Search results for: conformal symmetry

Authors: Jeremy Attard, Jordan François, Serge Lazzarini, Thierry Masson

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Gauge theories are the natural background for describing geometrically fundamental interactions using principal and associated fiber bundles as dynamical entities. The central notion of these theories is their local gauge symmetry implemented by the local action of a Lie group H. There exist several methods used to reduce the symmetry of a gauge theory, like gauge fixing, bundle reduction theorem or spontaneous symmetry breaking mechanism (SSBM). This paper is a presentation of another method of gauge symmetry reduction, distinct from those three. Given a symmetry group H acting on a fiber bundle and its naturally associated fields (Ehresmann (or Cartan) connection, curvature, matter fields, etc.) there sometimes exists a way to erase (in whole or in part) the H-action by just reconfiguring these fields, i.e. by making a mere change of field variables in order to get new (‘composite‘) fields on which H (in whole or in part) does not act anymore. Two examples: the re-interpretation of the BEHGHK (Higgs) mechanism, on the one hand, and the top-down construction of Tractor and Penrose's Twistor spaces and connections in the framework of conformal Cartan geometry, one the other, will be discussed. They have, of course, nothing to do with each other but the dressing field method can be applied on both to get a new insight. In the first example, it turns out, indeed, that generation of masses in the Standard Model can be separated from the symmetry breaking, the latter being a mere change of field variables, i.e. a dressing. This offers an interpretation in opposition with the one usually found in textbooks. In the second case, the dressing field method applied to the conformal Cartan geometry offer a way of understanding the deep geometric nature of the so-called Tractors and Twistors. The dressing field method, distinct from a gauge transformation (even if it can have apparently the same form), is a systematic way of finding and erasing artificial symmetries of a theory, by a mere change of field variables which redistributes the degrees of freedom of the theories.

Keywords: BEHGHK (Higgs) mechanism, conformal gravity, gauge theory, spontaneous symmetry breaking, symmetry reduction, twistors and tractors

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Authors: P. Y. Tsyba, O. V. Razina, E. Güdekli, R. Myrzakulov

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In this paper, we consider the equation of motion for the F(R,T) gravity on their property of conformal invariance. It is shown that in the general case such a theory is not conformally invariant. Special cases for the functions v and u, in which the properties of the theory can appear, were studied.

Keywords: conformal invariance, gravity, space-time, metric

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Patrascu Andrei Tudor

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One of the main problems in high energy physics is the fact that we do not have a complete understanding of the interaction between local and global effects in gauge theory. This has an increasing impact on our ability to access the non-perturbative regime of most of our theories. Our theories, while being based on gauge groups considered to be simple or semi-simple and connected, are expected to be described by their simple local linear approximation, namely the Lie algebras. However, higher homotopy properties resulting in gauge anomalies appear frequently in theories of physical interest. Our assumption that the groups we deal with are simple and simply connected is probably not suitable, and ways to go beyond such assumptions, particularly in gauge theories, where the Lie algebra linear approximation is prevalent, are not known. We approach this problem from two directions: on one side we are explaining the potential role of formal group laws in describing certain higher homotopical properties and interferences with local or perturbative effects, and on the other side, we employ a categorical approach leading to synthetic theory and a way of looking at gauge theories. The topos approach is based on a geometry where the fundamental logic is intuitionistic logic, and hence the ‘tertium non datur’ principle is abandoned. This has a remarkable impact on understanding conformal symmetry and its anomalies in string theory in various dimensions.

Keywords: Gauge theory, formal group laws, Topos theory, conformal symmetry

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Authors: Venkat Garigapati

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Cell-based therapies are limited due to underlying host immune system activity. Microencapsulation of living cells to overcome this issue has some serious drawbacks, such as limitations of nutrient and oxygen diffusion, which pose a threat to the function and longevity of cells. The conformal coating could overcome the issues which are generally involved in traditional microencapsulation. Some of the theoretical advantages of conformal coating include superior nutrient and oxygen supply to cells, prolonged lifespan, improved drug-secreting cell functionality and an opportunity to load high cell doses in small volumes. Despite several advantages to the conformal coating, there are no suitable methods available to apply to living cells. The ultra-thin conformal coating was achieved utilizing click-reactive methacryloyloxyethyl phosphorylcholine (MPC) polymers, which are capable of specifically reacting one polymer to another at neutral pH in the aqueous isotonic system at the desired temperature suitable for living cells without the need of deleterious initiators. ARPE-19 (Adult Retinal Pigment Epithelial cell line-19) cell-spheroids and rat pancreatic islets were used in the formulation studies. The in vitro studies of coated ARPE-19 cell-spheroids and rat islets indicate that the coat was intact; cells were viable and functioning. The in vitro study results revealed that the conformal coating technology seems promising and in vivo studies are being planned.

