Geometrical Computer Research Articles

Reconstruction of Historic Monuments—A Dual Approach

The proper maintenance of historical monuments and their use is one of the pillars of sustainable development. Over the years, historic architectural buildings have undergone numerous changes resulting from reconstruction, expansion, or damage caused both by natural and other disasters. Therefore, their contemporary appearance is the result of these changes. Thanks to the documentation of their transformations, one has the opportunity to get to know their history. Currently, thanks to advanced technology, it is becoming easier and easier to document various historical monuments. However, the method of their documentation, especially the possibility of their reconstruction and the creation of 3D models depends mostly on the data resources at one’s disposal. This article compares two extreme methods of recreating an architectural object that has undergone some changes throughout history. One of the methods is to reconstruct the object on the basis of a photograph using geometrical rules and computer aid, while the other is based on laser scanning. Due to the fact that the same object is being reconstructed by means of both methods, it is possible to evaluate and compare the applied methods and estimate their accuracy, as well as to draw conclusions about the transformations of the reconstructed object over the years.

Study of Power Parameters of Forming Profile Elliptical Screw Workpieces

Based on the power-saving technologies, the design of an installation for coiling elliptical screw workpieces is worked out. Theoretical dependences for determining power and structural parameters of coiling a screw profile workpiece (SPW) on the elliptical mandrel are developed with consideration of the material grade specification and the parameters of technological equipment. The dependences of the moment value of SPW bending to the elliptical mandrel on its rotation angle, thickness and width are defined. The challenge is to develop the progressive methods of manufacturing augers and their sub-type - L-shaped auger spirals (LSAS) with high precision geometrical dimensions Computer simulation of the tape workpiece winding process on ellipse mandrel with initial conditions, displacements, deformations and stresses that arising in the material of tape workpice after applying the simulated efforts to it, was shown. Given simulation showed ranges where maximum stresses of tension and compression arising in material of tape workpiece, and made it possible to determine the minimum radius of curvature during winding, which is advisable to take at least 20 mm.

Assessing the Effect of Dome Shape and Location on The Acoustical Performance of a Mosque by Using Computer Simulation

Architecturally, the dome is one evolutionary presence in most mosques of modern day. Besides mihrab, the dome is one of the architectural elements that has a phenomenon of concentration of energy by reflected sound waves from concave surfaces. The aim of this research is to compare the acoustical performance of different shapes of the dome and their respective locations by using geometrical approach computer simulation. Four types of dome that are commonly used on a mosque; Arabic, segmental, hemispherical, and onion, were modeled to compare their acoustical parameters i.e. reverberation time (RT) and speech transmission index (STI). It can be concluded that the shape of the dome does affect the RT. Furthermore, the shape of the dome also affects the STI - the larger the volume, the lower the STI value. However, the locations of a dome has little significance over acoustical parameter. The findings of this research may not limit to mosques only, but to any similar building that has similar typology.

Computer simulations of optical turbulence in the weak- and strong-scattering regime: angle-of-arrival fluctuations obtained from ray optics and wave optics

It is known that certain geometrical-optics predictions often agree well with optical turbulence field observations even though theoretical constraints for ignoring diffraction may be violated. Geometrical optics assumptions can simplify analyses, and ray optics can significantly reduce simulation computation time. Here, an investigation into angle-of-arrival fluctuations is presented involving wave optics and geometrical (ray) optics computer simulations of a plane wave of visible light propagating through a turbulent refractive-index field. The simulation and Rytov-based theory results for the variances of aperture-filtered angle-of-arrival fluctuations generally agree well for weak scattering (Rytov variance, σR2≲0.2), but for increasing Rytov variance, the simulation results demonstrate a positive slope that can be significantly shallower than that predicted by the theory. For weak-to-moderate scattering regimes (σR2≲2.67), a comparison of the ray and wave results show they match for aperture diameters greater than about two Fresnel lengths. This result is consistent with a previous theoretical analysis by Cheon and Muschinski. For the strongest scattering case studied (σR2=26.7), the wave and ray simulations match for aperture diameters greater than about 10 Fresnel lengths. For smaller apertures, we attribute the disparity between the wave and ray simulation results to a Fresnel filtering effect.

