6,902 research outputs found
A phase-field-crystal approach to critical nuclei
We investigate a phase-field-crystal model for homogeneous nucleation.
Instead of solving the time evolution of a density field towards equilibrium we
use a String Method to identify saddle points in phase space. The saddle points
allow to obtain the nucleation barrier and the critical nucleus. The advantage
of using the phase-field-crystal model for this task is its ability to resolve
atomistic effects. The obtained results indicate different properties of the
critical nucleus compared with bulk crystals and show a detailed description of
the nucleation process.Comment: 12 pages, 5 figures, submitte
Where are the parallel algorithms?
Four paradigms that can be useful in developing parallel algorithms are discussed. These include computational complexity analysis, changing the order of computation, asynchronous computation, and divide and conquer. Each is illustrated with an example from scientific computation, and it is shown that computational complexity must be used with great care or an inefficient algorithm may be selected
Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability
A two-dimensional crystal on the surface of a sphere experiences elastic
stress due to the incompatibility of the crystal axes and the curvature. A
common mechanism to relax elastic stress is the Asaro-Tiller-Grinfeld (ATG)
instability. With a combined numerical and analytical approach we demonstrate,
that also curvature induced stress in surface crystals can be relaxed by the
long wave length ATG instability. The numerical results are obtained using a
surface phase-field crystal (PFC) model, from which we determine the
characteristic wave numbers of the ATG instability for various surface
coverages corresponding to different curvature induced compressions. The
results are compared with an analytic expression for the characteristic wave
number, obtained from a continuum approach which accounts for hexagonal
crystals and intrinsic PFC symmetries. We find our numerical results in
accordance with the analytical predictions.Comment: 6 pages, 5 figure
Closing the gap between atomic-scale lattice deformations and continuum elasticity
Crystal lattice deformations can be described microscopically by explicitly
accounting for the position of atoms or macroscopically by continuum
elasticity. In this work, we report on the description of continuous elastic
fields derived from an atomistic representation of crystalline structures that
also include features typical of the microscopic scale. Analytic expressions
for strain components are obtained from the complex amplitudes of the Fourier
modes representing periodic lattice positions, which can be generally provided
by atomistic modeling or experiments. The magnitude and phase of these
amplitudes, together with the continuous description of strains, are able to
characterize crystal rotations, lattice deformations, and dislocations.
Moreover, combined with the so-called amplitude expansion of the phase-field
crystal model, they provide a suitable tool for bridging microscopic to
macroscopic scales. This study enables the in-depth analysis of elasticity
effects for macro- and mesoscale systems taking microscopic details into
account.Comment: 9 pages, 7 figures, Supporting Information availabl
A methodology for exploiting parallelism in the finite element process
A methodology is described for developing a parallel system using a top down approach taking into account the requirements of the user. Substructuring, a popular technique in structural analysis, is used to illustrate this approach
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
Design, development and use of the finite element machine
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
One of the major difficulties in employing phase field crystal (PFC) modeling
and the associated amplitude (APFC) formulation is the ability to tune model
parameters to match experimental quantities. In this work we address the
problem of tuning the defect core and interface energies in the APFC
formulation. We show that the addition of a single term to the free energy
functional can be used to increase the solid-liquid interface and defect
energies in a well-controlled fashion, without any major change to other
features. The influence of the newly added term is explored in two-dimensional
triangular and honeycomb structures as well as bcc and fcc lattices in three
dimensions. In addition, a finite element method (FEM) is developed for the
model that incorporates a mesh refinement scheme. The combination of the FEM
and mesh refinement to simulate amplitude expansion with a new energy term
provides a method of controlling microscopic features such as defect and
interface energies while simultaneously delivering a coarse-grained examination
of the system.Comment: 14 pages, 9 figure
The light CP-even MSSM Higgs mass resummed to fourth logarithmic order
We present the calculation of the light neutral CP-even Higgs mass in the
MSSM for a heavy SUSY spectrum by resumming enhanced terms through fourth
logarithmic order (NLL), keeping terms of leading order in the top Yukawa
coupling , and NNLO in the strong coupling . To this goal,
the three-loop matching coefficient for the quartic Higgs coupling of the SM to
the MSSM is derived to order by comparing the
perturbative EFT to the fixed-order expression for the Higgs mass. The new
matching coefficient is made available through an updated version of the
program Himalaya. Numerical effects of the higher-order resummation are studied
using specific examples, and sources of theoretical uncertainty on this result
are discussed.Comment: 26 pages, 3 figures, matches version published in EPJ
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