@article{11556,
  abstract     = {We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the
oscillations with respect to fluctuations and noise.},
  author       = {Kalinov, Aleksei and Osinskiy, A.I. and Matveev, S.A. and Otieno, W. and Brilliantov, N.V.},
  issn         = {0021-9991},
  journal      = {Journal of Computational Physics},
  keywords     = {Computer Science Applications, Physics and Astronomy (miscellaneous), Applied Mathematics, Computational Mathematics, Modeling and Simulation, Numerical Analysis},
  publisher    = {Elsevier},
  title        = {{Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics}},
  doi          = {10.1016/j.jcp.2022.111439},
  volume       = {467},
  year         = {2022},
}

@article{7763,
  abstract     = {An orthogonal wavelet basis is characterized by its approximation order, which relates to the ability of the basis to represent general smooth functions on a given scale. It is known, though perhaps not widely known, that there are ways of exceeding the approximation order, i.e., achieving higher-order error in the discretized wavelet transform and its inverse. The focus here is on the development of a practical formulation to accomplish this first for 1D smooth functions, then for 1D functions with discontinuities and then for multidimensional (here 2D) functions with discontinuities. It is shown how to transcend both the wavelet approximation order and the 2D Gibbs phenomenon in representing electromagnetic fields at discontinuous dielectric interfaces that do not simply follow the wavelet-basis grid.},
  author       = {Lombardini, Richard and Acevedo, Ramiro and Kuczala, Alexander and Keys, Kerry P. and Goodrich, Carl Peter and Johnson, Bruce R.},
  issn         = {0021-9991},
  journal      = {Journal of Computational Physics},
  pages        = {244--262},
  publisher    = {Elsevier},
  title        = {{Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena}},
  doi          = {10.1016/j.jcp.2015.10.035},
  volume       = {305},
  year         = {2016},
}