Search results for: finite quantum systems

Authors: Hasan Fatih Ertuğrul, Beytullah Okur, Huseyin Üvet, Kadir Erkan

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The objective of this paper is to analyze a 4-pole hybrid magnetic levitation system by using 3D finite element and analytical methods. The magnetostatic analysis of the system is carried out by using ANSYS MAXWELL-3D package. An analytical model is derived by magnetic equivalent circuit (MEC) method. The purpose of magnetostatic analysis is to determine the characteristics of attractive force and rotational torques by the change of air gap clearances, inclination angles and current excitations. The comparison between 3D finite element analysis and analytical results are presented at the rest of the paper.

Keywords: yoke hybrid electromagnet, 3D finite element analysis, magnetic levitation system, magnetostatic analysis

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Authors: Bruna G. M. Araújo, Pedro M. M. Q. Cruz

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In this letter, we review the literature of the major concepts that govern Gaussian quantum information. As we work with quantum information and computation with continuous variables, Gaussian states are needed to better describe these systems. Analyzing a single ion locked in a Paul trap we use the interaction picture to obtain a toolbox of Gaussian operations with the ion-laser interaction Hamiltionian. This is achieved exciting the ion through the combination of two lasers of distinct frequencies corresponding to different sidebands of the external degrees of freedom. First we study the case of a trap with 1 mode and then the case with 2 modes. In this way, we achieve different continuous variables gates just by changing the external degrees of freedom of the trap and combining the Hamiltonians of blue and red sidebands.

Keywords: Paul trap, ion-laser interaction, Gaussian operations

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Mojtaba Valinataj

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Reversible logic as a new favorable design domain can be used for various fields especially creating quantum computers because of its speed and intangible power consumption. However, its susceptibility to a variety of environmental effects may lead to yield the incorrect results. In this paper, because of the importance of multiplication operation in various computing systems, some novel reversible logic array multipliers are proposed with error detection capability by incorporating the parity-preserving gates. The new designs are presented for two main parts of array multipliers, partial product generation and multi-operand addition, by exploiting the new arrangements of existing gates, which results in two signed parity-preserving array multipliers. The experimental results reveal that the best proposed 4×4 multiplier in this paper reaches 12%, 24%, and 26% enhancements in the number of constant inputs, number of required gates, and quantum cost, respectively, compared to previous design. Moreover, the best proposed design is generalized for n×n multipliers with general formulations to estimate the main reversible logic criteria as the functions of the multiplier size.

Keywords: array multipliers, Baugh-Wooley method, error detection, parity-preserving gates, quantum computers, reversible logic

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Authors: Boukelkoul Lahcen

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The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: cost, finite state, Markov model, operation and maintenance

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Authors: Prawal Sinha, Peeyush Singh, Pravir Dutt

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Problems in elastohydrodynamic lubrication have attracted a lot of attention in the last few decades. Solving a two-dimensional problem has always been a big challenge. In this paper, a new discontinuous finite volume method (DVM) for two-dimensional point contact Elastohydrodynamic Lubrication (EHL) problem has been developed and analyzed. A complete algorithm has been presented for solving such a problem. The method presented is robust and easily parallelized in MPI architecture. GMRES technique is implemented to solve the matrix obtained after the formulation. A new approach is followed in which discontinuous piecewise polynomials are used for the trail functions. It is natural to assume that the advantages of using discontinuous functions in finite element methods should also apply to finite volume methods. The nature of the discontinuity of the trail function is such that the elements in the corresponding dual partition have the smallest support as compared with the Classical finite volume methods. Film thickness calculation is done using singular quadrature approach. Results obtained have been presented graphically and discussed. This method is well suited for solving EHL point contact problem and can probably be used as commercial software.

Keywords: elastohydrodynamic, lubrication, discontinuous finite volume method, GMRES technique

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Authors: Tokuei Sako

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Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

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Authors: Felix Givois, Nicolas R. Gauger, Matthias Kabel

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The efficient digital material characterization is of great interest to many fields of application. It consists of the following three steps. First, a 3D reconstruction of 2D scans must be performed. Then, the resulting gray-value image of the material sample is enhanced by image processing methods. Finally, partial differential equations (PDE) are solved on the segmented image, and by averaging the resulting solutions fields, effective properties like stiffness or conductivity can be computed. Due to the high resolution of current CT images, the latter is typically performed with matrix-free solvers. Among them, a solver that uses the explicit formula of the Green-Eshelby operator in Fourier space has been proposed by Moulinec and Suquet. Its algorithmic, most complex part is the Fast Fourier Transformation (FFT). In our talk, we will discuss the potential quantum advantage that can be obtained by replacing the FFT with the Quantum Fourier Transformation (QFT). We will especially show that the data transfer for noisy intermediate-scale quantum (NISQ) devices can be improved by using appropriate boundary conditions for the PDE, which also allows using semi-classical versions of the QFT. In the end, we will compare the results of the QFT-based algorithm for simple geometries with the results of the FFT-based homogenization method.