Keywords: cells, hydrogel, conformal coating, microencapsulation, insulin

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Authors: Michele Sinico

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The present research investigates the effect of symmetry on the perception of happiness and boredom in design products. Three experiments were carried out in order to verify the degree of the visual expressive value on different models of bookcases, wall clocks, and chairs. 60 participants directly indicated the degree of happiness and boredom using 7-point rating scales. The findings show that the participants acknowledged a different value of expressive quality in the different product models. Results show also that symmetry is not a significant constraint for an emotional design project.

Keywords: product experience, emotional design, symmetry, expressive qualities

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Authors: M. A. Alhubail, A. I. Alateyah, D. Alenezi, B. Aldousiri

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In this study conformal cooling channel (CCC) was employed to dissipate heat of, Polypropylene (PP) parts injected into the Stereolithography (SLA) insert to form tensile and flexural test specimens. The direct metal laser sintering (DMLS) process was used to fabricate a mould with optimised CCC, while optimum parameters of injection moulding were obtained using Optimal-D. The obtained results show that optimisation of the cooling channel layout using a DMLS mould has significantly shortened cycle time without sacrificing the part’s mechanical properties. By applying conformal cooling channels, the cooling time phase was reduced by 20 seconds, and also defected parts were eliminated.

Keywords: optimum parameters, injection moulding, conformal cooling channels, cycle time

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Authors: Jing Lin, Zou Yiming, Goei Ronn, Li Yun, Amanda Ong Jiamin, Alfred Tok Iing Yoong

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High-entropy alloy (HEA) coatings comprise multiple (five or more) principal elements that give superior mechanical, electrical, and thermal properties. However, the current synthesis methods of HEA coating still face huge challenges in facile and controllable preparation, as well as conformal integration, which seriously restricts their potential applications. Herein, we report a controllable synthesis of conformal quinary HEA coating consisting of noble metals (Rh, Ru, Ir, Pt, and Pd) by using the atomic layer deposition (ALD) with a post-annealing approach. This approach realizes low temperature (below 200 °C), precise control (nanoscale), and conformal synthesis (over complex substrates) of HEA coating. Furthermore, the resulting quinary HEA coating shows promising potential as a platform for catalysis, exhibiting substantially enhanced electrocatalytic hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) performances as compared to other noble metal-based structures such as single metal coating or multi-layered metal composites.

Keywords: high-entropy alloy, thin-film, catalysis, water splitting, atomic layer deposition

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Authors: Changyong Liu, Junda Tong, Feng Xu, Ninggui Huang

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In the injection molding process, the performance of cooling channels is crucial to the part quality. Through the application of conformal cooling channels fabricated via metal additive manufacturing, part distortion, warpage can be greatly reduced and cycle time can be greatly shortened. However, the properties of additively manufactured conformal cooling channels are quite different from conventional drilling processes such as the poorer dimensional accuracy and larger surface roughness. These features have significant influences on its cooling performance. In this study, test molds with the cooling channel diameters of φ2 mm, φ3 mm and φ4 mm were fabricated via selective laser melting and conventional drilling process respectively. A test system was designed and manufactured to measure the pressure difference between the channel inlet and outlet, the coolant flow rate and the temperature variation during the heating process. It was found that the cooling performance of SLM-fabricated channels was poorer than drilled cooling channels due to the smaller sectional area of cooling channels resulted from the low dimensional accuracy and the unmolten particles adhered to the channel surface. Theoretical models were established to determine the friction factor and heat transfer coefficient of SLM-fabricated cooling channels. These findings may provide guidance to the design of conformal cooling channels.

Keywords: conformal cooling channels, selective laser melting, cooling performance, injection molding

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Authors: K. C. R. Perera, B. M. Hapuwatte

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This paper presents an effective method to divide panels for mesh-less methods of source, vortex and doublet panel methods. In this research study the physical domain of air-foils were transformed into computational domain of a circle using conformal mapping technique of Joukowsky transformation. Then the circle is divided into panels of equal length and the co-ordinates were remapped into physical domain of the air-foil. With this method the leading edge and the trailing edge of the air-foil is panelled with a high density of panels and the rest of the body is panelled with low density of panels. The high density of panels in the leading edge and the trailing edge will increase the accuracy of the solutions obtained from panel methods where the fluid flow at the leading and trailing edges are complex.

