Related papers: On (Multi)-Collision Times
We examine the total number of collisions $C_n$ in the $\Lambda$-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $C_n$ are shown under the assumption of a power-like behaviour of the measure…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
Collision avoidance requires tradeoffs in planning time horizons. Depending on the planner, safety cannot always be guaranteed in uncertain environments given map updates. To mitigate situations where the planner leads the vehicle into a…
We present the first triangle mesh-based technique for tracking the evolution of general three-dimensional multimaterial interfaces undergoing complex topology changes induced by deformations and collisions. Our core representation is a…
In turbulent suspensions, collision rates determine how rapidly particles coalesce or react with each other. To determine the collision rate, many numerical studies rely on the 'Ghost Collision Approximation' (GCA), which simply records how…
The blocking problem naturally arises in transportation systems as multiple vehicles with different itineraries share available resources. In this paper, we investigate the impact of the blocking problem to the waiting time at the…
We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…
We model the disassembly of an excited nuclear system formed as a result of a heavy ion collision. We find that, as the beam energy in central collisions in varied, the dissociating system crosses a liquid-gas coexistence curve, resulting…
Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles…
Research in atomic and molecular collision processes and spectral line broadening has been very active since our last report, Peach, Dimitrijevic & Stancil 2009. Given the large volume of the published literature and the limited space…
Intersections constitute one of the most dangerous elements in road systems. Traffic signals remain the most common way to control traffic at high-volume intersections and offer many opportunities to apply intelligent transportation systems…
Time-to-Contact (TTC) estimation is a critical task for assessing collision risk and is widely used in various driver assistance and autonomous driving systems. The past few decades have witnessed development of related theories and…
The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…
Scheduling wireless links for simultaneous activation in such a way that all transmissions are successfully decoded at the receivers and moreover network capacity is maximized is a computationally hard problem. Usually it is tackled by…
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
A statistical-mechanical treatment of collision leads to a formal connection with transition-state theory, suggesting that collision theory and transition-state theory might be joined ultimately as a collision induced transition state…
We discuss the importance of initial state and early time effects with regard to the theoretical understanding of long range azimuthal correlations observed in high-multiplicity $p+p$ and $p+A$ collisions.
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
Onset of multifragmentation and vaporization in Au-Au collisions
A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles…