Search results for: singularities

Authors: Marc Diesse, Hochschule Heilbronn

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We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: linkages, configuration space-singularities, real algebraic geometry, analytic geometry

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: S. Srednyak

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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif

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This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: Hafdaoui Hichem, Mehadjebia Cherifa, Benatia Djamel

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In this paper, we propose a new method for Bulk detection of an acoustic microwave signal during the propagation of acoustic microwaves in a piezoelectric substrate (Lithium Niobate LiNbO3). We have used the classification by probabilistic neural network (PNN) as a means of numerical analysis in which we classify all the values of the real part and the imaginary part of the coefficient attenuation with the acoustic velocity in order to build a model from which we note the Bulk waves easily. These singularities inform us of presence of Bulk waves in piezoelectric materials. By which we obtain accurate values for each of the coefficient attenuation and acoustic velocity for Bulk waves. This study will be very interesting in modeling and realization of acoustic microwaves devices (ultrasound) based on the propagation of acoustic microwaves.

Keywords: piezoelectric material, probabilistic neural network (PNN), classification, acoustic microwaves, bulk waves, the attenuation coefficient

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Authors: Saad Bakkali

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Morocco is a major producer of phosphate, with an annual output of 19 million tons and reserves in excess of 35 billion cubic meters. This represents more than 75% of world reserves. Resistivity surveys have been successfully used in the Oulad Abdoun phosphate basin. A Schlumberger resistivity survey over an area of 50 hectares was carried out. A new field procedure based on analytic signal response of resistivity data was tested to deal with the presence of phosphate deposit disturbances. A resistivity map was expected to allow the electrical resistivity signal to be imaged in 2D. 2D wavelet is standard tool in the interpretation of geophysical potential field data. Wavelet transform is particularly suitable in denoising, filtering and analyzing geophysical data singularities. Wavelet transform tools are applied to analysis of a moroccan phosphate deposit ‘disturbances’. Wavelet approach applied to modeling surface phosphate “disturbances” was found to be consistently useful.

Keywords: resistivity, Schlumberger, phosphate, wavelet, Morocco

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Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

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The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

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Authors: Shyam Sunder Gupta

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The current theory for the creation of the universe, the Big Bang theory, is widely accepted but leaves some unanswered questions. It does not explain the origin of the singularity or what causes the Big Bang. The theory of the Big Bang also does not explain why there is such a huge amount of dark energy and dark matter in our universe. Also, there is a question related to one universe or multiple universes which needs to be answered. This research addresses these questions using the Bhagvat Puran and other Vedic scriptures as the basis. There is a Unique Pure Energy Field that is eternal, infinite, and finest of all and never transforms when in its original form. The Carrier Particles of Unique Pure Energy are Param-anus- Fundamental Energy Particles. Param-anus and a combination of these particles create bigger particles from which the Universe gets created. For creation to initiate, Unique Pure Energy is represented in three phases: positive phase energy, neutral phase eternal time energy and negative phase energy. Positive phase energy further expands in three forms of creative energies (CE1, CE2andCE3). From CE1 energy, three energy modes, mode of activation, mode of action, and mode of darkness, were created. From these three modes, 16 Principles, subtlest forms of energies, namely Pradhan, Mahat-tattva, Time, Ego, Intellect, Mind, Sound, Space, Touch, Air, Form, Fire, Taste, Water, Smell, and Earth, get created. In the Mahat-tattva, dominant in the Mode of Darkness, CE1 energy creates innumerable primary singularities from seven principles: Pradhan, Mahat-tattva, Ego, Sky, Air, Fire, and Water. CE1 energy gets divided as CE2 and enters, along with three modes and time, in each singularity, and primary Big Bang takes place, and innumerable Invisible Universes get created. Each Universe has seven coverings of 7 principles, and each layer is 10 times thicker than the previous layer. By energy CE2, space in Invisible Universe under the coverings is divided into two halves. In the lower half, the process of evolution gets initiated, and seeds of 24 elements get created, out of which 5 fundamental elements, building blocks of matter, Sky, Air, Fire, Water and Earth, create seeds of stars, planets, galaxies and all other matter. Since 5 fundamental elements get created out of the mode of darkness, it explains why there is so much dark energy and dark matter in our Universe. This process of creation, in the lower half of Invisible universe continues for 2.16 billion years. Further, in the lower part of the energy field, exactly at the Centre of Invisible Universe, Secondary Singularity is created, through which, by force of Mode of Action, Secondary Big Bang takes place and Visible Universe gets created in the shape of Lotus Flower, expanding into upper part. Visible matter starts appearing after a gap of 360,000 years. Within the Visible Universe, a small part gets created known as the Phenomenal Material World, which is our Solar System, the sun being in the Centre. Diameter of Solar planetary system is 6.4 billion km.

