Search results for: superposition

Authors: Zhang Jianrun, He Tangling

Abstract:

Superposition wave form automotive exhaust bellows is a new type of bellows, which has the characteristics of large compensation, good vibration isolation performance and long life. It has been paid more and more attention and applications in automotive exhaust pipe system. Aiming at the lack of current design methods of superposition wave form automotive exhaust bellows, this paper proposes a response surface parameter optimization method where the fatigue life and vibration transmissibility of the bellows are set as objectives. The parametric modeling of bellow structure is also adopted to achieve the high efficiency in the design. The approach proposed in this paper provides a new way for the design of superposition wave form automotive exhaust bellows. It embodies good engineering application value.

Keywords: superposition wave form, exhaust bellows, optimization, vibration, fatigue life

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Charles Mota Possatti Júnior, André Schwanz de Lima, Maurício Vicente Donadon, Alfredo Rocha de Faria

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An interlaminar damage model is combined with a beam element formulation based on global-local superposition to assess delamination in composite laminates. The variations in the mechanical properties in the laminate, generated by the presence of delamination, are calculated as a function of the displacements in the interface layers. The global-local superposition of displacement fields ensures the zig-zag behaviour of stresses and displacement, and the number of degrees of freedom (DOFs) is independent of the number of layers. The displacements and stresses are calculated as a function of DOFs commonly used in traditional beam elements. Finally, the finite element(FE) formulation is extended to handle cases of different thicknesses, and then the FE model predictions are compared with results obtained from analytical solutions and commercial finite element codes.

Keywords: delamination, global-local superposition theory, single beam element, zig-zag, interlaminar damage model

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Authors: Ammar Edress Mohamed, Mustafa Aziz, David Wright

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This paper analyses and calculates the head fields of asymmetrical 2D magnetic recording heads when the soft-underlayer is present using the appropriate Green's function to derive the surface potential/field by utilising the surface potential for asymmetrical head without underlayer. The results follow closely the corners, while the gap region shows a linear behaviour for d/g < 0.5 compared with the calculated fields from finite-element.

Keywords: magnetic recording, finite elements, asymmetrical magnetic heads, superposition, Laplace's equation

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Authors: Andre S. de Lima, Alfredo R. de Faria, Jose J. R. Faria

Abstract:

Accurate prediction of thermal stresses is particularly important for laminated composite structures, as large temperature changes may occur during fabrication and field application. The normal transverse deformation plays an important role in the prediction of such stresses, especially for problems involving thick laminated plates subjected to uniform temperature loads. Bearing this in mind, the present study aims to investigate the thermo-mechanical behavior of laminated composite structures using a new beam element based on global-local superposition, accounting for through-the-thickness effects. The element formulation is based on a global-local superposition in the thickness direction, utilizing a cubic global displacement field in combination with a linear layerwise local displacement distribution, which assures zig-zag behavior of the stresses and displacements. By enforcing interlaminar stress (normal and shear) and displacement continuity, as well as free conditions at the upper and lower surfaces, the number of degrees of freedom in the model is maintained independently of the number of layers. Moreover, the proposed formulation allows for the determination of transverse shear and normal stresses directly from the constitutive equations, without the need of post-processing. Numerical results obtained with the beam element were compared to analytical solutions, as well as results obtained with commercial finite elements, rendering satisfactory results for a range of length-to-thickness ratios. The results confirm the need for an element with through-the-thickness capabilities and indicate that the present formulation is a promising alternative to such analysis.

Keywords: composite beam element, global-local superposition, laminated composite structures, thermal stresses

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Authors: Thanida Sujarittham, Narumon Emarat, Jintawat Tanamatayarat, Kwan Arayathanitkul, Suchai Nopparatjamjomras

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Electric field is an important fundamental concept in electrostatics. In high-school, generally Thai students have already learned about definition of electric field, electric field due to a point charge, and superposition of electric fields due to multiple-point charges. Those are the prerequisite basic knowledge students holding before entrancing universities. In the first-year university level, students will be quickly revised those basic knowledge and will be then introduced to a more complicated topic—electric field due to continuous charged distributions. We initially found that our freshman students, who were from the Faculty of Science and enrolled in the introductory physic course (SCPY 158), often seriously struggled with the basic physics concepts—superposition of electric fields and inverse square law and mathematics being relevant to this topic. These also then resulted on students’ understanding of advanced topics within the course such as Gauss's law, electric potential difference, and capacitance. Therefore, it is very important to determine students' understanding of electric field due to continuous charged distributions. The open-ended question about sketching net electric field vectors from a uniformly charged insulating rod was administered to 260 freshman science students as pre- and post-tests. All of their responses were analyzed and classified into five levels of understandings. To get deep understanding of each level, 30 students were interviewed toward their individual responses. The pre-test result found was that about 90% of students had incorrect understanding. Even after completing the lectures, there were only 26.5% of them could provide correct responses. Up to 50% had confusions and irrelevant ideas. The result implies that teaching methods in Thai high schools may be problematic. In addition for our benefit, these students’ alternative conceptions identified could be used as a guideline for developing the instructional method currently used in the course especially for teaching electrostatics.

