Vacuum harmonic generation in slowly varying electromagnetic backgrounds

Relativistische Quantentheorie sagt die Existenz von virtuellen Elektron-Positron-Paaren vorher, die innerhalb einer typischen Zeitskala, der Compton-Zeit des Elektrons, erzeugt und wieder vernichtet werden. Diese virtuellen Dipole machen das Vakuum zu einem polarisierbaren Medium, was zu einer Abänderung der klassischen Maxwell-Gleichungen führt. Falls die Photonen eine Energie haben, welche deutlich kleiner ist als die Ruheenergie des Elektrons, werden diese Effekte durch die “Heisenberg-Euler”-Lagrange-Dichte im Rahmen der Quantenelektrodynamik beschrieben. Für Feldstärken, die klein sind im Vergleich zu dem “kritischen” Feld Ecr = 1.3 · 10^16 Vcm^−1, können diese Korrekturen zur Ausbreitung von elektromagnetischen Wellen explizit ausgewertet werden. In dieser Arbeit werden die Maxwell-Gleichungen mitsamt dieser Korrekturen für schwache Felder numerisch in einer Anregungs-Abfrage-Konfiguration von zwei zusammenstoßenden, ebenen Wellen gelöst. Die entsprechende Wellengleichung wird dann analytisch gelöst. Die Anfangsbedingungen bestehen dabei aus einem (optischen) gaußschen “Abfrage”-Puls, der sich entgegengesetzt der “Anregung” in Form eines nur schwach variierenden, starken Hintergrunds, ausbreitet. Dabei werden Vakuumpolarisations-Effekte wie Doppelbrechung und die Erzeugung von Harmonischen (ähnlich zu Prozessen in einem nichtlinearen Kerr-Medium) untersucht. Der erste Teil dieser Arbeit befasst sich mit der Analyse der zeitaufgelösten Dynamik der Kollision des Abfrage-Pulses mit einem gaußförmigen, starken Hintergrund. Dabei wird ein “Überlappungs”-Feld identifiziert, welches nur im Wechselwirkungsbereich vorhanden ist und verschwindet, wenn die Pulse weit voneinander entfernt sind. Der zweite Teil untersucht die Erzeugung von höheren Harmonischen im Vakuum, wobei der Hintergrund nun als ebene Welle mit verschwindender Frequenz gewählt wird. Falls die Weglänge des Abfrage-Pulses im externen Feld groß genug ist, können höhere Harmonische durch hintereinander stattfindende Streuprozesse erzeugt werden. Für parallele Polarisationen der beiden Pulse wird ein Multi-Skalen-Parameter identifiziert, welcher angibt, wann diese Selbstwechselwirkung relevant wird. Wenn dieser Parameter gegen eins strebt, entwickelt der Abfrage-Puls eine Unstetigkeit in der Trägerfrequenz, welche auch “Schock” genannt wird.Relativistic quantum theory predicts the existence of virtual electron-positron pairs that are generated and annihilated over a typical time scale given by the electron Compton time. These virtual dipoles render the vacuum a polarisable medium thereby modifying the classical Maxwell vacuum equations. For photons with energy much smaller than the electron rest energy, these effects are well-described by the “Heisenberg-Euler” Lagrangian within the framework of Quantum Electrodynamics. In the case of field strengths that are small compared to the “critical” field Ecr = 1.3 · 10^16 Vcm^−1, the resulting nonlinear corrections to the electromagnetic wave propagation can be evaluated explicitly. In this thesis, Maxwell equations that include these weak-field corrections are solved numerically for a “pump-probe” setup of two colliding plane waves. The corresponding wave equation is then solved analytically. The inital configuration is a weak (optical) Gaussian probe pulse that counterpropagates with a slowly-varying strong “background”. Vacuum polarisation effects such as birefringence and the generation of harmonics (similar to processes in a nonlinear Kerr-medium) are analysed. The first part of the thesis is dedicated to the study of the time-resolved dynamics when the probe collides with a Gaussian strong pulse and an “overlap” signal is identified, which is only present in the interaction region and disappears when the pulses are well separated. The second part of the thesis considers vacuum high harmonic generation in a plane wave background of vanishing frequency. If the propagation length of the probe in the external field is long enough, higher harmonics of the probe frequency can be generated due to multiple scattering events. For parallel polarisations of probe and strong pulse, a multi-scale parameter is identified which indicates when this self-interaction becomes important. If this parameter approaches unity, the probe pulse develops a discontinuity or “shock” in the carrier wave

Deadwood volume assessment in the third Swiss National Forest Inventory: methods and first results

