Category: Physics

Summary: Finding the bond density where a diluted triangular spring network becomes mechanically rigid.

Ordinary percolation asks when a network first becomes connected, but rigidity percolation asks a harder question: when does it acquire enough constraints to resist deformation? In a diluted spring network, that transition marks the onset of a nonzero shear response and connects to problems in gels, granular packings, and cytoskeletal materials.

The experiment constructs triangular-lattice spring networks at increasing sizes, forms their stiffness matrices, and bisects bond probability to locate the onset of rigidity. Because rigidity depends on the spectrum of the elastic operator rather than simple graph connectivity, each pass requires a full symmetric eigensolve.

The BOINC setup is useful because it can push the threshold bracket through multiple lattice deepening stages while keeping the memory footprint controlled. That makes it practical to map the finite-size critical region with much denser coverage than a one-off workstation run.

Method: Dense symmetric eigensolve of stiffness matrices with iterative deepening and bisection on bond probability.

What is measured: Critical bond probability, current lattice size, matrix dimension, bracket width, and number of eigendecompositions.