Magnetic confinement fusion (MCF) and inertial confinement fusion (ICF) are critically contrasted in the context of far-distant travels throughout solar system. Both are shown to potentially display superior capabilities for vessel maneuvering at high speed, which are unmatched by standard cryogenic propulsion (SCP). Costs constraints seem less demanding than for ground-based power plants. Main issue is the highly problematic takeoff from earth, in view of safety hazards concomitant to radioactive spills in case of emergency. So, it is recommended to assemble the given powered vessel at high earth altitude ∼ 700 km, above upper atmosphere. Fusion propulsion is also compared to fission powered one, which secures a factor of two improvement over SCP. As far a specific impulse (s) is considered, one expects 500–3000 from fission and as much as 104–105 from fusion through deuterium–tritium (D-T). Next, we turn attention to the most performing fusion reaction, i.e., proton–antiproton annihilation with specific impulse ∼ 103–106 and thrust–to–weight ratio ∼ 10−3–1. Production and costs are timely reviewed. The latter could drop by four orders of magnitude, which is possible with successful MCF or ICF. Appropriate vessel designs will be presented for fusion as well as for antimatter propulsion. In particular, ion compressed antimatter nuclear II (ICAN-II) project to Mars in 30 days with fusion catalyzed by 140 ng of antiprotons will be detailed (specific impulse ∼ 13500 s).

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

We consider one-dimensional processes in which particles annihilate their neighbours, grow until they meet their neighbours or are deposited onto surfaces. All of the models considered have the property that they are connected to exponential series often by an inclusion-exclusion argument.

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. It is shown that with initial configuration ℤ the distribution of particles at all times is a renewal process and that the probability that a site remains occupied for all time tends to 1/e. Time-dependent behaviour is also calculated for the tree 𝕋r.

Annihilation behaviors of athermal ω-phase crystals formed by cooling at 131 K for 10.8 ks under four different electron irradiation conditions of acceleration voltages of 200 kV and 160 kV, and beam currents of approximately 20 pA/cm2 and 5 pA/cm2 were investigated using in situ dark field and HREM observation methods at 131 K. The effect of acceleration voltages on the lifetimes is recognized, i.e., in the case of approximately equal electron beam current, lifetimes at 200 kV become shorter than those at 160 kV. Also, lifetimes depend on the electron beam current at 200 kV, i.e., the higher the beam currents, the shorter the lifetimes become. However, no distinct dependence can be seen at 160 kV. Since annihilations of athermal ω-phase crystals begin after the electron irradiation for a certain period in each condition, which depends on acceleration voltages and beam currents, it is suggested that the annihilation behaviors have incubation periods.

Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.

In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution vλ /(λ +1), the product measure with density λ/(1 +λ). It is shown that vλ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is vλ /(λ +1) provided the initial measure converges.