Model of the Geometrical Computer for Carrying Out Exact Calculations in Applied Tasks

In article possibility of creation of mathematical model of the geometrical computer on the example of the classical task consisting in finding of the cube having volume is considered it is twice more than a volume of an initial cube. The geometrical computer,manipulating points and beams, allows to receive result with an absolute accuracy, without use of usual operations (multiplication, division, exponentiation, extraction of a root, addition and subtraction) with numbers. Opportunity to experts of the widest profile, without algebra opens, to solve applied problems in various areas of science and equipment where usual methods are unacceptable.

Atomic scale strain relaxation in axial semiconductor III-V nanowire heterostructures.

Combination of mismatched materials in semiconductor nanowire heterostructures offers a freedom of bandstructure engineering that is impossible in standard planar epitaxy. Nevertheless, the presence of strain and structural defects directly control the optoelectronic properties of these nanomaterials. Understanding with atomic accuracy how mismatched heterostructures release or accommodate strain, therefore, is highly desirable. By using atomic resolution high angle annular dark field scanning transmission electron microscopy combined with geometrical phase analyses and computer simulations, we are able to establish the relaxation mechanisms (including both elastic and plastic deformations) to release the mismatch strain in axial nanowire heterostructures. Formation of misfit dislocations, diffusion of atomic species, polarity transfer, and induced structural transformations are studied with atomic resolution at the intermediate ternary interfaces. Two nanowire heterostructure systems with promising applications (InAs/InSb and GaAs/GaSb) have been selected as key examples.

Prediction of outdoor sound propagation by geometrical computer modeling

Prediction of outdoor sound propagation by geometrical computer modeling

A Trial of Auralization of Municipal Public Address Systems using Geometrical Computer Modeling and 6-channel Reproduction Technique

A Trial of Auralization of Municipal Public Address Systems using Geometrical Computer Modeling and 6-channel Reproduction Technique

The contributions of pairs of parallel surfaces in a simple analytical model of room reverberation

In a recent paper [Embrechts, “Searching for a theoretical relation between reverberation and the scattering coefficients of surfaces in a room,” in Proceedings of the Acoustics 2012 Nantes Conference (2012), 2397–2402], we derived an analytical model of the sound energy decay in a room from the acoustic radiative transfer equation. This model includes the surfaces' scattering properties and it is presently valid for rooms in which the cloud of image sources is approximately isotropic and constant for all receptor's positions. Its validity is extended in this paper by the inclusion of a pair of parallel surfaces. Indeed, it is known that parallel surfaces can introduce significant anisotropy in the cloud of image sources. We show that the room reverberation can be represented by a sum of exponential decays (except in its early part), each decay having its specific slope and amplitude depending on the surfaces' absorption and scattering properties. It is also shown how this simple model can be applied to speed up geometrical acoustics computer simulations.

Customized room acoustics simulations using scripting interfaces.

Geometrical computer modeling is commonly used in consulting practice to make predictions of room acoustical quality. A large number of new parameters have been created by academicians and acousticians in recent years—so much so that it has been difficult for room acoustics simulation providers to include them all. This presentation will demonstrate how customized scripted simulations in Rhinoceros (a CAD program), using Pachyderm (an open source geometrical acoustics simulation engine), can allow the use of new parameters, or parameter simulation types, without reliance on software vendors to explicitly release software versions implementing new code.

Axially Loaded Stainless Steel Columns in Case of Fire

The simple model of Eurocode 3, for the fire resistance evaluation of stainless steel members, are based on the procedures used for carbon steel structural elements. However, due to the existing differences in the constitutive laws of these two materials, it is expected that it would not be possible to use, in both materials, the same formulae for the member stability calculation, as proposed in Eurocode 3. This paper aims at increasing the knowledge on the behaviour of stainless steel axially loaded columns at elevated temperatures. For this purpose, a geometrical and material non linear computer code has been used to determine the buckling load of these elements. The Eurocode formulae are evaluated and a new proposal, that ensures accurate and conservative results when compared with the numerical simulations, is presented.

