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Register a new userOn the Glassy Behavior of Parking Lot Model
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Added by
Alexei V. Tkachenko
Publication date
1998
fields
Physics
and research's language is
English
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We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understood by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative picture for understanding recent granular compaction experiments and other glassy systems.
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The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers, but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed generalisations to the KA model where swap can be very effective. Here, we show that these models can in turn be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We successfully develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimise them. We provide several physical measurements indicating that the proposed algorithms considerably enhance mechanical and thermodynamic stability in the KA model, including a transition towards brittle yielding behaviour. Our results thus pave the way for future studies of stable glasses using the KA model.
We present the study of the landscape structure of athermal soft spheres both as a function of the packing fraction and of the energy. We find that, on approaching the jamming transition, the number of different configurations available to the system has a steep increase and that a hierarchical organization of the landscape emerges. We use the knowledge of the structure of the landscape to predict the values of thermodynamic observables on the edge of the transition.
Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions $N$ up to N=28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension $N$. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.
We use a new version of the reversible Parking Lot Model to study the compaction of vibrated polydisperse media. The particle sizes are distributed according to a truncated power law. We introduce a self-consistent desorption mechanism with a hierarchical initialization of the system. In this way, we approach densities close to unity. The final density depends on the polydispersity of the system as well as on the initialization and will reach a maximum value for a certain exponent in the power law.
Both structural glasses and disordered crystals are known to exhibit anomalous thermal, vibrational, and acoustic properties at low temperatures or low energies, what is still a matter of lively debate. To shed light on this issue, we studied the halomethane family C-Br_n-Cl_4-n (n = 0,1,2) at low temperature where, despite being perfectly translationally ordered stable monoclinic crystals, glassy dynamical features had been reported from experiments and molecular dynamics simulations. For n = 1,2 dynamic disorder originates by the random occupancy of the same lattice sites by either Cl or Br atoms, but not for the ideal reference case of CCl4. Measurements of the low-temperature specific heat (Cp) for all these materials are here reported, which provide evidence of the presence of a broad peak in Debye-reduced Cp/T^3 and in the reduced density of states g(w)/w^2 determined by means of neutron spectroscopy, as well as a linear term in Cp usually ascribed in glasses to two-level systems in addition to the cubic term expected for a fully ordered crystal. Being CCl4 a fully ordered crystal, we also performed density functional theory (DFT) calculations, which provide unprecedented detailed information about the microscopic nature of vibrations responsible for that broad peak, much alike the boson peak of glasses, finding it to essentially arise from a piling up (at around 3 - 4 meV) of low-energy optical modes together with acoustic modes near the Brillouin-zone limits.
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