Geometrically cohesive granular materials: Why can you move
through rice but not nails?
Our lab is looking at large aspect ratio (large length to diameter
ratio) granular materials. These materials' resistance to
disturbances is striking. One can easily run fingers through a bucket
of sand, but not through nails. When the aspect ratio is large, a
solid "plug" forms that holds its shape even when the initial
container is removed. This is seen in the pile below, which was
formed by putting acrylic rods (3" long, 1/16" in diameter) in a big
cylinder and then lifting the entire pile by a small (1/4'' ball at
the bottom. When the cylinder is removed, the pile retains its
cylindrical shape, supported only by the ball at the bottom.
This plug forms despite the presence of large voids into which
particles could move. The rigidity results from particle
entanglement, which greatly constrains the ability of particles to
rotate.

Physics Education Research: How Physicists
embed Meaning in Mathematics
Physics embeds conceptual meaning in mathematical formalism, and
attempts to separate the two seems arbitrary and artificial. To the
physicist, the concepts are the math and the math are
the concepts. The particulars of the math serves to emphasisze (or
deemphasize) particular concepts, and physicists manipulate equations
to highlight specific concepts. For example, the Newton's 2nd law
equation for a damped, driven harmonic oscillator written as
emphasizes the restoring and damping forces, as well as the
"partsofawhole" nature of the net force. Rewriting it as
changes the focus to one in which the variable x is now
constrained by the driving F(t) through an inhomogeneous
differential equation. This particular mathematical move refocuses
the classroom "frame" from a physicsoriented context to one in which
canonical mathematical approaches are more natural.
