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Simulation of relaxation processes in complex condensed matter systems: Algorithmic and physical aspets
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis summarizes interrelated simulation studies of three different physical phenomena. The three topics are: simulation of work hardening of materials using dislocation dynamics, investigation of anomalous diffusion in supercooled liquids using molecular dynamics,and kinetic Monte-Carlo simulation of annealing of radiation damaged materials. All three topics require special algorithms in order to enable physically relevant simulations. The author's contributionconsists of development, implementation, and optimization of these algorithms, as well as interpretation of simulation results.

Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , ix, 27 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2009:21
National Category
Condensed Matter Physics Computational Mathematics Materials Engineering Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-11574ISBN: 978-91-7415-515-0 (print)OAI: oai:DiVA.org:kth-11574DiVA: diva2:277783
Public defence
2009-12-10, D3, main building, Lindstedsvägen 3, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2010-08-05Bibliographically approved
List of papers
1. Enabling strain hardening simulations with dislocation dynamics
Open this publication in new window or tab >>Enabling strain hardening simulations with dislocation dynamics
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2007 (English)In: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 15, 553-595 p.Article in journal (Refereed) Published
Abstract [en]

Numerical algorithms for discrete dislocation dynamics simulations areinvestigated for the purpose of enabling strain hardening simulations of singlecrystals on massively parallel computers. The algorithms investigated includethe O(N) calculation of forces, the equations of motion, time integration,adaptive mesh refinement, the treatment of dislocation core reactions and thedynamic distribution of data and work on parallel computers. A simulationintegrating all these algorithmic elements using the Parallel DislocationSimulator (ParaDiS) code is performed to understand their behaviour in concertand to evaluate the overall numerical performance of dislocation dynamicssimulations and their ability to accumulate percent of plastic strain.

Keyword
plastic-deformation; elastic field; free-surface; fcc metals; crystals
National Category
Materials Engineering Condensed Matter Physics Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11564 (URN)10.1088/0965-0393/15/6/001 (DOI)000249392800001 ()
Note
QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2010-12-03Bibliographically approved
2. Matrix compression by common subexpression elimination
Open this publication in new window or tab >>Matrix compression by common subexpression elimination
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this report a method for common subexpression elimination in matrices isexplored. The method is applied to several types of matrices occurring in numericalsimulations. In all cases, the cost of a matrix-vector multiplication is reduced by asignificant amount. The amount of storage required for the eliminated matrices isalso less than that required for the original matrices. When the proposed method isapplied to the Fourier transform matrix, the output is equivalent to the fast Fouriertransform. For some matrices used in the fast multipole method for dislocationdynamics, the cost of a matrix-vector multiplication is reduced from O(p^6) to O(p^4.5),where p is the expansion order. Using an expansion order of 5, one can expect a factorof four speedup of the fast multipole part of a dislocation dynamics code.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11566 (URN)
Note
QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2010-08-05Bibliographically approved
3. Anomalous diffusion in supercooled liquids: A long-range localizationin particle trajectories
Open this publication in new window or tab >>Anomalous diffusion in supercooled liquids: A long-range localizationin particle trajectories
2009 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 131, 044510- p.Article in journal (Refereed) Published
Abstract [en]

A statistical analysis of the geometries of particle trajectories in the supercooled liquid state isreported. The analysis we present here is based on the statistics of the first-passage trajectory length.We examine two structurally different fragile glass-forming liquids simulated by moleculardynamics. In both liquids, the trajectories are found to reveal three distinct diffusion regimes. Ashort-range confinement to the cage of nearest neighbors is followed by a persistent diffusionregime. At a still larger spatial scale, the particle trajectories demonstrate a novel diffusion anomaly:a long-range localization distinct from the short-range localization. This phenomenon can beinterpreted in terms of the potential-energy landscape topography with the local energy minimacoalescing into metabasins—compact domains with low escape probability. We also demonstratethat the persistent diffusion regime can be linked to the exponential decay of the self-part of thevan Hove correlation function.

Keyword
Anomalous diffusion; Diffusion regimes; Escape probability; Exponential decays; First-passage; Fragile glass; Local energy minima; Metabasins; Nearest neighbors; Particle trajectories; Potential energy landscapes; Range localization; Spatial scale; Statistical analysis; Supercooled liquid state; Supercooled liquids; Trajectory length; Van Hove correlation
National Category
Condensed Matter Physics Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11567 (URN)10.1063/1.3184850 (DOI)000268613700068 ()2-s2.0-68249102273 (Scopus ID)
Note
QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2012-01-18Bibliographically approved
4. First-Passage Monte Carlo Algorithm: Diffusion without All the Hops
Open this publication in new window or tab >>First-Passage Monte Carlo Algorithm: Diffusion without All the Hops
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2006 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 97, 230602- p.Article in journal (Refereed) Published
Abstract [en]

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green’s functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hopsused in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicablet o many important physical situations in arbitrary integer dimensions.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11568 (URN)10.1103/PhysRevLett.97.230602 (DOI)000242708900007 ()2-s2.0-33845276991 (Scopus ID)
Note
PACS numbers: 05.10.Ln, 02.60.Cb, 02.70.Tt, 02.70.Uu QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2011-11-08Bibliographically approved
5. First-Passage Kinetic Monte Carlo method
Open this publication in new window or tab >>First-Passage Kinetic Monte Carlo method
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2009 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 80, no 6, 066701- p.Article in journal (Refereed) Published
Abstract [en]

We present a new effcient method for Monte Carlo simulations of diusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditionalsmall diusion hops and propagates the diusing particles over long distances through asequence of super-hops, one particle at a time. By partitioning the simulation space into nonoverlappingprotecting domains each containing only one or two particles, the algorithm factorizesthe N-body problem of collisions among multiple Brownian particles into a set of much simplersingle-body and two-body problems. Ecient propagation of particles inside their protective domainsis enabled through the use of time-dependent Green's functions (propagators) obtained assolutions for the rst-passage statistics of random walks. The resulting Monte Carlo algorithmis event-driven and asynchronous; each Brownian particle propagates inside its own protectivedomain and on its own time clock. The algorithm reproduces the statistics of the underlyingMonte-Carlo model exactly. Extensive numerical examples demonstrate that for an importantclass of diusion-reaction models the new algorithm is effcient at low particle densities, whereother existing algorithms slow down severely.

Keyword
Brownian motion; Green's function methods; Monte Carlo methods; N-body problems; reaction-diffusion systems
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11570 (URN)10.1103/PhysRevE.80.066701 (DOI)000273228000084 ()2-s2.0-72449169547 (Scopus ID)
Note
Uppdaterad från manuskript till artikel: 20100805 QC 20100805Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2012-01-18Bibliographically approved

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