Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability

The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of the origin. Previous, models of ballistic annihilation have particles that always react on contact, i.e. pair-reaction probability $p=1$. The evolution of such systems are wholly determined by the initial distribution of particles and therefore do not have a stochastic dynamics. However, in this paper the generalisation is made to $p<1$, allowing particles to pass through each other without necessarily reacting. In this way, the A and B particle domains overlap to form a fluctuating, finite-sized reaction zone where the product C is created. Fluctuations are also included in the currents of A and B particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by the `intrinsic reaction rate', seen in a single system, and the `extrinsic reaction rate', seen in an average over many systems. The intrinsic and extrinsic behaviours are examined and compared to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte

A probability-conserving cross-section biasing mechanism for variance reduction in Monte Carlo particle transport calculations

In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible to increase the cross section of nuclear reactions by factors exceeding 10^4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful, for example, in problems that involve computation of particle penetration deep into a target, such as occurs in atmospheric showers or in shielding

Liver tissue graft rejection in murine major histocompatibility complex mutants

Liver tissue grafts between seven H-2 mutants and their parental strains have been studied. Each of these mutants was originally identified by reciprocal mutant—parental strain skin graft rejection. However, liver grafts among mutants and parental standard strains are not uniformly rejected. Liver graft rejection also fails to correlate with mutant—parental stimulation in CML and MLC. In addition, the immune reaction pattern of female mutant animals against grafts of male liver differs from the reaction pattern found in parental standard strains. Several explanations for the differences between immune response to liver and skin grafts are proposed, including different T cell subsets involved in recognition, availability of antigenic sites to immunocompetent cells, and structural differences between mutant and parental H-2 antigens.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46738/1/251_2004_Article_BF00364259.pd