A new parameterization of aircraft icing accounting for microphysical properties of clouds

The effects of aircraft icing comprise of (i) simple inconveniences, like flight delays, (ii) increased fuel consumption and (iii) severe performance degradations, potentially resulting in the loss of control over the aircraft. The accretion of ice onto the aircraft is considered the reason for several documented fatal crashes. Because of this safety hazard for aviation, weather services around the world use aircraft icing prediction schemes to forecast the location and intensity of icing environments, based on the output of numerical weather prediction models. Although aircraft icing occurs by the freezing of supercooled liquid droplets impinging onto the aircraft’s surface, current icing prediction schemes do not consider microphysical quantities, like the droplets’ size or their spectrum, in their design. Analytical icing related algorithms tend to respect the droplets’ size, but in a simplified, heuristic way. The present work develops a new physically based aircraft icing parameterization employing the two main physical processes involved in aircraft icing, namely the droplet impingement and the freezing of the impinged droplets. The former is represented by the droplets’ impingement efficiency, which is computed by evaluating droplet trajectories in the vicinity of the object. The freezing model used in this new parameterization allows for the differentiation of different icing phases, a dry icing phase solely accreting rime ice and a wet icing phase accreting glaze ice and a liquid water film due to the release of latent heat whilst freezing, allowing for a more detailed forecast and analysis. This new aircraft icing parameterization is implemented in a numerical weather forecast model to simulate icing conditions for two former case studies and an additional icing incident. The simulations reproduce the results of the case studies properly and enhance them with additional icing related quantities. Contrary to currently used heuristic approaches to the impingement efficiency, this new physically based approach gives a greater differentiation of high impingement efficiency values. Using this new parameterization, the present work further investigates the role of microphysical quantities by conducting sensitivity studies focused on the explicit consideration of the droplet spectrum and the aerosol load, which is represented by the cloud droplet number density for one experiment and by the number density of aerosols acting as cloud condensation nuclei for the droplet nucleation parameterization for the other. Since the new aircraft icing parameterization introduces further influencing quantities, a further sensitivity investigation focusing on the relative airspeed is conducted. The present work shows that the explicit consideration of the cloud droplet spectrum affects the impingement and icing related quantities only minorly. The alteration of the cloud droplet number density, as a proxy for the effect of the aerosol load, has large implications for the impingement, accretion rates and amounts as well as composition of the accreted material. Altering the number density of cloud condensation nuclei instead affects the impingement mainly in low impinging environments and the composition of the accreted material due to impacts on the accretion of rime ice. Glaze ice and liquid water accretion are largely unaffected. The relative airspeed also affects the droplet impingement, but its largest effect is on the accretion rates caused by the impinging water and the composition of the accreted material. The newly developed physically based parameterization of aircraft icing also gives the possibility to design a new online icing prediction scheme, as it is implemented into an operatively used numerical weather forecast model. This requires additional efforts in designing an appropriate icing intensity scale as well as in testing, validating and tuning

