Numerical studies of transport in complex many-particle systems far from equilibrium
Julkaistu sarjassa
Research report / Department of Physics, University of JyväskyläTekijät
Päivämäärä
2012Oppiaine
FysiikkaIn this Thesis, transport in complex nonequilibrium many-particle systems is studied
using numerical master equation approach and Monte Carlo simulations. We focus
on the transport of the center-of-mass of deformable objects with internal structure.
Two physical systems are studied in detail: linear polymers using the Rubinstein-Duke
model and single-layer metal-on-metal atomic islands using a semi-empirical lattice
model. Polymers and islands are driven out of thermodynamic equilibrium by strong
static and time-dependent external forces. Topics covered in this work include introductions
to nonequilibrium statistical mechanics, master equations and computational
methods, with construction and numerical solving of master equations, and numerical
optimization. For small systems (up to ∼106 states), solving master equations numerically
is found to be efficient, especially when studying parameter sensitive and elusive
properties, such as drifts caused by the ratchet effect. Speed and accuracy of the
method allows optimization with respect to continuous model parameters and transition
cycles, which helps in understanding the coupling between the internal dynamics
of deformable objects and their center-of-mass displacement. Firstly, we study transport of polymers in spatially periodic time-dependent potentials
using a standard and relaxed versions of the Rubinstein-Duke model. Two types
of potentials, flashing and traveling, are considered with stochastic and deterministic
time-dependency schemes. Rich non-linear behavior for the transport velocity, diffusion
and energetic efficiency is found. By varying the polymer length, we find current
inversions caused by a ’rebound’ effect that is only present for objects with internal
structure. These results are different between reptating and non-reptating polymers.
Transport is found to become more coherent for deterministic time-dependency scheme
and as the polymer gets longer. The results show that small changes in the molecule
structure (e.g. the charge configuration) and the environment variables can lead to a
large change in the velocity.Secondly, we study transport of single-layer metal-on-metal islands using a semiempirical
lattice model for Cu atoms on Cu(001) surface. Two types of time-dependent
driving are considered: a pulsed rotated field and an alternating field with a zero average
force (an electrophoretic ratchet). The main results are that a pulsed field can
increase the velocity in both diagonal and axis directions as compared to a static field, and there exists a current inversion in an electrophoretic ratchet. In addition
to a ’magic size’ effect for islands in equilibrium, a stronger odd-even effect is found
in the presence of large fields. Master equation computations reveal nonmonotonous
behavior of the leading relaxation constant and effective Arrhenius parameters. Optimized
transition cycles shed light on microscopic mechanisms responsible for island
transport in strong fields.
...
Julkaisija
University of JyväskyläISBN
978-951-39-4787-3ISSN Hae Julkaisufoorumista
0075-465XJulkaisuun sisältyy osajulkaisuja
- Artikkeli I: Kauttonen, J., Merikoski, J., & Pulkkinen, O. (2008). Polymer dynamics in time-dependent periodic potentials. Physical Review E, 77(6), Article 061131. DOI: 10.1103/PhysRevE.77.061131
- Artikkeli II: Kauttonen, J., & Merikoski, J. (2010). Characteristics of the polymer transport in ratchet systems. Physical Review E, 81, 41112. DOI: 10.1103/PhysRevE.81.041112. JYX: jyx.jyu.fi/handle/123456789/46666
- Artikkeli III: Kauttonen, J., & Merikoski, J. (2012). Single-layer metal-on-metal islands driven by strong time-dependent fields. Physical Review E, 85, 11107. DOI: 10.1103/PhysRevE.85.011107 Arxiv
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