Non-Equilibrium Magnetization in a Ballistic Quantum Dot

We show that Aharonov-Bohm (AB) oscillations in the magnetic moment of an integrable ballistic quantum dot can be destroyed by a time dependent magnetic flux. The effect is due to a nonequilibrium population of perfectly coherent electronic states. For real ballistic systems the equilibrization process, which involves a special type of inelastic electron backscattering, can be so ineffective, that AB oscillations are suppressed when the flux varies with frequency $\omega\sim$ 10$^7$-10$^8$ s$^{-1}$. The effect can be used to measure relaxation times for inelastic backscattering.Comment: 11 pages LaTeX v3.14 with RevTeX v3.0, 3 post script figures available on request, APR 93-X2

Interferenzeffekte im Leitwert von metallischen Nanometer-Strukturen

SIGLEAvailable from TIB Hannover: DW 6419 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications.

Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, bringing controversies in treatment planning since aggressive treatment may lead to undesirable side effects. Thus, for management decisions it would be valuable to obtain early estimates of LGG growth potential. Here we propose a simple mathematical model of LGG growth and its response to chemotherapy which allows the growth of LGGs to be described in real patients. The model predicts, and our clinical data confirms, that the speed of response to chemotherapy is related to tumour aggressiveness. Moreover, we provide a formula for the time to radiological progression, which can be possibly used as a measure of tumour aggressiveness. Finally, we suggest that the response to a few chemotherapy cycles upon diagnosis might be used to predict tumour growth and to guide therapeutical actions on the basis of the findings

Elliptic differential equations: theory and numerical treatment

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics

Evolution of LGGs diameter—Results based on the simulations of FKE Eq (6) (black solid line), analytic equation of radius evolution Eq (11) (red dashed-dotted line) due to Skellam model (7) and asymptotic behaviour of radius as <i>t</i> → 0 Eq (16) (blue dotted line).

<p>The vertical dashed line denotes the time when malignant transformation was confirmed histopathologically. The model parameters and initial conditions were the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179999#pone.0179999.g003" target="_blank">Fig 3</a> for patients selected in this study.</p

Estimates of the onsets of malignant transformation:<i>t</i>_<i>OMT</i> (black solid line), <i>t</i>_{<i>OMT</i>,<i>S</i>} (blue dotted line) and <i>t</i>_{<i>OMT</i>,<i>L</i>} (red dashed-dotted line) for different values of diffusion rate <i>D</i>.

<p>The initial tumour cell densities and other parameters’ values are taken as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179999#pone.0179999.g001" target="_blank">Fig 1</a>.</p