arXiv subjects

Dieter W. Heermann

Publications and source records attributed to Dieter W. Heermann.

25 records · Page 2Linked to original sources

arXiv2002

Evidence for sharper than expected transition between metastable and unstable states

In mean-field theory, i.e. infinite-range interactions, the transition between metastable and unstable states of a thermodynamic system is sharp. The metastable and the unstable states are separated by a spinodal curve. For systems with short-range interaction the transition between metastable and unstable states has been thought of as gradual. We show evidence, that one can define a sharp border between the two regions. We have analysed the lifetimes of states by considering the relaxation trajectories following a quench. The average lifetimes, as a function of the quench depth into the two-phase region, shows a very sharp drop defining a limit of stability for metastable states. Using the limit of stability we define a line similar to a spinodal in the two-phase region.

cond-mat.stat-mech↗

arXiv1996

Modelling of amorphous polymer surfaces in computer simulation

We study surface effects in amorphous polymer systems by means of computer simulation. In the framework of molecular dynamics, we present two different methods to prepare such surfaces. {\em Free} surfaces are stabilized solely by van--der--Waals interactions whereas {\em confined} surfaces emerge in the presence of repelling plates. The two models are compared in various computer simulations. For free surfaces, we analyze the migration of end--monomers to the surface. The buildup of density and pressure profiles from zero to their bulk values depends on the surface preparation method. In the case of confined surfaces, we find density and pressure oszillations next to the repelling plates. We investigate the influence of surfaces on the coordination number, on the orientation of single bonds, and on polymer end--to--end vectors. Furthermore, different statistical methods to determine location and width of the surface region for systems of various chain lengths are discussed and applied. We introduce a ``height function'' and show that this method allows to determine average surface profiles only by scanning the outermost layer of monomers.

cond-mat↗

arXiv1996

Deformation of polymer films by bending forces

We study the deformation of nano--scale polymer films which are subject to external bending forces by means of computer simulation. The polymer is represented by a generalized bead--spring--model, intended to reproduce characteristic features of n--alkanes. The film is loaded by the action of a prismatic blade which is pressed into the polymer bulk from above and a pair of columns which support the film from below. The interaction between blade and support columns and the polymer is modelled by the repulsive part of a Lennard-Jones potential. For different system sizes as well as for different chainlengths, this nano--scale experiment is simulated by molecular dynamics methods. Our results allow us to give a first characterization of deformed states for such films. We resolve the kinetic and the dynamic stage of the deformation process in time and access the length scale between discrete particle and continuum mechanics behaviour. For the chainlengths considered here, we find that the deformation process is dominated by shear. We observe strangling effects for the film and deformation fluctuations in the steady state.

cond-mat↗

arXiv1995

Folding Transitions of Self-Avoiding Membranes

The phase structure of self-avoiding polymerized membranes is studied by extensive Hybrid Monte Carlo simulations. Several folding transitions from the flat to a collapsed state are found. Using a suitable order parameter and finite size scaling theory, these transitions are shown to be of {\em first order}. The phase diagram in the temperature-field plane is given.

cond-mat↗

arXiv1994

Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.

cond-mat↗

arXiv1993

Structural Properties of Two-Dimensional Polymers

We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and compared to the results of percolation theory. We also describe the dependence of the typical cluster structures on the reaction rate.

cond-mat↗

arXiv1993

The Crumpling Transition of Dynamically Triangulated Random Surfaces

We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We used longer runs than previous simulations and give new and more accurate estimates of critical exponents. Our data indicate a cusp singularity in the specific heat. The transition temperature, as well as the exponents are topology dependent.

hep-th↗