A simplified model of airway narrowing due to bronchial mucosal folding

Bronchial mucosal folding during bronchoconstriction can be a significant phenomenon, and a number of previous studies have provided models which examine a number of aspects of this important problem. Previous approaches include finite-element analyses, fluid-structure interaction, linear elasticity models, geometrical computer optimisation, and more. These models have focused on changes to the elastic properties of the airways due to mucosal folding, rather than airway narrowing, and suffer from too great a degree of computational complexity for use in multiscale, spatially distributed models of the lung now being developed. We propose a simplified, geometrical model of airway folding under the assumptions of fixed airway wall area, fixed basement membrane perimeter during constriction, specified shape and number of folds, and liquid filling of the mucosal folds, in the context of determining effective airway radius and hence airway impedance. We show that this model generates predictions in good agreement with existing models while being vastly simpler to solve.

The influence of absorption factors on the sensitivity of a virtual room’s sound field to scattering coefficients

Currently there is limited information on what scattering coefficients (SCs) to assign materials in geometrical room acoustic computer models. As a result, room modelers rely on general guidelines and intuition when assigning SCs. How sensitive is the predicted sound field to the user’s choice of scattering coefficients? The sound field’s sensitivity depends on its diffusivity (without SCs); the more diffuse the room’s sound field is, the less sensitive the virtual room is to the selection of SCs. In rooms with no fittings to diffuse sound energy, the sound field diffusivity is influenced by (1) room shape, (2) volume, (3) amount and (4) location of absorption, and (5) the choice of SCs. This investigation focuses only on the latter three factors. A rectangular room is modeled in ODEON v6.5 with 10 absorption schemes. These schemes vary in terms of the area of mirrored reflective surfaces, average absorption coefficient, and standard deviation of absorption. The amount of diffuse reflections at each room boundary as dictated by the SC is increased uniformly in each room. Changes in the room sound field, in particular in the reverberation time (T30), are examined at each step. Sound field diffusivity, and consequently a virtual room model’s sensitivity to SCs, is found to depend most on the area of mirrored reflective surfaces. Also, a proposed quantity called the Scattering Sensitivity Index appears to predict sound field diffusivity.

The Design of the IEEE 802.12 Coding Scheme

In 1995, the IEEE approved the 802.12 standard for data transmission at 100-Mbit/s using the Demand Priority Network Access protocol. 100 VG-AnyLAN products conforming to this standard offered an upgrade path for Ethernet and token ring networks, without requiring new building wiring. A key factor in the approval of the 802.12 standard was the demonstrated error detection properties of its coding scheme. In particular, the coding scheme allows the detection of error bursts affecting encoded data carried on four parallel conductors, using nothing more than the standard IEEE 32-bit cyclic redundancy check applied to the unencoded data. Although these error detection properties were presented for verification as part of the standards process, for many years commercial considerations prevented public disclosure of how the code was actually found. These considerations no longer apply, and, in this paper, we explain in detail the design principles of the code, combining geometrical insight, linear algebra, combinatorial reasoning, and computer search.

IMPS: A multianalyser detector system for the thermal three-axis spectrometer IN8

The primary spectrometer of the ILL's thermal-beam three-axis spectrometer IN8 has recently been rebuilt to increase the instrument flexibility as well as the monochromatic flux at the sample position. Further improvement of the instrument is now envisaged and consists in the installation of a multianalyser detector system to multiplex the secondary spectrometer. This will enable one to obtain images of selected regions in ( Q , ω ) space. The design of such a multiplexed secondary spectrometer is based on analytical results reflecting the geometrical considerations and computer simulations performed using the neutron ray-tracing package McStas.

