Imaginary Surfaces Research Articles

Magnetic Taylor-Proudman Constraint Explains Flows into the Tangent Cylinder.

Tangent cylinders (TCs) have shaped our understanding of planetary dynamos and liquid cores. The Taylor-Proudman constraint creates these imaginary surfaces because of planetary rotation, separating polar and equatorial regions, but cannot explain the flows meandering through them. Here, we establish and verify experimentally that magnetic fields aligned with rotation drive flows into TCs, linked to the flows along TCs by a magnetic Taylor-Proudman constraint. This constraint explains and quantifies how magnetic fields reshape rotating flows in planetary interiors and magnetorotating flows in general.

Identification of geological faults by geophysical methods for risk assessment in underground mining

High-accuracy prediction of geological faults, especially small-amplitude tectonic faults, is essential for an efficient and safe underground mining. Having such information about the location of tectonic faults in the rock mass reduces the likelihood of rock collapse and outburst, gas explosion, and water breakthrough during the mining operations. Modeling of the tectonic structure of the rock mass based on the data from the exploratory drilling and ground geophysical observations is of crucial importance to the extraction of mineral raw materials. Typically, in the areas of mineral extraction, tectonic faults in the rock mass are well studied using these data, but the predicted faults are represented by simplified imaginary surfaces that separate different structural parts of the rock mass and are not normally found by mining in such a form. The actual structure of tectonic faults is revealed in the course of mining, but the use of seismic survey is required for further prediction of such faults. The experience of applying these methods is shown in the examples of studies of tectonic faults of coal seams in the Donbass mines during the period from 2008 to 2012. To illustrate the capabilities of underground and surface 2D seismic surveys to accurately predict the location of faults, a site was chosen at the Dneprovskaya mine, which is characterized by the most amount of data collected from exploration drilling and geophysical methods. Also, in contrast to the mining practice when the coal seams areas are discarded based on the results of research due to difficult geological conditions or are not documented by geologists in the process of panel mining, this specific area is distinguished by the completeness of mapping of real faults exposed by mining operations. Predictions of faults obtained by preliminary and CDP seismic surveys are compared with the real faults exposed by mining operations. An example of research at the Krasnolimanskaya mine shown in this paper is among a few isolated cases utilizing 3D CDP seismic survey at mines. The results of the prediction of tectonic faults and the specifics of data processing and interpretation are examined. The research results considered in this paper can be used for further development of seismic survey methods for high-accuracy prediction of geological faults.

Novel Recurrence Relations for Volumes and Surfaces of n-Balls, Regular n-Simplices, and n-Orthoplices in Real Dimensions

This study examines n-balls, n-simplices, and n-orthoplices in real dimensions using novel recurrence relations that remove the indefiniteness present in known formulas. They show that in the negative, integer dimensions, the volumes of n-balls are zero if n is even, positive if n = −4k − 1, and negative if n = −4k − 3, for natural k. The volumes and surfaces of n-cubes inscribed in n-balls in negative dimensions are complex, wherein for negative, integer dimensions they are associated with integral powers of the imaginary unit. The relations are continuous for n ∈ ℝ and show that the constant of π is absent for 0 ≤ n < 2. For n < −1, self-dual n-simplices are undefined in the negative, integer dimensions, and their volumes and surfaces are imaginary in the negative, fractional ones and divergent with decreasing n. In the negative, integer dimensions, n-orthoplices reduce to the empty set, and their real volumes and imaginary surfaces are divergent in negative, fractional ones with decreasing n. Out of three regular, convex polytopes present in all natural dimensions, only n-orthoplices and n-cubes (and n-balls) are defined in the negative, integer dimensions.

Focus boom simulations using sBOOM and lossy nonlinear Tricomi equation solvers

The low-boom prediction committee, comprised of several research agencies and companies across the world, is organizing a special session dedicated to the prediction and comparison of focused sonic booms. This presentation will document and discuss focus boom simulations corresponding to the benchmark cases prescribed for this special session using a combination of sBOOM and lossy nonlinear Tricomi equation (LNTE) solvers. sBOOM is an augmented Burgers equation based sonic boom propagation solver that has been developed at NASA over the past decade. Focus boom simulations involve regions where simulations based solely on traditional ray theory approaches, such as those used in sBOOM, are inadequate. The results from sBOOM are, therefore, coupled with an LNTE solver that considers diffraction effects, which become dominant in the vicinity of imaginary surfaces (caustics) in the atmosphere on which singularities arise when using ray theory approaches. The LNTE solver used in this study has been developed and successfully demonstrated as part of the NASA's superboom caustic analysis and measurement project (SCAMP). Sonic boom focused signatures and other relevant metrics of the coupled simulations will be documented and discussed along with interesting observations.

