Novel and Unique Expression for the Radiation Reaction Force, Relevance of Newton's Third Law and Tunneling

We derive the radiation reaction by taking into account that the acceleration of the charge is caused by the interaction with some heavy source particle. In the non relativistic case this leads, in contrast to the usual approach, immediately to a result which is Galilei invariant. Simple examples show that there can be small regions of extremely low velocity where the energy requirements cannot be fulfilled, and which the charged particle can only cross by quantum mechanical tunneling. We also give the relativistic generalization which appears unique. The force is a four-vector, but only if the presence of the source is taken into account as well. It contains no third derivatives of the position as the Lorentz-Abraham-Dirac equation, and consequently no run away solutions. All examples considered so far give reasonable results.Comment: 9 page

Absence of simulation evidence for critical depletion in slit-pores

Recent Monte Carlo simulation studies of a Lennard-Jones fluid confined to a mesoscopic slit-pore have reported evidence for ``critical depletion'' in the pore local number density near the liquid-vapour critical point. In this note we demonstrate that the observed depletion effect is in fact a simulation artifact arising from small systematic errors associated with the use of long range corrections for the potential truncation. Owing to the large near-critical compressibility, these errors lead to significant changes in the pore local number density. We suggest ways of avoiding similar problems in future studies of confined fluids.Comment: 4 pages Revtex. Submitted to J. Chem. Phy

Tractatus logico-graphicus. Eine Philosophie der Malerei.

Wittgenstein sagt: (1) Die Welt ist alles, was der Fall ist. (2) Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten. (3) Das logische Bild der Tatsache ist der Gedanke. (4) Der Gedanke ist der sinnvolle Satz. (5) Der Satz ist eine Wahrheitsfunktion der Elementarsätze. (6) Die allgemeine Form der Wahrheitsfunktion ist [ p, ξ , N (ξ)]. (7) Wovon man nicht sprechen kann, darüber muss man schweigen. Ich ergänze: (1) Die Welt ist alles, was für die Malerei der Fall ist. (2) Was der Fall ist, die Tatsache, ist die Welt des Subjektes. (3) Das Abbild der Welt ist der Gedanke. (4) Der Gedanke ist das sinnvolle Bild (Gemälde). (5) Das Bild (Gemälde) ist eine Funktion der Elemente Farbe und Form. (6) Die allgemeine Form des Bildes (Gemäldes) ist : I (W). (7) Wovon man nicht sprechen kann, darüber muss man malen

Interconnect technologies for very large spiking neural networks

In the scope of this thesis, a neural event communication architecture has been developed for use in an accelerated neuromorphic computing system and with a packet-based high performance interconnection network. Existing neuromorphic computing systems mostly use highly customised interconnection networks, directly routing single spike events to their destination. In contrast, the approach of this thesis uses a general purpose packet-based interconnection network and accumulates multiple spike events at the source node into larger network packets destined to common destinations. This is required to optimise the payload efficiency, given relatively large packet headers as compared to the size of neural spike events. Theoretical considerations are made about the efficiency of different event aggregation strategies. Thereby, important factors are the number of occurring event network-destinations and their relative frequency, as well as the number of available accumulation buffers. Based on the concept of Markov Chains, an analytical method is developed and used to evaluate these aggregation strategies. Additionally, some of these strategies are stochastically simulated in order to verify the analytical method and evaluate them beyond its applicability. Based on the results of this analysis, an optimisation strategy is proposed for the mapping of neural populations onto interconnected neuromorphic chips, as well as the joint assignment of event network-destinations to a set of accumulation buffers. During this thesis, such an event communication architecture has been implemented on the communication FPGAs in the BrainScaleS-2 accelerated neuromorphic computing system. Thereby, its usability can be scaled beyond single chip setups. For this, the EXTOLL network technology is used to transport and route the aggregated neural event packets with high bandwidth and low latency. At the FPGA, a network bandwidth of up to 12 Gbit/s is usable at a maximum payload efficiency of 94 %. The latency has been measured in the scope of this thesis to a range between 1.6 μs and 2.3 μs across the network between two neuron circuits on separate chips. This latency is thereby mostly dominated by the path from the neuromorphic chip across the communication FPGA into the network and back on the receiving side. As the EXTOLL network hardware itself is clocked at a much higher frequency than the FPGAs, the latency is expected to scale in the order of only approximately 75 ns for each additional hop through the network. For being able to globally interpret the arrival timestamps that are transmitted with every spike event, the system time counters on the FPGAs are synchronised across the network. For this, the global interrupt mechanism implemented in the EXTOLL hardware is characterised and used within this thesis. With this, a synchronisation accuracy of ±40ns could be measured. At the end of this thesis, the successful emulation of a neural signal propagation model, distributed across two BrainScaleS-2 chips and FPGAs is demonstrated using the implemented event communication architecture and the described synchronisation mechanism