Uses and limitations of statistical and geometrical modeling of nonexponential decay curves in performance spaces

The conditions under which the high-frequency, diffuse-field model of coupled rooms is a valid approximation to geometrical acoustics have been examined by comparison with ray-tracing predictions of decay curves in two and three room systems. Results particular to coupled rooms were noted. Because nonexponential decay shape is sensitive to both decay rates and relative energy densities, corrections to these parameters meaningfully improved the diffuse-field model. Variations in the free-path distribution of each subroom, introduced by coupling, complicated the use of improved decay models. Also, the expected decrease in energy density with distance from the source was found to result in spatial dependence of decay shape for certain coupling geometries. Insights from this study were used in the construction of diffuse-field and geometrical computer models of Bass Hall, a 2056 seat multipurpose auditorium with an acoustically coupled stage house. Preliminary results indicate that high-frequency decay curves in each of the subrooms predicted by geometrical acoustics are well matched to the predictions of diffuse-field models. The use of both models as prediction and design tools is assessed by comparison at high frequencies with measurements made during occupied and unoccupied conditions. [Research supported by the Bass Foundation.]

Analysis and Synthesis of Schatz Six-Revolute Mechanisms.

Based on geometrical intuition and computer graphics, we present the formation of two kinds of Schatz six-revolute mechanisms and two types of algebraic surfaces on which the corresponding reciprocal screw axes lie under any possible configurations. Then, we derive the general kinematic closed-form solutions and show the absence of stationary configuration of both mechanisms using four-by-four matrix and differential algebra. Moreover, the parametric formulations of coupler-point motion provide a complete higher-order analysis of the coupler curve. In practical application, this mechanism is further used for the dimensional synthesis, path and motion generation synthesis, by the nonlinear programming optimization method. At last, two numerical examples are taken to illustrate the design algorithm.

A mathematically based classification of root canal curvatures on natural human teeth

Testing of root canal-shaping instruments on natural human teeth has many difficulties, because of the different anatomical forms of root canals. There is a lack of an internationally accepted and mathematically based classification of root canal morphology. The aim of this study was to give a mathematical description of root canal forms with the help of differentiated geometrical pattern analysis and computer graphics. The measurements of 433 roots were conducted on isometric radiographs taken from the clinical view. Measured points of the same radiographs were approximated using fourth degree polynomial functions describing the imaginary axis of canals. The classification of root canal morphology on the basis of Schneider's angle differs from the classification of geometrical pattern analysis. Fourth-degree function approximation as a new method for the description of the shape of root canal curvatures seems to be exact and reliably repeatable. This type of classification of root canals is suitable for standardizing test specimens, including natural human teeth used for testing root forms: I (straight), J (apical curve), C (entirely curved), or S (multicurved).

An improved geometrical sound field analysis in rooms using scattered sound and an audible room acoustic simulator

A geometrical computer simulation model and an audible room acoustic simulator, based on ray tracing with scattering effects, are presented. This calculation model classifies the receiving sound energy into three types. Direct sound energy is calculated with the inverse square law, and early reflected and diffuse sound energy are calculated with the effective geometrical reflection energy coefficient using a simple diffraction theory for a finite free reflecting panel. Two actual halls are used to compare measured and computed values of four acoustic parameters: Clarity (C), deutlichkeit (D), lateral efficiency (LE), and room response (RR). It has been found that the new calculation model is a better evaluator of C, D and RR than the traditional ray tracing method. The room acoustic simulator has been used to simulate sound in the halls using 15 channels. The simulator can judge acoustic impressions in the presence of reverberation, clarity and spaciousness.

Study on microengines: miniaturing stirling engines for actuators

This paper describes the micro Stirling engine, a miniaturized Stirling engine the length, width, or height of whose body measure no more than several centimeters. The steps taken both to establish the design concept and actually to produce a microactuator are discussed. Geometrical scale analysis and computer simulation are used to investigate how the design parameters change when the engine size is reduced. This analysis and simulation enable a micro Stirling engine with an approximately 0.05 cm 3 piston swept volume (equivalent ot the displacement of a gasoline is approximately 10 mW at 10 Hz. Problems of scaling down the engine to a maximum length of several millimeters are discussed.