Performance analyses of mesh-based local Finite Element Method and meshless global RBF Collocation Method for solving Poisson and Stokes equations

Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several criteria. The accuracy of Radial Basis Function Collocation Method with multiquadrics is enhanced by implementing a shape parameter optimization algorithm. For the time-dependent problems, time discretization is done using Backward Euler Method. The performances are assessed over the accuracy, runtime, condition number, and ease of implementation. Three error kinds considered; least square error, root mean square error and maximum relative error. To calculate the least square error using meshless Radial Basis Function Collocation Method, a novel technique is implemented. Imaginary numerical solution surfaces are created, then the volume between those imaginary surfaces and the analytic solution surfaces is calculated, ensuring a fair error calculation. Lastly, all results are put together and trends are observed. The change in runtime vs. accuracy and number of nodes; and the change in accuracy vs. the number of nodes is analyzed. The study indicates the criteria under which Finite Element Method performs better and conditions when Radial Basis Function Collocation Method outperforms its mesh dependent counterpart.

A novel approach for modelling fluid flow and heat transfer in an Open Volumetric Air Receiver using ANSYS-FLUENT

Open volumetric air receiver (OVAR) has great potential as a source of process heat for metals processing operations. The two major components of OVAR are the porous absorbers and the return air flow chamber (RAFC). Heat exchange between the “cooler” return air and the hot curved absorber surface in RAFC is critical as it prevents overheating of absorbers. Unfortunately, modeling of air flow in the RAFC is conspicuous by its absence. Calculations were performed in ANSYS-FLUENT using the local thermal non-equilibrium model for heat transfer in the porous absorber. Three dimensional flow and heat transfer simulations were carried out in the RAFC. Unfortunately, ANSYS decoupled heat exchange between the absorbers and return air by splitting the curved absorber surface into real and imaginary surfaces. Decoupling also meant that heat flux had to be specified separately on the absorber and the RAFC, which was a challenge since only the total input solar flux is known. Hence the major contribution of this paper has been to incorporate two innovations in the simulation methodology. One, to couple the absorber and RAFC thermally by mapping the temperature of the real surface to the imaginary surface. Two, the flux used for heating air in the absorber was calculated iteratively. Limited simulations suggest that in laboratory experiments, relatively inexpensive circumferential (Joule) heating of absorbers can reasonably mimic heating of absorbers by concentrated solar radiation.

Using a planar rack cutter with variable modulus to generate a spherical gear pair

In this study, an imaginary planar rack cutter with variable modulus and discrete conical teeth was used to generate a spherical gear pair with double degree of freedom. First, a geometric method was used to design the mathematical model of the imaginary planar rack cutter with variable modulus and discrete conical teeth. Next, the relationship of coordinate systems between the generating and generated surfaces was established. Then, the family of the imaginary planar rack cutter surfaces was obtained by homogeneous coordinate transformation matrix. Further, two equations of meshing between the generating and generated surfaces were determined by the two-parameter envelope theory. The mathematical model of spherical gear pair with variable modulus and discrete ring-involute teeth can be created by using the two equations of meshing and the family of the imaginary planar rack cutter surfaces. The mathematical models of the spherical gear pair with double degree of freedom and tooth contact analysis method were used to investigate the assembly errors of the gear pair in four cases.

특정 공항에서의 VFR 항공기 레이다 항적자료 분석 연구

Obstacle limitation surfaces are imaginary space surfaces that must be clear of obstacles for the aircraft to safely take off and land on the aerodrome. These surfaces are closely related to the safety of the VFR aircraft, which require a pilot to be able to see outside the cockpit, to control the aircraft

Using an Imaginary Planar Rack Cutter to Create a Spherical Gear Pair with Continue Involute Teeth

This paper presents an imaginary planar rack cutter having two parameters of motion to create a spherical gear pair with two degrees of freedom. The working region of the imaginary planar rack cutter is that of symmetrical straight lines. The relationship between the coordinate system of the imaginary planar rack cutter and that of the spherical gear pair having two parameters of motion is illustrated. The two-parameter family of imaginary planar rack cutter surfaces is obtained by using the homogeneous coordinate transformation matrix to transfer the coordinate system of the planar rack cutter to that of the spherical pinion or the spherical gear. Based on the two-parameter enveloping theory, the mathematical models of the spherical gear pair with two degrees of freedom were proposed. The developed mathematical model of the gear pair with two degrees of freedom can be used to analyze undercutting analysis of the imaginary planar rack cutter. Based on the undercutting equation, a minimum number of teeth of the spherical pinion are determined. A line of singular points on the spherical pinion’s teeth are displayed. Results show that a minimum number of teeth of the spherical pinion can be determined in order to avoid undercutting.