Keywords: conformal mapping, Joukowsky transformation, physical domain, computational domain

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Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: M. Kamel El-Sayed

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The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Keywords: information system, uncertain concept, membership function, similarity relation, degree of similarity

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Authors: Gayatri Ghosh

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In this work, a flavour theory of a neutrino mass model based on A_4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A_4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z_2 × Z_2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δ_CP phase, the neutrino oscillation probability P(νµ → νe), the effective Majorana mass |mee| and |meff νe |. A Z_2 × Z_2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ_13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δ_CP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A_4 × Z_2 × Z_2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the A_4 symmetry. In this context the implications for charged lepton flavour violation processes like µ → eγ, τ → eγ, τ → µγ are discussed.

Keywords: Z2 × Z2 invariant perturbations, CLFV, delta CP phase, tribimaximal neutrino mixing

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Authors: Mihriban Hacisalihoğlu Karadeniz, Figen Bozkuş, Tuğba Baran, Ümit Akar

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Creating the correct symmetry of conceptual knowledge about students, conceptual information about the symmetry of the instructors is important. However, teachers’, the students should be aware of the existing misconceptions and be able to develop strategies to correct these misconceptions. In this study, the purpose, the prospective teachers’, the students’ explanations for corrections of misconceptions and misconceptions were asked to be introduced. The working group during the 2012-2013 academic year, Kocaeli University Faculty of Education Mathematics Education consists of studying at the twenty-six prospective teachers. The study adopted a qualitative approach. The data prepared by the researchers were obtained with an open-ended test. As a result of analysis of the data, prospective with teaching the concept of symmetry observed in more developed practical solutions. These solutions are focused on the method, students utilization mirrors, paper folding, such as using a square piece of registration of events. Prospective teachers’ who think this way, students observed that overlooked the creation of conceptual knowledge.

Keywords: symmetry concepts, misconceptions, elementary mathematics, prospective teachers-students

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Authors: Kefaya Qaddoum

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The aim of this study is to predict breast cancer and to construct a supportive model that will stimulate a more reliable prediction as a factor that is fundamental for public health. In this study, we utilize general regression neural networks (GRNN) to replace the normal predictions with prediction periods to achieve a reasonable percentage of confidence. The mechanism employed here utilises a machine learning system called conformal prediction (CP), in order to assign consistent confidence measures to predictions, which are combined with GRNN. We apply the resulting algorithm to the problem of breast cancer diagnosis. The results show that the prediction constructed by this method is reasonable and could be useful in practice.

Keywords: neural network, conformal prediction, cancer classification, regression

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Authors: Nelson Nenuwe

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The behavior of interacting electrons in one dimension was studied by calculating correlation functions and critical exponents at zero and external magnetic fields for arbitrary band filling. The technique employed in this study is based on the conformal field theory (CFT). The charge and spin degrees of freedom are separated, and described by two independent conformal theories. A detailed comparison of the t-J model with the repulsive Hubbard model was then undertaken with emphasis on their Tomonaga-Luttinger (TL) liquid properties. Near half-filling the exponents of the t-J model take the values of the strong-correlation limit of the Hubbard model, and in the low-density limit the exponents are those of a non-interacting system. The critical exponents obtained in this study belong to the repulsive TL liquid (conducting phase) and attractive TL liquid (superconducting phase). The theoretical results from this study find applications in one-dimensional organic conductors (TTF-TCNQ), organic superconductors (Bechgaard salts) and carbon nanotubes (SWCNTs, DWCNTs and MWCNTs). For instance, the critical exponent at from this study is consistent with the experimental result from optical and photoemission evidence of TL liquid in one-dimensional metallic Bechgaard salt- (TMTSF)2PF6.

Keywords: critical exponents, conformal field theory, Hubbard model, t-J model

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: complex potential, conformal mapping, image well theory, Laplace’s equation, superposition principle

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Alpana Tiwari, N. K. Gaur

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We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: orientational glass, phonons, TR-coupling, lattice dynamics

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Authors: Saleh Elawgali

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In order to present the effect of the dynamic eccentricity on the stator currents of squirrel cage induction machines, the current spectrums of a 550 kW induction motor was calculated for the cases of full symmetry and dynamic eccentricity. The calculations presented in this paper are based on the Poly-Harmonic Model accounting for static and dynamic eccentricity, stator and rotor slotting, parallel branches as well as cage asymmetry. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums for full symmetry and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one.

