A Geometric Optics Experiment to Simulate the Betatronic Motion

Bazzani, Armando; Freguglia, Paolo; Fronzoni, Leone; Turchetti, G.

doi:10.1007/978-1-4757-4947-2_2

Cited by 2 publications

(5 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the sake of simplicity, let us use the modeling framework proposed by [26], where phenotypes are modelled through a finite number of parameters. Thus, we may say that our model assumes that the tumor immuno-phenotype has an average given by the vector f (t) = [p(t),k(t)], and a variance that is very small.…”

Section: Discussionmentioning

confidence: 99%

Simple biophysical model of tumor evasion from immune system control

d’Onofrio

Ciancio

2011

Phys. Rev. E

View full text Add to dashboard Cite

The competitive nonlinear interplay between a tumor and the host's immune system is not only very complex but is also time-changing. A fundamental aspect of this issue is the ability of the tumor to slowly carry out processes that gradually allow it to become less harmed and less susceptible to recognition by the immune system effectors. Here we propose a simple epigenetic escape mechanism that adaptively depends on the interactions per time unit between cells of the two systems. From a biological point of view, our model is based on the concept that a tumor cell that has survived an encounter with a cytotoxic T-lymphocyte (CTL) has an information gain that it transmits to the other cells of the neoplasm. The consequence of this information increase is a decrease in both the probabilities of being killed and of being recognized by a CTL. We show that the mathematical model of this mechanism is formally equal to an evolutionary imitation game dynamics. Numerical simulations of transitory phases complement the theoretical analysis. Implications of the interplay between the above mechanisms and the delivery of immunotherapies are also illustrated.

show abstract

Section: Discussionmentioning

confidence: 99%

Simple biophysical model of tumor evasion from immune system control

d’Onofrio

Ciancio

2011

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Symmetric mapping models of Hamiltonian systems proposed in this work should also be useful in some important problems of accelerator physics and dynamical astronomy. The symplectic mapping models have been important tools to study the long-term stability of particle motion in accelerators (see [29][30][31][32]). In most cases, they have been constructed in a nonsymmetric form, which is less compatible with the original Hamiltonian system.…”

Section: Discussionmentioning

confidence: 99%

“…Only in the case when the function H 1 does not depend on the action variable ψ, i.e. ∂H 1 /∂ψ = g(ψ, ϑ) ≡ 0, does the angle ϑ become continuous along ϕ, and the integration gives rise to the map (29) which is known as a radial twist map when the frequency ω(ψ) is a monotonic function of ψ.…”

Section: Conventional Methodsmentioning

confidence: 99%

“…However, for the system (24) they are not defined at these sections. Therefore, the variables of the map (29) are not identical to those of the original system. The approach that we have presented to construct symplectic maps does not allow us to find the relation between the variables of the original system and the ones in the map (29).…”

Section: Conventional Methodsmentioning

confidence: 99%

“…Mappings are also extensively used in accelerator physics to study the stability of single-particle motion in accelerator devices [29][30][31][32]. In dynamical astronomy different symplectic mapping methods have been proposed to simulate the long-term evolution of planetary systems in the Solar System (see [33][34][35][36][37][38] and references therein).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On mapping models of field lines in a stochastic magnetic field

Abdullaev¹

2004

Nucl. Fusion

View full text Add to dashboard Cite

Mapping models of Hamiltonian systems are discussed using the example of magnetic field lines in magnetically confined fusion plasmas. They are usually constructed in a certain symplectic form by imposing several constraints that make them compatible with a toroidal geometry. The possible symplectic forms of model mappings for Hamiltonian systems are derived using the recently developed method for the construction of symplectic mappings (Abdullaev S.S. 2002 J. Phys. A 35 2811). It is shown that the symplectic mappings may have symmetric and nonsymmetric forms. The generating function of the symmetric mapping depends only on the perturbation field while the one for the nonsymmetric map depends also on the safety factor (or winding number). Mapping models, particularly, a global mapping model in a toroidal system, the tokamap (Balescu R. et al 1998 Phys. Rev. E 58 951), usually used in plasma physics are reviewed and their relations with continuous Hamiltonian systems are discussed. The symmetric form of the tokamap is proposed and compared with the conventional tokamap. The symmetric and nonsymmetric mapping models for field lines in ergodic divertor tokamaks are also considered. It is shown that symmetric mappings closely describe original Hamiltonian systems in comparison with nonsymmetric mappings.

show abstract

A Geometric Optics Experiment to Simulate the Betatronic Motion

Cited by 2 publications

References 3 publications

Simple biophysical model of tumor evasion from immune system control

Simple biophysical model of tumor evasion from immune system control

On mapping models of field lines in a stochastic magnetic field

Contact Info

Product

Resources

About