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A convergence result and numerical study for a nonlinear piezoelectric material in a frictional contact process with a conductive foundation

El-Hassan Benkhira, Rachid Fakhar, Youssef Mandyly (2021)

Applications of Mathematics

We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky's law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed to be frictional, and the foundation is electrically conductive. The contact is modeled with the...

Coexisting cycles in a class of 3-D discrete maps

Anna Agliari (2012)

ESAIM: Proceedings

In this paper we consider the class of three-dimensional discrete maps M (x, y, z) = [φ(y), φ(z), φ(x)], where φ : ℝ → ℝ is an endomorphism. We show that all the cycles of the 3-D map M can be obtained by those of φ(x), as well as their local bifurcations. In particular we obtain that any local bifurcation is of co-dimension 3, that is three eigenvalues cross simultaneously the unit circle. As the map M exhibits coexistence...

Discrete anisotropic curvature flow of graphs

Klaus Deckelnick, Gerhard Dziuk (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.

Intensified Doxorubicin-Based Regimen Efficacy in Residual Non-Hodgkin's Lymphoma Disease: Towards a Computationally Supported Treatment Improvement

Y. Kogan, B. Ribba, K. Marron, N. Dahan, V. Vainstein, Z. Agur (2010)

Mathematical Modelling of Natural Phenomena

Despite recent advances, treatment of patients with aggressive Non-Hodgkin's lymphoma (NHL2) has yet to be optimally designed. Notwithstanding the contribution of molecular treatments, intensification of chemotherapeutic regimens may still be beneficial. Hoping to aid in the design of intensified chemotherapy, we put forward a mathematical and computational model that analyses the effect of Doxorubicin on NHL over a wide range of patho-physiological conditions. The model represents tumour growth...

Pointwise representation method.

Osipov, Vladimir Mihajlovich, Osipov, Vladimir Vladimirovich (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Vibrational properties of nanographene

Sandeep Kumar Singh, F.M. Peeters (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

The eigenmodes and the vibrational density of states of the ground state configuration of graphene clusters are calculated using atomistic simulations. The modified Brenner potential is used to describe the carbon-carbon interaction and carbon-hydrogen interaction in case of H-passivated edges. For a given configuration of the C-atoms the eigenvectors and eigenfrequencies of the normal modes are obtained after diagonalisation of the dynamical matrix whose elements are the second derivative of the...

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