Finite Cylinder Research Articles

A low-energy limit of Yang-Mills theory on de Sitter space

We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder mathcal{I} × S3, where mathcal{I} = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → mathcal{I} × S3 which are framed over the temporal boundary ∂ mathcal{I} × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂ mathcal{I} × S3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along mathcal{I} is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space mathcal{M} vac of gauge-inequivalent Yang-Mills vacua on S3. Since mathcal{M} vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.

Influence of rounding corners on the wake of a finite-length cylinder: An experimental study

This study aims to investigate experimentally the influence of rounding corners (r) as well as aspect ratio (AR) on the flow structures of a surface-mounted finite cylinder. The cylinders with sharp (r* = r/D = 0) and rounded corners (r*=0.167, 0.25 and 0.5) and aspect ratio or height-to-width/diameter ratio (AR = H/D) between 2 and 7 are utilized. The experiments are based on the five-hole probe and hot-wire measurements as well as the oil flow visualization. Wake measurements are made in an open return wind tunnel at the Reynolds number, Re = 1.6 × 104, where Re is defined based on the side width/diameter (D) of the cylinder cross-section and the freestream velocity. It is found that r* and AR have significant effects on the flow structure from the perspective of wake topology, strength of streamwise vortices, and vortex shedding frequency. For all r* considered, the wake is characterized by a quadrupole type (both the tip and base vortices are present) at AR = 7, while a dipole type occurs for AR = 2 and 4 (the base vortices are absent). The strength (circulation) of the streamwise vortex structures is affected by r*. For all AR examined in the present study, the strengths of tip and base vortex structures decrease with increasing r*. The oil flow visualization demonstrates that the features of the horseshoe vortex are sensitive to r* and AR. With increasing r*, the location of the separation line moves downstream and the distance between horseshoe vortex legs decreases. Velocity measurements reveal that the downwash flow enhances with increasing r*. It is also found that the Strouhal number increases progressively by 60% as r* increases from 0 to 0.5, regardless of AR.

Accurate Calculation of Capacitance for Three-Dimensional Axisymmetric Conductors with Arbitrary Profile

This paper presents a rigorous mathematical approach to the analysis of electrostatic problems for three-dimensional objects of revolution. A cavity can be formed by rotation of an arbitrarily shaped generating curve and has coaxial apertures on both ends. Such flexibility allows to consider a wide class of previously studied conductors and stimulate design of new ones. The accurate free space capacitance calculations for finite open cylinders and truncated cones are performed and the results are compared to the known data from the literature.

К расчету поля конечного магнитного цилиндра с внутренним соосным цилиндрическим дефектом

Using the grid method, a numerical solution of the direct problem of magnetostatics for calculating the field of a finite cylinder with a constant magnetic permeability containing an internal inclusion in the form of a coaxial cylinder with a different magnetic permeability is carried out. The algorithm is created for an arbitrary external field. In order to assess the reliability and accuracy of the solution method, the results were tested using precisely solved problems. A comparison is also made with the results of the previously solved problem of a finite defect-free cylinder. The coordinate dependences of the components of the resulting field are constructed for different source data. The program adds to the library of magnetic control problems and can be used for high-quality verification with the results of model experiments, as well as for evaluating the geometric characteristics of an internal defect.

The use of the variational method of homogeneous solutions in an axisymmetric elasticity problem for a finite cylinder under its weight

The use of the variational method of homogeneous solutions in an axisymmetric elasticity problem for a finite cylinder under its weight

Vortex induced vibrations of a pivoted finite height cylinder at low Reynolds number

The vortex induced vibrations (VIVs) of a pivoted cylinder with finite height have been numerically investigated. A mathematical model is introduced and described, and the resulting equations are numerically solved for low Reynolds number Re = 100, 200 and several combinations of the governing parameters. Results on the solid body trajectories, the maximum amplitude of the oscillations, the hydrodynamic force coefficients, the wake structure, and details on the vortex shedding near the cylinder are presented and discussed. The numerical results compare reasonably well with the canonical system of VIV of two-degrees of freedom circular cylinder in the laminar regime. Also, qualitative similarities with closely related VIV systems at larger Re suggest interesting lines of future research. Analytical approximations for limiting cases are done and an excellent agreement with the numerical results is obtained.

