423 research outputs found
Free energy surface of ST2 water near the liquid-liquid phase transition
We carry out umbrella sampling Monte Carlo simulations to evaluate the free
energy surface of the ST2 model of water as a function two order parameters,
the density and a bond-orientational order parameter. We approximate the
long-range electrostatic interactions of the ST2 model using the reaction-field
method. We focus on state points in the vicinity of the liquid-liquid critical
point proposed for this model in earlier work. At temperatures below the
predicted critical temperature we find two basins in the free energy surface,
both of which have liquid-like bond orientational order, but differing in
density. The pressure and temperature dependence of the shape of the free
energy surface is consistent with the assignment of these two basins to the
distinct low density and high density liquid phases previously predicted to
occur in ST2 water.Comment: 8 pages, 9 figure
Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
We present a simple off-lattice hard-disc model that exhibits glassy
dynamics. The inherent structures are enumerated exactly, transitions between
metabasins are well understood, and the particle configurations that act to
facilitate dynamics are easily identified. The model readily maps to a coarse
grained dynamic facilitation description.Comment: 5 pages, 5 figures, submitted to PR
Design analysis of the bearing component of the hip joint prosthesis to improve distribution of forces and frictional wear.
This is a design analysis project aimed at reducing wear of the hip joint components by improvement of distribution of forces. Though there have been celebrated achievements in the total hip arthroplasty (THA) procedure that have brought much relief, challenges as- sociated with wear, hip joint stresses and adverse biological response have greatly affected the longevity of the implants.
Prosthetic wear is a problem that has overshadowed the tremendous gains in the THA and has resulted in implants loosening so much that corrective revision surgeries were necessary. Previously THA has been known to be confined to the older patients but has recently crept downwards to include those in the twenties. This has increased demand and quality of the implants. The project analyses the forces that are active at the hip joint articular surfaces and by use of computer simulation, finite element analysis (FEA) was performed on the models where upon material and proposed design of the bearing were recommended.
The finite element analysis was also compared to the Herztian contact method where it can be concluded that low stresses are achievable by maximising the contact area. This was followed by the model design optimization that gave the final specifications of the proposed design. The proposed design managed to lower contact stresses from a peak of 22 MPa which was equatorial contact to 3MPa over a considerable wide area due alterations in the geometry, diameters sizes and clearances. However the model still needs to be tested in vitro to ascertain the wear characteristics
"Swarm relaxation": Equilibrating a large ensemble of computer simulations
It is common practice in molecular dynamics and Monte Carlo computer
simulations to run multiple, separately-initialized simulations in order to
improve the sampling of independent microstates. Here we examine the utility of
an extreme case of this strategy, in which we run a large ensemble of
independent simulations (a "swarm"), each of which is relaxed to equilibrium.
We show that if is of order , we can monitor the swarm's relaxation
to equilibrium, and confirm its attainment, within , where
is the equilibrium relaxation time. As soon as a swarm of this size
attains equilibrium, the ensemble of final microstates from each run is
sufficient for the evaluation of most equilibrium properties without further
sampling. This approach dramatically reduces the wall-clock time required,
compared to a single long simulation, by a factor of several hundred, at the
cost of an increase in the total computational effort by a small factor. It is
also well-suited to modern computing systems having thousands of processors,
and is a viable strategy for simulation studies that need to produce
high-precision results in a minimum of wall-clock time. We present results
obtained by applying this approach to several test cases.Comment: 12 pages. To appear in Eur. Phy. J. E, 201
Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics
In simulations of supercooled, high-density liquid silica we study a range of
temperature T in which we find both crystal nucleation, as well as the
characteristic dynamics of a glass forming liquid, including a breakdown of the
Stokes-Einstein relation. We find that the liquid cannot be observed below a
homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than
it can equilibrate. We show that the HNL would occur at lower T, and perhaps
not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy
dynamics plays a central role in setting a crystallization limit on the liquid
state in this case. We also explore the relation of the HNL to the Kauzmann
temperature, and test for spinodal-like effects near the HNL.Comment: 4 pages, 4 figure
The liquid-glass transition of silica
We studied the liquid-glass transition of by means of replica theory,
utilizing an effective pair potential which was proved to reproduce a few
experimental features of silica. We found a finite critical temperature ,
where the system undergoes a phase transition related to replica symmetry
breaking, in a region where experiments do not show any transition. The
possible sources of this discrepancy are discussed.Comment: 14 pages, 6 postscript figures. Revised version accepted for
pubblication on J.Chem.Phy
Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation
We investigate a non-equilibrium reaction-diffusion model and equivalent
ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The
exact energy spectrum and the n-point hole correlations are considered with the
help of the Jordan-Wigner fermionization and the inter-particle distribution
function method. Although the Hamiltonian has no explicit translational
symmetry, the translational invariance is recovered after long time due to the
diffusion. We see the scaling relations for the concentration and the two-point
function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge
Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density ~g/cm, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate , the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that , the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC
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