Search results for "Euler"
showing 10 items of 159 documents
N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant
1991
We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of…
TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS
1991
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal G}$ of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces and introduce supersymmetric quantum mechanics actions modelling the Riemannian geometry of submersions and embeddings, relevant to the projections ${\cal A}\rightarrow {\cal A}/{\cal G}$ and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ respectively. We explain the relation between Donal…
Dimensional interpolation and the Selberg integral
2019
Abstract We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non–integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.
Nonlinear Kelvin waves on a quantized vortex line in superfluid helium
2013
In this paper we show an exact solution (Kelvin wave) of an approximated dynamical equation for a quantized vortex line in helium superfluid at finite temperature. It is shown that the applied heat flux interacts with the vortex line, and the amplitude of the Kelvin wave can grow (the so-called Donnelly instability) or decrease according with the mutual direction between heat flux and wave vector.
Khovanov homology for signed divides
2009
The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles in a [math] –disc, one can associate a strongly invertible link in the [math] –sphere. This can be generalized to signed divides: divides with [math] or [math] sign assignment to each crossing point. Conversely, to any link [math] that is strongly invertible for an involution [math] , one can associate a signed divide. Two strongly invertible links that are isotopic through an isotopy respecting the involution are called strongly equivalent. Such isotopi…
Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations
1998
This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.
Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution
1998
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…
A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air’ method
2012
SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air’ approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosityfluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostati…
Aerodynamics of an isolated ski jumping ski
2019
A single isolated ski was suspended from a six-component wind tunnel balance and three angles, the angle of attack, the yaw angle and the edge angle were adjustable during the test. Increasing yaw angle from 0 to 15° increased the lift coefficient CL from 0.42 to 0.90 at edge angle 0° and from 0.70 to 0.87 at edge angle 10°, respectively. Increasing yaw angle also increased the sensitivity of the ski to changes in edge angle, i.e., increasing the edge angle (20°–45°) decreased the CL and the ratio $$C_{L}^{2}/{C_D}$$ with large yaw angles. However, to maximize the lift-to-drag ratio with a typical angle of attack of 30° in ski jumping, it may be reasonable to have an edge angle of 5°–10° on…
Numerical Simulation as a Tool for Design Optimization of Two-Phase Swirl Flow Atomizers
2021
This study aims to analyze the hydrodynamics in two-phase swirl flow conical atomizers. The Euler-Euler model was used for the calculations. Numerical simulations were performed to provide information about the fluid velocity distribution and the atomizer’s internal flow. The numerical calculations confirmed the experimental data. This data was found based on the consistency of the spray angles obtained by both methods. Assuming the correctness of the numerical simulations performed, they can be treated as a tool for further analysis of mass and energy exchange along with the atomizer and optimizing the atomizer’s design depending on the requirements. The influence of the swirl chamber geom…