Contour instabilities in early tumor growth models

Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.     

Dynamical study of fractional order differential equations of predator‐pest models

To explore the impact of pest‐control strategy through a fractional derivative, we consider three predator‐prey systems by simple modification of Rosenzweig‐MacArthur model. First, we consider fractional‐order Rosenzweig‐MacArthur model. Allee threshold phenomena into pest population is considered for the second case. Finally, we consider additional food to the predator and harvesting in prey population. The main objective of the present investigation is to observe which model is most suitable for the pest control. To achieve this goal, we perform the local stability analysis of the equilibrium points and observe the basic dynamical properties of all the systems. We observe fractional‐order system has the ability to stabilize Rosenzweig‐MacArthur model with low pest density from oscillatory state. In the numerical simulations, we focus on the bistable regions of the second and third model, and we also observe the effect of the fractional order α throughout the stability region of the system. For the third model, we observe a saddle‐node bifurcation due to the additional food and Allee effect to the pest densities. Also, we numerically plot two parameter bifurcation diagram with respect to the harvesting parameter and fractional order of the system. We finally conclude that fractional‐order Rosenzweig‐MacArthur model and the modified Rosenzweig‐MacArthur model with additional food for the predator and harvested pest population are more suitable models for the pest management.     

Instabilities in elastomers and in soft tissues

Biological soft tissues exhibit elastic properties that canbe dramatically different from rubber-type materials (elastomers).To gain a better understanding of the role of constitutive relationshipsin determining material responses under loads we compare threedifferent types of instabilities (two in compression, one inextension) in hyperelasticity for various forms of strain-energyfunctions typically used for elastomers and for soft tissues.Surprisingly, we find that the strain-hardening property ofsoft tissues does not always stabilize the material. In particularwe show that the stability analyses for a compressed half-spaceand for a compressed spherical thick shell can lead to oppositeconclusions: a soft tissue material is more stable than an elastomerin the former case and less stable in the latter case.     

Quantum stationary state of class A Bianchi universe

Padmanabhan derived a differential equation for the stationary state for the class A Bianchi model and obtained some approximate solutions. Here we reduce the differential equation to a standard, well-known, solvable linear differential equation and indicate some exact explicit particular solutions.     

Biclosure and bistability in a balanced bipartite graph

The k-biclosure of a balanced bipartite graph wiht color classes A and B is the graph obtained from G by recursively joining pairs of nonadjacent vertices respectively taken in A and B whose degree sum is at least k, until no such pair remains. A property P defined on all the balanced bipartite graphs of order 2n is k-bistable if whenever G + ab has property P and d_G(b) ≧ k then G itself has property P. We present a synthesis of results involving, for some properties, P, the bistability of P, the k-biclosure of G, the number of edges and the minimum degree. © 1995 John Wiley & Sons, Inc.     

Mechanical behavior and tensile fractography of compatible vinylchloride–vinylacetate–maleic acid terpolymer and nitrocellulose blends

Vinylchloride–vinylacetate–maleic acid terpolymer (VMCH) and nitrocellulose (NC) were blended at 10% (W/V) concentration is cyclohexanone at different weight fractions. Compatible blends were obtained at all weight fractions. This paper reports the mechanical behavior of solvent cast blend films of VMCH and NC. The films were prepared by solution blending and subsequent casting on a mercury surface. Depending on the composition, the tensile behavior ranged from brittle to ductile. The effect of the blend ratio on the properties shows that within the Hookeian region the modulus and strength have a positive deviation from linearity, whereas the elongation has a negative deviation. The effect of the blend ratio on the ultimate properties of the materials shows a positive deviation in strength up to 63 wt% VMCH composition and a negative deviation in elongation and toughness. The tensile fractography of the pure VMCH and VMCH/NC blends shows the presence of peaks, foldings of fibrils along with cavities or voids, which indicate a ductile mode of failure with craze-initiated fracture. Fractography of the pure NC Indicates a brittle mode of failure wit h craze-initiated fracturing.     

Sur le principe de superposition et l'équation de Riccati

In this Note we study the conditions under which a system of ordinary differential equations admits a nonlinear superposition of the solutions, and also the linearization of such systems. A particular study is established for the Riccati equation. To cite this article: S. Rezzag et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Collinear laser spectroscopy at ionic beams of argon and chlorine

Metastable ions of argon and chlorine were accelerated to form a beam which was led antiparallel to dye-laser beam. When the laser beam was tuned to transitions from the metastables to higher states and the accelerating voltage was set to compensate for the remaining shift, fluorescence from the ions could be detected. Scanning the voltage excitation spectra of the ions could be obtained which allowed to determine the isotope shift of the lines the laser excited.