Kinematic performance of a parabolic gear tooth with two parabolic coefficients

This paper presents design imaginary skew rack cutters having teeth of two parabolic coefficients to generate spur and helical gears. First, a mathematical model of the imaginary rack cutter having teeth of two parabolic coefficients is derived using geometric relations and coordinate transformation. After the relationship between the coordinate system of the imaginary rack cutter and that of the helical gear pair is set up, a family of imaginary rack cutter surfaces is obtained using the homogeneous coordinate transformation matrix to transfer the coordinate system of the rack cutters to that of the helical gear. Based on the gear theory, the equations of meshing between the rack cutter and the helical gear are determined. Substituting the equations of meshing into the family of imaginary rack cutter surfaces, a pinion and a gear are generated and their geometries are plotted using an in-house software package. Based on the assembly errors, tooth contact analysis is performed to determine the influences of kinematic assembly errors and the parabolic coefficients. Results show that maximum parabolic coefficient value of the imaginary skew rack cutter exists in order to avoid undercutting and it can be determined.

Design and kinematics evaluation of a gear pair with asymmetric parabolic teeth

This paper presents design of imaginary spur and skew rack cutters having teeth of asymmetric parabolic profiles to generate spur and helical gear pairs, respectively. First, a mathematical model of the imaginary rack cutter having teeth of an asymmetric parabolic profile is derived using geometric relations and coordinate transformation. After the relationship between the coordinate system of the imaginary rack cutter and that of the gear pair is set up, a family of imaginary rack cutter surfaces is obtained using the homogeneous coordinate transformation matrix to transfer the coordinate system of the rack cutter to that of the gear pair. Substituting the equations of meshing into the family of imaginary rack cutter surfaces, a pinion and a gear are generated and their geometries are plotted using an in-house software package. Based on the derived mathematical model of the gear pair with assumed assembly errors, tooth contact analysis is performed to determine the influences of kinematic errors and the asymmetric tooth profile. A helical gear pair made by CNC machining is used to verify the influences of asymmetric parabolic tooth profiles on contact conditions and kinematic performance.

Simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies

A new optimization strategy for eigenfrequency optimization of functionally graded (FG) structures within the framework of isogeometric analysis (IGA) approach is introduced. The proposed methodology which utilizes a concurrent procedure by combining the shape and material composition optimization of these structures employs an extended form of the standard IGA method by allowing for gradation of material properties through patches. The distributions of the graded material properties are considered as imaginary surfaces over the computational domain and captured in a fully isogeometric formulation using the same NURBS-based parameterization which is employed for the geometry modeling as well as the solution approximation. Considering the in-plane coordinates of the control points defining the design boundary surfaces as well as the applicates of all the control points describing the variations of material properties as design variables, we subsequently adopt a mathematical programming algorithm to simultaneously find the optimum shape and material composition of FG structures. A couple of illustrative numerical examples in 2D elasticity with eigenfrequencies as their either constraints or objective functions are presented to demonstrate the high performance of the proposed methodology. It will be seen that the obtained results by this concurrent optimization procedure have much better dynamic performance compared to the optimal results of the simple shape or material composition design.

An improved isogeometrical analysis approach to functionally graded plane elasticity problems

The isogeometric analysis method is extended for addressing the plane elasticity problems with functionally graded materials. The proposed method which employs an improved form of the isogeometric analysis approach allows gradation of material properties through the patches and is given the name Generalized Iso-Geometrical Analysis (GIGA). The gradations of materials, which are considered as imaginary surfaces over the computational domain, are defined in a fully isoparametric formulation by using the same NURBS basis functions employed for the construction of the geometry and the approximation of the solution. The basic concept of the developed approach is concisely explained and its relation to the standard isogeometric analysis method is pointed out. It is shown that the difficulties encountered in the finite element analysis of the functionally graded materials are alleviated to a large degree by employing the mentioned method. Different numerical examples are presented and compared with available analytical solutions as well as the conventional and graded finite element methods to demonstrate the performance and accuracy of the proposed approach. The presented procedure can also be employed for solving other partial differential equations with non-constant coefficients.

