Singularities in Hessian element distributions of amorphous media
We show that the distribution of elements H in the Hessian matrices associated with amorphous materials exhibit singularities P(H)∼|H|^{γ} with an exponent γ<0, as |H|→0. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.042025 |
| _version_ | 1797211210727292928 |
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| author | Vishnu V. Krishnan Smarajit Karmakar Kabir Ramola |
| author_facet | Vishnu V. Krishnan Smarajit Karmakar Kabir Ramola |
| author_sort | Vishnu V. Krishnan |
| collection | DOAJ |
| description | We show that the distribution of elements H in the Hessian matrices associated with amorphous materials exhibit singularities P(H)∼|H|^{γ} with an exponent γ<0, as |H|→0. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that γ depends only on the degree of smoothness n of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix. |
| first_indexed | 2024-04-24T10:22:52Z |
| format | Article |
| id | doaj.art-7017836584a94352a37e15358f320854 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:22:52Z |
| publishDate | 2020-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7017836584a94352a37e15358f3208542024-04-12T17:03:28ZengAmerican Physical SocietyPhysical Review Research2643-15642020-11-012404202510.1103/PhysRevResearch.2.042025Singularities in Hessian element distributions of amorphous mediaVishnu V. KrishnanSmarajit KarmakarKabir RamolaWe show that the distribution of elements H in the Hessian matrices associated with amorphous materials exhibit singularities P(H)∼|H|^{γ} with an exponent γ<0, as |H|→0. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that γ depends only on the degree of smoothness n of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.http://doi.org/10.1103/PhysRevResearch.2.042025 |
| spellingShingle | Vishnu V. Krishnan Smarajit Karmakar Kabir Ramola Singularities in Hessian element distributions of amorphous media Physical Review Research |
| title | Singularities in Hessian element distributions of amorphous media |
| title_full | Singularities in Hessian element distributions of amorphous media |
| title_fullStr | Singularities in Hessian element distributions of amorphous media |
| title_full_unstemmed | Singularities in Hessian element distributions of amorphous media |
| title_short | Singularities in Hessian element distributions of amorphous media |
| title_sort | singularities in hessian element distributions of amorphous media |
| url | http://doi.org/10.1103/PhysRevResearch.2.042025 |
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