Keywords: invisible universe, phenomenal material world, primary Big Bang, secondary Big Bang, singularities, visible universe

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Authors: Manuel Urueña Palomo

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In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Jinyong Yao, Hongzhi Li, Chao Du, Jiao Li

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Reliability of long-term storage products is related to the availability of the whole system, and the evaluation of storage life is of great necessity. These products are usually highly reliable and little failure information can be collected. In this paper, an analytical method based on data from accelerated storage life test is proposed to evaluate the reliability index of the long-term storage products. Firstly, singularities are eliminated by data normalization and residual analysis. Secondly, with the pre-processed data, the degradation path model is built to obtain the pseudo life values. Then by life distribution hypothesis, we can get the estimator of parameters in high stress levels and verify failure mechanisms consistency. Finally, the life distribution under the normal stress level is extrapolated via the acceleration model and evaluation of the true average life available. An application example with the camera stabilization device is provided to illustrate the methodology we proposed.

Keywords: accelerated storage life test, failure mechanisms consistency, life distribution, reliability

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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Authors: Paolo Russu

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This paper investigates the economic and ecological dynamics that emerge in Protected Areas (PAs) as a result of interactions between visitors to the area and the animals that live there. We suppose that the PAs contain two species whose interactions are determined by the Lotka-Volterra equations system. Visitors' decisions to visit PAs are influenced by the entrance cost required to enter the park as well as the chance of witnessing the species that live there. Visitors have contradictory effects on the species and thus on the sustainability of the protected areas: on the one hand, an increase in the number of tourists damages the natural habitat of the areas and thus the species living there; on the other hand, it increases the total amount of entrance fees that the managing body of the PAs can use to perform defensive expenditures that protect the species from extinction. For a given set of parameter values, the existence of saddle-node bifurcation, Hopf bifurcation, homoclinic orbits, and a Bogdanov–Takens bifurcation of codimension two has been investigated. The system displays periodic doubling and chaotic solutions, as demonstrated by numerical examples. Pontryagin's Maximum Principle was utilized to develop an optimal admission charge policy that maximized both social gain and ecosystem conservation.

Keywords: environmental preferences, singularities point, dynamical system, chaos

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Authors: C. S. Sona, Makrand A. Khanwale, Channamallikarjun S. Mathpati

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New generation nuclear power plants are currently being developed to be highly economical, to be passive safe, to produce hydrogen. An important feature of these reactors will be the use of coolants at temperature higher than that being used in current nuclear reactors. The molten fluoride salt with a eutectic composition of 46.5% LiF - 11.5% NaF - 42% KF (mol %) commonly known as FLiNaK is a leading candidate for heat transfer coolant for these nuclear reactors. CFD simulations were carried out using large eddy simulations to investigate the flow characteristics of molten FLiNaK at 850°C at a Reynolds number of 10,500 in a cylindrical pipe. Simulation results have been validated with the help of mean velocity profile using direct numerical simulation data. Transient velocity information was used to identify and characterise turbulent structures which are important for transfer of heat across solid-fluid interface. A wavelet transform based methodology called wavelet transform modulus maxima was used to identify and characterise the singularities. This analysis was also used for flow visualisation, and also to calculate the heat transfer coefficient using small eddy model. The predicted Nusselt number showed good agreement with the available experimental data.

