Model In Cylindrical Geometry Research Articles

Modeling non-confined coronal flares: Dynamics and X-ray diagnostics

Long-lasting, intense, stellar X–ray flares may approach conditions of breaking magnetic confinement and evolving in open space. In the perspective of searching for possible tracers of non-confinement, we explore this hypothesis with hydrodynamic simulations of flares occurring in a non-confined corona: model flares are triggered by a transient impulsive heating injected in a plane-parallel stratified corona. The plasma evolution is described by means of a numerical 2-D model in cylindrical geometry $R,Z$. We explore the space of fundamental parameters. As a reference model, we consider a flare triggered by a heating pulse of 10 erg cm -3 s -1 lasting 150 s and released in a region ~ 10 9 cm wide and at a height ~$ 2 \times 10^9$ cm from the base of the stellar surface. The pressure at the base of the corona of the unperturbed atmosphere is 0.1 dyne cm -2 . The heating would cause a 20 MK flare if delivered in a 40 000 km long closed loop. The modeled plasma evolution in the heating phase involves the propagation of a 10 MK conduction front and the evaporation of a shocked bow density front upwards from the chromosphere. As the heating is switched off, the temperature drops in few seconds while the density front still propagates, expanding, and gradually weakening. This kind of evolution is shared by other simulations with different coronal initial pressure, and location, duration and intensity of the heating. The X-ray emission, spectra and light curves at the ASCA/SIS focal plan, and in two intense X–ray lines (Mg XI at 9.169 A and Fe XXI at 128.752 A), have been synthesized from the models. The results are discussed and compared to features of confined events, and scaling laws are derived. The light curves invariably show a very rapid rise, a constant phase as long as the constant heating is on, and then a very fast decay, on time scales of few seconds, followed by a more gradual one (few minutes). We show that this evolution of the emission, and especially the fast decay, together with other potentially observable effects, are intrinsic to the assumption of non–confinement. Their lack indicates that observed long–lasting stellar X–ray flares should involve plasma strongly confined by magnetic fields.

Modelling micro-level volume expansion during reactive melt infiltration using non-isothermal unreacted-shrinking core models

Reactive melt infiltration is a process used to manufacture silicon carbide fibre-reinforced silicon carbide (SiC/SiC) composites. The present stage of research on reactive infiltration is primarily experimental, wherein complete infiltration is rarely achieved and unreacted silicon still remains in the composite. This paper deals with the micro-modelling aspect of reactive melt infiltration and estimates volume expansion due to mass transfer and reaction for cylindrical fibres. The thickness of the reaction product layer forming the matrix in the composite is determined by using an unreacted-shrinking core (URSC) model for cylindrical geometry in terms of physical parameters (diffusivity of the reactants and temperature) and non-dimensional physical quantities (such as the Sherwood number, Nusselt number and Thiele modulus). The effectiveness factors for the chemical reaction are determined as a function of time for various sets of physical parameters. The amount of volume expansion is found by determining the growth of the radius of the reaction product layer. It is concluded that lower initial temperatures of the solid reactant and higher ratios of heat capacity of reaction product to heat of reaction are favourable for infiltration. Determining the volume expansion in a single particle will later help in determining the transient permeability in a fibre preform during infiltration and also in optimizing this process.

Kinetics of cortical bone demineralization: Controlled demineralization—a new method for modifying cortical bone allografts

We investigated the kinetics of hydrochloric acid demineralization of human cortical bone with the objective of developing a method of controlled demineralization for structural bone allografts. It is known that the demineralization of cortical bone is a diffusion rate limited process with a sharp advancing reaction front. The demineralization kinetics of human cortical bone, described as the advance of the reaction front versus immersion time, were determined by measuring extraction of bone mineral in both planar and cylindrical geometries. Mathematical models based on diffusional mass transfer were developed to predict this process. The experimental data fit well with the behavior predicted by the model. The model for planar geometry is applicable to controlled demineralization of cortical bone allografts of irregular shapes such as cortical struts. The model for cylindrical geometry is appropriate when curved surfaces are involved such as in diaphyseal bone allografts. This method of demineralization has direct application to clinical modification of cortical bone allografts to potentially enhance their osteoinductive properties. © 1996 John Wiley & Sons, Inc.

Kinetics of cortical bone demineralization: Controlled demineralization?a new method for modifying cortical bone allografts

We investigated the kinetics of hydrochloric acid demineralization of human cortical bone with the objective of developing a method of controlled demineralization for structural bone allografts. It is known that the demineralization of cortical bone is a diffusion rate limited process with a sharp advancing reaction front. The demineralization kinetics of human cortical bone, described as the advance of the reaction front versus immersion time, were determined by measuring extraction of bone mineral in both planar and cylindrical geometries. Mathematical models based on diffusional mass transfer were developed to predict this process. The experimental data fit well with the behavior predicted by the model. The model for planar geometry is applicable to controlled demineralization of cortical bone allografts of irregular shapes such as cortical struts. The model for cylindrical geometry is appropriate when curved surfaces are involved such as in diaphyseal bone allografts. This method of demineralization has direct application to clinical modification of cortical bone allografts to potentially enhance their osteoinductive properties.