Keywords: alternative conceptions, electric field of continuous charged distributions, inverse square law, levels of student understandings, superposition principle

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Authors: Xin Tong, Jin-sheng Xu, Xiong Chen, Ya Zheng

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The aim of this paper is to study the mechanical properties of HTPB (Hydroxyl-terminated polybutadiene) composite propellant under harsh conditions. It describes two tests involving uniaxial tensile tests of various strain rates (ranging from 0.0005 s^-1 to 1.5 s^-1), temperatures (ranging from 223 K to 343 K) and high-cycle fatigue tests under low-temperature (223 K, frequencies were set at 50, 100, 150 Hz) using DMA (Dynamic Mechanical Analyzer). To highlight the effect of small pre-strain on fatigue properties of HTPB propellant, quasi-static stretching was carried out before fatigue loading, and uniaxial tensile tests at constant strain rates were successively applied. The results reveal that flow stress of propellant increases with reduction in temperature and rise in strain rate, and the strain rate-temperature equivalence relationship could be described by TTSP (time-temperature superposition principle) incorporating a modified WLF equation. Moreover, the rate of performance degradations and damage accumulation of propellant during fatigue tests increased with increasing strain amplitude and loading frequencies, while initial quasi-static loading has a negative effect on fatigue properties by comparing stress-strain relations after fatigue tests.

Keywords: fatigue, HTPB propellant, tensile properties, time-temperature superposition principle

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Authors: K. A. Weidenmann, M. Grigo, B. Brylka, P. Elsner, T. Böhlke

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In order to reduce fuel consumption, the weight of automobiles has to be reduced. Fiber reinforced polymers offer the potential to reach this aim because of their high stiffness to weight ratio. Additionally, the use of fiber reinforced polymers in automotive applications has to allow for an economic large-scale production. In this regard, long fiber reinforced thermoplastics made by direct processing offer both mechanical performance and processability in injection moulding and compression moulding. The work presented in this contribution deals with long glass fiber reinforced polypropylene directly processed in compression moulding (D-LFT). For the use in automotive applications both the temperature and the time dependency of the materials properties have to be investigated to fulfill performance requirements during crash or the demands of service temperatures ranging from -40 °C to 80 °C. To consider both the influence of temperature and time, quasistatic tensile tests have been carried out at different temperatures. These tests have been complemented by high speed tensile tests at different strain rates. As expected, the increase in strain rate results in an increase of the elastic modulus which correlates to an increase of the stiffness with decreasing service temperature. The results are in good accordance with results determined by dynamic mechanical analysis within the range of 0.1 to 100 Hz. The experimental results from different testing methods were grouped and interpreted by using different time temperature shift approaches. In this regard, Williams-Landel-Ferry and Arrhenius approach based on kinetics have been used. As the theoretical shift factor follows an arctan function, an empirical approach was also taken into consideration. It could be shown that this approach describes best the time and temperature superposition for glass fiber reinforced polypropylene manufactured by D-LFT processing.

Keywords: composite, dynamic mechanical analysis, long fibre reinforced thermoplastics, mechanical properties, time temperature superposition

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Authors: V. V. Fomin, A. P. Mikhailovich, E. M. Agapitov, V. E. Rogachev, E. A. Kostousova, E. S. Perekhodova

