Metodologia badań politologicznych na przykładzie eurazjatyzmu

The text answers the following question: what is the point of conducting political science research? The research can make a lot of sense when you are strongly motivated and, motivation is just as important as your knowledge how to do it. In the latter case, you must proceed in the correct order. Firstly, the boundaries of the research field should be set, and secondly, original and unconventional research problems and hypotheses should be defined. Thirdly, the proper selection of primary and secondary sources is necessary. Fourthly, you choose appropriate research methods and techniques, and then construct a research tool or tools. After the determining of the level of accuracy and relevance of data collected, it is possible to proceed to the verification of hypotheses. The more thorough the process and the more inquisitive researcher, the more interesting research results are obtained.Tekst odpowiada na pytanie: jaki jest sens prowadzenia badań politologicznych? Wtedy, gdy ma się odpowiednią motywację i (co równie ważne) wie się, jak to można zrobić. W tym drugim przypadku musi się postępować w odpowiedniej kolejności. Po pierwsze, należy wyznaczyć granice pola badawczego, a po drugie, określić oryginalne, niebanalne problemy i hipotezy badawcze. Po trzecie, konieczny jest odpowiedni dobór i sposób selekcji źródeł pierwotnych i ewentualnie wtórnych. Czwartym etapem jest dobranie adekwatnych metod i technik badawczych, a następnie skonstruowanie narzędzia lub narzędzi badawczych. Po określeniu poziomu prawdziwości i stosowalności zebranych informacji możliwe jest dopiero przystąpienie do weryfikacji hipotez. Im bardziej ten ostatni proces będzie rzetelny, a badacz dociekliwy, tym ciekawsze uzyska się rezultaty badawcze

Optimal neuronal tuning for finite stimulus spaces

The efficiency of neuronal encoding in sensory and motor systems has been proposed as a first principle governing response properties within the central nervous system. We present a continuation of a theoretical study presented by Zhang and Sejnowski, where the influence of neuronal tuning properties on encoding accuracy is analyzed using information theory. When a finite stimulus space is considered, we show that the encoding accuracy improves with narrow tuning for one- and two-dimensional stimuli. For three dimensions and higher, there is an optimal tuning width

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths

Homoclinic points of 2-D and 4-D maps via the Parametrization Method

An interesting problem in solid state physics is to compute discrete breather solutions in $\mathcal{N}$ coupled 1--dimensional Hamiltonian particle chains and investigate the richness of their interactions. One way to do this is to compute the homoclinic intersections of invariant manifolds of a saddle point located at the origin of a class of $2\mathcal{N}$--dimensional invertible maps. In this paper we apply the parametrization method to express these manifolds analytically as series expansions and compute their intersections numerically to high precision. We first carry out this procedure for a 2--dimensional (2--D) family of generalized Henon maps ($\mathcal{N}$=1), prove the existence of a hyperbolic set in the non-dissipative case and show that it is directly connected to the existence of a homoclinic orbit at the origin. Introducing dissipation we demonstrate that a homoclinic tangency occurs beyond which the homoclinic intersection disappears. Proceeding to $\mathcal{N}=2$, we use the same approach to determine the homoclinic intersections of the invariant manifolds of a saddle point at the origin of a 4--D map consisting of two coupled 2--D cubic H\'enon maps. In dependence of the coupling the homoclinic intersection is determined, which ceases to exist once a certain amount of dissipation is present. We discuss an application of our results to the study of discrete breathers in two linearly coupled 1--dimensional particle chains with nearest--neighbor interactions and a Klein--Gordon on site potential.Comment: 24 pages, 10 figures, videos can be found at https://comp-phys.tu-dresden.de/supp

Coupling of bouncing-ball modes to the chaotic sea and their counting function

We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach. Agreement with numerically determined rates is found for the stadium and the cosine billiard. We use this result to predict the asymptotic behavior of the counting function N_bb(E) ~ E^\delta. For the stadium billiard we find agreement with the previous result \delta = 3/4. For the cosine billiard we derive \delta = 5/8, which is confirmed numerically and is well below the previously predicted upper bound \delta=9/10.Comment: 10 pages, 6 figure

Temporal flooding of regular islands by chaotic wave packets

We investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist. For wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling. This flooding weight initially increases linearly and saturates to a value which varies from torus to torus. We demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard. This universality is reproduced by a suitable random matrix model