We consider strictly positive solutions to a class of fourth-order conservative quasilinear SPDEs on the $d$-dimensional torus modeled after the stochastic thin-film equation. We prove local Lipschitz estimates in Bessel potential spaces under minimal assumptions on the parameters and corresponding stochastic maximal $L^p$-regularity estimates for thin-film type operators with measurable in-time coefficients. As a result, we deduce local well-posedness of the stochastic thin-film equation as well as blow-up criteria and instantaneous regularization for the solution. In dimension one, we additionally close $\alpha$-entropy estimates and subsequently an energy estimate for the stochastic thin-film equation with an interface potential so that global well-posedness follows. We allow for a wide range of mobility functions including the power laws $u^n$ for $n\in [0,6)$ as long as the interface potential is sufficiently repulsive.

Antonio Agresti Max Sauerbrey

It is shown how laboratory experiments performed with high intensity femtosecond lasers can probe the physics of black holes in the near-horizon regime. The acceleration generated by the high intensity laser ranging from $10^{13}$g to more than $10^{18}$g is identified with the gravitational acceleration at stretched horizons. In the black-hole's asymptotic region, the stretched-horizon-reflected light shows a measurable universal phase acceleration of $c^4/4GM$. PACS numbers: 04.70.Bw, 97.60.Lf, 52.40.Nk, 52.50.Jm

G. Schäfer R. Sauerbrey

We suggest an experiment to observe vacuum birefringence induced by intense laser fields. A high-intensity laser pulse is focused to ultra-relativistic intensity and polarizes the vacuum which then acts like a birefringent medium. The latter is probed by a linearly polarized x-ray pulse. We calculate the resulting ellipticity signal within strong-field QED assuming Gaussian beams. The laser technology required for detecting the signal will be available within the next three years.

T. Heinzl B. Liesfeld K. -U. Amthor H. Schwoerer R. Sauerbrey A. Wipf

We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum FEL in the high-gain mode and avoids the experimental challenges of an X-ray FEL oscillator. Moreover, we study the intensity fluctuations of the emitted radiation which turn out to be super-Poissonian.

Peter Kling Enno Giese C. Moritz Carmesin Roland Sauerbrey Wolfgang P. Schleich

We solve the long-time dynamics of a high-gain free-electron laser in the quantum regime. In this regime each electron emits at most one photon on average, independently of the initial field. In contrast, the variance of the photon statistics shows a qualitatively different behavior for different initial states of the field. We find that the realization of a seeded Quantum FEL is more feasible than self-amplified spontaneous emission.

Peter Kling Enno Giese C. Moritz Carmesin Roland Sauerbrey Wolfgang P. Schleich

We study frequency shifts in a piezoelectric quartz resonator induced by a surface mass layer for sensor applications. The scalar differential equations for thickness-shear modes in a quartz plate are used. A first-order perturbation analysis is performed. The frequency shift is obtained and is expressed by a perturbation integral. It produces the well-known Sauerbrey equation for mass sensitivity in the special case of a uniform mass layer. As an application of the perturbation integral, frequency shifts due to a nonuniform mass layer are calculated.

Jiashi Yang

How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc 'traditional' approaches to variable selection have been in use for at least 50 years. Similarly, methods for determining functional forms for continuous variables were first suggested many years ago. More recently, many alternative approaches to address these two challenges have been proposed, but knowledge of their properties and meaningful comparisons between them are scarce. To define a state-of-the-art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge many outstanding issues in multivariable modelling remain. Our main aims are to identify and illustrate such gaps in the literature and present them at a moderate technical level to the wide community of practitioners, researchers and students of statistics. We briefly discuss general issues in building descriptive regression models, strategies for variable selection, different ways of choosing functional forms for continuous variables, and methods for combining the selection of variables and functions. We discuss two examples, taken from the medical literature, to illustrate problems in the practice of modelling. Our overview revealed that there is not yet enough evidence on which to base recommendations for the selection of variables and functional forms in multivariable analysis. Such evidence may come from comparisons between alternative methods. In particular, we highlight seven important topics that require further investigation and make suggestions for the direction of further research.

Willi Sauerbrei Aris Perperoglou Matthias Schmid Michal Abrahamowicz Heiko Becher Harald Binder Daniela Dunkler Frank E. Harrell Jr Patrick Royston Georg Heinze

Quantum electrodynamics predicts the vacuum to behave as a non-linear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly non-linear measurement schemes - while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

N. Ahmadiniaz T. E. Cowan R. Sauerbrey U. Schramm H. -P. Schlenvoigt R. Schützhold

The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible sub-micron-sized suspended spheres, and with experimental results for adsorbed micron-sized colloids which yield a "negative acoustic mass". The parallel behaviour unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should in most cases include hydrodynamics.

M. Meléndez A. Vázquez-Quesada R. Delgado-Buscalioni

In a quantum mechanical description of the free-electron laser (FEL) the electrons jump on discrete momentum ladders, while they follow continuous trajectories according to the classical description. In order to observe the transition from quantum to classical dynamics, it is not sufficient that many momentum levels are involved. Only if additionally the initial momentum spread of the electron beam is larger than the quantum mechanical recoil, caused by the emission and absorption of photons, the quantum dynamics in phase space resembles the classical one. Beyond these criteria, quantum signatures of averaged quantities like the FEL gain might be washed out.

C. Moritz Carmesin Peter Kling Enno Giese Roland Sauerbrey Wolfgang P. Schleich