Search results for: collinear

Authors: Michele Sinico

Abstract:

In the Giovanelli illusion, some collinear dots appear misaligned, when each dot lies within a circle and the circles are not collinear. In this illusion, the role of the frame of reference, determined by the circles, is considered a crucial factor. Three experiments were carried out to study the influence of directionality of the circles on the misalignment. The adjustment method was used. Participants changed the orthogonal position of each dot, from the left to the right of the sequence, until a collinear sequence of dots was achieved. The first experiment verified the illusory effect of the misalignment. In the second experiment, the influence of two different directionalities of the circles (-0.58° and +0.58°) on the misalignment was tested. The results show an over-normalization on the sequences of the dots. The third experiment tested the misalignment of the dots without any inclination of the sequence of circles (0°). Only a local illusory effect was found. These results demonstrate that the directionality of the circles, as a global factor, can increase the misalignment. The findings also indicate that directionality and the frame of reference are independent factors in explaining the Giovanelli illusion.

Keywords: Giovannelli illusion, visual illusion, directionality, misalignment, the frame of reference

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Authors: Inigo Beckett

Abstract:

In forensic investigations, it is often the case that the most potentially useful recorded evidence derives from coincidental imagery, recorded immediately before or during an incident, and that during the incident (e.g. a ‘failure’ or fire event), the evidence is changed or destroyed. To an image analysis expert involved in photogrammetric analysis for Civil or Criminal Proceedings, traditional computer vision methods involving calibrated cameras is often not appropriate because image metadata cannot be relied upon. This paper presents an approach for resolving this problem, considering in particular and by way of a case study, the angle of a simple ladder shown in a photograph. The UK Health and Safety Executive (HSE) guidance document published in 2014 (INDG455) advises that a leaning ladder should be erected at 75 degrees to the horizontal axis. Personal injury cases can arise in the construction industry because a ladder is too steep or too shallow. Ad-hoc photographs of such ladders in their incident position provide a basis for analysis of their angle. This paper presents a direct approach for ascertaining the position of the camera and the angle of the ladder simultaneously from the photograph(s) by way of a workflow that encompasses a novel application of projective geometry and matrix analysis. Mathematical analysis shows that for a given pixel ratio of directly measured collinear points (i.e. features that lie on the same line segment) from the 2D digital photograph with respect to a given viewing point, we can constrain the 3D camera position to a surface of a sphere in the scene. Depending on what we know about the ladder, we can enforce another independent constraint on the possible camera positions which enables us to constrain the possible positions even further. Experiments were conducted using synthetic and real-world data. The synthetic data modeled a vertical plane with a ladder on a horizontally flat plane resting against a vertical wall. The real-world data was captured using an Apple iPhone 13 Pro and 3D laser scan survey data whereby a ladder was placed in a known location and angle to the vertical axis. For each case, we calculated camera positions and the ladder angles using this method and cross-compared them against their respective ‘true’ values.

Keywords: image analysis, projective geometry, homography, photogrammetry, ladders, Forensics, Mathematical modeling, planar geometry, matrix analysis, collinear, cameras, photographs

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Authors: Rajib Mia, Badam Singh Kushvah

Abstract:

The present research was motivated by the recent discovery of the binary star systems. In this paper, we use the restricted three-body problem in the binary stellar systems, considering photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. The stability and periodic orbits of collinear points and the stability and trajectories of the triangular points are studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16 systems. A detailed comparison is made among periodic orbits and trajectories.

Keywords: exoplanetary systems, lagrangian points, periodic orbit, restricted three body problem, stability

Procedia PDF Downloads 397

Authors: O. Maximova, I. L. Danilovich, E. B. Deeva, K. Y. Bukhteev, A. A. Vorobyova, I. V. Morozov, O. S. Volkova, E. A. Zvereva, I. V. Solovyev, S. A. Nikolaev, D. Phuyal, M. Abdel-Hafiez, Y. C. Wang, J. Y. Lin, J. M. Chen, D. I. Gorbunov, K. Puzniak, B. Lake, A. N. Vasiliev

Abstract:

