A coagulation–disintegration model of Oort–Hulst cluster-formation

Wattis, Jonathan A. D.

doi:10.1088/1751-8113/45/42/425001

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…The equation (2) includes two major events, collision followed by coagulation. There are various examples of the phenomenon explained by the Oort-Hulst-Safronov equation, namely, the collision of asteroids [11], formation of saturn's rings [12], formation of protoplanetary disc around a newly formed star [13]. There are several real-world problems caused by particle coagulation such as the health hazards of sand and dust storms [14], the analysis of nano-metal dust explosions [15] and the impact on glacier mass as a result of volcanic dust accumulation [16].…”

Section: Prologuementioning

confidence: 99%

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Kaushik¹,

Kumar²

2022

Preprint

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The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients φ such that φ i,j ≤ ij ∀ i, j ∈ N. Both conservative and non-conservative truncated systems are used to analyse the infinite system of ODEs. In the conservative case, Helly's selection theorem is used to prove the global existence while for the non-conservative part, we make use of the refined version of De la Vallée-Poussin theorem to establish the existence. Further, it is shown that these solutions conserve density. Finally, the solutions are shown to be unique when the kernel φ i,j ≤ min{i η , j η } where η ∈ [0, 2].

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Section: Prologuementioning

confidence: 99%

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Kaushik¹,

Kumar²

2022

Preprint

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“…represents the breakage into the debris l ¼ fl 1 ; …l n g. The collision-controlled fragmentation underlies, e.g., the Oort-Hulst models [49][50][51][52][53]. Generally, the process (2) describes the breakup of an aggregate in a collision with energetic monomers [21,[54][55][56][57].…”

mentioning

confidence: 99%

Nonextensive Supercluster States in Aggregation with Fragmentation

2021

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Systems evolving through aggregation and fragmentation may possess an intriguing supercluster state (SCS). Clusters constituting this state are mostly very large, so the SCS resembles a gelling state, but the formation of the SCS is controlled by fluctuations and in this aspect, it is similar to a critical state. The SCS is nonextensive, that is, the number of clusters varies sublinearly with the system size. In the parameter space, the SCS separates equilibrium and jamming (extensive) states. The conventional methods, such as, e.g., the van Kampen expansion, fail to describe the SCS. To characterize the SCS we propose a scaling approach with a set of critical exponents. Our theoretical findings are in good agreement with numerical results.

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“…The collision-controlled fragmentation underlies e.g. the Oort-Hulst models [49][50][51][52][53]. Generally, the process (2) describes the break-up of an aggregate in a collision with energetic monomers [21,[54][55][56][57].…”

mentioning

confidence: 99%

Non-extensive super-cluster states in aggregation with fragmentation

Brilliantov,

Otieno,

Krapivsky

2021

Preprint

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Systems evolving through aggregation and fragmentation may possess an intriguing super-cluster state (SCS). Clusters constituting this state are mostly large, so the SCS resembles a gelling state. The formation of the SCS is controlled by fluctuations and in this aspect, it is similar to a critical state. The SCS is non-extensive as the number of clusters varies sub-linearly with the system size. In the parameter space, the SCS separates equilibrium and jamming (extensive) states. The conventional methods such as the van Kampen expansion fail to describe the SCS. To characterize the SCS, we propose a scaling approach with a set of critical exponents. Our theoretical findings are in good agreement with numerical results.

show abstract

A coagulation–disintegration model of Oort–Hulst cluster-formation

Cited by 8 publications

References 24 publications

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Nonextensive Supercluster States in Aggregation with Fragmentation

Non-extensive super-cluster states in aggregation with fragmentation

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