scholarly journals Vibrational density of states and boson peak in two-dimensional frictional granular assemblies

2016 ◽  
Vol 65 (3) ◽  
pp. 036301
Author(s):  
Niu Xiao-Na ◽  
Zhang Guo-Hua ◽  
Sun Qi-Cheng ◽  
Zhao Xue-Dan ◽  
Dong Yuan-Xiang
Keyword(s):  
Density Of States ◽  
Boson Peak ◽  
Two Dimensional ◽  
Vibrational Density Of States ◽  
Granular Assemblies ◽  
Vibrational Density

scholarly journals Применение теории случайных матриц для описания бозонного пика в двумерных системах

2020 ◽  
Vol 62 (4) ◽  
pp. 603
Author(s):  
Д.А. Конюх ◽  
Я.М. Бельтюков
Keyword(s):  
Density Of States ◽  
Disordered Systems ◽  
Degrees Of Freedom ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Amorphous Solids ◽  
Boson Peak ◽  
Two Dimensional ◽  
Reduced Density ◽  
Vibrational Density

The random matrix theory is applied to describe the vibrational properties of two-dimensional disordered systems with a large number of degrees of freedom. It is shown that the most significant mechanical properties of amorphous solids can be taken into account using the correlated Wishart ensemble. In this ensemble, an excess vibrational density of states over the Debye law is observed as a peak in the reduced density of states g(ω)/ω. Such a peak is known as the boson peak, which was observed in many experiments and numerical simulations for two-dimensional and three-dimensional disordered systems. It is shown that two-dimensional systems have a number of differences in the asymptotic behavior of the boson peak.

scholarly journals Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity

2020 ◽  
Vol 43 (11) ◽  
Author(s):  
Bingyu Cui ◽  
Alessio Zaccone
Keyword(s):  
Internal Stress ◽  
Density Of States ◽  
Power Law ◽  
Elastic Constants ◽  
Boson Peak ◽  
Internal Stresses ◽  
Logarithmic Correction ◽  
Spatial Correlations ◽  
Vibrational Density Of States ◽  
Vibrational Density

Abstract. A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D($\omega$ ω ) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $ \sim -\omega^{2}\ln\omega$ ∼ - ω 2 ln ω is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a $ \sim\omega^{4}$ ∼ ω 4 regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory. Graphical abstract

scholarly journals Anomalies in the low frequency vibrational density of states for a polymer with intrinsic microporosity – the Boson peak of PIM-1

2018 ◽  
Vol 20 (3) ◽  
pp. 1355-1363 ◽  
Author(s):  
Reiner Zorn ◽  
Huajie Yin ◽  
Wiebke Lohstroh ◽  
Wayne Harrison ◽  
Peter M. Budd ◽  
...  
Keyword(s):  
Density Of States ◽  
Low Frequency ◽  
Boson Peak ◽  
Vibrational Density Of States ◽  
First Time ◽  
Intrinsic Microporosity ◽  
Vibrational Density

For the first time the low frequency vibrational density of states is reported for a polymer with intrinsic microporosity.

scholarly journals Excess vibrational density of states and the brittle to ductile transition in crystalline and amorphous solids

Soft Matter ◽  
2016 ◽  
Vol 12 (4) ◽  
pp. 1210-1218 ◽  
Author(s):  
Jeetu S. Babu ◽  
Chandana Mondal ◽  
Surajit Sengupta ◽  
Smarajit Karmakar
Keyword(s):  
Mechanical Loading ◽  
Density Of States ◽  
Amorphous Solids ◽  
Vibrational Density Of States ◽  
Brittle To Ductile Transition ◽  
Active Research ◽  
Vibrational Density

The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers.

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