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Ground-level landscape photos can be used as a source of objective data on woody vegetation and vegetation dynamics. We proposed a method for processing, analyzing, and presenting ground photographs, which has the following advantages: 1) researcher has to form holistic representation of the study area in form of a set of interlapping ground-level landscape photographs; 2) it is necessary to define or obtain characteristics of the landscape, objects, and phenomena present on the photographs; 3) it is necessary to create new or supplement existing textual descriptions and annotations for the ground-level landscape photographs; 4) single or multiple ground-level landscape photographs can be used to develop specialized geoinformation layers, schematic maps or thematic maps; 5) it is necessary to determine quantitative data that describes both images as a whole, and displayed objects and phenomena, using algorithms for automated image analysis. It is suggested to match each photo with a polygonal geoinformation layer, which is a sector consisting of areas corresponding with parts of the landscape visible in the photos. Calculation of visibility areas is performed in a geoinformation system within a sector using a digital model of a study area relief and visibility analysis functions. Superposition of the visibility sectors corresponding with various camera viewpoints allows matching landscape photos with each other to create a complete and wholesome representation of the space in question. It is suggested to user-defined data or phenomenons on the images with the following superposition over the visibility sector in the form of map symbols. The technology of geoinformation layers’ spatial superposition over the visibility sector creates opportunities for image geotagging using quantitative data obtained from raster or vector layers within the sector with the ability to generate annotations in natural language. The proposed method has proven itself well for relatively open and clearly visible areas with well-defined relief, for example, in mountainous areas in the treeline ecotone. When the polygonal layers of visibility sectors for a large number of different points of photography are topologically superimposed, a layer of visibility of sections of the entire study area is formed, which is displayed in the photographs. Also, as a result of this overlapping of sectors, areas that did not appear in the photo will be assessed as gaps. According to the results of this procedure, it becomes possible to obtain information about the photos that display a specific area and from which points of photography it is visible. This information may be obtained either as a query on the map or as a query for the attribute table of the layer. The method was tested using repeated photos taken from forty camera viewpoints located on Ray-Iz mountain massif (Polar Urals, Russia) from 1960 until 2023. It has been successfully used in combination with other ground-based and remote sensing methods of studying the climate-driven dynamics of woody vegetation in the Polar Urals. Acknowledgment: This research was collaboratively funded by the Russian Ministry for Science and Education project No. FEUG-2023-0002 (image representation) and Russian Science Foundation project No. 24-24-00235 (automated textual description).

Keywords: woody, vegetation, repeated, photographs

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Authors: Jay Xiong, Li Lin

Abstract:

Existing software modeling and visualization approaches using UML are outdated, which are outcomes of reductionism and the superposition principle that the whole of a system is the sum of its parts, so that with them all tasks of software modeling and visualization are performed linearly, partially, and locally. This paper introduces revolutionary solutions for modeling and visualization of complex software systems, which make complex software systems much easy to understand, test, and maintain. The solutions are based on complexity science, offering holistic, automatic, dynamic, virtual, and executable approaches about thousand times more efficient than the traditional ones.

Keywords: complex systems, software maintenance, software modeling, software visualization

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Authors: Abir Abdessalem, Sahbi Tamboura, J. Fitoussi, Hachmi Ben Daly, Abbas Tcharkhtchi

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Dynamic mechanical analysis (DMA) is one of the most used experimental techniques to investigate the temperature and frequency dependence of the mechanical behavior of viscoelastic materials. The measured data are generally shifted by the application of the principle of the time– temperature superposition (TTS) to obtain the viscoelastic system’s master curve. The aim of this work is to show the methodology to define the horizontal shift factor to be applied to the storage modulus measured in order to indicate the validity of (TTS) principle for this material system. This principle was successfully used to determine the long-term properties of the Sheet Moulding Compound (SMC) composites.

Keywords: composite material, dynamic mechanical analysis, SMC composites, viscoelastic behavior, modeling

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Authors: Etienne K. Ngoy

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This analysis suggests that the comprehensive degradation caused by any environmental factor on fiber reinforced plastics under mechanical stress can be measured as a change in viscoelastic properties of the material. The change in viscoelastic characteristics is experimentally determined as a time-dependent function expressing the amplification of the stress relaxation. The variation of this experimental function provides a measure of the environmental degradation rate. Where real service environment conditions can be reliably simulated in the laboratory, it is possible to generate master curves that include environmental degradation effect and hence predict the durability of the fiber reinforced plastics under environmental degradation.

Keywords: environmental effects, fiber reinforced plastics durability, prediction, stress effect

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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: Djamal Hamadi, Ashraf Ayoub, Ounis Abdelhafid, Chebili Rachid

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In this paper, a new computationally-efficient rectangular flat shell finite element named 'ACM_RSBEC' is presented. The formulated element is obtained by superposition of a new rectangular membrane element 'RSBEC' based on the strain approach and the well known plate bending element 'ACM'. This element can be used for the analysis of thin shell structures, no matter how the geometrical shape might be. Tests on standard problems have been examined. The convergence of the new formulated element is also compared to other types of quadrilateral shell elements. The presented shell element ‘ACM_RSBEC’ has been demonstrated to be effective and useful in analysing thin shell structures.