The low-dimensional magnetic systems tend to reveal exotic spin liquid ground states or form peculiar types of long-range order. Among systems of vivid interest are those characterized by the triangular motif in two dimensions. The realization of either ordered or disordered ground state in a triangular, honeycomb, or kagome lattices is are dictated by the competition of exchange interactions, also being sensitive to anisotropy and the spin value of magnetic ions. While the low-spin Heisenberg systems may arrive at a spin liquid long-range entangled quantum state with emergent gauge structures, the high-spin Ising systems may establish the rigid non-collinear structures. This study presents the case of chiral non-coplanar inverted umbrella-type ferrimagnet formed in cobalt nitrate Co(NO₃)₂ below T

Keywords: chiral magnetic structures, low dimensional magnetic systems, umbrella-type ferrimagnets, chiral non-coplanar magnetic structures

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Authors: Mariana Gomez Gomez, Maria Elena Sanchez Vergara

Abstract:

Many sustainable approaches to generate electric energy have emerged in the last few decades; one of them is through solar cells. Yet, this also has the disadvantage of highly polluting inorganic semiconductor manufacturing processes. Therefore, the use of molecular semiconductors must be considered. In this work, allene compounds C24H26O4 and C24H26O5 were used as dopants to manufacture semiconductors films based on PbPc by high-vacuum evaporation technique. IR spectroscopy was carried out to determine the phase and any significant chemical changes which may occur during the thermal evaporation. According to UV-visible spectroscopy and Tauc’s model, the deposition process generated thin films with an activation energy range of 1.47 to 1.55 eV for direct transitions and 1.29 to 1.33 eV for indirect transitions. These values place the manufactured films within the range of low bandgap semiconductors. The flexible devices were manufactured: polyethylene terephthalate (PET), Indium tin oxide (ITO)/organic semiconductor/ Cubic Close Packed (CCP). The characterization of the devices was carried out by evaluating electrical conductivity using the four-probe collinear method. I-V curves were obtained under different lighting conditions at room temperature. OS1 (PbPc/C24H26O4) showed an Ohmic behavior, while OS2 (PbPc/C24H26O5) reached higher current values ​​at lower voltages. The results obtained show that the semiconductors devices doped with allene compounds can be used in the manufacture of optoelectronic devices.

Keywords: electrical properties, optical gap, phthalocyanine, thin film.

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Authors: Vaishakh Medikeri

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Lightning, the marvelous, spectacular and the awesome truth of nature is one of the greatest energy sources left unharnessed since ages. A single lightning bolt of lightning contains energy of about 15 billion joules. This huge amount of energy cannot be harnessed completely but partially. This paper proposes to harness the energy from lightning strikes. Throughout the globe the frequency of lightning is 40-50 flashes per second, totally 1.4 billion flashes per year; all of these flashes carrying an average energy of about 15 billion joules each. When a lightning bolt strikes the ground, tremendous amounts of energy is transferred to earth which propagates in the form of concentric circular energy waves. These waves have a frequency of about 7.83Hz. Harvesting the lightning bolt directly seems impossible, but harvesting the energy waves produced by the lightning is pretty easier. This can be done using a tricoil energy harnesser which is a new device which I have invented. We know that lightning bolt seeks the path which has minimum resistance down to the earth. For this we can make a lightning rod about 100 meters high. Now the lightning rod is attached to the tricoil energy harnesser. The tricoil energy harnesser contains three coils whose centers are collinear and all the coils are parallel to the ground. The first coil has one of its ends connected to the lightning rod and the other end grounded. There is a secondary coil wound on the first coil with one of its end grounded and the other end pointing to the ground and left unconnected and placed a little bit above the ground so that this end of the coil produces more intense currents, hence producing intense energy waves. The first coil produces very high magnetic fields and induces them in the second and third coils. Along with the magnetic fields induced by the first coil, the energy waves which are currents also flow through the second and the third coils. The second and the third coils are connected to a generator which in turn is connected to a capacitor which stores the electrical energy. The first coil is placed in the middle of the second and the third coil. The stored energy can be used for transmission of electricity. This new technique of harnessing the lightning strikes would be most efficient in places with more probability of the lightning strikes. Since we are using a lightning rod sufficiently long, the probability of cloud to ground strikes is increased. If the proposed apparatus is implemented, it would be a great source of pure and clean energy.

