Axial Symmetric Geometry Research Articles

Modeling the effect of shape deformation induced by gravity on the evaporation of pendant and sessile drops

Pendant and sessile drops form a spherical cap only in the absence of gravity. The effect of gravity on drop shape is often neglected on the basis of the assumption that the drop size is smaller than the capillary length [Lc=(σ/gρ)1/2], although the deformation may not be fully negligible even in those cases. This paper focuses on evaluation of the effect that deformation due to gravity has on the evaporation characteristics of pendant and sessile drops. The drop shape is described by the Bashforth–Adams equation, a non-linear second order ordinary differential equation, which is solved numerically using a Runge–Kutta method with variable time steps. Under quasi-steady approximation, the species and energy conservation equations in the gas phase have analytical solutions, even for temperature-dependent gas thermophysical properties, once the solution of a basic Laplace problem is known. The Laplace equation is solved in axial symmetric geometry by using COMSOL Multiphysics®, for a wide range of drop sizes and contact angles, yielding vapor distribution, vapor fluxes, and evaporation rates. Comparison with the results from drops of same size in microgravity (i.e., having a spherical cap shape) shows that the effect is also perceptible for drops with a size smaller than the capillary length and that it can become quite important for those with larger sizes. Complementary results are found for sessile and pendant drops with respect to wall wettability, suggesting that the phenomenon can be analyzed using a unitary approach.

Computer Simulation of Explosive Emission Processes in Strong Electromagnetic Fields

The paper discusses the problem of computer simulation of explosive emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell’s equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Компьютерное моделирование процессов электронной эмиссии в сильных электромагнитных полях

The paper discusses the problem of computer simulation of electron emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell's equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Quasi-static approximation in the study of compact stars

This paper is devoted to the evaluation of the quasi-static approximation of the hydro-dynamics of compact stars in the energy–momentum squared gravity. This theory allows for the presence of a scalar created by the stress–energy tensor as T2=TγλTγλ in the generalized action of the theory. For this purpose, we investigate the anisotropic and dissipative fluid composition in axial and reflection symmetric geometry. To grasp the idea of the proposed approximation, a collection of invariant velocities is defined. As a result, the evolution of compact stars is presented in this approximation by examining the associated generalized field, dynamical, and scalar equations to elicit all possible outcomes. The generalized heat-transport equation is evaluated to study the thermodynamics of the chosen system. In the context of energy–momentum squared gravity, the role of structure scalars in the dynamics of the compact stars is also investigated. Furthermore, the proposed approximation is used to determine the significance of kinematical variables, generalized heat-fluxes, and structure scalars for the evolution of self-gravitating compact stars.

PiCOPIC: 2.5-D PARTICLE-IN-CELL CODE, OPTIMIZED FOR SIMULATION OF BEAM-PLASMA INTERACTIONS

Original code optimized forsimulation of interactions between plasma and charged particles beams and bunches, based on particle in cell method described. The code is electromagnetic and fully relativistic with 2.5D axial symmetric geometry. Binary coulomb particle collisions are taken into account. The code is fully parallelized and designed for computer systems with shared memory. Ability to extend supported platforms to systems with distributed memory (like computer clusters or grids) is embedded into code architecture.

Mechanical effects of distributed fibre orientation in the periodontal ligament of an idealised geometry

In this study, we computationally assess the effects of the distributed fibre orientation in the periodontal ligament (PDL) on mechanical responses of the tooth-PDL complex. An idealised axial-symmetric geometry of a tooth-PDL complex was constructed. The fibre orientation in the PDL was modelled as a trigonometric function based on anatomical knowledge, and the PDL was modelled as a transversely isotropic hyperelastic material dependent on fibre orientations. Parametric studies of the fibre orientation on the mechanical responses of the tooth-PDL complex were conducted. Obtained results showed that the anatomically consistent fibre orientation functions as a supporting structure against not only vertical but also horizontal loads.

