3 resultados para Lyapunov Exponents

em Helda - Digital Repository of University of Helsinki


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Civil War Hero Burials the funerals of the fallen White in Finland in 1918 This study focuses on the burial with honours of fallen White combatants during the Finnish Civil War of 1918, as well as on the reasons underpinning the practice. The main sources of the study included the archives of the White army, the Civil Guard organisation and the Church, as well as the newspapers. The genetic method of history research was used. Both the existing tradition of military burials and the ecclesiastical burial culture influenced the burials of those who fell during the Civil War. The first war hero funerals took place as early as the beginning of February 1918, and the first larger-scale collective funerals were organised in Laihia and Vaasa in the Ostrobothnia province, with the latter attended by the supreme civil and military leaders of White Finland. From early on, these funerals assumed their characteristic features, such as the lion flag a design for the Finnish national flag proposed immediately upon the declaration of the country s independence military parades, lines of honour guards, eulogies, salutes and common war hero graves. As a result of the general offensive begun in mid-March 1918, the numbers of the fallen multiplied, so special organisations were established to handle the burials of the fallen. At the same time, the war hero funerals became more frequent and diffused, and the numbers of the buried grew throughout the country. In early March, the advocates of the republican system of government published their appeal in the newspapers, requesting that collective graves for those who fell in the war prepared in every locality. They motivated their request by stating that it was the funerals in particular that had inspired many men to join the ranks voluntarily in the first place, and that the large collective soldiers graves increased the numbers of those who answered the call and left for the front. The Civil Guard organisation arranged the burials of war heroes. The clergy contributed by officiating the religious service and by clearly aligning themselves with the Whites in their eulogies. The teachings of the Lutheran Church suggest that they found the Whites to be the temporal authority instituted by God, and therefore authorised raising the sword against the Reds. Speaking at the funerals with great pomp and sentimental power, the leaders of the Civil Guard and the exponents of the learned classes instigated their audiences against the Reds. The funeral speeches idealised the war hero s death by recalling military history since the times of ancient Greece. Being of the emblematic colour of the Whites, the white coffin assumed a particular importance connected to ideas of biblical purity and innocence. By the end of May 1918, almost 3,300 Whites were buried in the soldiers graves prepared by the burial organisation in some 400 localities. Only about 200 men remained missing in action or unidentified. The largest common graves accommodated over 60 fallen combatants. Thus, the traditions of the 1918 Civil War directly influenced war hero burial practices, which continued into the Finnish Winter War of 1939.

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Aerosols impact the planet and our daily lives through various effects, perhaps most notably those related to their climatic and health-related consequences. While there are several primary particle sources, secondary new particle formation from precursor vapors is also known to be a frequent, global phenomenon. Nevertheless, the formation mechanism of new particles, as well as the vapors participating in the process, remain a mystery. This thesis consists of studies on new particle formation specifically from the point of view of numerical modeling. A dependence of formation rate of 3 nm particles on the sulphuric acid concentration to the power of 1-2 has been observed. This suggests nucleation mechanism to be of first or second order with respect to the sulphuric acid concentration, in other words the mechanisms based on activation or kinetic collision of clusters. However, model studies have had difficulties in replicating the small exponents observed in nature. The work done in this thesis indicates that the exponents may be lowered by the participation of a co-condensing (and potentially nucleating) low-volatility organic vapor, or by increasing the assumed size of the critical clusters. On the other hand, the presented new and more accurate method for determining the exponent indicates high diurnal variability. Additionally, these studies included several semi-empirical nucleation rate parameterizations as well as a detailed investigation of the analysis used to determine the apparent particle formation rate. Due to their high proportion of the earth's surface area, oceans could potentially prove to be climatically significant sources of secondary particles. In the lack of marine observation data, new particle formation events in a coastal region were parameterized and studied. Since the formation mechanism is believed to be similar, the new parameterization was applied in a marine scenario. The work showed that marine CCN production is feasible in the presence of additional vapors contributing to particle growth. Finally, a new method to estimate concentrations of condensing organics was developed. The algorithm utilizes a Markov chain Monte Carlo method to determine the required combination of vapor concentrations by comparing a measured particle size distribution with one from an aerosol dynamics process model. The evaluation indicated excellent agreement against model data, and initial results with field data appear sound as well.

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Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.