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Abstract: Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells…) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species. [Copyright &y& Elsevier]

Abstract: The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. [Copyright &y& Elsevier]

Quality of the cutting machining process of martensitic steel is analysed as a function of the cutting speed. This analysis is performed by topographical measurement of tooled surfaces. A statistical analysis taking into account more than hundred roughness parameters allows us to prove that the mean slope value of the profile is the best parameter to characterise the cutting speed effect on the surface topography. This roughness parameter discriminates the cutting speed threshold between two cutting stages and moreover, discriminates also the cutting process in each stage (the usual Ra parameter is unable to do it). A mathematical treatment based on the chaos theory is then processed. From the profile of the machined surface, a two-dimensional attractor is constructed. Thanks to an original method, it is shown that this attractor depends on two mathematical functions: the first one characterises the work hardening during the cutting process and the second is related to thermal softening. For a critical cutting speed, these two mechanisms are linked together and lead to a single attracting final state. This stage is governed by generalised work hardening. Above this critical speed, the attractor will present a two branches bifurcation, which means that the cutting process is now alternating between the two different states. This chaotic mode is related to the instability between work hardening and thermal softening. This instability is confirmed by a fractal analysis based on the reconstructed profiles from the attractor : the higher the cutting speed, the higher the fractal dimension. [ABSTRACT FROM AUTHOR]

In this work, we study the diffusion of particle accelerated in an electromagnetic wave packet, through a numerical simulation of the relativistic standard map. We contribute to the field of stochastic diffusion of accelerated particles as a function of the stochastic parameter K, specially the transition between partial and global stochasticity, and we also compare our theoretical computation of the diffusion with numerical results. [ABSTRACT FROM AUTHOR]

A direct numerical simulation is carried out to describe the amplitude vacillation phenomena appearing between two successive steady regular waves flows in an air-filled differentially heated rotating annulus. For a fixed temperature difference, ΔT=30 K, when varying progressively the rotation rate, we have obtained the occurrence of the two amplitude vacillation instabilities observed experimentally by Read et al. (J. Fluid Mech. 238 (1992) 599–632) with a high Prandtl number fluid. The first one, denoted AV is characterized by a doubly periodic temporal behaviour with a periodic variation of wave amplitudes, while the second one corresponds to a torus-3 quasi-periodic or chaotic motion with the presence of a modulation in the wave amplitudes evolution. To cite this article: P. Maubert, A. Randriamampianina, C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]