Matrix method

دسترسی آزاد مقاله

1 - One-dimensional Fibonacci fractal photonic crystals and their optical characteristics
Mehdi Tavakoli Yousef Seyed Jalili

10.1007/s40094-014-0113-0

AbstractFibonacci fractal structures have been already studied. However, more special fractal structures could be beneficial in specific applications. In this paper, we create three variations of Fibonacci fractal photonic crystals as well as original structure, includi چکیده کامل

AbstractFibonacci fractal structures have been already studied. However, more special fractal structures could be beneficial in specific applications. In this paper, we create three variations of Fibonacci fractal photonic crystals as well as original structure, including: inverse Fibonacci fractal photonic crystal, mirror symmetry Fibonacci fractal photonic crystal (MSFFPC), and finally folded Fibonacci fractal photonic crystal. The transmission spectra of these structures are simulated and analyzed. Our findings show that presented structures have their own characteristics, therefore, can be used for different applications according to required specifications. Some MSFFPC structures, for instance, could be used to develop resonant microcavities with high Q factor that can be applicable in design and construction of ultrasensitive optical sensors with very high quality factor requirements. The narrower resonance peaks and the smaller amount of interfaces lead to a higher sensitivity for this structure. پرونده مقاله

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2 - Butterfly-like phase shift: a novel gauge for critical coupling of add–drop resonator
Mahdi Bahadoran Preecha Yupapin

10.1007/s40094-018-0291-2

AbstractOptical transfer function for add–drop resonator is derived in the presence of coupling loss using the scattering matrix method. A critical coupling condition for ADR is calculated. The response of the ADR under variation of coupling losses and coupling coeffici چکیده کامل

AbstractOptical transfer function for add–drop resonator is derived in the presence of coupling loss using the scattering matrix method. A critical coupling condition for ADR is calculated. The response of the ADR under variation of coupling losses and coupling coefficients is studied. The number of allowed states under the critical condition is determined. The full width at half maximum as sharp as 0.17 nm is achieved. It is found that the relative phase shifts of through and drop ports show the same responses under the critical coupling condition. This response emerges in a butterfly-like phase shift, which can be considered as a new evaluating factor for checking the system in critical coupling condition. پرونده مقاله

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3 - یک روش ماتریسی جهت برآورد ضرایب رگرسیون خطی مبتنی بر اعداد-زاده
سمیه ایزدی توفیق الهویرنلو

در این مقاله، یک روش جدید جهت برآورد تقریب ضرایب رگرسیون خطی مبتنی بر اعداد- زاده ارائه میشود. در این مدل مشاهدات اعداد حقیقی هستند و ضرایب رگرسیون و متغیر وابسته (y) مقادیری با ارزشگذاری اعداد-زاده هستند. جهت برآورد ضرایب این مدل ابتدا مدل رگرسیون خطی مبتنی بر اعد چکیده کامل

در این مقاله، یک روش جدید جهت برآورد تقریب ضرایب رگرسیون خطی مبتنی بر اعداد- زاده ارائه میشود. در این مدل مشاهدات اعداد حقیقی هستند و ضرایب رگرسیون و متغیر وابسته (y) مقادیری با ارزشگذاری اعداد-زاده هستند. جهت برآورد ضرایب این مدل ابتدا مدل رگرسیون خطی مبتنی بر اعداد-زاده را به دو مدل رگرسیون خطی فازی تبدیل کرده سپس دو مدل را به صورت دستگاه Ax=y  تبدیل میکنیم که در آن A ضریب رگرسیون خطی و x متغیر مستقل و y متغیر وابسته است.  در نهایت برای مینیمم سازی دستگاه فوق از روش مجموع مربعات خطا مبتنی بر فاصله d استفاده میکنیم. طی دو مثال نشان میدهیم که روش پیشنهادی از دقت مطلوبی جهت برآورد رگرسیون بر اساس اعداد فازی برخوردار است. پرونده مقاله

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4 - یافتن تجزیه‌ی قطبی یک ماتریس به وسیله‌ی یک روش تکراری کارا
فرشاد کیومرثی

هدف از این مقاله، مطالعه‌ی ساختن یک روش تکرار ماتریسی مرتبه بالاتر برای محاسبه‌ی تجزیه‌ی قطبی یک ماتریس مناسب می‌باشد. به‌طور تحلیلی نشان داده می‌شود که روش جدید همگراست و دارای مرتبه‌ی بالا است. نتایج مقاله به وسیله‌ی مثال‌های عددی به تصویر کشیده می‌شوند.