A study on simultaneous photolimitation and photoinhibition in dense microalgal cultures taking into account incident and averaged irradiances

From chemostat cultures of the marine microalga Isochrysis galbana (CCAP 927/15) simultaneous photolimitation and photoinhibition was observed. The extent of each phenomenon depends on the light gradient inside the culture and therefore on the incident irradiance. Variations in biomass concentration and average irradiance inside the culture with dilution rate at three incident irradiances, I o , were studied (from I o = 820 to 3270 μE m −2 s −1). At I o above 1630 μE m −2 s −1 a photoinhibition effect was observed, although the specific growth rate remained a hyperbolic function of average irradiance regardless of incident irradiance. To calculate average irradiance, a three-dimensional irradiance distribution model for cylindrical geometry is proposed, improving the estimation of the irradiance field inside culture with regard to other methods used up to now since the variations in illumination along the vertical axis are considered. Lastly, a new approach to model simultaneous photolimitation and photoinhibition is proposed by considering that specific growth rate is related to average irradiance and that parameters representing the cell adaptability to light are a function of the maximum irradiation at which cells are exposed, that is, the incident irradiance.

Global waves in resistive and hot tokamak plasmas

Maxwell's equations are solved in a toroidal axisymmetric plasma. The numerical method implemented in the PENN code is based on a formulation in terms of the electromagnetic potentials and a discretization with standard bilinear or bicubic Hermite finite elements. Two models for the dielectric tensor operator yield different physical problems, which can be used comparatively to study small amplitude plasma perturbations down to the Alfvén range of frequencies. The first treats the plasma as resistive fluids and gives results that are in good agreement with toroidal fluid codes. The second is a kinetic model taking into account the finite size of the Larmor radii; it is here successfully tested against a similar model in cylindrical geometry. New results are obtained for kinetic effects in toroidal geometry, showing that it might be difficult to use an Alfvén wave heating scheme to heat a plasma up to temperatures that are relevant for a tokamak reactor.

Heating of underdense plasmas by intense short-pulse lasers.

A one-dimensional model in cylindrical geometry which incorporates tunnel ionization, nonlinear inverse bremsstrahlung, and radial heat conduction is used to predict the spatial and temporal temperature distribution in an undercritical plasma irradiated axially by a short-pulse laser. Results from the calculation are compared to available experimental data using a 12 ps KrF laser and to previous work in a regime relevant to proposed recombination optical-field ionized xuv lasers in the transient regime, e.g., Li-like neon. The calculated temperature is too high for lasing to the ground state because of the large contribution from inverse bremsstrahlung for pulse lengths greater than 100 fs. It is shown that for small filaments, additional cooling by supersonic heat conduction on a few picosecond time scale could be used efficiently to generate inversion between excited states in the quasi-steady-state regime.

Plasma density profile and electron temperature in discharge positive columns at intermediate pressures: examination of Ingold's approximation

Ingold's model (1978) for the medium pressure positive column is examined and compared with the original quasi-neutral theory of Self (1966). The model for cylindrical geometry is extended to plane and spherical cases, and their plasma balance equations (PBE) are further simplified without loss of accuracy. It is found that Ingold's model is inappropriate to predict the plasma density profiles, producing lower values than the exact curves. For helium plane and cylindrical positive columns, it is shown that the electron temperatures obtained from Ingold's and simplified PBES are accurate within several percent of the exact values and are in good agreement with reported observations.

Isothermal release of tritium from neutron-irradiated Li 2O pellets

Li 2O pellets irradiated with thermal neutrons were isothermally annealed to release tritium in a helium atmosphere at temperatures ranging from 673 to 1073 K. The release rates were found to significantly increase at elevated temperatures and to depend on the density of the Li 2O pellet. The overall diffusion coefficients of the release process were calculated using the cylindrical geometry model for the pellets as D (cm 2 s −1) = 1.02 × 10 −3 exp(−51.0 kJ mol −1/RT ) (90% theoretical density pellets), and D (cm 2 s −1) = 2.64 × 10 −3 exp(−46.5 kJ mol −1/RT ) (ca. 80% T.D. pellets) over the region 773≤ T ≤ 1073 K. The result of the release experiment at 673 K suggested that the diffusion rate was controlled by the decomposition of lithium hydroxide on the surface of Li 2O grains.

Uniqueness of the even correlation functions for the two-dimensional Ising model in cylindrical geometry at low temperature

Uniqueness of the even correlation functions for the two-dimensional Ising model in cylindrical geometry at low temperature