Keywords: current spectrum, dynamic eccentricity, harmonics, Induction machine, slot harmonic zone.

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Authors: Saurabh Basu, Sudin Ganguly

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Conductance in graphene nanoribbons (GNR) in presence of magnetic (for example, Iron) and non-magnetic (for example, Gold) adatoms are explored theoretically within a Kane-Mele model for their possible spintronic applications and topologically non-trivial properties. In our work, we have considered the magnetic adatoms to induce a Rashba spin-orbit coupling (RSOC) and an exchange bias field, while the non-magnetic ones induce an RSOC and an intrinsic spin-orbit (SO) coupling. Even though RSOC is present in both, they, however, represent very different physical situations, where the magnetic adatoms do not preserve the time reversal symmetry, while the non-magnetic case does. This has important implications on the topological properties. For example, the non-magnetic adatoms, for moderately strong values of SO, the GNR denotes a quantum spin Hall insulator as evident from a 2e²/h plateau in the longitudinal conductance and presence of distinct conducting edge states with an insulating bulk. Since the edge states are protected by time reversal symmetry, the magnetic adatoms in GNR yield trivial insulators and do not possess any non-trivial topological property. However, they have greater utility than the non-magnetic adatoms from the point of view of spintronic applications. Owing to the broken spatial symmetry induced by the presence of adatoms of either type, all the x, y and z components of the spin-polarized conductance become non-zero (only the y-component survives in pristine Graphene owing to a mirror symmetry present there) and hence become suitable for spintronic applications. However, the values of the spin polarized conductances are at least two orders of magnitude larger in the case of magnetic adatoms than their non-magnetic counterpart, thereby ensuring more efficient spintronic applications. Further the applications are tunable by altering the adatom densities.

Keywords: magnetic and non-magnetic adatoms, quantum spin hall phase, spintronic applications, spin polarized conductance, time reversal symmetry

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Authors: Hubert Klar

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High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: correlation, resonances, threshold ionization, Cooper pair

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Authors: Ravi Kiran Pothamsetty, Radha Rani Ghosh, Baby Paul Thaliath

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Radiation therapy has undergone many advancements and evloved from 2D to 3D. Recently, with rapid pace of drug discoveries, cutting edge technology, and clinical trials has made innovative advancements in computer technology and treatment planning and upgraded to intensity modulated radiotherapy (IMRT) which delivers in homogenous dose to tumor and normal tissues. The present study was a hospital-based experience comparing two different conformal radiotherapy techniques for brain tumors. This analytical study design has been conducted at Regional Cancer Centre, India from January 2014 to January 2015. Ten patients have been selected after inclusion and exclusion criteria. All the patients were treated on Artiste Siemens Linac Accelerator. The tolerance level for maximum dose was 6.0 Gyfor lenses and 54.0 Gy for brain stem, optic chiasm and optical nerves as per RTOG criteria. Mean and standard deviation values of PTV98%, PTV 95% and PTV 2% in IMRT were 93.16±2.9, 95.01±3.4 and 103.1±1.1 respectively; for 3DCRT were 91.4±4.7, 94.17±2.6 and 102.7±0.39 respectively. PTV max dose (%) in IMRT and 3D-CRT were 104.7±0.96 and 103.9±1.0 respectively. Maximum dose to the tumor can be delivered with IMRT with acceptable toxicity limits. Variables such as expertise, location of tumor, patient condition, and TPS influence the outcome of the treatment.

Keywords: brain tumors, intensity modulated radiotherapy (IMRT), three dimensional conformal radiotherapy (3D-CRT), radiation therapy oncology group (RTOG)

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Authors: Yuen Yee Li Sip, Lei Zhai

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Biofilms are formed by the attachment of microorganisms onto substrates via self-synthesized extracellular polymeric substances. They have been observed in the International Space Stations (ISS), in which biofilms can jeopardize the performance of key equipment and can pose health threats to the astronauts. This project aims at building conformal nanoporous surfaces that are infused with lubricant and decorated with antimicrobial nanoparticles while simultaneously evaluating their efficacy in preventing biofilm formation. Lubricant-impregnated surfaces (LIS) are fabricated by using a layer-by-layer assembly of silica nanoparticles to generate conformal nanoporous coatings on substrates and fill the films with fluorinated fluids. LIS has demonstrated excellent repellency to a broad range of liquids, preventing microbe adhesion (anti-biofouling). Silver or copper nanoparticles were deposited on the coatings prior to lubricant infusion in order to provide antimicrobial characteristics to the coating. Surface morphology and biofilm growth were characterized to understand how the coating morphology affects the LIS stability and anti-biofouling behaviors (stationary and in a flow).