Optical Properties of Quasiperiodically Arranged Semiconductor Nanostructures

This work consists of two parts which are entitled "One-Dimensional Resonant Fibonacci Quasicrystals" and "Resonant Tunneling of Light in Silicon Nanostructures". A microscopic theory has been applied to investigate the optical properties of the respective semiconductor nanostructures. The studied one-dimensional resonant Fibonacci quasicrystals consist of GaAs quantum wells (QW) that are separated by either a large spacer L or a small one S. These spacers are arranged according to the Fibonacci sequence LSLLSLSL... The average spacing satisfies a generalized Bragg condition with respect to the 1s-exciton resonance of the QWs. A theory, that makes use of the transfer-matrix method and that allows for the microscopic description of many-body effects such as excitation-induced dephasing caused by the Coulomb scattering of carriers, has been applied to compute the optical spectra of such structures. Based on an appropriate single set of fixed sample parameters, the theory provides reflectance spectra that are in excellent agreement with the corresponding measured linear and nonlinear spectra. A pronounced sharp reflectivity minimum is found in the vicinity of the heavy-hole resonance both in the measured as well as in the calculated linear 54-QW spectra. Such sharp spectral features are suitable for application as optical switches or for slow-light effects. Hence, their properties have been studied in detail. Specifically, the influence of the carrier density, of the QW arrangement, of a detuning away from the exact Bragg condition, of the average spacing as well as of the ratio of the optical path lengths of the large and small spacers L and S, respectively, and of the QW number on the optical properties of the samples have been studied. The features of measured spectra could have been attributed to different sample properties related to the sample setup. Additionally, self-similarity among reflection spectra corresponding to different QW numbers that exceed a Fibonacci number by one is observed, which identifies certain spectral features as true fingerprints of the Fibonacci spacing. In the second part, resonant tunneling of light in stacked structures consisting of alternating parallel layers of silicon and air have been studied theoretically. While usually total internal reflection is expected for light shined on a silicon-air interface under an angle larger than the critical angle, light may tunnel through the air barrier due to the existence of evanescent waves inside the air layers if the neighboring silicon layer is close enough. This tunneling of light is in analogy to the well-known tunneling of a quantum particle through a potential barrier. In particular, the wave equation and the stationary Schrödinger equation are of the same form. Hence, the resonant tunneling of light can be understood in analogy to the resonant tunneling of e.g. electrons as well. The characteristic feature of resonant tunneling is a complete transmission through the barrier at certain resonance energies. The transmission, reflection, and propagation properties of the samples have been determined numerically using a transfer-matrix method. Analytical expressions for the energetic resonance positions have been derived and are in excellent agreement with the numerical simulations. Special attention has been drawn to the lowest resonance out of a series of resonant-tunneling resonances. There, light has been observed to be concentrated within silicon layers the extension of which is smaller than the corresponding wavelength of the light. Specifically, the quality factor is large at the resonance energies, so that the resonant light leaves the sample delayed, which allows for the study of slow light. A detailed investigation of how the sample geometry influences the optical properties of the sample has been presented. In particular, it has been outlined how to design a sample to obtain certain desired optical properties. The optical properties that are related to the resonant tunneling strongly rely on the (mirror-)symmetry of the samples. If asymmetries - especially of the silicon wells inside the air barrier - are present in the sample setup, the resonant-tunneling efficiency is diminished. Such asymmetries are unavoidable in the production of the samples. Therefore, a parameter range has been identified in which reasonable transmission above a transmission probability of 50% can be expected taking typical fluctuations caused by the production process into account. Silicon-based resonant-tunneling structures of a setup proposed by the presented theory have already been fabricated and first experiments are under way. This will allow for theory-experiment comparisons

Complexity of searching an immobile hider in a graph

AbstractWe study the computational complexity of certain search-hide games on a graph. There are two players, called searcher and hider. The hider is immobile and hides in one of the nodes of the graph. The searcher selects a starting node and a search path of length at most k. His objective is to detect the hider, which he does with certainty if he visits the node chosen for hiding. Finding the optimal randomized strategies in this zero-sum game defines a fractional path covering problem and its dual, a fractional packing problem. If the length k of the search path is arbitrary, then the problem is NP-hard. The problem remains NP-hard if the searcher may freely revisit nodes that he has seen before. In that case, the searcher selects a connected subgraph of k nodes rather than a path of k nodes. If k is logarithmic in the number of nodes of the graph, then the problem can be solved in polynomial time. This is shown using a recent technique called color-coding due to Alon, Yuster and Zwick. The same results hold for edges instead of nodes, that is, if the hider hides in an edge and the searcher searches k edges on a path or on a connected subgraph

When Do Subpollen Particles Become Relevant for Ice Nucleation Processes in Clouds?

