• Corpus ID: 211532760

Do spatially non-uniform phases of matter with no long-range order exist?

@article{Tth2020DoSN,
  title={Do spatially non-uniform phases of matter with no long-range order exist?},
  author={Gyula I. T{\'o}th},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
  • G. Tóth
  • Published 21 February 2020
  • Mathematics
  • arXiv: Statistical Mechanics
In this Letter, the existence of spatially non-uniform phases with no long-range order is investigated in continuum models of first order phase transitions with quartic non-linearity. The central result of the paper is the development of a mathematical method allowing to find "disordered" solutions (infinite sets of spatially non-uniform analytical solutions with no long range order) to partial differential equations. The new method is applied for the Gaussian measure, and it has been found… 

Figures from this paper

References

SHOWING 1-10 OF 26 REFERENCES

Theory of structural glasses and supercooled liquids.

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the

Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line

Summary. We give a rigorous derivation of the time-dependent one-dimensional Ginzburg—Landau equation. As in the work of Iooss, Mielke, and Demay [11] (who derived the steady Ginzburg-Landau

On radial solutions of the Swift-Hohenberg equation

We study radial solutions to the generalized Swift-Hohenberg equation on the plane with an additional quadratic term. We find stationary localized radial solutions that decay at infinity and

Highly ordered noncrystalline metallic phase.

We report the characterization of a unique metallic glass that, during rapid cooling of an Al-Fe-Si melt, forms by nucleation, followed by growth normal to a moving interface between the solid and

Spots in the Swift-Hohenberg Equation

The existence of stationary localized spots for the planar and the three-dimensional Swift--Hohenberg equations is proved using geometric blow-up techniques. The spots found in this paper have a much

Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics

Preface 1. General notions. The principle of conservation of extension-in-phase 2. Application of the principle of conservation of extension-in-phase to the theory of errors 3. Application of the

High density amorphous ice at room temperature

High density amorphous (HDA) ice is formed from metastable ice VII in the stability field of ice VI under rapid compression using dynamic-diamond anvil cell (d-DAC) and results from structural similarities between HDA and ice VII, indicating that structural instabilities of parent ice VII and Ih drive the pressure-induced amorphization.

Modeling elasticity in crystal growth.

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales in a natural manner and enables access to time scales much larger than conventional atomic methods.

Concentration of measure and isoperimetric inequalities in product spaces

The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product ΩN of probability spaces has measure at least one half, “most” of the points of Ωn are “close”