Keywords: FLiNaK, heat transfer, molten salt, turbulent structures

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Amal Ait El Djoudi

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A thermodynamical model of coexisting hadronic and quark–gluon plasma (QGP) phases is used to study the thermally driven deconfining phase transition occurring between the two phases. A color singlet partition function is calculated for the QGP phase with two massless quarks, as in our previous work, but now the finite extensions of the hadrons are taken into account in the equation of state of the hadronic phase. In the present work, the finite-size effects on the system are examined by probing the behavior of some thermodynamic quantities, called response functions, as order parameter, energy density and their derivatives, on a range of temperature around the transition at different volumes. It turns out that the finiteness of the system size has as effects the rounding of the transition and the smearing of all the singularities occurring in the thermodynamic limit, and the additional finite-size effect introduced by the requirement of exact color-singletness involves a shift of the transition point. This shift as well as the smearing of the transition region and the maxima of both susceptibility and specific heat show a scaling behavior with the volume characterized by scaling exponents. Another striking result is the large similarity noted between the behavior of these response functions and that of the cumulants of the probability density. This similarity is worked to try to extract information concerning the occurring phase transition.

Keywords: equation of state, thermodynamics, deconfining phase transition, quark–gluon plasma (QGP)

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

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Authors: Diala Bitar, Emmanuel Gourdon, Claude H. Lamarque, Manuel Collet

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Acoustic absorber devices play an important role reducing the noise at the propagation and reception paths. An electroacoustic absorber consists of a loudspeaker coupled to an electric shunt circuit, where the membrane is playing the role of an absorber/reflector of sound. Although the use of linear shunt resistors at the transducer terminals, has shown to improve the performances of the dynamical absorbers, it is nearly efficient in a narrow frequency band. Therefore, and since nonlinear phenomena are promising for their ability to absorb the vibrations and sound on a larger frequency range, we propose to couple a nonlinear electric shunt circuit at the loudspeaker terminals. Then, the equivalent model can be described by a 2 degrees of freedom system, consisting of a primary linear oscillator describing the dynamics of the loudspeaker membrane, linearly coupled to a cubic nonlinear energy sink (NES). The system is analytically treated for the case of 1:1 resonance, using an invariant manifold approach at different time scales. The proposed methodology enables us to detect the equilibrium points and fold singularities at the first slow time scales, providing a predictive tool to design the nonlinear circuit shunt during the energy exchange process. The preliminary results are promising; a significant improvement of acoustic absorption performances are obtained.

Keywords: electroacoustic absorber, multiple-time-scale with small finite parameter, nonlinear energy sink, nonlinear passive shunt

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: Ramish, Farhan Khalique Awan

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Kinematic redundancy within the manipulators presents extended dexterity and manipulability to the manipulators. Redundant serial robotic manipulators are very popular in industries due to its competencies to keep away from singularities during normal operation and fault tolerance because of failure of one or more joints. Such fault tolerant manipulators are extraordinarily beneficial in applications where human interference for repair and overhaul is both impossible or tough; like in case of robotic arms for space programs, nuclear applications and so on. The design of this sort of fault tolerant serial 3 DoF manipulator is presented in this paper. This work was the extension of the author’s previous work of designing the simple 3R serial manipulator. This work is the realization of the previous design with optimizing the link lengths for incorporating the feature of fault tolerance. Various measures have been followed by the researchers to quantify the fault tolerance of such redundant manipulators. The fault tolerance in this work has been described in terms of the worst-case measure of relative manipulability that is, in fact, a local measure of optimization that works properly for certain configuration of the manipulators. An optimum fault tolerant Jacobian matrix has been determined first based on prescribed null space properties after which the link parameters have been described to meet the given Jacobian matrix. A solid model of the manipulator was then developed to realize the mathematically rigorous design. Further work was executed on determining the dynamic properties of the fault tolerant design and simulations of the movement for various trajectories have been carried out to evaluate the joint torques. The mathematical model of the system was derived via the Euler-Lagrange approach after which the same has been tested using the RoboAnalyzer© software. The results have been quite in agreement. From the CAD model and dynamic simulation data, the manipulator was fabricated in the workshop and Advanced Machining lab of NED University of Engineering and Technology.