When exposed to sufficiently humid environments, pollen grains burst and release large quantities of small subpollen particles (SPPs) which carry ice nucleating macromolecules. In this study, for the first time we develop a physically based parameterization describing the bursting process of pollen by applying a turgor pressure parameterization and quantify the impact SPPs have on overall ice nucleation in clouds. SPPs are generated from simulated birch pollen emissions over Europe for a 10-day case study in spring. We found SPP concentrations to surpass pollen grain concentrations by 4–6 orders of magnitude leading to an abundance of biological ice nuclei from SPPs in the range of 103−104\ua0m−3. However, it is found that these concentrations lead to only small changes in hydrometeor number densities and precipitation. Addressing the question when SPPs become relevant for ice nucleation in clouds, we conducted a sensitivity investigation. We find that amplifying ice nucleation efficiency of biological particles by factors greater 100 increases the ice particle numbers by up to 25% (T\ua0≈\ua0268\ua0K). Strong reductions show in cloud droplet number concentration and water vapor at these temperatures while water vapor is increasing at 600\ua0m. Overall, we found a net reduction of water in the atmosphere as liquid and particularly water vapor density is reduced, while frozen water mass density increases above 257\ua0K. Findings indicate an alteration of mixed-phase cloud composition and increased precipitation (up to 6.2%) when SPPs are considered as highly efficient biological ice nuclei

When Do Subpollen Particles Become Relevant for Ice Nucleation Processes in Clouds?

When exposed to sufficiently humid environments, pollen grains burst and release large quantities of small subpollen particles (SPPs) which carry ice nucleating macromolecules. In this study, for the first time we develop a physically based parameterization describing the bursting process of pollen by applying a turgor pressure parameterization and quantify the impact SPPs have on overall ice nucleation in clouds. SPPs are generated from simulated birch pollen emissions over Europe for a 10-day case study in spring. We found SPP concentrations to surpass pollen grain concentrations by 4–6 orders of magnitude leading to an abundance of biological ice nuclei from SPPs in the range of 10$^3$−10$^4$ m$^{−3}$. However, it is found that these concentrations lead to only small changes in hydrometeor number densities and precipitation. Addressing the question when SPPs become relevant for ice nucleation in clouds, we conducted a sensitivity investigation. We find that amplifying ice nucleation efficiency of biological particles by factors greater 100 increases the ice particle numbers by up to 25% (T ≈ 268 K). Strong reductions show in cloud droplet number concentration and water vapor at these temperatures while water vapor is increasing at 600 m. Overall, we found a net reduction of water in the atmosphere as liquid and particularly water vapor density is reduced, while frozen water mass density increases above 257 K. Findings indicate an alteration of mixed-phase cloud composition and increased precipitation (up to 6.2%) when SPPs are considered as highly efficient biological ice nuclei

Resonant Photonic Quasicrystalline and Aperiodic Structures

We have theoretically studied propagation of exciton-polaritons in deterministic aperiodic multiple-quantum-well structures, particularly, in the Fibonacci and Thue-Morse chains. The attention is concentrated on the structures tuned to the resonant Bragg condition with two-dimensional quantum-well exciton. The superradiant or photonic-quasicrystal regimes are realized in these structures depending on the number of the wells. The developed theory based on the two-wave approximation allows one to describe analytically the exact transfer-matrix computations for transmittance and reflectance spectra in the whole frequency range except for a narrow region near the exciton resonance. In this region the optical spectra and the exciton-polariton dispersion demonstrate scaling invariance and self-similarity which can be interpreted in terms of the ``band-edge'' cycle of the trace map, in the case of Fibonacci structures, and in terms of zero reflection frequencies, in the case of Thue-Morse structures.Comment: 13 pages, 9 figures, submitted to Phys. Rev.