The Swiss National Forest Inventory (NFI) is expected to provide reliable data about the current state of the Swiss forests and recent changes. Since the first Swiss NFI (1982-1986) a deadwood assessment has been part of the inventory. However, the definition of deadwood used was restricted and only parts of the total deadwood volume were assessed. A broader definition was therefore used in the second NFI (1993-1995) and coarse wood debris (CWD) was also assessed using line intersect sampling in the third NFI (2004-2006). This paper discusses the development of the definition of deadwood from the first to the third Swiss NFI, as well as the tally rules and estimators used in assessing deadwood in the ongoing third NFI. Different definitions of deadwood were applied in two Swiss regions and the resulting volume estimates were compared. The definition of deadwood appears to be crucial for the estimate of deadwood volumes, which were significantly underestimated in the first and second Swiss NFI. The minimum diameter and other limits applied must be chosen with special care. Up to 30m3/ha of deadwood was found in Swiss forests varying with the region. There was little evidence of significant correlations between deadwood volume and such forest parameters as management, site or stand attributes. The proposed target values for the volume of deadwood have been generally reached, whereas the number of snags per hectare has no

THE STRUCTURAL ANCHORING OF IS/IT INNOVATION MANAGEMENT: TOWARD AN ORGANIZATIONAL DESIGN THEORY

The importance of information systems and information technology (IS/IT) is growing constantly, reaching top positions on agendas of CEOs, which is fueled by current discussions about digitization and digital transformation. To gain or maintain competitive advantages, many organizations have started conducting systematic IS/IT innovation management. Empirical research has shown that cur-rent initiatives are still immature and unsuccessful. An analysis of the obstacles shows that a missing or inadequate organizational structure is one of the main challenges. Nevertheless, research on this issue is still scarce. This gap motivates our research, which aims to develop a design theory for insti-tutionalizing IS/IT innovation management. To derive our results, we conducted an exploratory inter-view study, comprising ten expert interviews. We identified eight meta-requirements for a successful institutionalization. We also found that there is no “one-fits-all solution”, therefore we present six design variants and formulate propositions about the implications of each variant for the fulfillment of the meta-requirements. As a next research step, we will initiate an evaluation cycle to increase our theory’s validity and utility. Our design theory helps practitioners to find the right variant for institu-tionalizing IS/IT innovation management and contributes to the nascent body of knowledge on IS/IT innovation management

Symbolic Analysis of Cryptographic Protocols

We rely on the security properties of cryptographic protocols every day while browsing the Internet or withdrawing money from an ATM. However, many of the protocols we use today were standardized without a proof of security. Serious flaws in protocols restrict the level of security we can reach for applications. This thesis motivates why we should strive for proofs of security and provides a framework that makes using automated tools to conduct such proofs more feasible

De verwoestingen van Babylon door Darius i en Xerxes in het licht van Babylonische en bijbelse bronnen.

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Vacuum high-harmonic generation and electromagnetic shock

When one takes into account the presence of virtual charged states in the quantum vacuum, a nonlinear self-interaction can arise in the propagation of electromagnetic fields. This self-interaction is often referred to as 'real photon-photon scattering'. When the centre-of-mass energy of colliding photons is much lower than the rest energy of an electron-positron pair, this quantum effect can be included in the classical field equations of motion as a vacuum current and charge density using the Heisenberg-Euler Lagrangian. Using analytical and numerical methods for subcritical fields, the intrinsic solution to Maxwell's equations has been found for counter propagating probe and pump plane waves in the presence of vacuum four and six-wave mixing. In the corresponding all-order solution for the scattered probe, a route to vacuum high-harmonic generation is identified in which a long phase length can compensate for the weakness of interacting fields. The resulting shocks in the probe carrier wave and envelope are studied for different parameter regimes and polarisation set-ups. In this special issue, we study two additional set-ups: that of a slowly varying single-cycle background to highlight the effect of an oscillating background on the probe harmonic spectrum, and that of a few-cycle probe to highlight the smoothing of the harmonic peaks produced by a wider spectrum of probe photons. We also correct sign errors in an earlier publication

MergeMAC:A MAC for Authentication with Strict Time Constraints and Limited Bandwidth

This paper presents MergeMAC, a MAC that is particularly suitable for environments with strict time requirements and extremely limited bandwidth. MergeMAC computes the MAC by splitting the message into two parts. We use a pseudorandom function (PRF) to map messages to random bit strings and then merge them with a very efficient keyless function. The advantage of this approach is that the outputs of the PRF can be cached for frequently needed message parts. We demonstrate the merits of MergeMAC for authenticating messages on the CAN bus where bandwidth is extremely limited and caching can be used to recover parts of the message counter instead of transmitting it. We recommend an instantiation of the merging function MERGE and analyze the security of our construction. Requirements for a merging function are formally defined and the resulting EUF-CMA security of MergeMAC is proven

