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- W2003131812 abstract "Abstract To study the collisional evolution of asteroidal groups we can use an analytical solutionfor the self-similar collision cascades. This solution is suitable to study the steady-state massdistribution of the collisional fragmentation. However, out of the steady-state conditions, thissolution is not satisfactory for some values of the collisional parameters. In fact, for some valuesfor the exponent of the mass distribution power law of an asteroidal group and its relation to theexponent of the function which describes how rocks break we arrive at singular points for theequation which describes the collisional evolution. These singularities appear since someapproximations are usually made in the laborious evaluation of many integrals that appear in theanalytical calculations. They concern the cutoff for the smallest and the largest bodies. Thesesingularities set some restrictions to the study of the analytical solution for the collisionalequation. To overcome these singularities we performed an algebraic computationconsidering the smallest and the largest bodies and we obtained the analytical expressions for theintegrals that describe the collisional evolution without restriction on the parameters. However,the new distribution is more sensitive to the values of the collisional parameters. In particular thesteady-state solution for the differential mass distribution has exponents slightly different from11⧸6 for the usual parameters in the Asteroid Belt. The sensitivity of this distribution with respectto the parameters is analyzed for the usual values in the asteroidal groups. With anexpression for the mass distribution without singularities, we can evaluate also its time evolution.We arrive at an analytical expression given by a power series of terms constituted by a smallparameter multiplied by the mass to an exponent, which depends on the initial power lawdistribution. This expression is a formal solution for the equation which describes the collisionalevolution. Furthermore, the first-order term for this solution is the time rate of the distribution atthe initial time. In particular the solution shows the fundamental importance played by theexponent of the power law initial condition in the evolution of the system." @default.
- W2003131812 created "2016-06-24" @default.
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- W2003131812 date "1999-05-01" @default.
- W2003131812 modified "2023-09-27" @default.
- W2003131812 title "Collisional evolution—an analytical study for the nonsteady-state mass distribution" @default.
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- W2003131812 doi "https://doi.org/10.1016/s0032-0633(98)00133-0" @default.
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