DIFFERENCES AND COMPARISON BETWEEN FAA AND ICAO OBSTACLE RESTRICTION REGULATIONS

FAR Part 77 “Objects Affecting Navigable Airspace” is commonly only used in the US, whereas ICAO Annex14 “Obstacle Restriction and Removal” is accepted by all other countries. These two systems were constructed with a different baseline, restrictive area and height. Since government regulations or research publications usually adopt one of them exclusively, users and researchers may perceive ambiguous figures. The purpose of this paper is to compare safety airspaces and identify differences. The results indicate that the FAA imaginary surfaces system specifies a more extensive obstruction clearance than ICAO’s. We also show that airports which apply the FAA regulations restrict urban development around airports more.

Airport obstacle surfaces

AbstractThe most commonly used criteria to determine complicated airport obstacle surfaces are FAR Part 77 imaginary surfaces, TERPS, and the one engine inoperative obstacle identification surface for air carriers. For each obstacle surface there are tradeoffs encountered in our practice between the obstruction penetration and extension of runway, change of flight profile, and allowable aircraft maximum payloads. For the purposes of both airport engineering and airport planning, a better understanding of these different obstacle surfaces and their application is important. In this paper, the differences and relationships between these surfaces are addressed. The conditions for the use of each criterion are discussed. In addition, the FAA's Obstruction Evaluation / Airport Airspace Analysis (OE/AAA) process is reviewed.

Optimal selection of aspheric surfaces in optical design

Optical systems frequently use aspheric surfaces to improve performance. Typically the designer uses a combination of experience and trail and error to decide which surfaces to make aspheric, then the shape of the aspheric surface is optimized as part of the optical system. In this paper, a method of optimally choosing which surfaces are to be made aspheric is developed. This is implemented by allowing the surface number of the asphere to become a variable in the optimization. Imaginary surfaces are used as an intermediary to make the problem continuous for the optimization. The method of implementation and design examples are given.

Planetary cratering 2: Studies of saturation equilibrium

Abstract— A realistic computer model has been developed to display images of imaginary cratered surfaces, taking into account empirically measured input size distributions of primary and secondary craters, ejecta blanket morphology including feathering with distance, obliteration due to ejecta from outside the imaged area, lighting effects, etc. The model allows us to track surface evolution of morphology as new craters are added.Using the model as well as lunar photos, we have studied the approach to saturation equilibrium (defined as a condition when no further proportionate increase in crater density occurs as input cratering increases). We find that an identifiable saturation equilibrium occurs close to a level previously identified for this state (Hartmann, 1984), typically fluctuating around a crater density from ∼0.4 to 2 times that level. This result is fairly robust vis‐à‐vis the range of model parameters we have chosen. Flooding, basin ejecta blankets, and other obliterative effects can introduce structure and oscillations within this range, even after saturation equilibrium is achieved.These findings may constrain or revise certain earlier interpretations of satellite and planet surface evolution and impactor populations, which were predicated on the assumed absence of saturation equilibrium.In our fourth experimental run, we found that suppression of “sandblasting” by subresolution impacts allows the smallest secondaries to rise above the saturation equilibrium line, a result that might be relevant to a similar situation on Gaspra and perhaps some other asteroids.

Acoustic wave propagation over a depressed road having finite impedances.

It is very important to pre-estimate the sound pressure levels around the roads before the construction. We have derived the formulas to estimate the sound pressure levels on the banks of a depressed road with finite acoustic impedances. The formulas were produced by setting two imaginary boundary surfaces on the break-lines of the depressed road and applying Green's theorem. These formulas are used to estimate the effect of the finite acoustic impedances peculiar to the surfaces of the depressed road. The agreement between the theory and the experiments is excellent.

Evaluation of biaxial stress failure surfaces for a glass fabric reinforced polyester resin under static and fatigue loading

In an attempt to evaluate failure theories for a glass fabric reinforced polyester resin over 370 tests have been conducted on thin-walled tubes under combined axial loading and internal pressure, both for static and fatigue loading. For plane stress the results are considered in relation to imaginary failure surfaces inσ1,σ2,σ6 space. A limited measure of agreement between theories and results can be obtained after highly subjective selection of data. Only those theories which involve complex stress properties provide a reasonable fit. The behaviour of tubular specimens is strongly influenced by the presence of joints in the reinforcements.

K theorii imaginárných křivek a ploch druhého stupně

K theorii imaginárných křivek a ploch druhého stupně