Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Granular Impact Model as an Energy-Depth Relation   Velocity-squared drag forces are common in describing an object moving
through a granular material. The resulting force law is a nonlinear
differential equation, and closed-form solutions of the dynamics are typically
obtained by making simplifying assumptions. Here, we consider a generalized
version of such a force law which has been used in many studies of granular
impact. We show that recasting the force law into an equation for the kinetic
energy versus depth, K(z), yields a linear differential equation, and thus
general closed-form solutions for the velocity versus depth. This approach also
has several advantages in fitting such models to experimental data, which we
demonstrate by applying it to data from 2D impact experiments. We also present
new experimental results for this model, including shape and depth dependence
of the velocity-squared drag force.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org