2,427 research outputs found
On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use \bH(\div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new \tilde\bH^{-1/2}(\div)-conforming p-interpolation operator that assumes only \bH^r\cap\tilde\bH^{-1/2}(\div)-regularity () and for which we show quasi-stability with respect to polynomial degrees
Contributions to the mixed-alkali effect in molecular dynamics simulations of alkali silicate glasses
The mixed-alkali effect on the cation dynamics in silicate glasses is
analyzed via molecular dynamics simulations. Observations suggest a description
of the dynamics in terms of stable sites mostly specific to one ionic species.
As main contributions to the mixed--alkali slowdown longer residence times and
an increased probability of correlated backjumps are identified. The slowdown
is related to the limited accessibility of foreign sites. The mismatch
experienced in a foreign site is stronger and more retarding for the larger
ions, the smaller ions can be temporarily accommodated. Also correlations
between unlike as well as like cations are demonstrated that support
cooperative behavior.Comment: 10 pages, 12 figures, 1 table, revtex4, submitted to Phys. Rev.
Nonlinear Ionic Conductivity of Thin Solid Electrolyte Samples: Comparison between Theory and Experiment
Nonlinear conductivity effects are studied experimentally and theoretically
for thin samples of disordered ionic conductors. Following previous work in
this field the {\it experimental nonlinear conductivity} of sodium ion
conducting glasses is analyzed in terms of apparent hopping distances. Values
up to 43 \AA are obtained. Due to higher-order harmonic current density
detection, any undesired effects arising from Joule heating can be excluded.
Additionally, the influence of temperature and sample thickness on the
nonlinearity is explored. From the {\it theoretical side} the nonlinear
conductivity in a disordered hopping model is analyzed numerically. For the 1D
case the nonlinearity can be even handled analytically. Surprisingly, for this
model the apparent hopping distance scales with the system size. This result
shows that in general the nonlinear conductivity cannot be interpreted in terms
of apparent hopping distances. Possible extensions of the model are discussed.Comment: 7 pages, 6 figure
Non Markovian persistence in the diluted Ising model at criticality
We investigate global persistence properties for the non-equilibrium critical
dynamics of the randomly diluted Ising model. The disorder averaged persistence
probability of the global magnetization is found to decay
algebraically with an exponent that we compute analytically in a
dimensional expansion in . Corrections to Markov process are
found to occur already at one loop order and is thus a novel
exponent characterizing this disordered critical point. Our result is
thoroughly compared with Monte Carlo simulations in , which also include a
measurement of the initial slip exponent. Taking carefully into account
corrections to scaling, is found to be a universal exponent,
independent of the dilution factor along the critical line at , and
in good agreement with our one loop calculation.Comment: 7 pages, 4 figure
Energy landscape, two-level systems and entropy barriers in Lennard-Jones clusters
We develop an efficient numerical algorithm for the identification of a large
number of saddle points of the potential energy function of Lennard- Jones
clusters. Knowledge of the saddle points allows us to find many thousand
adjacent minima of clusters containing up to 80 argon atoms and to locate many
pairs of minima with the right characteristics to form two-level systems (TLS).
The true TLS are singled out by calculating the ground-state tunneling
splitting. The entropic contribution to all barriers is evaluated and
discussed.Comment: 4 pages, RevTex, 2 PostScript figure
Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model
An algoritm for the simulation of the 3--dimensional random field Ising model
with a binary distribution of the random fields is presented. It uses
multi-spin coding and simulates 64 physically different systems simultaneously.
On one processor of a Cray YMP it reaches a speed of 184 Million spin updates
per second. For smaller field strength we present a version of the algorithm
that can perform 242 Million spin updates per second on the same machine.Comment: 13 pp., HLRZ 53/9
Aging effects manifested in the potential energy landscape of a model glass former
We present molecular dynamics simulations of a model glass-forming liquid
(the binary Kob-Anderson Lennard-Jones model) and consider the distributions of
inherent energies and metabasins during aging. In addition to the typical
protocol of performing a temperature jump from a high temperature to a low
destination temperature, we consider the temporal evolution of the
distributions after an 'up-jump', i.e. from a low to a high temperature. In
this case the distribution of megabasin energies exhibits a transient two-peak
structure. Our results can qualitatively be rationalized in terms of a trap
model with a Gaussian distribution of trap energies. The analysis is performed
for different system sizes. A detailed comparison with the trap model is
possible only for a small system because of major averging effects for larger
systems.Comment: 16 pages, 14 figure
The Potential for Student Performance Prediction in Small Cohorts with Minimal Available Attributes
The measurement of student performance during their progress through university study provides academic leadership with critical information on each student’s likelihood of success. Academics have traditionally used their interactions with individual students through class activities and interim assessments to identify those “at risk” of failure/withdrawal. However, modern university environments, offering easy on-line availability of course material, may see reduced lecture/tutorial attendance, making such identification more challenging. Modern data mining and machine learning techniques provide increasingly accurate predictions of student examination assessment marks, although these approaches have focussed upon large student populations and wide ranges of data attributes per student. However, many university modules comprise relatively small student cohorts, with institutional protocols limiting the student attributes available for analysis. It appears that very little research attention has been devoted to this area of analysis and prediction. We describe an experiment conducted on a final-year university module student cohort of 23, where individual student data are limited to lecture/tutorial attendance, virtual learning environment accesses and intermediate assessments. We found potential for predicting individual student interim and final assessment marks in small student cohorts with very limited attributes and that these predictions could be useful to support module leaders in identifying students potentially “at risk.”.Peer reviewe
A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reporte
The mortar boundary element method
This thesis is primarily concerned with the mortar boundary element method (mortar BEM). The mortar finite element method (mortar FEM) is a well established numerical scheme for the solution of partial differential equations. In simple terms the technique involves the splitting up of the domain of definition into separate parts. The problem may now be solved independently on these separate parts, however there must be some sort of matching condition between the separate parts. Our aim is to develop and analyse this technique to the boundary element method (BEM). The first step in our journey towards the mortar BEM is to investigate the BEM with Lagrangian multipliers. When approximating the solution of Neumann problems on open surfaces by the Galerkin BEM the appropriate boundary condition (along the boundary curve of the surface) can easily be included in the definition of the spaces used. However, we introduce a boundary element Galerkin BEM where we use a Lagrangian multiplier to incorporate the appropriate boundary condition in a weak sense. This is the first step in enabling us to understand the necessary matching conditions for a mortar type decomposition. We next formulate the mortar BEM for hypersingular integral equations representing the elliptic boundary value problem of the Laplace equation in three dimensions (with Neumann boundary condition). We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. We present numerical results which confirm and underline the theory presented concerning the BEM with Lagrangian multipliers and the mortar BEM. Finally we discuss the application of the mortaring technique to the hypersingular integral equation representing the equations of linear elasticity. Based on the assumption of ellipticity of the appearing bilinear form on a constrained space we prove the almost quasi-optimal convergence of the scheme.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
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