Fractal neutrons diffusion equation: Uniformization of heat and fuel burn-up in nuclear reactor

In this study, the fractal neutrons diffusion equation is constructed based on the concept of fractal anisotropy and product-like fractal measure introduced by Li and Ostoja-Starzewski using the method of dimensional regularization. In this approach, the global forms of dynamical equations are cast in forms involving integer-order integrals while the local forms are expressed by partial differential equations with derivatives of integer order. This theory is characterized by an effective buckling which varies with distance and a diffusion damping characterized by a spatially variable coefficient. These terms are major in nuclear reactor physics since the magnitude of energy dissipation in fission depends on the position and nature of interaction. We have discussed the cases of parallelepiped and finite cylinder reactors. In both geometrical types of reactors, it was observed that the ratio of the maximum flux to the average flux is too small since the uniformization of the heat fabrication and the fuel burn-up in the nuclear reactor is potential. This has important consequences on safety of the fuel operation and on the types of nuclear materials used in nuclear engineering reactors. Further details are discussed as well.

Functional renormalization group study of the Kitaev- Γ model on the honeycomb lattice and emergent incommensurate magnetic correlations

The theoretical inception of the Kitaev honeycomb model has had defining influence on the experimental hunt for quantum spin liquids, bringing unprecedented focus onto the synthesis of materials with bond-directional interactions. Numerous Kitaev materials, which are believed to harbor ground states parametrically close to the Kitaev spin liquid, have been investigated since. Yet, in these materials the Kitaev interaction often comes hand in hand with off-diagonal $\Gamma$ interactions -- with the competition of the two potentially giving rise to a magnetically ordered ground state. In an attempt to aid future material investigations, we study the phase diagram of the spin-1/2 Kitaev-$\Gamma$ model on the honeycomb lattice. Employing a pseudofermion functional renormalization group approach which directly operates in the thermodynamic limit and captures the joint effect of thermal and quantum fluctuations, we unveil the existence of extended parameter regimes with emergent incommensurate magnetic correlations at finite temperature. We supplement our results with additional calculations on a finite cylinder geometry to investigate the impact of periodic boundary conditions on the incommensurate order, thereby providing a perspective on previous numerical studies on finite systems.

Analysis of The 2-D Transient Heat Conduction in a Composite Finite Cylinder with Heat Generation.(Dept.M)

The objective of this paper is to study the 2-D transient temperature behavior in a composite finite cylinder with internal heat generation. For this purpose, a new dimensionless 2-D finite difference technique in the axial and radial directions is developed. The developed technique is then applied to obtain the time development of temperature profiles in a complex composite cylinder.

Transient Thermal and Mechanical Stress Analysis of 2D-Functionally Graded Finite Cylinder: A Truly Meshless Formulation

Transient Thermal and Mechanical Stress Analysis of 2D-Functionally Graded Finite Cylinder: A Truly Meshless Formulation

Time-resolved wake dynamics of finite wall-mounted circular cylinders submerged in a turbulent boundary layer

Abstract

Insertion loss of regular finite cylinder arrays with porous layers between the rows.

