GENERIC RIGIDITY OF NETWORK GLASSES

In this paper, we have tried to collect together some of the more important results regarding floppy modes and constraint counting in glasses that have emerged in the past decade. This work has provided a useful conceptual framework within which to discuss some of the physical properties of glasses. Some of the arguments in this area are subtle and still controversial.

[1]  P. Boolchand,et al.  Direct Evidence for Stiffness Threshold in Chalcogenide Glasses , 1997 .

[2]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[3]  Jacobs,et al.  Generic rigidity percolation: The pebble game. , 1995, Physical review letters.

[4]  C. Moukarzel An efficient algorithm for testing the generic rigidity of graphs in the plane , 1996 .

[5]  Bruce Hendrickson,et al.  Conditions for Unique Graph Realizations , 1992, SIAM J. Comput..

[6]  J. C. Phillips,et al.  Topology of covalent non-crystalline solids II: Medium-range order in chalcogenide alloys and ASi(Ge) , 1981 .

[7]  J L Beeby,et al.  Physics of amorphous materials , 1984 .

[8]  M. Thorpe Bulk and surface floppy modes , 1995 .

[9]  Wooten,et al.  Computer model of tetrahedral amorphous diamond. , 1995, Physical review. B, Condensed matter.

[10]  C. Fortuin,et al.  On the random-cluster model: I. Introduction and relation to other models , 1972 .

[11]  Claude M. Penchina,et al.  The physics of amorphous solids , 1983 .

[12]  G. Döhler,et al.  A topological-dynamical model of amorphycity , 1980 .

[13]  J. Troadec,et al.  Non-local and non-linear problems in the mechanics of disordered systems: application to granular media and rigidity problems , 1990 .

[14]  P. N. Keating,et al.  Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure , 1966 .

[15]  Duxbury,et al.  Stressed backbone and elasticity of random central-force systems. , 1995, Physical review letters.

[16]  Thorpe,et al.  Glass-forming tendency, percolation of rigidity, and onefold-coordinated atoms in covalent networks. , 1994, Physical review. B, Condensed matter.

[17]  Donald J. Jacobs,et al.  Generic rigidity in three-dimensional bond-bending networks , 1998 .

[18]  Deborah S. Franzblau Combinatorial Algorithm for a Lower Bound on Frame Rigidity , 1995, SIAM J. Discret. Math..

[19]  Feng,et al.  Effective-medium theory of percolation on central-force elastic networks. , 1985, Physical review. B, Condensed matter.

[20]  Lindsay,et al.  Fragility of Ge-As-Se glass-forming liquids in relation to rigidity percolation, and the Kauzmann paradox. , 1990, Physical review letters.

[21]  L. Lovász,et al.  On Generic Rigidity in the Plane , 1982 .

[22]  Day,et al.  Rigid backbone: A new geometry for percolation. , 1986, Physical review letters.

[23]  Roux,et al.  Universality class of central-force percolation. , 1989, Physical review. B, Condensed matter.

[24]  M. Sahimi,et al.  On the universality of geometrical and transport exponents of rigidity percolation , 1992 .

[25]  Cai,et al.  Floppy modes in network glasses. , 1989, Physical review. B, Condensed matter.

[26]  D. Jacobs,et al.  Comment on “infinite-cluster geometry in central-force networks” , 1998 .

[27]  Michael Thorpe,et al.  Continuous deformations in random networks , 1983 .

[28]  J. C. Phillips,et al.  Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys , 1979 .

[29]  Zhang,et al.  Influence of one-fold-coordinated atoms on mechanical properties of covalent networks. , 1996, Physical review. B, Condensed matter.

[30]  G. Laman On graphs and rigidity of plane skeletal structures , 1970 .

[31]  Thorpe,et al.  Elastic properties of glasses. , 1985, Physical review letters.

[32]  J. W. Essam,et al.  Percolation theory , 1980 .

[33]  Shechao Feng,et al.  Percolation on Elastic Networks: New Exponent and Threshold , 1984 .

[34]  Phillip M. Duxbury,et al.  INFINITE-CLUSTER GEOMETRY IN CENTRAL-FORCE NETWORKS , 1997 .

[35]  J. Angus,et al.  Dense ‘‘diamondlike’’ hydrocarbons as random covalent networks , 1988 .