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Biomedical subjects

Raphael Blumenfeld

Publications and source records attributed to Raphael Blumenfeld.

4 recordsLinked to original sources

Isostaticity and controlled force transmission in the cytoskeleton: A model awaiting experimental evidence.

A new model is proposed for force transmission through the cytoskeleton (CSK). A general discussion is first presented on the physical principles that underlie the modeling of this phenomenon. Some fundamental problems of conventional models--continuous and discrete--are examined. It is argued that mediation of focused forces is essential for good control over intracellular mechanical signals. The difficulties of conventional continuous models in describing such mediation are traced to a fundamental assumption rather than to their being continuous. Relevant advantages and disadvantages of continuous and discrete modeling are discussed. It is concluded that favoring discrete models is based on two misconceptions, which are clarified. The model proposed here is based on the idea that focused propagation of mechanical stimuli in frameworks over large distances (compared to the mesh size) can only occur when considerable regions of the CSK are isostatic. The concept of isostaticity is explained and a recently developed continuous isostaticity theory is briefly reviewed. The model enjoys several advantages: it leads to good control over force mediation; it explains nonuniform stresses and action at a distance; it is continuous, making it possible to model force propagation over long distances; and it enables prediction of individual force paths. To be isostatic, or nearly so, CSK networks must possess specific structural characteristics, and these are quantified. Finally, several experimental observations are interpreted using the new model and implications are discussed. It is also suggested that this approach may give insight into the dynamics of reorganization of the CSK. Many of the results are amenable to experimental measurements, providing a testing ground for the proposed picture, and generic experiments are suggested.

Animals↗

Stresses in isostatic granular systems and emergence of force chains.

Progress is reported on several questions that bedevil understanding of granular systems: (i) Are the stress equations elliptic, parabolic, or hyperbolic? (ii) How can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How do we relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains, and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to nonisostatic and more realistic granular assemblies.

Computer Simulation↗

Granular entropy: explicit calculations for planar assemblies.

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It leads to the identification of a conveniently small phase space. The utility of the volume function is demonstrated on several case studies, for which we calculate explicitly the mean volume and the volume fluctuations.

Journal Article↗

Stress field in granular systems: loop forces and potential formulation.

The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. This leads to a local constitutive equation coupling the stress tensor to fluctuations in the local geometry. For a disordered pile of rough grains this means the stress tensor components are coupled in a frustrated manner. In piles of rough grains with long range staggered order, frustration is avoided and a simple linear theory follows. We show that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.

Journal Article↗