Competition Between Self-birth and Catalyzed Death in Aggregation Growth with Catalysis Injection

• 出 处: Communications in Theoretical Physics
• 发表日期: 2009年12期
• 关键词: birth aggregate monomer kernel aggregation exponential exchanges periodical domi

We propose two irreversible aggregation growth models of aggregates of two distinct species (A and B)to study the interactions between virus aggregates and medicine efficacy aggregates in the virus-medicine cooperativeevolution system. The A-species aggregates evolve driven by self monomer birth and B-species aggregate-catalyzedmonomer death in model Ⅰ and by self birth, catalyzed death, and self monomer exchange reactions in model Ⅱ, whilethe catalyst B-species aggregates are assumed to be injected into the system sustainedly or at a periodic time-dependentrate. The kinetic behaviors of the A-species aggregates are investigated by the rate equation approach based on themean-field theory with the self birth rate kernel I_A(k) = Ik, catalyzed death rate kernel J_(AB)(k) = Jk and self exchangerate kernel K_A(k,l) = Kkl. The kinetic behaviors of the A-species aggregates are mainly dominated by the competitionbetween the two effects of the self birth (with the effective rate I) and the catalyzed death (with the effective rate JB_0),while the effects of the self exchanges of the A-species aggregates which appear in an effective rate K A_0 play importantroles in the cases of I > J B_0 and I = J B_0. The evolution behaviors of the total mass M_1~A(t) and the total aggregatenumber M_0~A(t) are obtained, and the aggregate size distribution a_k(t) of species A is found to approach a generalizedscaling form in the case of I ≥ J B_0 and a special modified scaling form in the case of I < J B_0. The periodical evolutionof the B-monomers concentration plays an exponential form of the periodic modulation. We propose two irreversible aggregation growth models of aggregates of two distinct species (A and B) to study the interactions between virus aggregates and medicine efficacy aggregates in the virus-medicine cooperative evolution system. The A-species aggregates evolve driven by self monomer birth and B catalyzed death, and self monomer exchange reactions in model II, while the catalyst B-species aggregates are assumed to be injected into the system sustainedly or at a periodic time-dependent rate. kinetic behaviors of the A-species aggregates are investigated by the rate equation approach based on themean-field theory with the self-birth rate kernel I_A (k) = Ik, catalyzed death rate kernel J_ (AB) (k) = Jk and self exchangerate Kinetic behaviors of the A-species aggregates are mainly dominated by the competitionbetween the two effects of the self birth (with the effective rate I) and the catalyzed death (with the effective rate JB_0), while the effects of the self exchanges of the A-species aggregates which appear in an effective rate K A_0 play importantroles in the cases of I> J B_0 and I = J B_0. The evolution behaviors the aggregate size distribution a_k (t) of species A is found to approach a generalizedscaling form in the case of I ≥ J B_0 and a special modified scaling form in the case of I