Keywords: fault tolerant, Graham matrix, Jacobian, kinematics, Lagrange-Euler

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Authors: H. Daaou Nedjari, O. Guerri, M. Saighi

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A numerical study was conducted to optimize the positioning of wind turbines over complex terrains. Thus, a two-dimensional disk model was used to calculate the flow velocity deficit in wind farms for both flat and complex configurations. The wind turbine wake was assessed using the hybrid methods that combine CFD (Computational Fluid Dynamics) with the actuator disc model. The wind turbine rotor has been defined with a thrust force, coupled with the Navier-Stokes equations that were resolved by an open source computational code (Code_Saturne V3.0 developed by EDF) The simulations were conducted in atmospheric boundary layer condition considering a two-dimensional region located at the north of Algeria at 36.74°N longitude, 02.97°E latitude. The topography elevation values were collected according to a longitudinal direction of 1km downwind. The wind turbine sited over topography was simulated for different elevation variations. The main of this study is to determine the topography effect on the behavior of wind farm wake flow. For this, the wake model applied in complex terrain needs to selects the singularity effects of topography on the vertical wind flow without rotor disc first. This step allows to determine the existence of mixing scales and friction forces zone near the ground. So, according to the ground relief the wind flow waS disturbed by turbulence and a significant speed variation. Thus, the singularities of the velocity field were thoroughly collected and thrust coefficient Ct was calculated using the specific speed. In addition, to evaluate the land effect on the wake shape, the flow field was also simulated considering different rotor hub heights. Indeed, the distance between the ground and the hub height of turbine (Hhub) was tested in a flat terrain for different locations as Hhub=1.125D, Hhub = 1.5D and Hhub=2D (D is rotor diameter) considering a roughness value of z0=0.01m. This study has demonstrated that topographical farm induce a significant effect on wind turbines wakes, compared to that on flat terrain.

Keywords: CFD, wind turbine wake, k-epsilon model, turbulence, complex topography

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Authors: Margarida Franca

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The influence of the ‘cultural turn’ movement and the consequent deconstruction of scientific thought allowed geography and other social sciences to open or deepen their studies based on the analysis of multiple identities, on singularities, on what is particular or what marks the difference between individuals. In the context of postmodernity, the geography of religion has gained a favorable scientific, thematic and methodological focus for the qualitative and subjective interpretation of various religious identities, sacred places, territories of belonging, religious communities, among others. In the context of ‘late modernity’ or ‘net modernity’, sacred places and the definition of a network of sacred territories allow believers to attain the ‘ontological security’. The integration on a religious group or a local community, particularly a religious community, allows human beings to achieve a sense of belonging, familiarity or solidarity and to overcome, in part, some of the risks or fears that society has discovered. The importance of sacred places comes not only from their inherent characteristics (eg transcendent, mystical and mythical, respect, intimacy and abnegation), but also from the possibility of adding and integrating members of the same community, creating bonds of belonging, reference and individual and collective memory. In addition, the formation of different networks of sacred places, with multiple scales and dimensions, allows the human being to identify and structure his times and spaces of daily life. Thus, each individual, due to his unique identity and life and religious paths, creates his own network of sacred places. The territorial expression of religious identity allows to draw a variable and unique geography of sacred places. Through the case study of the practicing Catholic population in the diocese of Coimbra (Portugal), the aim is to study the territorial expression of the religious identity of the different local communities of this city. Through a survey of six parishes in the city, we sought to identify which factors, qualitative or not, define the different territorial expressions on a local, national and international scale, with emphasis on the socioeconomic profile of the population, the religious path of the believers, the religious group they belong to and the external interferences, religious or not. The analysis of these factors allows us to categorize the communities of the city of Coimbra and, for each typology or category, to identify the specific elements that unite the believers to the sacred places, the networks and religious territories that structure the religious practice and experience and also the non-representational landscape that unifies and creates memory. We conclude that an apparently homogeneous group, the Catholic community, incorporates multitemporalities and multiterritorialities that are necessary to understand the history and geography of a whole country and of the Catholic communities in particular.

Keywords: geography of religion, sacred places, territoriality, Catholic Church

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Authors: Efrain Rodriguez, Cristhian Riano, Alberto Alvares

