Optimal life strategies in organisms exposed to recurrent critical events

The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion.     

A novel approach for introducing particulate matter into thermal plasmas: The triple-cathode arc

A coalesced high-intensity dc discharge is maintained between three cathodes and a single anode, stabilized by using resistors on each cathode leg. Jets of plasma gas are produced from either the cathode area or the anode area of the device. Cathode jets are generated by the self-induced pumping at the cathode tips and augmented by central gas injection. Arc voltage-current characteristics show classical convection-stabilized arc behavior. Anode heat transfer rates may be substantially increased by central gas injection toward the anode. Temperature fields in the coalesced, axially symmetric portion of the arc are determined spectrometrically and compared to those of a classical single-cathode free-burning arc.     

New lower bounds on the size of (n,r)‐arcs in PG(2,q)

An $\left(n,r\right)$‐arc in $\text{PG}\left(2,q\right)$ is a set of $n$ points such that each line contains at most $r$ of the selected points. It is well known that $\left(n,r\right)$‐arcs in $\text{PG}\left(2,q\right)$ correspond to projective linear codes. Let $m_r\left(2,q\right)$ denote the maximal number $n$ of points for which an $\left(n,r\right)$‐arc in $\text{PG}\left(2,q\right)$ exists. In this paper we obtain improved lower bounds on $m_r\left(2,q\right)$ by explicitly constructing $\left(n,r\right)$‐arcs. Some of the constructed $\left(n,r\right)$‐arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.     

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.

     

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

From Field Emission to Vacuum Arc Ignition: A New Tool for Simulating Copper Vacuum Arcs

Understanding plasma initiation in vacuum arc discharges can help to bridge the gap between nano‐scale triggering phenomena and the macroscopic surface damage caused by vacuum arcs. We present a new twodimensional particle‐in‐cell tool to simulate plasma initiation in direct‐current (DC) copper vacuum arc discharges starting from a single, strong field emitter at the cathode. Our simulations describe in detail how a sub‐micron field emission site can evolve to a macroscopic vacuum arc discharge, and provide a possible explanation for why and how cathode spots can spread on the cathode surface. Furthermore, the model provides us with a prediction for the current and voltage characteristics, as well as for properties of the plasma like densities, fluxes and electric potentials in a simple DC discharge case, which are in agreement with the known experimental values. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A geometric approach to Mathon maximal arcs

In 1969 Denniston [3] gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon [8] gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of isomorphism classes of Mathon maximal arcs of degree 8 in PG(2,h²), h prime.     

A 100-kW three-phase AC plasma furnace for spheroidization of aluminum silicate particles

A 100-kW three-phase ac plasma furnace with sheathed copper electrodes (sheathing gas: air) is presented. It is used for spheroidizing chamotte (refractory-fired clay) particles having a smooth, pore-free surface. A simple, one-dimensional numerical model for the heat transfer to the particles explains the maximum processing rate and the detrimental influence of an inhomogeneous particle size distribution.     

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.This research was supported by the National Science Foundation under Grant Nos. GK-30115 and ENG 74-21618 and by the National Aeronautics and Space Administration under Contract No. NAS 9-12872.     

Singular differential game numerical techniques

This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.