On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Proactive heuristic procedures for robust project scheduling: An experimental analysis

Solution-robust project scheduling is a growing research field aiming at constructing proactive schedules to cope with multiple disruptions during project execution. When stochastic activity durations are considered, including time buffers between activities is a proven method to improve the stability of a baseline schedule.     

Electric field assisted charge carrier photogeneration in poly(spirobifluorene-co-benzothiadiazole)

The dynamics of charge carrier generation in poly(spirobifluorene-co-benzothiadiazole) was investigated by electric field-induced fluorescence quenching and differential absorption measurements. Three different time domains of carrier generation have been identified: an ultrafast phase, a subnanosecond phase, and an entire lifetime phase. The charge generation efficiencies during the first and second phases were found to be almost independent of temperature, being about 25% and 10%, respectively, at an applied electric field of 1.3×10(6)?V/cm, while the generation efficiency during the third phase increases from 2% at 80 K to 10% at room temperature. The results of transient spectroscopy measurements and quantum chemical calculations suggest an intramolecular charge transfer for about 1 ps from the alkoxy-substituted fluorene side group to the benzothiadiazole subunit of the main chain. The formation and evolution of the resulting charge transfer states determine the way of charge carrier generation.     

Free-carrier generation in aggregates of single-wall carbon nanotubes by photoexcitation in the ultraviolet regime

We present evidence for the generation of free carriers in aggregated single-wall carbon nanotubes by photoexcitation in the energetic range of the π→π(*) transition associated with the M saddle point of the graphene lattice. The underlying broad absorption culminating at 4.3 eV can be fit well with a Fano line shape that describes strong coupling of a saddle-point exciton to an underlying free electron-hole pair continuum. Moreover, it is demonstrated that transitions in this energetic region autoionize into the continuum by detecting features unique to the presence of free charges in the transient transmission spectra of the continuum-embedded second sub-band exciton, S(2).     

Tiling Convex Polygons with Congruent Equilateral Triangles

We study the sets $\mathcal{T}_{v}=\{m \in\{1,2,\ldots\}: \mbox{there is a convex polygon in }\mathbb{R}^{2}\mbox{ that has }v\mbox{ vertices and can be tiled with $m$ congruent equilateral triangles}\}$ , v=3,4,5,6. $\mathcal{T}_{3}$ , $\mathcal{T}_{4}$ , and $\mathcal{T}_{6}$ can be quoted completely. The complement $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ of $\mathcal{T}_{5}$ turns out to be a subset of Euler’s numeri idonei. As a consequence, $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ can be characterized with up to two exceptions, and a complete characterization is given under the assumption of the Generalized Riemann Hypothesis.     

Ultrafast dynamics in the excited hydrogen atom transfer states of ammonia clusters

Neutral ammonia clusters (NH₃)_m are photo-excited to the electronic state by a deep UV femtosecond laser pump pulse. Within a few hundred femtoseconds a significant fraction of the clusters rearrange to form an H-transfer state (NH₃)_m-2NH₄(3s)NH₂ with the subunit NH₄ in its 3s electronic ground state. This state is then electronically excited by a time-delayed infrared control pulse of variable wavelength. Finally, a third (probe) pulse in the UV ionizes the clusters for detection. The lifetime of the excited (NH₃)_m-2NH₄(3p)NH₂ states is found to vary between 2.7 and 0.13 ps depending on cluster size and excitation energy. It increases drastically upon deuteration. The corresponding cluster size-dependent photoelectron spectra allow us to disentangle the underlying energetics of the excitation and ionization process and reveal additional processes, such as nonresonant ionization or dissociative ionization. The experimental findings suggest that the excited H-transfer ammonia complexes with m > 2 are deactivated by an internal conversion process back to the electronically lowest H-transfer state followed by fast dissociation. Received 22 September 2001 and Received in final form 31 January 2002     

Lower Semi-continuous Function Frames

It has never been systematically studied under which algebraic actions lower semi-continuity is a stable property. This is despite the fact that this continuity variant is commonly used, in different branches of mathematics. In this note we propose an abstraction of the lower semi-continuous function frame on a topological space and describe this as the Eilenberg–Moore algebras of a Hom-functor monad. We also point out the connection with approach frames and with classical frame theory. Thereby we obtain several different characterizations of the introduced category.     

Ultrafast photoelectron spectroscopy: Femtosecond pump-probe coincidence detection of ammonia cluster ions and electrons

A new type of experiment is described, in which the femtosecond pump-probe method is combined with the photoelectron-photoion coincidence technique and time-of-flight photoelectron energy analysis. The experimental conditions for observing true coincidences are discussed. The performance of the new time resolved, ultrafast photoelectron spectroscopy is exemplified by studying the excited state dynamics of ammonia molecules and clusters.     

Mode launching on a multimode slab-waveguide by a plane wave

Mode launching on a symmetrical multimode slab-waveguide by a plane wave incident onto the front side of the guide is investigated theoretically and experimentally. A single plane wave always excites a whole set of modes. Among these are, in general, three adjacent modesm-1, m, m+1 which are excited most strongly. The relative power launched into these modes is approximately given by the ratio 0.4:1:0.4. The theoretical results are confirmed by qualitative observations of the far-field mode patterns. In the far field the modes are separated by using a wedge-type waveguide.