From mean-motion resonances to scattered planets: Producing the Solar System, eccentric exoplanets and Late Heavy Bombardments

We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We show that this can lead to a variety of outcomes; some cases resemble the Solar System, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar Late Heavy Bombardment. Thus, it may be that a large-scale dynamical instability, with more or less cataclysmic results, is an evolutionary step common to many planetary systems, including our own.Comment: 12 pages, 7 figures, submitted to Ap

Overcoming migration during giant planet formation

In the core accretion model, gas giant formation is a race between growth and migration; for a core to become a jovian planet, it must accrete its envelope before it spirals into the host star. We use a multizone numerical model to extend our previous investigation of the "window of opportunity" for gas giant formation within a disk. When the collision cross-section enhancement due to core atmospheres is taken into account, we find that a broad range of protoplanetary disks posses such a window.Comment: 4 pages, 3 figs, accepted to ApJ

Modeling the Formation of Giant Planet Cores I: Evaluating Key Processes

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the the solar nebula dispersed. The most popular model of giant planet formation is the so-called 'core accretion' model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments we have included: 1) aerodynamic gas drag, 2) collisional damping between planetesimals, 3) enhanced embryo cross-sections due to their atmospheres, 4) planetesimal fragmentation, and 5) planetesimal driven migration. We find that the gravitational interaction between the embryos and the planetesimals lead to the wholesale redistribution of material - regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near that embryos is cleared of planetesimals before much growth can occur. The remaining 10%, however, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~100,000 years, the outer embryo can migrate ~6 AU and grow to roughly 30 Earth-masses. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth.Comment: Accepted to AJ, 62 pages 11 figure

Saving Planetary Systems: Dead Zones & Planetary Migration

The tidal interaction between a disk and a planet leads to the planet's migration. A long-standing question regarding this mechanism is how to stop the migration before planets plunge into their central stars. In this paper, we propose a new, simple mechanism to significantly slow down planet migration, and test the possibility by using a hybrid numerical integrator to simulate the disk-planet interaction. The key component of the scenario is the role of low viscosity regions in protostellar disks known as dead zones, which affect planetary migration in two ways. First of all, it allows a smaller-mass planet to open a gap, and hence switch the faster type I migration to the slower type II migration. Secondly, a low viscosity slows down type II migration itself, because type II migration is directly proportional to the viscosity. We present numerical simulations of planetary migration by using a hybrid symplectic integrator-gas dynamics code. Assuming that the disk viscosity parameter inside the dead zone is (alpha=1e-4-1e-5), we find that, when a low-mass planet (e.g. 1-10 Earth masses) migrates from outside the dead zone, its migration is stopped due to the mass accumulation inside the dead zone. When a low-mass planet migrates from inside the dead zone, it opens a gap and slows down its migration. A massive planet like Jupiter, on the other hand, opens a gap and slows down inside the dead zone, independent of its initial orbital radius. The final orbital radius of a Jupiter mass planet depends on the dead zone's viscosity. For the range of alpha's noted above, this can vary anywhere from 7 AU, to an orbital radius of 0.1 AU that is characteristic of the hot Jupiters.Comment: 38 pages, 14 figures, some changes in text and figures, accepted for publication in Ap