Symmetry-broken effects on electron momentum spectroscopy caused by adiabatic vibration

The vibronic coupling effect is usually studied by invoking the breakdown of Born-Oppenheimer approximation. The present study shows that the symmetry-broken effect induced by nuclei vibrations can also lead strong impact on the electronic states under the framework of Born-Oppenheimer approximation. This adiabatic-invoking vibrational effect on electron momentum spectroscopy of ethylene (C2H4), ethane (C2H6) and methanol (CH3OH) was studied with quantum mechanical method. The results show that electron momentum spectroscopy of localized electrons, especially core electrons in axial symmetric geometry molecules can be affected unusually and strongly by several asymmetric vibrational modes.

2.5D relativistic electromagnetic PIC code for simulation of the beam interaction with plasma in axial-symmetric geometry

2.5D relativistic electromagnetic PIC code for simulation of the beam interaction with plasma in axial-symmetric geometry was developed. Accurate charge weighting scheme and difference schemes near the system axis were introduced. Simulation tests of electromagnetic wave interaction with inhomogeneous plasma were carried out.

A Multi-Physics Model for Solid Oxide Iron-Air Redox Flow Battery

A rigorous physics-based mathematical model for a solid oxide iron-air redox flow battery system is presented in this paper. The modeled flow battery system combines a Fe-FeO redox couple as the energy storage unit and a regenerative solid oxide fuel cell as the electrical functioning unit in a 2D axial symmetric geometry. This model was developed from fundamental theories of reaction engineering in which basic transport phenomena and chemical/electrochemical kinetics are included. The model shows good agreement with the experimental data. Simulation results for the chemical, electrochemical and transport behavior of the battery are discussed.

A Multi-Physics Model for Solid Oxide Iron-Air Redox Flow Battery: Simulation of Discharge Behavior at High Current Density

A rigorous physics-based mathematical model for a solid oxide iron-air redox flow battery system is presented in this paper. The modeled flow battery system combines a Fe-FeO redox couple as the energy storage unit and a regenerative solid oxide fuel cell as the electrical functioning unit in a 2D axial symmetric geometry. This model was developed from fundamental theories of reaction engineering in which basic transport phenomena and chemical/electrochemical kinetics are included. The model shows good agreement with the experimental data. Simulation results for the chemical, electrochemical and transport behavior of the battery are discussed.

Modeling Microscopic Chemical Sensors in Capillaries

Nanotechnology-based microscopic robots could provide accurate in vivo measurement of chemicals in the bloodstream for detailed biological research and as an aid to medical treatment. Quantitative performance estimates of such devices require models of how chemicals in the blood diffuse to the devices. This paper models microscopic robots and red blood cells (erythrocytes) in capillaries using realistic distorted cell shapes. The models evaluate two sensing scenarios: robots moving with the cells past a chemical source on the vessel wall, and robots attached to the wall for longer-term chemical monitoring of chemicals released into the bloodstream. Using axial symmetric geometry with realistic flow speeds and diffusion coefficients, we compare detection performance with a simpler model that does not include the cells. The average chemical absorption is quantitatively similar in both models, indicating the simpler model is an adequate design guide to sensor performance in capillaries. However, determining the variation in forces and absorption as cells move requires the full model.

