Secondary bifurcation of a shearable rod with nonlinear spring supports

The mechanisms by which sister chromatids maintain biorientation on the metaphase spindle are critical to the fidelity of chromosome segregation. Active force interplay exists between predominantly extensional microtubule-based spindle forces and restoring forces from chromatin. These forces regulate tension at the kinetochore that silences the spindle assembly checkpoint to ensure faithful chromosome segregation. Depletion of pericentric cohesin or condensin has been shown to increase the mean and variance of spindle length, which have been attributed to a softening of the linear chromatin spring. Models of the spindle apparatus with linear chromatin springs that match spindle dynamics fail to predict the behavior of pericentromeric chromatin in wild-type and mutant spindles. We demonstrate that a nonlinear spring with a threshold extension to switch between spring states predicts asymmetric chromatin stretching observed in vivo. The addition of cross-links between adjacent springs recapitulates coordination between pericentromeres of neighboring chromosomes.

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Intermittency, Secondary Bifurcation and Mixed Mode Oscillations in a Swirl-Stabilized Annular Combustor: Experiments and Modeling

10.1115/1.0003125v ◽

2021 ◽

Author(s):

Samarjeet Singh ◽

Amitesh Roy ◽

K V Reeja ◽

Asalatha A. S. Nair ◽

Swetaprovo Chaudhuri ◽

...

Keyword(s):

Mixed Mode ◽

Mixed Mode Oscillations ◽

Annular Combustor ◽

Secondary Bifurcation

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SOFTENING BRANCHES OF A TWO-DEGREE-OF-FREEDOM SYSTEM INDUCED BY SPATIAL BUCKLING

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455406002088 ◽

2006 ◽

Vol 06 (04) ◽

pp. 493-512 ◽

Cited By ~ 2

Author(s):

NOËL CHALLAMEL

Keyword(s):

Structural Model ◽

Structural Parameters ◽

Degree Of Freedom ◽

Lateral Loading ◽

Load Parameter ◽

Imperfection Sensitivity ◽

Softening Effect ◽

Out Of Plane ◽

Secondary Bifurcation ◽

Two Degree Of Freedom

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.

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