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In recent years, robots manipulators with parallel architectures are used in additive manufacturing processes – 3D printing. These robots have advantages such as speed and lightness that make them suitable to help with the efficiency and productivity of these processes. Consequently, the interest for the development of parallel robots for additive manufacturing applications has increased. This article deals with the conceptual design and dimensional synthesis of the linear delta robot for additive manufacturing. Firstly, a methodology based on structured processes for the development of products through the phases of informational design, conceptual design and detailed design is adopted: a) In the informational design phase the Mudge diagram and the QFD matrix are used to aid a set of technical requirements, to define the form, functions and features of the robot. b) In the conceptual design phase, the functional modeling of the system through of an IDEF0 diagram is performed, and the solution principles for the requirements are formulated using a morphological matrix. This phase includes the description of the mechanical, electro-electronic and computational subsystems that constitute the general architecture of the robot. c) In the detailed design phase, a digital model of the robot is drawn on CAD software. A list of commercial and manufactured parts is detailed. Tolerances and adjustments are defined for some parts of the robot structure. The necessary manufacturing processes and tools are also listed, including: milling, turning and 3D printing. Secondly, a dimensional synthesis method applied on design of the linear delta robot is presented. One of the most important key factors in the design of a parallel robot is the useful workspace, which strongly depends on the joint space, the dimensions of the mechanism bodies and the possible interferences between these bodies. The objective function is based on the verification of the kinematic model for a prescribed cylindrical workspace, considering geometric constraints that possibly lead to singularities of the mechanism. The aim is to determine the minimum dimensional parameters of the mechanism bodies for the proposed workspace. A method based on genetic algorithms was used to solve this problem. The method uses a cloud of points with the cylindrical shape of the workspace and checks the kinematic model for each of the points within the cloud. The evolution of the population (point cloud) provides the optimal parameters for the design of the delta robot. The development process of the linear delta robot with optimal dimensions for additive manufacture is presented. The dimensional synthesis enabled to design the mechanism of the delta robot in function of the prescribed workspace. Finally, the implementation of the robotic platform developed based on a linear delta robot in an additive manufacturing application using the Fused Deposition Modeling (FDM) technique is presented.

Keywords: additive manufacturing, delta parallel robot, dimensional synthesis, genetic algorithms

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Authors: Dragan Ribarić

Abstract:

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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Authors: Yan Torres, Fernanda Simoes, Francisco Petrucci-Fonseca, Freddie-Jeanne Richard

Abstract:

The non-invasive samples are an alternative of collecting genetic samples directly. Non-invasive samples are collected without the manipulation of the animal (e.g., scats, feathers and hairs). Nevertheless, the use of non-invasive samples has some limitations. The main issue is degraded DNA, leading to poorer extraction efficiency and genotyping. Those errors delayed for some years a widespread use of non-invasive genetic information. Possibilities to limit genotyping errors can be done using analysis methods that can assimilate the errors and singularities of non-invasive samples. Genotype matching and population estimation algorithms can be highlighted as important analysis tools that have been adapted to deal with those errors. Although, this recent development of analysis methods there is still a lack of empirical performance comparison of them. A comparison of methods with dataset different in size and structure can be useful for future studies since non-invasive samples are a powerful tool for getting information specially for endangered and rare populations. To compare the analysis methods, four different datasets used were obtained from the Dryad digital repository were used. Three different matching algorithms (Cervus, Colony and Error Tolerant Likelihood Matching - ETLM) are used for matching genotypes and two different ones for population estimation (Capwire and BayesN). The three matching algorithms showed different patterns of results. The ETLM produced less number of unique individuals and recaptures. A similarity in the matched genotypes between Colony and Cervus was observed. That is not a surprise since the similarity between those methods on the likelihood pairwise and clustering algorithms. The matching of ETLM showed almost no similarity with the genotypes that were matched with the other methods. The different cluster algorithm system and error model of ETLM seems to lead to a more criterious selection, although the processing time and interface friendly of ETLM were the worst between the compared methods. The population estimators performed differently regarding the datasets. There was a consensus between the different estimators only for the one dataset. The BayesN showed higher and lower estimations when compared with Capwire. The BayesN does not consider the total number of recaptures like Capwire only the recapture events. So, this makes the estimator sensitive to data heterogeneity. Heterogeneity in the sense means different capture rates between individuals. In those examples, the tolerance for homogeneity seems to be crucial for BayesN work properly. Both methods are user-friendly and have reasonable processing time. An amplified analysis with simulated genotype data can clarify the sensibility of the algorithms. The present comparison of the matching methods indicates that Colony seems to be more appropriated for general use considering a time/interface/robustness balance. The heterogeneity of the recaptures affected strongly the BayesN estimations, leading to over and underestimations population numbers. Capwire is then advisable to general use since it performs better in a wide range of situations.

Keywords: algorithms, genetics, matching, population

Procedia PDF Downloads 138