Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Highly conductive molecular junctions based on direct binding of benzene to platinum electrodes

Highly conductive molecular junctions were formed by direct binding of benzene molecules between two Pt electrodes. Measurements of conductance, isotopic shift in inelastic spectroscopy and shot noise compared with calculations provide indications for a stable molecular junction where the benzene molecule is preserved intact and bonded to the Pt leads via carbon atoms. The junction has a conductance comparable to that for metallic atomic junctions (around 0.1-1 Go), where the conductance and the number of transmission channels are controlled by the molecule's orientation at different inter-electrode distances.Comment: 4 pages, 4 figure

Parameterized optimized effective potential for atoms

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both single configuration and multi configuration trial wave functions are implemented. Applications to several atomic systems are presented improving previous works. The results here obtained are very close to those calculated in either the Hartree-Fock and the multi configurational Hartree-Fock framework.Comment: 8 pages, 3 figure

Thinking in action: Need for cognition predicts self-control together with action orientation

Need for Cognition describes relatively stable interindividual differences in cognitive motivation. Previous research has shown relations of Need for Cognition to Self-Control–a capacity that can be broadly defined as resistance to temptation–yet, the processes underlying this relation remain unclear. One explanation for the prediction of Self-Control by Need for Cognition can be an increased motivation to invest cognitive effort with higher levels of Need for Cognition. Another possible link could be that individual differences in the implementation of Self-Control intentions may play a moderating or mediating role for the predictive value of Need for Cognition. Such individual differences in the self-motivated initiation and maintenance of intentions are described by dispositional Action Orientation. Therefore, in the present study, Action Orientation was examined with regard to its possible role in explaining the relation of Need for Cognition to Self-Control. In a sample of 1209 young adults, Self-Control was assessed with two different self-report instruments and moderation and mediation models of the relationship between Need for Cognition, Action Orientation, and Self-Control were tested. While there was no evidence for a moderating role of Action Orientation in explaining the relation of Need for Cognition and Self-Control, Action Orientation was found to partly mediate this relation with a remaining direct effect of Need for Cognition on Self-Control. These results add to the conceptual understanding of Need for Cognition and demonstrate the relevance of trait variables to predict Self-Control

Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices

We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model, and the properties of the solutions are analyzed. An expression for the current is obtained. Finally, Zener-tunneling in a two-band tight-binding model is considered. The present work gives the background and an extension of the theoretical framework underlying our recent Letter [J. Rotvig {\it et al.}, Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache

Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure