Comparison of threaded connections on parts manufactured with 3D printing

Tato práce se zabývá analýzou problému použití závitových spojení u plastových výtisků vyrobených metodou 3D tisku. Cílem práce je popsat jednotlivé druhy a vlastnosti závitových spojení, které lze použít na výtiscích při dané metodě. V experimentální části je popsaná a testovaná výroba dílčích vzorků v laboratorních podmínkách. Následně jsou dle získaných informací určeny závěry a doporučení pro nasazení.This Bachelor thesis deals with the analysis of the problem of using threaded connections in plastic parts produced by 3D printing. The aim of this work is to describe the various types and properties of threaded connections that could be used in a given method of printed parts. In the experimental part is described and tested production of partial samples under laboratory conditions. Consequently, according to the obtained information are determined conclusions and recommendations for deployment

Higher dimensional uniformisation and W-geometry

We formulate the uniformisation problem underlying the geometry of W_n-gravity using the differential equation approach to W-algebras. We construct W_n-space (analogous to superspace in supersymmetry) as an (n-1) dimensional complex manifold using isomonodromic deformations of linear differential equations. The W_n-manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in CP^{n-1}. The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W_n-manifold. We discuss how the Teichmuller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W_n-manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ``generic'' W-algebras.Comment: LaTeX file; 25/13 pages in b/l mode ; version to appear in Nuc. Phys.

The spectra of the spherical and euclidean triangle groups

We derive the spectrum of the Laplace-Beltrami operator on the quotient orbifold of the non hyperbolic triangle groups.Comment: accepted in the Journal of the Australian Mathematical Societ

Quantum mechanics and quantum Hall effect on Riemann surfaces

The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of the $\theta$-bundle, and the wave functions of the Landau levels in the case of the the Poincar{\' e} metric. The degeneracy of the the Landau levels is obtained by using the Riemann-Roch theorem. Then we construct the Laughlin wave function on Riemann surfaces and discuss the mathematical structure hidden in the Laughlin wave function. Moreover the degeneracy of the Laughlin states is also discussed.Comment: 24 pages, Late

Transient Effects on High Voltage Diode Stack under Reverse Bias

This article deals with a description and analysis of the fast transient processes which can occur during a local non-destructive breakdown in a circuit arranged by serial connection of reverse biased high-voltage silicon diodes. The existence of the non-destructive breakdown was observed at some measurements of reverse current-voltage characteristics of individual diodes. However, the study of this phenomenon is very difficult for many serial connected diodes in stack. That is why, a physical model was created for reflection of individual local breakdown in this case. Validity of this model was verified by means of circuit simulation of the investigated process. Further, statistical significance of this process was considered with respect to reliability and lifetime of high-voltage diode stack (HVDS)

Arithmetic and equidistribution of measures on the sphere

Motivated by problems of mathematical physics (quantum chaos) questions of equidistribution of eigenfunctions of the Laplace operator on a Riemannian manifold have been studied by several authors. We consider here, in analogy with arithmetic hyperbolic surfaces, orthonormal bases of eigenfunctions of the Laplace operator on the two dimensional unit sphere which are also eigenfunctions of an algebra of Hecke operators which act on these spherical harmonics. We formulate an analogue of the equidistribution of mass conjecture for these eigenfunctions as well as of the conjecture that their moments tend to moments of the Gaussian as the eigenvalue increases. For such orthonormal bases we show that these conjectures are related to the analytic properties of degree eight arithmetic L-functions associated to triples of eigenfunctions. Moreover we establish the conjecture for the third moments and give a conditional (on standard analytic conjectures about these arithmetic L-functions) proof of the equdistribution of mass conjecture.Comment: 18 pages, an appendix gives corrections to the article "On the central critical value of the triple product L-function" (In: Number Theory 1993-94, 1-46. Cambridge University Press 1996) by Siegfried Boecherer and Rainer Schulze-Pillot. Revised version (minor revisions, new abstract), paper to appear in Communications in Mathematical Physic

Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.Comment: 18 pages, 10 figure

Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis

We prove the non-integrability (non-existence of additional analytic conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU) lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method about the variational equations. The key to this analysis is that the normal variational equations along a certain solution happen to be in a type of Lam\'e equations. We also introduce the classification problem towards non-homogeneous nonlinear lattices including FPU lattices using non-integrability preserving transformation.Comment: Latex, 21 pages, to appear in Physica D (1996), ps.Z file available at http://www.bip.riken.go.jp/irl/chaosken/reulam.ps.

Supersymmetric quantum cosmological billiards

D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.Comment: 4 pages. v2: Added ref. Version to be published in PR