Effects Of Cylindrical Geometry Research Articles

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possible to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.

Jet launching from accretion discs in the local approximation

The acceleration of an outflow along inclined magnetic field lines emanating from an accretion disc can be studied in the local approximation, as employed in the computational model known as the shearing box. By including the slow magnetosonic point within the computational domain, the rate of mass loss in the outflow can be calculated. The accretion rates of mass and magnetic flux can also be determined, although some effects of cylindrical geometry are omitted. We formulate a simple model for the study of this problem and present the results of one-dimensional numerical simulations and supporting calculations. Quasi-steady solutions are obtained for relatively strong poloidal magnetic fields for which the magnetorotational instability is suppressed. In this regime the rate of mass loss decreases extremely rapidly with increasing field strength, or with decreasing surface density or temperature. If the poloidal magnetic field in an accretion disc can locally achieve an appropriate strength and inclination then a rapid burst of ejection may occur. For weaker fields it may be possible to study the launching process in parallel with the magnetorotational instability, but this will require three-dimensional simulations.

Characterization and Modeling of 1/$f$ Noise in Si-nanowire FETs: Effects of Cylindrical Geometry and Different Processing of Oxides

In this paper, the volume trap densities Nt are extracted from gate-all-around silicone-nanowire FETs with different gate oxides, using a cylindrical-coordinate-based flicker noise model developed. For extracting Nt, the drain-current power spectral densities were measured from a large number of identical devices and averaged over, thereby mimicking the spatial distribution of trap sites inducing 1/f curve. Also, effective mobility and threshold voltage were simultaneously extracted with the series resistance to characterize the 1/f noise in terms of intrinsic values of these two channel parameters. The volume trap densities thus extracted from different oxides (in situ steam-generated oxide/rapid thermal oxide/nitride-gated oxide) are compared and further examined using hot-carrier stress data. Finally, radius dependence of the cylindrical 1/f model developed is discussed.

Study of skin model and geometry effects on thermal performance of thermal protective fabrics

Thermal protective clothing has steadily improved over the years as new materials and improved designs have reached the market. A significant method that has brought these improvements to the fire service is the NFPA 1971 standard on structural fire fighters’ protective clothing. However, this testing often neglects the effects of cylindrical geometry on heat transmission in flame resistant fabrics. This paper deals with methods to develop cylindrical geometry testing apparatus incorporating novel skin bioheat transfer model to test flame resistant fabrics used in firefighting. Results show that fabrics which shrink during the test can have reduced thermal protective performance compared with the qualities measured with a planar geometry tester. Results of temperature differences between skin simulant sensors of planar and cylindrical tester are also compared. This test method provides a new technique to accurately and precisely characterize the thermal performance of thermal protective fabrics.

Diffusion of azimuthal magnetic fields into a cylindrical plasma

Simple analytic models have been developed to describe the current density and magnetic field profiles in a cylindrically symmetric plasma carrying a z-directional current. Solutions are obtained for time varying boundary magnetic fields characteristic of imploding liner and gas puff plasma implosions. The cylindrical models are compared with previously developed planar solutions. Applications to electromagnetically imploded plasma shells show a small variation in the magnetic field profiles at early times and large radius. These variations become more pronounced as the implosion moves to smaller radius. In general, the effects of cylindrical geometry become significant only when the outer radius reaches the same order as the magnetic field gradient scale length.

The break-up of axisymmetric liquid sheets

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.