Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collision-avoiding in the singular Cucker-Smale model with nonlinear
  velocity couplings   Collision avoidance is an interesting feature of the Cucker-Smale (CS) model
of flocking that has been studied in many works, e.g. [1, 2, 4, 6, 7, 20, 21,
22]. In particular, in the case of singular interactions between agents, as is
the case of the CS model with communication weights of the type
$\psi(s)=s^{-\alpha}$ for $\alpha \geq 1$, it is important for showing global
well-posedness of the underlying particle dynamics. In [4], a proof of the
non-collision property for singular interactions is given in the case of the
linear CS model, i.e. when the velocity coupling between agents $i,j$ is
$v_{j}-v_{i}$. This paper can be seen as an extension of the analysis in [4].
We show that particles avoid collisions even when the linear coupling in the CS
system has been substituted with the nonlinear term $\Gamma(\cdot)$ introduced
in [12] (typical examples being $\Gamma(v)=v|v|^{2(\gamma -1)}$ for $\gamma \in
(\frac{1}{2},\frac{3}{2})$), and prove that no collisions can happen in finite
time when $\alpha \geq 1$. We also show uniform estimates for the minimum
inter-particle distance, for a communication weight with expanded singularity
$\psi_{\delta}(s)=(s-\delta)^{-\alpha}$, when $\alpha \geq 2\gamma$, $\delta
\geq 0$.

9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
19
The categories of this paper are: eess
16
The categories of this paper are: stat