Keywords: finite element, flat shell element, strain based approach, static condensation

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Authors: H. Babou, S. Ridjla, B. Amerate, R. Ferhoum, M. Aberkane

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This work is devoted to the experimental study of thermal ageing effect on the mechanical and micro structural behavior of polycarbonate (PC). A simple compression tests, micro hardness and an IRTF analysis were completed in order to characterize the response of material on specimens after ageing at a temperature of order 100 C° and for serval maintain duration 72, 144 and 216 hours. These investigations showed a decrease of the intrinsic properties of polycarbonate (Young modulus, yield stress, etc.); the superposition of spectra IRTF shows that the intensity of chemical connections C=C, C-O, CH3 and C-H are influenced by the duration of thermal ageing; in addition, an increase of 30 % of micro hardness was detected after 216 hour of ageing.

Keywords: amorphous polymer, polycarbonate, mechanical behavior, compression test, thermal ageing

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Authors: Kittipong Tripetch

Abstract:

This paper proposes for the first time symbolic formula of the power spectrum of cross couple oscillator and its modified circuit. Many principle existed to derived power spectrum in microwave textbook such as impedance, admittance parameters, ABCD, H parameters, etc. It can be compared by graph of power spectrum which methodology is the best from the point of view of practical measurement setup such as condition of impedance parameter which used superposition of current to derived (its current injection of the other port of the circuit is zero, which is impossible in reality). Four Graphs of impedance parameters of cross couple oscillator is proposed. After that four graphs of Scattering parameters of cross couple oscillator will be shown.

Keywords: optimization, power spectrum, impedance parameters, scattering parameter

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Authors: Mandip Singh

Abstract:

Quantum entanglement plays a fundamental role in our understanding of counter-intuitive aspects of quantum reality. If classical physics is an approximation of quantum physics, then quantum entanglement should persist at a macroscopic scale. In this paper, a thought experiment is presented where a free falling spin polarized Bose-Einstein condensate interacts with a quantum superimposed magnetic field of nonzero gradient. In contrast to the semiclassical Stern-Gerlach experiment, the magnetic field and the spin degrees of freedom both are considered to be quantum mechanical in a generalized scenario. As a consequence, a Bose-Einstein condensate can be prepared at distinct locations in space in a sense of quantum superposition. In addition, the generation of Schrodinger-cat like quantum states shall be presented.

Keywords: Schrodinger-cat quantum states, macroscopic entanglement, macroscopic quantum fields, foundations of quantum physics

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Sven Krabbenhoft, Kristian Krabbenhoft, Lars Damkilde

Abstract:

The problem of determining the bearing capacity of a strip foundation located near a slope of infinite height has been dealt with by several authors. Very often in practical problems the slope is of limited height, and furthermore the resulting load may be inclined at an angle to the horizontal, and in such cases the bearing capacity of the footing cannot be found using the existing methods. The present work comprises finite element based upper- and lower-bound calculations, using the geotechnical software OptumG2 to investigate the effect of the slope height and horizontal forces on the total bearing capacity, both without and with using superposition as presupposed in the traditional bearing capacity equation. The results for friction angles 30, 35 and 40 degrees, slope inclinations 1:2, 1:3 and 1:4, for selfweight and surcharge are given as charts showing the slope inclination factors suitable for design.

Keywords: footings, bearing capacity, slopes, cohesionnless soil

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Authors: Kittipong Tripetch

Abstract:

This paper proposes studies of input impedance of two types of the CMOS active inductor. It derives two input impedance formulas. The first formula is the input impedance of a grounded active inductor. The second formula is an input impedance of floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of a fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption

Keywords: grounded active inductor, floating active inductor, fully differential bandpass amplifier

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Authors: Asma Ben Yaghlane, Mohamed Naceur Azaiez

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In this paper, we treat a model that falls in the area of protecting targeted systems from intelligent threats including terrorism. We introduce the concept of system survivability, in the context of continuous attacks, as the probability that a system under attack will continue operation up to some fixed time t. We define a constant attack rate (CAR) process as an attack on a targeted system that follows an exponential distribution. We consider the superposition of several CAR processes. From the attacker side, we determine the optimal attack strategy that minimizes the system survivability. We also determine the optimal strengthening strategy that maximizes the system survivability under limited defensive resources. We use operations research techniques to identify optimal strategies of each antagonist. Our results may be used as interesting starting points to develop realistic protection strategies against intentional attacks.