Divide-and-conquer-Algorithmen auf dem Hyperwürfel

Wir haben in dieser Arbeit einige Probleme auf Objekten betrachtet, deren Struktur wohlgeformten Klammerworten entspricht. Dies waren spezielle Routing-Probleme, das Umformen und Auswerten algebraischer Ausdrücke, sowie die Berechnung korrespondierender Symbole zweier Ausdrücke. Eine effiziente Lösung dieser Probleme gelang durch einen rekursiven Divide-and-Conquer Ansatz, der auf Grund der “natürlichen” rekursiven Definition der betrachteten Objekte auch nahe liegt. Im Divide-Schritt wurde das jeweilige Problem in viele wesentlich kleinere Teilprobleme zerlegt, so daß die gesamte Laufzeit des Algorithmus asymptotisch gleich der des Divide-Schrittes und des Conquer-Schrittes blieb. Das Zerlegen der Probleme erfolgte im wesentlichen unter Anwendung bekannter Routing-Algorithmen für monotone Routings und Bit-Permute-Complement Permutationen. Im Conquer-Schritt für das Klammerrouting und das Knotenkorrespondenzproblem wurden nur die Datenbewegungen des Divide-Schrittes rückwärts ausgeführt. Für das Tree-Contraction-Problem wurde dagegen im Conquer-Schritt die Hauptarbeit geleistet. Die Methode der Simulation eines PRAMAlgorithmus durch die Berechnung seiner Kommunikationsstruktur und eine entsprechende Umordnung der Datenelemente konnte sowohl für eine effiziente Implementierung des Tree-Contraction Conquer-Schrittes auf dem Hyperwürfel als auch für die Konstruktion eines einfachen NC1-Schaltkreises zum Auswerten Boolescher Formeln angewandt werden. In einer Implementierung eines Divide-and-Conquer Algorithmus auf einem Netzwerk müssen den generierten Teilproblemen für ihre weitere Bearbeitung Teile des Netzwerks zugeordnet werden. Um die weiteren Divide-Schritte nach der gleichen Methode ausführen zu können, sollte die Struktur dieser Teilnetzwerke analog zu der des gesamten Netzwerks sein. Wir haben das Teilnetzwerk-Zuweisungsproblem für den Hyperwürfel und einige hyperwürfelartige Netzwerke untersucht. Der Hyperwürfel und das Butterfly-Netzwerk können so in Teilnetzwerke vorgegebener Größen aufgeteilt werden, daß nur ein geringer Anteil der Prozessoren ungenutzt bleibt, und die Teilprobleme können schnell in die ihnen zugeordneten Teilnetzwerke gesendet werden. Unter Anwendung dieser Teilnetzwerk-Zuweisungs-Algorithmen haben wir optimale Implementierungen für eine große Klasse von Divide-and-Conquer Algorithmen auf dem Hyperwüfel und hyperwürfelartigen Netzwerken erhalten. Wir konnten garantieren, daß die Laufzeit der gesamten Implementierung des Divide-and-Conquer Algorithmus asymptotisch gleich der Laufzeit ist, die sich aus dem gegebenen Divide-Schritt und Conquer-Schritt ergibt, wenn man alle mit der Teilnetzwerk-Zuweisung verbundenen Probleme außer acht läßt. Wir haben die hier vorgestellte allgemeine Divide-and-Conquer Implementierung im optimalen Teilwürfel-Zuweisungs-Algorithmus, im Klammerrouting-Algorithmus, der selbst ein wesentlicher Teil des Tree-Contraction-Algorithmus ist, und im Algorithmus für das Knotenkorrespondenzproblem eingesetzt

On the Security of Server-aided RSA Protocols

. In this paper we investigate the security of the server-aided RSA protocols RSA-S1 and RSA-S1M proposed by Matsumoto, Kato and Imai ([MKI89]) and Matsumoto, Imai, Laih and Yen ([MILY93]), respectively. In these protocols a smart card calculates an RSA signature with the aid of an untrusted powerful server. We focus on generic attacks, that is, passive attacks that do not exploit any special properties of the encoding of the group elements. Generic algorithms have been introduced by Nechaev ([Nec94]) and Shoup ([Sho97]). We prove lower bounds for the complexity of generic attacks on these two protocols and show that the bounds are sharp by describing attacks that almost match our lower bounds. To the best of our knowledge these are the first security proofs for efficient server-aided RSA protocols. Keywords: server-aided secret computation, RSA, signature, generic algorithms 1 Introduction In this paper, we investigate the security of server-aided secret computations of R..