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Localized soft modes and the supercooled liquid’s irreversible passage through its configuration space
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Image of FIG. 1.
FIG. 1.

The probability distributions for the minimum number of “lost” initial neighbors after having first lost neighbors. Note that after losing neighbors, the probability of recovering all of the initial neighbors (i.e., having ) is essentially zero. The distributions show peaks at suggesting that particles typically recover two of their initial neighbors. These calculations where carried out over a time interval of at .

Image of FIG. 2.
FIG. 2.

Distribution of times at which particles first lose their fourth nearest neighbor (data averaged over isoconfigurational ensembles of 100 runs for a total of ten initial configurations of particles at ).

Image of FIG. 3.
FIG. 3.

Contour plots of the probability of a particle losing four original neighbors, the criterion for IR, over 100 isoconfigurational runs for six different initial configurations.

Image of FIG. 4.
FIG. 4.

Contour plots of the participation fraction summed over the 30 lowest frequency modes for the quenched initial configurations of the same six configurations used in Fig. 3.

Image of FIG. 5.
FIG. 5.

Maps of the participation fractions for the 11 lowest frequency normal modes of the local potential energy minimum associated with a single initial configuration. Modes with a participation ratio are colored red while the more delocalized modes are colored blue. The intensity of the color increases with the magnitude of the squared amplitude. The corresponding irreversibility map for this configuration is provided for comparison.

Image of FIG. 6.
FIG. 6.

A comparison of the particle displacements averaged over the isoconfigurational ensemble and the displacements associated with the four lowest frequency normal modes. The first column labeled “displacements” contains the same displacement map repeated for ease of comparison. The vectors are proportional to the isoconfigurational average of the particle displacement over . The middle column labeled “Mode Displacements” shows the 4 lowest frequency normal modes of the initial configuration. The vectors are proportional to the mode polarization vector on each particle. Those vectors colored blue are correlated with displacement map vectors with an angle of less than while the red regions are anticorrelated with angle greater than It should be noted that each eigenvector provides us with lines in space along which particle moves with the actual forward or backward direction depending on the (arbitrary) phase of the vibration. The third column labeled “comparison” shows plots of the scalar product of the mode polarization vector on each particle with the average displacement vector. Darker colors signify greater magnitude of the scalar product, with blue (red) signifying positive (negative) signs of the scalar product.

Image of FIG. 7.
FIG. 7.

Contour plots of the low frequency mode participation (as in Fig. 3), overlaid with the location of particles (white circles) whose isoconfigurational probability of losing four initial nearest neighbors within is greater than or equal to 0.01.

Image of FIG. 8.
FIG. 8.

Plots of the participation fraction in the 30 lowest frequency normal modes for quenched configurations taken every along a trajectory from the initial configuration. The color code is the same as previous figures. While there are clearly variations occurring in the distribution of modes (and hence in the identity of the quenched minimum or inherent structure) over , substantial elements of the mode distribution persist. The top left map is the IR map for the initial configuration, included for comparison.

Image of FIG. 9.
FIG. 9.

(a) Contour plot of the participation fraction summed over the 30 lowest frequency modes for a quenched configuration. (b) Contour plot of the maximum value of the participation fraction observed over five runs starting from the configuration in Fig. 10(a). (c) Particles whose isoconfigurational probability of losing four initial nearest neighbors within is greater than or equal to 0.01 (white circles) overlaid on the participation fraction map for the initial configuration. d) As in (c) except that the overlay is over the map of the maximum participation fraction shown in (b).

Image of FIG. 10.
FIG. 10.

A comparison of the sum of the participation fractions of the normal modes with imaginary frequency with the sum of participation fraction of the same number of quenched normal modes, along with the map of the local DW factor and a map with vectors representing the motion of each particle from the instantaneous configuration to the IS.

Image of FIG. 11.
FIG. 11.

For the 2D system, the overlap of the 10% of particles with the largest DW factors with (black dots) the top 10% of clustered particles with the largest amplitudes in the sum of the lowest 30 normal modes and with (red squares) a random selection of 10% of the particles, all maps have had clusters of less than eliminated.

Image of FIG. 12.
FIG. 12.

Similar to Fig. S6 for the 3D system, in this dimension the minimum cluster size is .


Generic image for table
Table I.

Comparison of the degree of similarity in the sum of low-frequency quenched normal modes and imaginary frequency instantaneous normal mode maps for ten configurations. The left two columns give the percentage of particles with a value of the amplitude of the sum of the mode polarization vectors on each particle greater than 25% of the minimum value (the “active portions”). The overlap column lists the percentages of those particles that are presented in both the left and middle columns.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Localized soft modes and the supercooled liquid’s irreversible passage through its configuration space