Keywords: most likelihood amplitude estimation (MLQAE), numerical homogenization, quantum Fourier transformation (QFT), NISQ devises

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Authors: Pavan K. Rallabandi, Kailash C. Patidar

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In this paper, we present an optimization technique or a learning algorithm using the hybrid architecture by combining the most popular sequence recognition models such as Recurrent Neural Networks (RNNs) and Hidden Markov models (HMMs). In order to improve the sequence or pattern recognition/ classification performance by applying a hybrid/neural symbolic approach, a gradient descent learning algorithm is developed using the Real Time Recurrent Learning of Recurrent Neural Network for processing the knowledge represented in trained Hidden Markov Models. The developed hybrid algorithm is implemented on automata theory as a sample test beds and the performance of the designed algorithm is demonstrated and evaluated on learning the deterministic finite state automata.

Keywords: hybrid systems, hidden markov models, recurrent neural networks, deterministic finite state automata

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Jing-Gang Xie

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The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: general relativity theory, particles, photons, Quantum Gravity Model, gravitational frequency shift

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Tobias Horstmann, Thomas Le Garrec, Daniel-Ciprian Mincu, Emmanuel Lévêque

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Despite the efficiency and low dissipation of the stream-collide formulation of the Lattice Boltzmann (LB) algorithm, which is nowadays implemented in many commercial LBM solvers, there are certain situations, e.g. mesh transition, in which a classical finite-volume or finite-difference formulation of the LB algorithm still bear advantages. In this paper, we present an algorithm that combines the node-based streaming of the distribution functions with a second-order finite volume discretization of the advection term of the BGK-LB equation on a uniform D2Q9 lattice. It is shown that such a coupling is possible for a multi-domain approach as long as the overlap, or buffer zone, between two domains, is achieved on at least 2Δx. This also implies that a direct coupling (without buffer zone) of a stream-collide and finite-volume LB algorithm on a single grid is not stable. The critical parameter in the coupling is the CFL number equal to 1 that is imposed by the stream-collide algorithm. Nevertheless, an explicit filtering step on the finite-volume domain can stabilize the solution. In a further investigation, we demonstrate how such a coupling can be used for mesh transition, resulting in an intrinsic conservation of mass over the interface.

Keywords: algorithm coupling, finite volume formulation, grid refinement, Lattice Boltzmann method

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Authors: H. R. Fazlollahi

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Dark Energy origin is unknown and so describing this mysterious component in large scale structure needs to manipulate our theories in general relativity. Although in most models, dark energy arises from extra terms through modifying Einstein-Hilbert action, maybe its origin traces back to fundamental aspects of ground energy of space-time given in quantum mechanics. Hence, diluting space-time in general relativity with quantum mechanics properties leads to the Karolyhazy relation corresponding energy density of quantum fluctuations of space-time. Through generalized uncertainty principle and an eye to Karolyhazy approach in this study we extend energy density of quantum fluctuations of space-time. Also, the application of this idea is considered in late time evolution and we have shown how extra term in generalized uncertainty principle plays as a plausible interaction term role in suggested model.

Keywords: generalized uncertainty principle, karolyhazy approach, agegraphic dark energy, cosmology

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Authors: Woosuk Lee

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We controlled the electron injection rate in inverted quantum dot light-emitting diode (QLED) by inserting PEIE layer between ZnO electron transport layer(ETL) and quantum dots(QDs) layer and successfully demonstrated high efficiency of QLEDs. The inverted QLED has the layer structure of ITO(cathode)/ ZnO NPs/PEIE/QDs/PEIE/P-TPD/MoO3/Al(anode). The PEIE between poly-TPD hole transport layer (HTL) and quantum dot emitting layer protects QD EML during HTL coating process and improves the surface morphology. In addition, the hole injection barrier is reduced by upshifting the valence band maximum (VBM) of QDs. An additional layer of PEIE was introduced between ZnO and QD to balance charge within QD emissive layer in device, which serves as an effective electron blocking layer without changing device operating condition such as turn-on voltage and emissive spectra. As a result, the optimized QLED with 5nm PEIE shows a ~36% improved current efficiency and external quantum efficiency (EQE) compared to the QLED without PEIE.(maximum current efficiency, and EQE are achieved 70cd/A and 17.3%, respectively). In particular, the maximum brightness of the optimized QLED dramatically improved by a factor of 2.3 relative to the QLED without PEIE. The main reasons for these QLED performance improvement are due to the suppressing the leakage current across the device and well confined exciton by inserting PEIE layers.

