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Hybrid modeling of tumor-induced angiogenesis.
TLDR
This work sets up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derives a mean field approximation for their densities, which leads to a deterministic integropartial differential system that describes the formation of the Stochastic vessel network.
On the mathematical modelling of tumor-induced angiogenesis.
TLDR
The outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the ``propagation of chaos" assumption cannot be applied to obtain a deterministic mean field approximation.
Chaos-based true random number generators
TLDR
A mathematical model is explained to describe spontaneous chaos in semiconductor superlattices at room temperature, solved numerically to reveal the origin and characteristics of chaotic oscillations, and the limitations of the model are discussed in view of known experiments.
Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models.
TLDR
The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments, and to determine more accurately the time-dependent characteristics of superLattices, in particular their current density.
Noise-enhanced spontaneous chaos in semiconductor superlattices at room temperature
Physical systems exhibiting fast spontaneous chaotic oscillations are used to generate high-quality true random sequences in random number generators. The concept of using fast practical entropy
Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in
Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices
A two miniband model for electron transport in semiconductor superlattices that includes scattering and interminiband tunnelling is proposed. The model is formulated in terms of Wigner functions in a
Nonlinear Electron and Spin Transport in Semiconductor Superlattices
TLDR
Numerical solutions show stable self-sustained oscillations of the current and the spin polarization through a voltage biased lateral superlattice thereby providing an example of superlATTice spin oscillator.
Nonlinear Electron and Spin Transport in Semiconductor Superlattices
Nonlinear charge transport in strongly coupled semiconductor super lattices is described by two-miniband Wigner-Poisson kinetic equations with BGK collision terms. The hyperbolic limit, in which the
Spatially confined Bloch oscillations in semiconductor superlattices
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that convective nonlinearities may compensate it and Bloch oscillations persist
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