Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9906248

Voronoi-Delaunay analysis of normal modes in a simple model glass

V. A. Luchnikov·N. N. Medvedev·Yu. I. Naberukhin·H. R. Schober
View original source ↗Read source document ↗Export metadata ↓

Abstract

We combine a conventional harmonic analysis of vibrations in a one-atomic model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the structure. ``Structure potentials'' (tetragonality, sphericity or perfectness) are introduced to describe the shape of the local atomic configurations (Delaunay simplices) as function of the atomic coordinates. Apart from the highest and lowest frequencies the amplitude weighted ``structure potential'' varies only little with frequency. The movement of atoms in soft modes causes transitions between different ``perfect'' realizations of local structure. As for the potential energy a dynamic matrix can be defined for the ``structure potential''. Its expectation value with respect to the vibrational modes increases nearly linearly with frequency and shows a clear indication of the boson peak. The structure eigenvectors of this dynamical matrix are strongly correlated to the vibrational ones. Four subgroups of modes can be distinguished.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

V. A. Luchnikov, N. N. Medvedev, Yu. I. Naberukhin, H. R. Schober. 1999-06-16. Voronoi-Delaunay analysis of normal modes in a simple model glass. https://doi.org/10.1103/physrevb.62.3181

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Embedding stochastic dynamics in latent manifolds of recurrent neural networks

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits through their ability to support rich time-dependent behaviour. Whilst high-dimensional by construction, they can be used to encode low-dimensional dynamical systems, for example by restricting to low-rank connectivity, hence mirroring the emergence of latent neural manifolds found in empirical neural data. Here, we exploit a relationship between RNNs and a class of universal approximators to train networks that can represent arbitrary, nonlinear stochastic differential equations (SDEs), with given drift and diffusion coefficients, within a low-dimensional latent subspace. We show that RNNs can faithfully embed the drift and diffusion of a given SDE, including nonlinear and nonequilibrium dynamics such as chaotic attractors. We apply this approach by constructing RNN realisations of stochastic systems that transiently explore various attractors through both input-driven switching and autonomous transitions driven by nonequilibrium currents, which we interpret as models of associative and sequential (episodic) memory. To elucidate how these dynamics are encoded in the network, we introduce decompositions of the RNN based on its asymmetric connectivity and its time-irreversibility. Our results show that neural populations can implement a broad class of stochastic dynamics within low-dimensional manifolds, unifying ideas from the dynamics of neural computation, the theory of neural manifolds, associative memory, and nonequilibrium statistical mechanics.

cond-mat.dis-nn↗
arXiv2026

Deep-layered machines have a built-in Occam's razor

Many complex systems map vast numbers of microscopic descriptions onto far fewer macroscopic outcomes. Surprisingly, these input-output maps strongly favor simple outputs. In an exactly solvable deep-layered machine, we prove that simplicity bias strengthens with every layer. The probability of an output function $F$ approaches $\Pr(F)\propto 2^{-K(F)}$, where $K$ is the Kolmogorov complexity. Our results show that hierarchical composition alone can generate an intrinsic Occam's razor, suggesting a general mechanism for simplicity bias in learning and evolution.

cond-mat.dis-nn↗
arXiv2026

Cup and Cap Topological Neural Network

Topological Deep Learning (TDL) is designed to learn features associated not only with nodes but also with edges, triangles and higher dimensional simplices. However, most TDL approaches, being based on boundary operators and Hodge Laplacians, have the limitation that features and signals cannot be lifted or lowered across more than one dimension per layer. To overcome this limitation, in this work, we propose the adoption of the cup and cap products. Specifically, we formulate the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (or 0-cochains) by taking into account their many-body interactions (e.g. triangles) present in the data. We validate CCNN by assessing its performance on the TopoBench datasets, demonstrating its competitive performance with respect to other simplicial complex neural networks.

cond-mat.dis-nn↗