Keywords: CAR processes, defense/attack strategies, exponential failure, survivability

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Authors: S. Levitsky, R. Bergman

Abstract:

Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.

Keywords: elastic tube, sound propagation, temperature effect, viscoelastic liquid

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Authors: Susmita Panda, Arnab Banerjee, Ajinkya Baxy, Bappaditya Manna

Abstract:

The design of short to medium-span high-speed bridges in critical locations is an essential aspect of vehicle-bridge interaction. Due to dynamic interaction between moving load and bridge, mathematical models or finite element modeling computations become time-consuming. Thus, to reduce the computational effort, a universal approximator using an artificial neural network (ANN) has been used to evaluate the dynamic response of the bridge. The data set generation and training of surrogate models have been conducted over the results obtained from mathematical modeling. Further, the robustness of the surrogate model has been investigated, which showed an error percentage of less than 10% with conventional methods. Additionally, the dependency of the dynamic response of the bridge on various load and bridge parameters has been highlighted through a parametric study.

Keywords: artificial neural network, mode superposition method, moving load analysis, surrogate models

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Ahmed Hammed, Wady Naanaa

Abstract:

In this paper, we propose a general approach to deal with the problem of a convolutive mixture of images. We use a direct blind source separation method by adding only one non-statistical justified constraint describing the relationships between different mixing matrix at the aim to make its resolution easy. This method can be applied, provided that this constraint is known, to degraded document affected by the overlapping of text-patterns and images. This is due to chemical and physical reactions of the materials (paper, inks,...) occurring during the documents aging, and other unpredictable causes such as humidity, microorganism infestation, human handling, etc. We will demonstrate that this problem corresponds to a convolutive mixture of images. Subsequently, we will show how the validation of our method through numerical examples. We can so obtain clear images from unreadable ones which can be caused by pages superposition, a phenomenon similar to that we find every often in archival documents.

Keywords: blind source separation, convoluted mixture, degraded documents, text-patterns overlapping

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Authors: G. Balogh, I. A. Szabó, P.Z. Kovács

Abstract:

Mechanical stress has a strong effect on the magnitude of the Barkhausen-noise in structural steels. Because the measurements are performed at the surface of the material, for a sample sheet, the full effect can be described by a biaxial stress field. The measured Barkhausen-noise is dependent on the orientation of the exciting magnetic field relative to the axis of the stress tensor. The sample inhomogenities including the residual stress also modifies the angular dependence of the measured Barkhausen-noise. We have developed a laboratory device with a cross like specimen for bi-axial bending. The measuring head allowed performing excitations in two orthogonal directions. We could excite the two directions independently or simultaneously with different amplitudes. The simultaneous excitation of the two coils could be performed in phase or with a 90 degree phase shift. In principle this allows to measure the Barkhausen-noise at an arbitrary direction without moving the head, or to measure the Barkhausen-noise induced by a rotating magnetic field if a linear superposition of the two fields can be assumed.

Keywords: Barkhausen-noise, bi-axial stress, stress measuring, stress dependency

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Authors: Mona Mihailescu, Rebeca Tudor, Irina A. Paun, Cristian Kusko, Eugen I. Scarlat, Mihai Kusko

