arXiv subjects

Nicholas B. Weingartner

Publications and source records attributed to Nicholas B. Weingartner.

5 recordsLinked to original sources

arXiv2018

The Stochastic Replica Approach to Machine Learning: Stability and Parameter Optimization

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as expansions in terms of various stochastic functions. The algorithm predicts the classification/regression values of new data by combining (via voting) the outputs of these numerous linear expansions in randomly chosen functions. The few parameters (typically only one parameter is used in all studied examples) that this model has may be automatically optimized. The algorithm has been tested on 10 diverse training data sets of various types and feature space dimensions. It has been shown to consistently exhibit high accuracy and readily allow for optimization of parameters, while simultaneously avoiding pitfalls of existing algorithms such as those associated with class imbalance. We very briefly speculate on whether spatial coordinates in physical theories may be viewed as emergent "features" that enable a robust machine learning type description of data with generic low order smooth functions.

stat.ML↗

arXiv2017

Critical assessment of the equilibrium melting-based, energy distribution theory of supercooled liquids and application to jammed systems

Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is to understand the remarkable increase of the viscosity with supercooling. Recently, a new theory of supercooled liquids has been proposed that starts from first principles, using elementary statistical mechanics arguments, to derive a form for the viscosity that contains only a single fitting parameter in its simplest form. In this we demonstrate that this exact same form may be derived from a different starting point, and then critically examine its performance. In the process we find that functional form proposed fits the viscosity data of a diverse group of 45 liquids exceptionally well over a wide temperature range, and uncover a number of interesting correlations of the single parameter with various thermodynamic quantities, ultimately allowing for the prediction of low temperature viscosity from high temperature data. Additionally, we find that similar physical reasoning can be used to derive a similar, single parameter form for the viscosity of hard-sphere/jammed liquids. We demonstrate that this form accurately reproduces the viscosity of hard-spheres, suggesting an underlying universality in metastable dynamics.

cond-mat.dis-nn↗

arXiv2016

A phase space approach to supercooled liquids and a universal collapse of their viscosity

A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed which explain and reproduce the temperature dependence of the viscosity of supercooled liquids. Each of these frameworks appears only applicable to specific classes of glassformers and each possess a number of variable parameters. Here we describe a classical framework for explaining the dynamical behavior of supercooled liquids based on statistical mechanical considerations, and possessing only a single variable parameter. This parameter varies weakly from liquid to liquid. Furthermore, as predicted by this new classical theory and its earlier quantum counterpart, we find with the aid of a small dimensionless constant that varies in size from $\sim 0.05-0.12$, a universal (16 decade) collapse of the viscosity data as a function of temperature. The collapse appears in all known types of glass forming supercooled liquids (silicates, metallic alloys, organic systems, chalcogenide, sugars, and water).

cond-mat.soft↗

arXiv2016

A Dramatically Growing Shear Rigidity Length Scale in a Supercooled Glass Former ($NiZr_2$)

Finding a suitably growing length scale that increases in tandem with the immense viscous slowdown of supercooled liquids is an open problem associated with the glass transition. Here, we define and demonstrate the existence of one such length scale which may be experimentally verifiable. This is the length scale over which external shear perturbations appreciably penetrate into a liquid as the glass transition is approached. We provide simulation based evidence of its existence, and its growth by at least an order of magnitude, by using molecular dynamics simulations of NiZr2, a good fragile glass former. On the probed timescale, upon approaching the glass transition temperature from above, this length scale, ξ is also shown to be consistent with Ising-like scaling. Furthermore, we demonstrate the possible scaling of ξ about the temperature at which super-Arrhenius growth of viscosity, and a marked growth of the penetration depth sets in. Our simulation results suggest that upon supercooling, marked initial increase of the shear penetration depth in fluids may occur in tandem with the breakdown of the Stokes-Einstein relation.

cond-mat.mtrl-sci↗

arXiv2016

Probing Local Structure in Glass by the Application of Shear

The glass transition remains one of the great unsolved mysteries of contemporary condensed matter physics. When crystallization is bypassed by rapid cooling, a supercooled liquid, retaining amorphous particle arrangment, results. The physical phenomenology of supercooled liquids is as vast as it is interesting. Most significant, the viscosity of the supercooled liquid displays an incredible increase over a narrow temperature range. Eventually, the supercooled liquid ceases to flow, becomes a glass, and gains rigidity and solid-like behaviors. Understanding what underpins the monumental growth of viscosity, and how rigidity results without long range order is a long-sought goal. Many theories of the glassy slowdown require the growth of static lengthscale related to structure with lowering of the temperature. To that end, we have proposed a new, natural lengthscale- "the shear penetration depth". This lengthscale quantifies the structural connectivity of the supercooled liquid. The shear penetration depth is defined as the distance up to which a shear perturbation applied to the boundary propagates into the liquid. We provide numerical data, based on the simulations of $NiZr_2$, illustrating that this length scale exhibits dramatic growth and eventual divergence upon approach to the glass transition. We further discuss this in relation to percolating structural connectivity and a new theory of the glass transition.

cond-mat.mtrl-sci↗