MULTI2D – a computer code for two-dimensional radiation hydrodynamics

Simulation of radiation hydrodynamics in two spatial dimensions is developed, having in mind, in particular, target design for indirectly driven inertial confinement energy (IFE) and the interpretation of related experiments. Intense radiation pulses by laser or particle beams heat high-Z target configurations of different geometries and lead to a regime which is optically thick in some regions and optically thin in others. A diffusion description is inadequate in this situation. A new numerical code has been developed which describes hydrodynamics in two spatial dimensions (cylindrical R – Z geometry) and radiation transport along rays in three dimensions with the 4 π solid angle discretized in direction. Matter moves on a non-structured mesh composed of trilateral and quadrilateral elements. Radiation flux of a given direction enters on two (one) sides of a triangle and leaves on the opposite side(s) in proportion to the viewing angles depending on the geometry. This scheme allows to propagate sharply edged beams without ray tracing, though at the price of some lateral diffusion. The algorithm treats correctly both the optically thin and optically thick regimes. A symmetric semi-implicit (SSI) method is used to guarantee numerical stability. Program summary Program title: MULTI2D Catalogue identifier: AECV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 151 098 No. of bytes in distributed program, including test data, etc.: 889 622 Distribution format: tar.gz Programming language: C Computer: PC (32 bits architecture) Operating system: Linux/Unix RAM: 2 Mbytes Word size: 32 bits Classification: 19.7 External routines: X-window standard library (libX11.so) and corresponding heading files (X11/*.h) are required. Nature of problem: In inertial confinement fusion and related experiments with lasers and particle beams, energy transport by thermal radiation becomes important. Under these conditions, the radiation field strongly interacts with the hydrodynamic motion through emission and absorption processes. Solution method: The equations of radiation transfer coupled with Lagrangian hydrodynamics, heat diffusion and beam tracing (laser or ions) are solved, in two-dimensional axial-symmetric geometry ( R – Z coordinates) using a fractional step scheme. Radiation transfer is solved with angular resolution. Matter properties are either interpolated from tables (equations-of-state and opacities) or computed by user routines (conductivities and beam attenuation). Restrictions: The code has been designed for typical conditions prevailing in inertial confinement fusion (ns time scale, matter states close to local thermodynamical equilibrium, negligible radiation pressure, …). Although a wider range of situations can be treated, extrapolations to regions beyond this design range need special care. Unusual features: A special computer language, called r94, is used at top levels of the code. These parts have to be converted to standard C by a translation program (supplied as part of the package). Due to the complexity of code (hydro-code, grid generation, user interface, graphic post-processor, translator program, installation scripts) extensive manuals are supplied as part of the package. Running time: 567 seconds for the example supplied.

Influence of external magnetic field geometry on flux and current distribution in superconducting thin films

Flux density distributions in superconducting thin films exposed to external magnetic fields can be studied very suitable by magneto-optics. In conventionally applied homogeneous magnetic fields, which are oriented perpendicular to the film surface, the influence of the macroscopic sample geometry dominates the flux B z ( x, y) as well as the induced current distribution j( x, y) in the superconductor. We have studied flux and current distribution in different kinds of inhomogeneous field geometries (radial or axial symmetric). In this case flux and current distribution depend on the symmetry of the magnetic field and the ratio of field gradients b z y / b z x , with b z x =(∂ B/∂ z) x and b z y =(∂ B/∂ z) y . In radial symmetric fields ( b z y / b z x ≈1) the domination of sample geometry can be observed in analogy to the homogeneous case. The magneto-optically observed current discontinuity lines can be understood within the Bean model and indicate an isotropic critical current distribution j c( x, y). This could be confirmed by calculating the current distribution from the magneto-optically detected flux distribution. A strong difference occurs by changing to an axial symmetric field geometry ( b z y / b z x ≠1). In this case, the field induced current distribution is strongly anisotropic, even in the fully penetrated state. This could not be explained by the Bean model. As a result the j c( x, y)-distribution in an intrinsic in-plane-isotropic superconductor can be anisotropically affected by the magnetic surroundings. This should be considered in the conception of high-current HTS-devices.

Properties of Knots in Cooling Stellar Jets

Modelling the formation of the maximal emission regions in Herbig-Haro flows, the so-called ‘knots,’ remains a main challenge in the investigation of the YSO's outflows. Recent HST images of optical regions reveal their wide morphological variety. Knotty structures and arc-like regions coexist, suggesting that several mechanisms could be responsible for the global scenario. Arc-like emissions are probably due to other mini-working surfaces or non-axially symmetric interaction of the kinking jet matter with the external medium, while knots seen in [SII] are mostly axially symmetric objects and may have a different origin. In this paper we show that a pattern of regularly spaced, knotty emission regions forms in stationary jets, with emissivity and kinematic features consistent with observations. To this purpose, numerical simulations of non-equilibrium, radiative, hydrodynamical jets in axial symmetric geometry have been performed.