Keywords: quantum dot light-emitting diodes, interfacial layer, charge-injection balance, suppressing QD charging

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Authors: Yang Cao

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Analyzing the oral production of Chinese-speaking learners of English as a second language (L2), we can find a large variety of verb inflections – Why does it seem so hard for them to use consistent correct past morphologies in obligatory past contexts? Failed Functional Features Hypothesis (FFFH) attributes the rather non-target-like performance to the absence of [±past] feature in their L1 Chinese, arguing that for post puberty learners, new features in L2 are no more accessible. By contrast, Missing Surface Inflection Hypothesis (MSIH) tends to believe that all features are actually acquirable for late L2 learners, while due to the mapping difficulties from features to forms, it is hard for them to realize the consistent past morphologies on the surface. However, most of the studies are limited to the verb morphologies in finite clauses and few studies have ever attempted to figure out these learners’ performance in non-finite clauses. Additionally, it has been discussed that Chinese learners may be able to tell the finite/infinite distinction (i.e. the [±finite] feature might be selected in Chinese, even though the existence of [±past] is denied). Therefore, adopting a self-paced reading task (SPR), the current study aims to analyze the processing patterns of Chinese-speaking learners of L2 Russian, in order to find out if they are sensitive to misuse of tense morphologies in both finite and non-finite clauses and whether they are sensitive to the finite/infinite distinction presented in Russian. The study targets L2 Russian due to its systematic morphologies in both present and past tenses. A native Russian group, as well as a group of English-speaking learners of Russian, whose L1 has definitely selected both [±finite] and [±past] features, will also be involved. By comparing and contrasting performance of the three language groups, the study is going to further examine and discuss the two theories, FFFH and MSIH. Preliminary hypotheses are: a) Russian native speakers are expected to spend longer time reading the verb forms which violate the grammar; b) it is expected that Chinese participants are, at least, sensitive to the misuse of inflected verbs in non-finite clauses, although no sensitivity to the misuse of infinitives in finite clauses might be found. Therefore, an interaction of finite and grammaticality is expected to be found, which indicate that these learners are able to tell the finite/infinite distinction; and c) having selected [±finite] and [±past], English-speaking learners of Russian are expected to behave target-likely, supporting L1 transfer.

Keywords: features, finite clauses, morphosyntax, non-finite clauses, past morphologies, present morphologies, Second Language Acquisition, self-paced reading task, verb inflections

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Authors: Deborah Eric, Abbas Ahmad Khan

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Lead halide perovskites quantum dots have attracted immense scientific and technological interest for successful photovoltaic applications because of their remarkable optoelectronic properties. In this paper, we have simulated CsMAPbI3-xBrx based quantum dots to implement their use in intermediate band solar cells (IBSC). These types of materials exhibit optical and electrical properties distinct from their bulk counterparts due to quantum confinement. The conceptual framework provides a route to analyze the electronic properties of quantum dots. This layer of quantum dots optimizes the position and bandwidth of IB that lies in the forbidden region of the conventional bandgap. A three-dimensional MAPbI3 quantum dot (QD) with geometries including spherical, cubic, and conical has been embedded in the CsPbBr3 matrix. Bound energy wavefunction gives rise to miniband, which results in the formation of IB. If there is more than one miniband, then there is a possibility of having more than one IB. The optimization of QD size results in more IBs in the forbidden region. One band time-independent Schrödinger equation using the effective mass approximation with step potential barrier is solved to compute the electronic states. Envelope function approximation with BenDaniel-Duke boundary condition is used in combination with the Schrödinger equation for the calculation of eigen energies and Eigen energies are solved for the quasi-bound states using an eigenvalue study. The transfer matrix method is used to study the quantum tunneling of MAPbI3 QD through neighbor barriers of CsPbI3. Electronic states are computed using Schrödinger equation with effective mass approximation by considering quantum dot and wetting layer assembly. Results have shown the varying the quantum dot size affects the energy pinning of QD. Changes in the ground, first, second state energies have been observed. The QD is non-zero at the center and decays exponentially to zero at boundaries. Quasi-bound states are characterized by envelope functions. It has been observed that conical quantum dots have maximum ground state energy at a small radius. Increasing the wetting layer thickness exhibits energy signatures similar to bulk material for each QD size.

