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We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ withequal species diffusivities in the system where an island of particles $A$ issurrounded by the uniform sea of particles $B$. We show that once the initialnumber of particles in the island is large enough, then at any system'sdimensionality $d$ the death of the majority of particles occurs in the {\ituniversal scaling regime} within which $\approx 4/5$ of the particles die atthe island expansion stage and the remaining $\approx 1/5$ at the stage of itssubsequent contraction. In the quasistatic approximation the scaling of thereaction zone has been obtained for the cases of mean-field ($d \geq d_{c}$)and fluctuation ($d < d_{c}$) dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Diffusion-controlled annihilation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mn>0</mml:mn></mml:math>with initially separated reactants: The death of an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>particle island in the<mml:…

Diffusion-controlled annihilationA+B→0with initially separated reactants: The death of anAparticle island in the