Kinetics of muonic hydrogen drift in axial symmetric geometry

The kinetics of muonic atoms of hydrogen isotopes in an axially symmetric trap is studied. The problem of the determination of the initial kinetic energy distribution of µp and µd atoms from time-of-flight spectra is discussed. The effects of the scattering of muonic atoms from gas and of the stopping distribution are evaluated. When the collision length is much larger than the target radius, the moments of the kinetic energy distribution are shown to be determined by the time-of-flight spectrum in a model-independent way.

An Assessment of In SituRadon Exhalation Measurements, and the Relation Between Free and Bound Exhalation Rates

By solving the diffusion equation for the axial-symmetric geometry of in situ radon exhalation measurements, the effect of the presence of the measuring device on the exhalation rate was determined. From analyses of the calculated growth curves of the radon concentration in the device it turned out that exhalation rates deduced from measurements underestimate the 'free' exhalation rate by at most a factor of 2. Analyses of a few measurements showed that erroneous results can be avoided by analysing the full growth curves.

An Assessment of In Situ Radon Exhalation Measurements, and the Relation Between Free and Bound Exhalation Rates

By solving the diffusion equation for the axial-symmetric geometry of in situ radon exhalation measurements, the effect of the presence of the measuring device on the exhalation rate was determined. From analyses of the calculated growth curves of the radon concentration in the device it turned out that exhalation rates deduced from measurements underestimate the 'free' exhalation rate by at most a factor of 2. Analyses of a few measurements showed that erroneous results can be avoided by analysing the full growth curves.

Development of General Next Event Surface Crossing Estimators for Monte Carlo Method

General NXTEVT's (next event surface crossing estimators), which have no restriction for detector location and orientation setting, have been developed for the Monte Carlo method of radiation transport calculation. The detectors are of ring, spherical band, cylinder and rhomboid geometry. The detailed formulas of flux scoring are described for each detector geometry. Two sample problems are analyzed in order to study the applicability of NXTEVT's to radiation shielding analysis. First, through the analysis of a simple one-velocity problem for an infinite isotropic scattering medium with an isotropic radiation source, using the spherical band type NXTEVT, the accuracy of the results is verified. Second, a problem of neutron transport in the system with an axial symmetric geometry is solved by using the cylinder and ring type NXTEVT's. The results shows NXTEVT is more efficient to obtain the solution in such a system than the point detector and boundary crossing estimators.

Development of general next event surface crossing estimators for Monte Carlo method.

General NXTEVT's (next event surface crossing estimators), which have no restriction for detector location and orientation setting, have been developed for the Monte Carlo method of radiation transport calculation. The detectors are of ring, spherical band, cylinder and rhomboid geometry. The detailed formulas of flux scoring are described for each detector geometry. Two sample problems are analyzed in order to study the applicability of NXTEVT's to radiation shielding analysis. First, through the analysis of a simple one-velocity problem for an infinite isotropic scattering medium with an isotropic radiation source, using the spherical band type NXTEVT, the accuracy of the results is verified. Second, a problem of neutron transport in the system with an axial symmetric geometry is solved by using the cylinder and ring type NXTEVT's. The results shows NXTEVT is more efficient to obtain the solution in such a system than the point detector and boundary crossing estimators.

Formulas for the inductance of coaxial busses comprised of square tubular conductors

BY virtue of its axial symmetric geometry, the coaxial tubular bus possesses certain very desirable electrical and mechanical characteristics. Low inductance contributes to good voltage regulation. Reduced skin and proximity effects minimize line losses and average temperature rise under load. Axial-symmetric distribution of skin and proximity effects reduces current density distortion and attendant hot-spot concentrations, hence enables a greater current rating for a specified maximum copper temperature. As electromagnetic forces between conductors are eliminated largely, mechanical bracing against short-circuit forces correspondingly can be reduced. The nested conductors require less space for installation and a smaller supporting structure than they would if arranged side by side.