هدف از این مقاله، مطالعه‌ی ساختن یک روش تکرار ماتریسی مرتبه بالاتر برای محاسبه‌ی تجزیه‌ی قطبی یک ماتریس مناسب می‌باشد. به‌طور تحلیلی نشان داده می‌شود که روش جدید همگراست و دارای مرتبه‌ی بالا است. نتایج مقاله به وسیله‌ی مثال‌های عددی به تصویر کشیده می‌شوند. پرونده مقاله

دسترسی آزاد مقاله

5 - Free Torsional Vibration Analysis of Hollow and Solid Non-Uniform Rotating Shafts Using Distributed and Lumped Modeling Technique
A Saghafi M .A Azizi

10.22034/jsm.2021.1899087.1591

In this paper, the torsional free vibration of solid and hollow rotating shafts with non-uniform tapered elements are investigated. To this end, the exact solution and also transfer matrix for the free torsional vibration of a hollow tapered shaft element with uniform t چکیده کامل

In this paper, the torsional free vibration of solid and hollow rotating shafts with non-uniform tapered elements are investigated. To this end, the exact solution and also transfer matrix for the free torsional vibration of a hollow tapered shaft element with uniform thickness and also solid element are firstly obtained. Then, the natural frequencies are determined based on distributed and lumped modeling technique (DLMT). This technique is similar to transfer matrix method (TMM) but the exact solution is employed to obtain the transfer matrixes of the distributed element, therefore, there is no approximation and the natural frequencies and mode shapes are the exact values. To confirm the reliability of the presented method, the simulation results are compared with the results obtained from the other methods such as finite element method. It is shown that the proposed method provides highly accurate results and it can be simply applied to the complex torsional systems. پرونده مقاله

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6 - Dynamic Analysis of Offshore Wind Turbine Towers with Fixed Monopile Platform Using the Transfer Matrix Method
M Feyzollahzadeh M.J Mahmoodi

In this paper, an analytical method for vibrations analysis of offshore wind turbine towers with fixed monopile platform is presented. For this purpose, various and the most general models including CS, DS and AF models are used for modeling of wind turbine foundation a چکیده کامل

In this paper, an analytical method for vibrations analysis of offshore wind turbine towers with fixed monopile platform is presented. For this purpose, various and the most general models including CS, DS and AF models are used for modeling of wind turbine foundation and axial force is modeled as a variable force as well. The required equations for determination of wind turbine tower response excited by the Morrison force are derived based on Airy wave theory. The transfer matrix is derived for each element of the tower using Euler-Bernoulli’s beam differential equation and the global transfer matrix is obtained considering boundary conditions of the tower and constructing the point matrix. The effective wave force is intended in several case studies and Persian Gulf Environmental conditions are examined for the installation of wind farms. Finally, the obtained results by the transfer matrix method are compared with the results of the finite elements method and experimental data which show good agreement in spite of low computational cost. پرونده مقاله

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7 - Whirling Analysis of Axial-Loaded Multi-Step Timoshenko Rotor Carrying Concentrated Masses
K Torabi H Afshari H Najafi

In this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward f چکیده کامل

In this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward frequencies and corresponding modes are obtained using transfer matrix method (TMM). The effect of the angular velocity of spin, value of the translational and rotational inertia, position of the attached elements and applied axial force on the natural frequencies are investigated for various boundary conditions. پرونده مقاله

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8 - Generalization of Dodgson's "Virtual Center" Method; an Efficient Method for Determinant Calculation
Elyas Shivanian Alireza Soleimani

Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the چکیده کامل

Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtual center". پرونده مقاله

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9 - Designing real-time biosensors and chemical sensors based on symmetrical photonic crystal heterostructures
maryam sharifi Habib Tajalli Hamid Pashaei Adl Payman Tajalli