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Specific intensity distributions in the laser beams are required in many fields: optical communications, material processing, microscopy, optical tweezers. In optical communications, the information embedded in specific beams and the superposition of multiple beams can be used to increase the capacity of the communication channels, employing spatial modulation as an additional degree of freedom, besides already available polarization and wavelength multiplexing. In this regard, optical vortices present interest due to their potential to carry independent data which can be multiplexed at the transmitter and demultiplexed at the receiver. Also, in the literature were studied their combinations: 1) axial or perpendicular superposition of multiple optical vortices or 2) with other laser beam types: Bessel, Airy. Optical vortices, characterized by stationary ring-shape intensity and rotating phase, are achieved using computer generated holograms (CGH) obtained by simulating the interference between a tilted plane wave and a wave passing through a helical phase object. Here, we propose a method to combine information through the reunion of two CGHs. One is obtained using the helical phase distribution, characterized by its topological charge, m. The other is obtained using conical phase distribution, characterized by its radial factor, r0. Each CGH is obtained using plane wave with different tilts: km and kr for CGH generated from helical phase object and from conical phase object, respectively. These reunions of two CGHs are calculated to be phase optical elements, addressed on the liquid crystal display of a spatial light modulator, to optically process the incident beam for investigations of the diffracted intensity pattern in far field. For parallel reunion of two CGHs and high values of the ratio between km and kr, the bright ring from the first diffraction order, specific for optical vortices, is changed in an asymmetric intensity pattern: a number of circle arcs. Both diffraction orders (+1 and -1) are asymmetrical relative to each other. In different planes along the optical axis, it is observed that this asymmetric intensity pattern rotates around its centre: in the +1 diffraction order the rotation is anticlockwise and in the -1 diffraction order, the rotation is clockwise. The relation between m and r0 controls the diameter of the circle arcs and the ratio between km and kr controls the number of arcs. For perpendicular reunion of the two CGHs and low values of the ratio between km and kr, the optical vortices are multiplied and focalized in different planes, depending on the radial parameter. The first diffraction order contains information about both phase objects. It is incident on the phase masks placed at the receiver, computed using the opposite values for topological charge or for the radial parameter and displayed successively. In all, the proposed method is exploited in terms of constructive parameters, for the possibility offered by the combination of different types of beams which can be used in robust optical communications.

Keywords: asymmetrical diffraction orders, computer generated holograms, conical phase distribution, optical vortices, spatial light modulator

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Authors: Svetlana Nikitenkova, Dmitry Kovriguine

Abstract:

Stationary energy partition between waves in a one dimensional carbyne chain at ambient temperatures is investigated. The study is carried out by standard asymptotic methods of nonlinear dynamics in the framework of classical mechanics, based on a simple mathematical model, taking into account central and noncentral interactions between carbon atoms. Within the first-order nonlinear approximation analysis, triple-mode resonant ensembles of quasi-harmonic waves are revealed. Any resonant triad consists of a single primary high-frequency longitudinal mode and a pair of secondary low-frequency transverse modes of oscillations. In general, the motion of the carbyne chain is described by a superposition of resonant triads of various spectral scales. It is found that the stationary energy distribution is obeyed to the classical Rayleigh–Jeans law, at the expense of the proportional amplitude dispersion, except a shift in the frequency band, upwards the spectrum.

Keywords: resonant triplet, Rayleigh–Jeans law, amplitude dispersion, carbyne

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Authors: Souici Abdelaziz, Tehami Mohamed, Rahal Nacer, Said Mohamed Bekkouche, Berthet Jean-Fabien

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In this paper, the influence of the concrete slab creep on the initial deformability of a bent composite beam is modelled. This deformability depends on the rate of creep. This means the rise in value of the longitudinal strain ε c(x,t), the displacement D eflec(x,t) and the strain energy E(t). The variation of these three parameters can easily affect negatively the good appearance and the serviceability of the structure. Therefore, an analytical approach is designed to control the status of the deformability of the beam at the instant t. This approach is based on the Boltzmann’s superposition principle and very particularly on the irreversible law of deformation. For this, two conditions of compatibility and two other static equilibrium equations are adopted. The two first conditions are set according to the rheological equation of Dischinger. After having done a mathematical arrangement, we have reached a system of two differential equations whose integration allows to find the mathematical expression of each generalized internal force in terms of the ability of the concrete slab to creep.

Keywords: composite section, concrete, creep, deformation, differential equation, time

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Authors: Yehuda Roth

Abstract:

In quantum theory, a system’s time evolution is predictable unless an observer performs measurement, as the measurement process can randomize the system. This randomness appears when the measuring device does not accurately describe the measured item, i.e., when the states characterizing the measuring device appear as a superposition of those being measured. When such a mismatch occurs, the measured data randomly collapse into a single eigenstate of the measuring device. This scenario resembles the interpretation process in which the observer does not experience an objective reality but interprets it based on preliminary descriptions initially ingrained into his/her mind. This distinction is the motivation for the present study in which the collapse scenario is regarded as part of the interpretation process of the observer. By adopting the formalism of the quantum theory, we present a complete mathematical approach that describes the interpretation process. We demonstrate this process by applying the proposed interpretation formalism to the ambiguous image "My wife and mother-in-law" to identify whether a woman in the picture is young or old.

Keywords: quantum-like interpretation, ambiguous image, determination, quantum-like collapse, classified representation

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