10 research outputs found
Evaporation, lifetime, and robustness studies of liquid marbles for collision-based computing
© 2018 American Chemical Society. Liquid marbles (LMs) have recently attracted interest for use as cargo carriers in digital microfluidics and have successfully been implemented as signal carriers in collision-based unconventional computing circuits. Both application domains require LMs to roll over substantial distances and to survive a certain number of collisions without degrading. To evaluate the lifetime of LMs being subjected to movement and impact stresses, we have selected four types of coating to investigate: polytetrafluoroethylene (PTFE), ultrahigh density polyethylene (PE), Ni, and a mixture of Ni with PE (Ni-PE). Hierarchies of robustness have been constructed which showed that pure PE LMs survived the longest when stationary and in motion. Pure PTFE LMs were shown to be the least resilient to multiple impacts. The PTFE coating provided minimal protection against evaporative losses for small LM volumes (2 and 5 μL) however, larger LMs (10 μL) were shown to have good evaporative stabilities when stationary. Conversely, PE LMs showed a remarkable ability to withstand multiple impacts and were also stable when considering just passive evaporation. Hybrid Ni-PE LMs exhibited more resilience to multiple impacts compared to Ni LMs. Thus, when designing LM devices, it is paramount to determine impact pathways and select appropriate coating materials
The firing squad synchronization problem for graphs
AbstractIn this paper, we give a solution of the Firing Squad Synchronization Problem for graphs. The synchronization times of solutions which have been obtained are proportional to the number of nodes of a graph. The synchronization time of our solution is proportional to the radius rG of a graph (G (3rG + 1 or 3rG time units, where rG, is the longest distance between the general and any other node of G. This synchronization time is minimum for an infinite number of graphs
A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata
The firing squad synchronization problem (FSSP) on cellular automata has been
studied extensively for more than forty years, and a rich variety of
synchronization algorithms have been proposed for not only one-dimensional
arrays but two-dimensional arrays. In the present paper, we propose a simple
recursive-halving based optimum-time synchronization algorithm that can
synchronize any rectangle arrays of size m*n with a general at one corner in
m+n+max(m, n)-3 steps. The algorithm is a natural expansion of the well-known
FSSP algorithm proposed by Balzer [1967], Gerken [1987], and Waksman [1966] and
it can be easily expanded to three-dimensional arrays, even to
multi-dimensional arrays with a general at any position of the array.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Cellular Automata on Group Sets
We introduce and study cellular automata whose cell spaces are
left-homogeneous spaces. Examples of left-homogeneous spaces are spheres,
Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform
tilings acted on by symmetries; vertex-transitive graphs, in particular, Cayley
graphs, acted on by automorphisms; groups acting on themselves by
multiplication; and integer lattices acted on by translations. For such
automata and spaces, we prove, in particular, generalisations of topological
and uniform variants of the Curtis-Hedlund-Lyndon theorem, of the
Tarski-F{\o}lner theorem, and of the Garden-of-Eden theorem on the full shift
and certain subshifts. Moreover, we introduce signal machines that can handle
accumulations of events and using such machines we present a time-optimal
quasi-solution of the firing mob synchronisation problem on finite and
connected graphs.Comment: This is my doctoral dissertation. It consists of extended versions of
the articles arXiv:1603.07271 [math.GR], arXiv:1603.06460 [math.GR],
arXiv:1603.07272 [math.GR], arXiv:1701.02108 [math.GR], arXiv:1706.05827
[math.GR], and arXiv:1706.05893 [cs.FL