Keywords: biofilm, coatings, nanoporous, antifouling

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Authors: Anas Ibrahim Yahaya, Christophe Soligo

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A substantial body of literature has reported on facial symmetry and asymmetry and their role in human mate choice. However, major gaps persist, with nearly all data originating from the WEIRD (Western, Educated, Industrialised, Rich and Developed) populations, and results remaining largely equivocal when compared across studies. This study is aimed at quantifying facial asymmetry from the 3D faces of the Hausa of northern Nigeria and also aimed at determining their (Hausa) perceptions and judgements of standardised facial images with different levels of asymmetry using questionnaires. Data were analysed using R-studio software and results indicated that individuals with lower levels of facial asymmetry (near facial symmetry) were perceived as more attractive, more suitable as marriage partners and more caring, whereas individuals with higher levels of facial asymmetry were perceived as more aggressive. The study conclusively asserts that all faces are asymmetric including the most beautiful ones, and the preference of less asymmetric faces was not just dependent on single facial trait, but rather on multiple facial traits; thus the study supports that physical attractiveness is not just an arbitrary social construct, but at least in part a cue to general health and possibly related to environmental context.

Keywords: face, asymmetry, symmetry, Hausa, preference

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Authors: Rinku Maji, Joydeep Chakrabortty, Stephen F. King

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The grand unified theory (GUT) rationales the arbitrariness of the standard model (SM) and explains many enigmas of nature at the outset of a single gauge group. The GUTs predict the proton decay and, the spontaneous symmetry breaking (SSB) of the higher symmetry group may lead to the formation of topological defects, which are indispensable in the context of the cosmological observations. The Super-Kamiokande (Super-K) experiment sets sacrosanct bounds on the partial lifetime (τ) of the proton decay for different channels, e.g., τ(p → e+ π0) > 1.6×10³⁴ years which is the most relevant channel to test the viability of the nonsupersymmetric GUTs. The GUTs based on the gauge groups SO(10) and E(6) are broken to the SM spontaneously through one and two intermediate gauge symmetries with the manifestation of the left-right symmetry at least at a single intermediate stage and the proton lifetime for these breaking chains has been computed. The impact of the threshold corrections, as a consequence of integrating out the heavy fields at the breaking scale alter the running of the gauge couplings, which eventually, are found to keep many GUTs off the Super-K bound. The possible topological defects arising in the course of SSB at different breaking scales for all breaking chains have been studied.

Keywords: grand unified theories, proton decay, threshold correction, topological defects

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Authors: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Sajjad Esmaeili, Robert Krause, Lukas Gerlich, Alireza Mohammadian Kia, Benjamin Uhlig

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This investigation aims to develop the feasible and qualitative process parameters for the thin films fabrication into ultra-large through-silicon-vias (TSVs) as vertical interconnections. The focus of the study is on TSV metallization and its challenges employing new materials for the purpose of rapid signal propagation in the microsystems technology. Cobalt metal-organic chemical vapor deposition (Co-MOCVD) process enables manufacturing an adhesive and excellent conformal ultra-thin film all the way through TSVs in comparison with the conventional non-conformal physical vapor deposition (PVD) process of copper (Cu) seed layer. Therefore, this process provides a Cu seed-free layer which is capable of direct Cu electrochemical deposition (Cu-ECD) on top of it. The main challenge of this metallization module is to achieve the proper alternative seed layer with less roughness, sheet resistance and granular organic contamination (e.g. carbon) which intensify the Co corrosion under the influence of Cu electrolyte.

Keywords: Cobalt MOCVD, direct Cu electrochemical deposition (ECD), metallization technology, through-silicon-via (TSV)

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Wenhao Lan, Ning Li, Qiang Tong

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To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

Keywords: mirror symmetry, oriented bounding box, point cloud registration, PointNetLK-OBB

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