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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.
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
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.
Coherence Resonance and Stochastic Resonance in an Excitable Semiconductor Superlattice.
TLDR
The device-dependent critical current for the coherence resonance is determined from experiments and numerical simulations and it is described through numerical simulations how a coherence Resonance triggers a stochastic resonance when its oscillation mode becomes locked to a weak ac external voltage signal.
One-dimensional overdriven detonations with branched-chain kinetics
The dynamics of time-dependent, planar propagation of gaseous detonations is addressed on the basis of a three-step chemistry model that describes branched-chain processes. Relevant nondimensional
Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model
TLDR
A mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues is presented and it is demonstrated that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.
Soliton driven angiogenesis
TLDR
A stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density.
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