Keywords: perovskite, intermediate bandgap, quantum dots, miniband formation

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Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi

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This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

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Authors: Jean Marriz M. Manzano, Marc D. Rosales, Magdaleno R. Vasquez Jr., Maria Theresa G. De Leon

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This paper discusses the effects of surface roughness on a cantilever beam vibrational energy harvester. A silicon sample was fabricated using MEMS fabrication processes. When etching silicon using deep reactive ion etching (DRIE) at large etch depths, rougher surfaces are observed as a result of increased response in process pressure, amount of coil power and increased helium backside cooling readings. To account for the effects of surface roughness on the characteristics of the cantilever beam, finite element method (FEM) modeling was performed using actual roughness data from fabricated samples. It was found that when etching about 550um of silicon, root mean square roughness parameter, Sq, varies by 1 to 3 um (at 100um thick) across a 6-inch wafer. Given this Sq variation, FEM simulations predict an 8 to148 Hz shift in the resonant frequency while having no significant effect on the output power. The significant shift in the resonant frequency implies that careful consideration of surface roughness from fabrication processes must be done when designing energy harvesters.

Keywords: deep reactive ion etching, finite element method, microelectromechanical systems, multiphysics analysis, surface roughness, vibrational energy harvester

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Authors: Riya Roy, Anjana Bhasi

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Column-supported embankments provide a practical and efficient solution for construction on soft soil due to the low cost and short construction times. In the recent years, geosynthetic have been used in combination with column systems to support embankments. The load transfer mechanism in these systems is a combination of soil arching effect, which occurs between columns and membrane effect of the geosynthetic. This paper aims at the study of soil arching effect on columnar embankments using finite element software, ABAQUS. An axisymmetric finite element model is generated and using this model, parametric studies are carried out. Thus the effects of various factors such as height of embankment fill, elastic modulus of pile and tensile stiffness of geosynthetic, on soil arching have been studied. The development of negative skin friction along the pile-soil interface have also been studied and the results obtained from this study are compared with the current design methods.

Keywords: ABAQUS, geosynthetic, negative skin friction, soil arching

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Authors: Nikhil Padhye, Ellen Kintz, Dan Dorci

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Recent years have seen a rising interest in study and applications of materially uniform thin-structures (plates/shells) subject to finite-bending and stretching deformations. We introduce a well-posed 2D-model involving finite-bending and stretching of thin-structures to approximate the three-dimensional equilibria. Key features of this approach include: Non-Uniform Rational B-Spline (NURBS)-based spatial discretization for finite elements, method of dynamic relaxation to predict stable equilibria, and no a priori kinematic assumption on the deformation fields. The approach is validated against the benchmark problems,and the use of NURBS for spatial discretization facilitates exact spatial representation and computation of curvatures (due to C1-continuity of interpolated displacements) for this higher-order accuracy 2D-model.

Keywords: Isogeometric Analysis, Plates/Shells , Finite Element Methods, Dynamic Relaxation

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Authors: Temami Oussama, Bessais Lakhdar, Hamadi Djamal, Abderrahmani Sifeddine

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The analysis of complex structures encourages the engineer to make simplifying assumptions, sometimes attempting the analysis of the whole structure as complex as it is, and it can be done using the finite element method (FEM). In the modeling of complex structures by finite elements, various elements can be used: beam element, membrane element, solid element, plates and shells elements. These elements formulated according to the classical formulation and do not generally share the same nodal degrees of freedom, which complicates the development of a compatible model. The compatibility of the elements with each other is often a difficult problem for modeling complicated structure. This compatibility is necessary to ensure the convergence. To overcome this problem, we have proposed finite elements with a rotational degree of freedom. The study used is based on the strain approach formulation with 2D and 3D formulation with different degrees of freedom at each node. For the comparison and confrontation of results; the finite elements available in ABAQUS/Standard are used.

Keywords: compatibility requirement, complex structures, finite elements, modeling, strain approach

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

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Authors: Michael Danilov, Sergei Iskakov, Vladimir Mazurenko

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The present paper describes a high-performance parallel realization of an exact diagonalization solver for quantum-electron models in a shared memory computing system. The proposed algorithm contains a storage format for efficient computing eigenvalues and eigenvectors of a quantum electron Hamiltonian matrix. The results of the test calculations carried out for 15 sites Hubbard model demonstrate reduction in the required memory and good multiprocessor scalability, while maintaining performance of the same order as compressed row storage.