Keywords: generator, lightning rod, tricoil energy harnesser, harvesting energy

Procedia PDF Downloads 352

Authors: E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glele Kakai, E. M. Qannari

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A new definition of a latent variable associated with a dataset makes it possible to propose variants of the PLS2 regression and the multi-block PLS (MB-PLS). We shall refer to these variants as Rd-PLS regression and Rd-MB-PLS respectively because they are inspired by both Redundancy analysis and PLS regression. Usually, a latent variable t associated with a dataset Z is defined as a linear combination of the variables of Z with the constraint that the length of the loading weights vector equals 1. Formally, t=Zw with ‖w‖=1. Denoting by Z' the transpose of Z, we define herein, a latent variable by t=ZZ’q with the constraint that the auxiliary variable q has a norm equal to 1. This new definition of a latent variable entails that, as previously, t is a linear combination of the variables in Z and, in addition, the loading vector w=Z’q is constrained to be a linear combination of the rows of Z. More importantly, t could be interpreted as a kind of projection of the auxiliary variable q onto the space generated by the variables in Z, since it is collinear to the first PLS1 component of q onto Z. Consider the situation in which we aim to predict a dataset Y from another dataset X. These two datasets relate to the same individuals and are assumed to be centered. Let us consider a latent variable u=YY’q to which we associate the variable t= XX’YY’q. Rd-PLS consists in seeking q (and therefore u and t) so that the covariance between t and u is maximum. The solution to this problem is straightforward and consists in setting q to the eigenvector of YY’XX’YY’ associated with the largest eigenvalue. For the determination of higher order components, we deflate X and Y with respect to the latent variable t. Extending Rd-PLS to the context of multi-block data is relatively easy. Starting from a latent variable u=YY’q, we consider its ‘projection’ on the space generated by the variables of each block Xk (k=1, ..., K) namely, tk= XkXk'YY’q. Thereafter, Rd-MB-PLS seeks q in order to maximize the average of the covariances of u with tk (k=1, ..., K). The solution to this problem is given by q, eigenvector of YY’XX’YY’, where X is the dataset obtained by horizontally merging datasets Xk (k=1, ..., K). For the determination of latent variables of order higher than 1, we use a deflation of Y and Xk with respect to the variable t= XX’YY’q. In the same vein, extending Rd-MB-PLS to the path modeling setting is straightforward. Methods are illustrated on the basis of case studies and performance of Rd-PLS and Rd-MB-PLS in terms of prediction is compared to that of PLS2 and MB-PLS.

Keywords: multiblock data analysis, partial least squares regression, path modeling, redundancy analysis

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Authors: Bipin Popat Sonawane

Abstract:

After 1988 Electron muon Collaboration (EMC) announcement of measurement of spin dependent structure function, it has been found that it has become a need to understand spin structure of a hadron. In the study of three-dimensional spin structure of a proton, we need to understand the foundation of quantum field theory in terms of electro-weak and strong theories using rigorous mathematical theories and models. In the process of understanding the inner dynamical stricture of proton we need understand the mathematical formalism in perturbative quantum chromodynamics (pQCD). In QCD processes like proton-proton collision at high energy we calculate cross section using conventional collinear factorization schemes. In this calculations, parton distribution functions (PDFs) and fragmentation function are used which provide the information about probability density of finding quarks and gluons ( partons) inside the proton and probability density of finding final hadronic state from initial partons. In transverse momentum dependent (TMD) PDFs and FFs, collectively called as TMDs, take an account for intrinsic transverse motion of partons. The TMD factorization in the calculation of cross sections provide a scheme of hadronic and partonic states in the given QCD process. In this study we review Transverse Momentum Dependent (TMD) factorization scheme using Collins-Soper-Sterman (CSS) Formalism. CSS formalism considers the transverse momentum dependence of the partons, in this formalism the cross section is written as a Fourier transform over a transverse position variable which has physical interpretation as impact parameter. Along with this we compare this formalism with improved CSS formalism. In this work we study the TMD evolution schemes and their comparison with other schemes. This would provide description in the process of measurement of transverse single spin asymmetry (TSSA) in hadro-production and electro-production of J/psi meson at RHIC, LHC, ILC energy scales. This would surely help us to understand J/psi production mechanism which is an appropriate test of QCD.

Keywords: QCD, PDF, TMD, CSS

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