It has been demonstrated recently via simulations in a duct that the sound transmission loss of porous materials can be increased with embedded periodic scatterers [Jena and Qiu, J. Acoust. Soc. Am. 147, 978-983 (2020)]. In this paper, the insertion loss (IL) of two types of finite size structures constructed by installing two parallel porous sheets within rows of periodic scatterers is investigated in free field. One structure uses rigid cylindrical shells, while the other uses split ring shells, which are obtained by making uniform vertical slits in cylindrical shells. The simulation results show that the mixed structure has larger IL than the summation of the ILs of the individual periodic scatterers and two parallel porous sheets in the frequency range after the first bandgap due to Bragg diffraction, and an additional peak in IL is introduced for the split ring scatterers due to their local resonance. The amplitude, frequency, and bandwidth of the resonance peak can be tuned by changing the geometry of the slit for some specific broadband sound absorption. Finally, the experiment results obtained in an anechoic chamber are presented to support the simulation results and analyses.

One Approach to the Numerical Solution of the Basic Equation of Magnetostatics for a Finite Cylinder in an Arbitrary External Field

One Approach to the Numerical Solution of the Basic Equation of Magnetostatics for a Finite Cylinder in an Arbitrary External Field

Characterization of normal and deformed red blood cells using simulated differential photoacoustic cross-section spectral data

Frequency dependent differential photoacoustic cross-section (DPACS) over a large frequency band (100–1000 MHz) has been computed and subsequently, morphological parameters of photoacoustic (PA) source have been quantified. Green’s function method has been employed for computing the DPACS for a series of ellipsoidal droplets (with varying aspect ratio), Chebyshev particles (with different waviness (n) and deformation (ϵ) parameters), healthy red blood cell (RBC) and cells suffering from hereditary disorders (spherocytosis, elliptocytosis and stomatocytosis). The tri-axial ellipsoid form factor (TAEFF), finite cylinder form factor (CFF) and toroid form factor (TFF) models have been used to fit the DPACS spectrum to obtain size and shape information of the PA source. The TAEFF model estimates the shape parameters of the ellipsoidal droplets accurately (error < 5%). It is found that volume estimation is better (error < 10%) for lower order (n = 2, ϵ = ± 0.25) and very higher order (n = 35, 45, ϵ = ± 0.05) Chebyshev particles compared to those of n = 4, 6 and ϵ = ± 0.25. The TAEFF model predicts shape parameters of stomatocyte with volume error ≈15% but it is ≤6% for other cells. The opposite trend is observed for the CFF model. The TFF model is able to estimate the shape parameters efficiently for normal erythrocyte and stomatocyte but gives relatively large errors (>15%) for other deformed RBCs. The inverse problem framework may motivate to develop a PA-based technology to assess single cell morphology.

Insights into low Reynolds flow past finite curved cylinders

Spectral proper orthogonal decomposition (SPOD) is applied to experimental digital visualizations to scrutinize the properties of the wake flow behind curved cylinders. This technique has been applied to the image data of Shang et al. [“Flow past finite cylinders of constant curvature,” J. Fluid Mech. 837, 896–915 (2018)] to emphasize the main features of the flow and to extract the most energetically and dynamically relevant space-time coherent structures. The study considers different Reynolds numbers and angles of curvature for two cylinder aspect ratios. It is first shown that the SPOD structures reproduce the base flow topology of the digital visualizations, confirming the presence of a single oblique shedding regime for a low aspect ratio and both normal and oblique regimes for a high aspect ratio. The appearance of the instabilities typical of straight cylinders, usually referred to as type-A and -B in literature, is identified as well. As principal results obtained for curved cylinders, increasing the Reynolds number the analysis of SPOD spectra has revealed two reductions in the oscillation frequency of the leading coherent structures, attributed to the occurrence of type-A instability when the wake is still laminar, and to the development of a one-sided vortex dislocation in turbulent regime. The study has also highlighted the gradual transfer of energy between flow structures during the transition from type-A to type-B instabilities, accompanied by high-frequency scales excitement. Some peculiar aspects of SPOD field reconstruction are outlined here, which are suggested by the physical characteristics of the flow.

