Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

Privman, Vladimir; Cadilhe, A.; Glasser, M. Lawrence

doi:10.1007/bf02179297

Cited by 48 publications

(45 citation statements)

References 32 publications

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“…A large fraction of analytical studies belong to low-dimensional (specially one-dimensional) systems, as solving lowdimensional systems should in principle be easier. [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable reaction diffusion models on a Cayley tree

2007

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The most general reaction-diffusion model on a Cayley tree with nearestneighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.

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Section: Introductionmentioning

confidence: 99%

Exactly solvable reaction diffusion models on a Cayley tree

2007

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“…A large fraction of analytical studies, belong to low-dimensional (specially one-dimensional) systems, where solving low-dimensional systems should in principle be easier. [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Models solvable through the empty-interval method

Aghamohammadi

Khorrami²

2005

Eur. Phys. J. B

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The most general one dimensional reaction-diffusion model with nearestneighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is shown that turning on the reactions which generate particles from two adjacent empty sites, results in a gap in the spectrum of the evolution operator (or equivalently a finite relaxation time).

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“…The solution of such equations usually poses great mathematical difficulties; however, the simple topology of the one-dimensional lattice frequently allows derivation of exact solutions [1][2][3][4][5][6]. These results may be used to test the validity of various approximations.…”

Section: Introductionmentioning

confidence: 99%

Lattice kinetics of diffusion-limited coalescence and annihilation with sources

Abad

Masser

ben‐Avraham

2002

J. Phys. A: Math. Gen.

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Abstract:We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.

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Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

Cited by 48 publications

References 32 publications

Exactly solvable reaction diffusion models on a Cayley tree

Exactly solvable reaction diffusion models on a Cayley tree

Models solvable through the empty-interval method

Lattice kinetics of diffusion-limited coalescence and annihilation with sources

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