Keywords: sparse matrix, compressed format, Hubbard model, Anderson model

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Authors: Yehuda Roth

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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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Authors: Hyun-Ho Lee, Kee-Won Kim

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The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: Wenjun Hou, Marek Perkowski

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The Traveling Salesman problem is famous in computing and graph theory. In short, it asks for the Hamiltonian cycle of the least total weight in a given graph with N nodes. All variations on this problem, such as those with K-bounded-degree nodes, are classified as NP-complete in classical computing. Although several papers propose theoretical high-level designs of quantum algorithms for the Traveling Salesman Problem, no quantum circuit implementation of these algorithms has been created up to our best knowledge. In contrast to previous papers, the goal of this paper is not to optimize some abstract complexity measures based on the number of oracle iterations, but to be able to evaluate the real circuit and time costs of the quantum computer. Using the emerging quantum programming language Q# developed by Microsoft, which runs quantum circuits in a quantum computer simulation, an implementation of the bounded-degree problem and its respective quantum circuit were created. To apply Grover’s algorithm to this problem, a quantum oracle was designed, evaluating the cost of a particular set of edges in the graph as well as its validity as a Hamiltonian cycle. Repeating the Grover algorithm with an oracle that finds successively lower cost each time allows to transform the decision problem to an optimization problem, finding the minimum cost of Hamiltonian cycles. N log₂ K qubits are put into an equiprobablistic superposition by applying the Hadamard gate on each qubit. Within these N log₂ K qubits, the method uses an encoding in which every node is mapped to a set of its encoded edges. The oracle consists of several blocks of circuits: a custom-written edge weight adder, node index calculator, uniqueness checker, and comparator, which were all created using only quantum Toffoli gates, including its special forms, which are Feynman and Pauli X. The oracle begins by using the edge encodings specified by the qubits to calculate each node that this path visits and adding up the edge weights along the way. Next, the oracle uses the calculated nodes from the previous step and check that all the nodes are unique. Finally, the oracle checks that the calculated cost is less than the previously-calculated cost. By performing the oracle an optimal number of times, a correct answer can be generated with very high probability. The oracle of the Grover Algorithm is modified using the recalculated minimum cost value, and this procedure is repeated until the cost cannot be further reduced. This algorithm and circuit design have been verified, using several datasets, to generate correct outputs.

Keywords: quantum computing, quantum circuit optimization, quantum algorithms, hybrid quantum algorithms, quantum programming, Grover’s algorithm, traveling salesman problem, bounded-degree TSP, minimal cost, Q# language

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Authors: Yuriy A. Shevchenko, Konstantin V. Nefedev

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We consider the antiferromagnetic systems of Ising spins located at the sites of the hexagonal, triangular and pyrochlore lattices. Such systems can be diluted to a certain concentration level by randomly replacing the magnetic spins with nonmagnetic ones. Quite recently we studied density of states (DOS) was calculated by the Wang-Landau method. Based on the obtained data, we calculated the dependence of the residual entropy (entropy at a temperature tending to zero) on the dilution concentration for quite large systems (more than 2000 spins). In the current study, we obtained the same data for small systems (less than 20 spins) by a complete search of all possible magnetic configurations and compared the result with the result for large systems. The shape of the curve remains unchanged in both cases, but the specific values of the residual entropy are different because of the finite size effect.

Keywords: entropy, pyrochlore, spin ice, Wang-Landau algorithm

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Authors: Sourabh R. Dinde, Rajshekar S. Talikoti

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According to the structural point of view Industrial Pallet rack structure can be considered typical steel framed structure. This work presents a general analysis of an industrial pallet rack structure, evaluating the influence of each of the components on the global stability. An analytical study for the sensitivity of pallet rack configuration in linear static equivalent lateral loads. The aim is to braced/unbraced frames were design and their analytical models are to be built in software. The finite element analysis is used to determine axial forces in beam and column, maximum storey displacement and buckling loads on braced/unbraced pallet rack structure. Bracing systems are mostly provided to enhance the stiffness factor of the structures with the seismic loads. Unbraced systems have mostly translational modes of failure and are very flexible due to excessive loads.

Keywords: buckling capacity, cold formed steel, finite element analysis, pallets Rrack, seismic design

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