10.30495/ijbbo.2021.689422

In this paper, we introduce and analytically demonstrate a novel biosensor based on the light-matter interaction in a classic topological photonic crystal (PC) heterostructure, which consists of two opposite-facing 5-period PCs separated by a microfluidic channel. Becau چکیده کامل

In this paper, we introduce and analytically demonstrate a novel biosensor based on the light-matter interaction in a classic topological photonic crystal (PC) heterostructure, which consists of two opposite-facing 5-period PCs separated by a microfluidic channel. Because of the excitation of topological edge mode (TEM) at the interface of the two PCs, the strong coupling between incident light and TEM produces a high-quality resonance peak, which can be used to detect very small changes in the refractive index of biomaterials such as Jurkat Cells inside the microfluidic channel. The proposed biosensor has a sensitivity as high as 240 nm/RIU and figure of merit (FOM) higher than 250. پرونده مقاله

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10 - 1D Photonic Crystal Based-Biosensor for Multiple Biomarkers Detection
Farzaneh Bayat Kazem Jamshidi-Ghaleh

10.30495/ijbbe.2023.1974383.1019

In this work, a highly sensitive 1D photonic crystal (1DPC) based biosensor is introduced and theoretically studied using the transfer matrix method, which has the capability of detecting multiple biomarkers, simultaneously. An m by n gradient refractive index (GRIN) le چکیده کامل

In this work, a highly sensitive 1D photonic crystal (1DPC) based biosensor is introduced and theoretically studied using the transfer matrix method, which has the capability of detecting multiple biomarkers, simultaneously. An m by n gradient refractive index (GRIN) lens array is introduced to the center of a 1DPC structure as a defect layer that is surrounded by two microfluidic channels. By irradiating a white light source to the structure, a multiplex array of the concentric rainbow appears on the output plane. The frequency range of these rainbows is highly dependent on the effective refractive index of the fluid inside the two microfluidic channels. By functionalizing the surfaces around the channels with an m by n antibody array and interacting with the various biomarkers with them, each element of the rainbow array displays the changes in the concentration of a different biomarker. Any change in the concentration of the biomarkers can cause a variation in the effective refractive index of the fluid and it leads to a shift in the produced rainbow frequency range on the output plane. The size and number of the generated rainbow array can be engineered by the central defect layer's refractive index distribution function. پرونده مقاله

دسترسی آزاد مقاله

11 - 1D Photonic Crystal-Based Biosensor for Multiple Biomarkers Detection
Farzaneh Bayat Kazem Jamshidi-Ghaleh

10.30495/ijbbe.2023.699745

In this paper, a highly sensitive 1D photonic crystal (1DPC) based biosensor is introduced and theoretically studied using the transfer matrix method, which has the capability of detecting multiple biomarkers, simultaneously. An m by n gradient refractive index (GRIN) l چکیده کامل

In this paper, a highly sensitive 1D photonic crystal (1DPC) based biosensor is introduced and theoretically studied using the transfer matrix method, which has the capability of detecting multiple biomarkers, simultaneously. An m by n gradient refractive index (GRIN) lens array is introduced to the center of a 1DPC structure as a defect layer that is surrounded by two microfluidic channels. By irradiating a natural light source to the structure, a multiple array of the concentric rainbow appears on the output plane. The frequency range of these rainbows is highly dependent on the effective refractive index of the fluid inside the two microfluidic channels. By functionalizing the surfaces around the channels with an m by n antibody array along with the interaction of the various biomarkers, each element of the rainbow array displays the changes in the concentration of a different biomarker. Any change in the concentration of the biomarkers can cause a variation in the effective refractive index of the fluid and thus lead to a shift in the generated rainbow frequency range of the output. The size and number of the generated rainbow array may be engineered by using the central defect layer's refractive index distribution function. پرونده مقاله

دسترسی آزاد مقاله

12 - Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
Sara Davaeifar Jalil Rashidinia

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Us چکیده کامل

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising non linear system, the Bernstein coefficients can be determined to obtain the finite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach. Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno- mials and series; Collocation points. 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20. پرونده مقاله

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