О задаче идентификации термомеханических характеристик конечного функционально-градиентного цилиндра

The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables. A set of canonical linear systems of differential equations of the 1st order is obtained, the solution of each of which is obtained numerically using the shooting method. The coefficient inverse problem of finding the thermomechanical characteristics of a finite length cylinder using additional information in Laplace transforms, given on the outer surface of the cylinder, is posed. The dimensionless thermomechanical characteristics of the cylinder were restored in two stages. At the first stage, the initial approximation was determined in the class of positive bounded functions. At the second stage, based on the solution of the corresponding Fredholm integral equations of the 1st kind, corrections of the reconstructed functions were found, and an iterative process of their refinement was constructed. In the course of computational experiments, it was found that monotonic characteristics are restored with good accuracy; the reconstruction procedure is resistant to input information noise.

Singular Limit for Rotating Compressible Fluids with Centrifugal Force in a Finite Cylinder

In this paper, we consider a rotating compressible Navier–Stokes system in a finite cylinder, by incorporating the effect of centrifugal force. The Mach number and Froude number admit the same scale. By using the relative entropy method, we prove that the scaled problem approaches the static profile as the Mach and Reynolds numbers tend to zero and infinity respectively, with well-prepared initial data. In particular, the property of radial symmetry resulting from the centrifugal force is crucial in the whole analysis.

Effects of size ratio and inter-cylinder spacing on wake transition in flow past finite inline circular cylinders mounted on plane surface

Three-dimensional numerical computations have been carried out in flow past two inline finite-height circular cylinders using Open Source Field Operation and Manipulation. Investigations have been carried out for the varying Reynolds number (Re) ranging from 150 to 300. The diameter of the upstream cylinder is varied in such a way that the size ratio (SR, ratio of the diameter of the upstream cylinder to that of the downstream cylinder) takes values of 0.25, 0.5, and 1.0. For each size of the upstream cylinder, the downstream cylinder is placed at different locations in the streamwise direction. Effects of Re, SR, and inter-cylinder spacing (S) on three-dimensional unsteady wake characteristics behind upstream and downstream cylinders have been examined using iso-Q surfaces. Unsteady wake oscillations in both the wakes are analyzed qualitatively and quantitatively in terms of Hilbert spectra and the degree of stationarity using the transverse velocity component in the wake. Different flow regimes for upstream and downstream wakes have been identified and discussed with the change in Re, SR, and S. Transitions in the wake flow are illustrated using vorticity contours, frequency spectra, and bifurcation diagram. The level of wake synchronization in the upstream wake, downstream wake, and between both the wakes has been identified with the help of the cross correlation function.

Experimental Investigation on Effects of Elastic Agitator to Turbulence Enhancement

The conventional method to promote mass, momentum and energy transport between fluid particles is to introduce a disturbance to the flow. An ultrasonic velocity profiler, UVP experiment was used to study the mean and fluctuating flow properties in the near wake of the rigid and flexible protruding surface in a water tunnel under the Reynolds number of 4000, 6000 and 8000. In the current study, circular finite cylinders (cantilevers) with various aspect ratios (AR = 10, 12, 14 and 16) and materials were used as the geometry of the rigid and protruding surface. The motion of the cylinder alters the fluid flow significantly. The increment of the wake region (~10 larger in the flexible cylinder compared to the rigid case, for AR = 16) is due to the weakening of the influence of downwash caused by the stream-wise deflection of the flexible cylinder. As a mean to quantify turbulence, the turbulent intensity, Ti, was studied. In general, the flexible cylinders show better capability in augmenting the turbulence than the rigid cylinder. The stream-wise turbulent intensity for AR = 16 and Re = 8000 can be as high as 97 for the flexible cylinder compared to only 26 for the rigid case. The normalized amplitude response graph, which records the cross-flow oscillation of the flexible cylinder was also analyzed. Under the same Reynolds number, the turbulence enhancement increases with the structural velocity. An organized oscillating motion is in favor of a higher performance of turbulence enhancement. © 2020 All Rights Reserved

On the origins of steady streaming in precessing fluids

Abstract