Vacuum harmonic generation in slowly varying electromagnetic backgrounds

Relativistische Quantentheorie sagt die Existenz von virtuellen Elektron-Positron-Paaren vorher, die innerhalb einer typischen Zeitskala, der Compton-Zeit des Elektrons, erzeugt und wieder vernichtet werden. Diese virtuellen Dipole machen das Vakuum zu einem polarisierbaren Medium, was zu einer Abänderung der klassischen Maxwell-Gleichungen führt. Falls die Photonen eine Energie haben, welche deutlich kleiner ist als die Ruheenergie des Elektrons, werden diese Effekte durch die “Heisenberg-Euler”-Lagrange-Dichte im Rahmen der Quantenelektrodynamik beschrieben. Für Feldstärken, die klein sind im Vergleich zu dem “kritischen” Feld Ecr = 1.3 · 10^16 Vcm^−1, können diese Korrekturen zur Ausbreitung von elektromagnetischen Wellen explizit ausgewertet werden. In dieser Arbeit werden die Maxwell-Gleichungen mitsamt dieser Korrekturen für schwache Felder numerisch in einer Anregungs-Abfrage-Konfiguration von zwei zusammenstoßenden, ebenen Wellen gelöst. Die entsprechende Wellengleichung wird dann analytisch gelöst. Die Anfangsbedingungen bestehen dabei aus einem (optischen) gaußschen “Abfrage”-Puls, der sich entgegengesetzt der “Anregung” in Form eines nur schwach variierenden, starken Hintergrunds, ausbreitet. Dabei werden Vakuumpolarisations-Effekte wie Doppelbrechung und die Erzeugung von Harmonischen (ähnlich zu Prozessen in einem nichtlinearen Kerr-Medium) untersucht. Der erste Teil dieser Arbeit befasst sich mit der Analyse der zeitaufgelösten Dynamik der Kollision des Abfrage-Pulses mit einem gaußförmigen, starken Hintergrund. Dabei wird ein “Überlappungs”-Feld identifiziert, welches nur im Wechselwirkungsbereich vorhanden ist und verschwindet, wenn die Pulse weit voneinander entfernt sind. Der zweite Teil untersucht die Erzeugung von höheren Harmonischen im Vakuum, wobei der Hintergrund nun als ebene Welle mit verschwindender Frequenz gewählt wird. Falls die Weglänge des Abfrage-Pulses im externen Feld groß genug ist, können höhere Harmonische durch hintereinander stattfindende Streuprozesse erzeugt werden. Für parallele Polarisationen der beiden Pulse wird ein Multi-Skalen-Parameter identifiziert, welcher angibt, wann diese Selbstwechselwirkung relevant wird. Wenn dieser Parameter gegen eins strebt, entwickelt der Abfrage-Puls eine Unstetigkeit in der Trägerfrequenz, welche auch “Schock” genannt wird.Relativistic quantum theory predicts the existence of virtual electron-positron pairs that are generated and annihilated over a typical time scale given by the electron Compton time. These virtual dipoles render the vacuum a polarisable medium thereby modifying the classical Maxwell vacuum equations. For photons with energy much smaller than the electron rest energy, these effects are well-described by the “Heisenberg-Euler” Lagrangian within the framework of Quantum Electrodynamics. In the case of field strengths that are small compared to the “critical” field Ecr = 1.3 · 10^16 Vcm^−1, the resulting nonlinear corrections to the electromagnetic wave propagation can be evaluated explicitly. In this thesis, Maxwell equations that include these weak-field corrections are solved numerically for a “pump-probe” setup of two colliding plane waves. The corresponding wave equation is then solved analytically. The inital configuration is a weak (optical) Gaussian probe pulse that counterpropagates with a slowly-varying strong “background”. Vacuum polarisation effects such as birefringence and the generation of harmonics (similar to processes in a nonlinear Kerr-medium) are analysed. The first part of the thesis is dedicated to the study of the time-resolved dynamics when the probe collides with a Gaussian strong pulse and an “overlap” signal is identified, which is only present in the interaction region and disappears when the pulses are well separated. The second part of the thesis considers vacuum high harmonic generation in a plane wave background of vanishing frequency. If the propagation length of the probe in the external field is long enough, higher harmonics of the probe frequency can be generated due to multiple scattering events. For parallel polarisations of probe and strong pulse, a multi-scale parameter is identified which indicates when this self-interaction becomes important. If this parameter approaches unity, the probe pulse develops a discontinuity or “shock” in the carrier wave