Archive

Abstract:

Most of the functional responses which have been incorporated to formulate mathematical biology consider individual contact or predator cooperation. In this study, we have introduced a different functional response that describes the prey-predator system when predators form a line and cooperatively attack a group of predators. We have also described the effect of prey on this system. Additionally, we find all the equilibrium points and their local stability behaviour.

Keywords:

Predator cooperation,Prey predator system,Equilibrium points,Local stability behaviour,

Refference:

I. C. Cosner, D. L. DeAngelis, J. S. Ault, D. B. Olson, Effects of spatial grouping on the functional response of predators, Theoretical population biology 56 (1) (1999) 65–75.
II. C. S. Holling, Some characteristics of simple types of predation and parasitism1, The Canadian Entomologist 91 (7) (1959) 385–398.
III. C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, The Memoirs of the Entomological Society of Canada 97 (S45) (1965) 5–60.
IV. D. L. DeAngelis, R. Goldstein, R. V. O’Neill, A model for tropic interaction, Ecology 56 (4) (1975) 881–892.
V. D. Xiao, S. Ruan, Codimension two bifurcations in a predator–prey system with group defense, International Journal of Bifurcation and Chaos 11 (08) (2001) 2123–2131.
VI. H. I. Freedman, G. S. Wolkowicz, Predator-prey systems with group defence: the paradox of enrichment revisited, Bulletin of Mathematical Biology 48 (5-6) (1986) 493–508.
VII. J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, The Journal of Animal Ecology (1975) 331–340.
VIII. K.-S. Cheng, S.-B. Hsu, S.-S. Lin, Some results on global stability of a predator-prey system, Journal of Mathematical Biology 12 (1) (1982) 115–126.
IX. R. Arditi, L. R. Ginzburg, H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratio-dependent predation models, The American Naturalist 138 (5) (1991) 1287–1296.

FIXATION OF THE RELATION BETWEEN FREQUENCY AND AMPLITUDE FOR NONLINEAR OSCILLATOR HAVING FRACTIONAL TERM APPLYING MODIFIED MICKENS’ EXTENDED ITERATION METHOD

Authors:

M. M. Ayub Hossain, B M Ikramul Haque

DOI NO:

https://doi.org/10.26782/jmcms.2022.01.00007

Abstract:

A modified extended iteration procedure is applied to compute the analytical periodic solutions of the nonlinear oscillator having fractional terms. A nonlinear oscillator with force is given to demonstrate the eﬀectiveness and expediency of the iteration scheme. Mickens’ extended iteration method is a well-established method for studying random oscillations. The method is also simple and straightforward to accomplish approximate frequency and the corresponding periodic solution of the strongly nonlinear oscillator. The method gives high validity for both small and large initial amplitudes of oscillations. We have used an appropriate truncation of the obtained Fourier cosine series in each step of iterations to determine the approximate analytic solution of the oscillators. The second, third, and fourth approximate frequencies of the truly nonlinear oscillator with force show a good agreement with their exact values. Also, we have compared the calculated results with some of the existing results. We have shown that the method performs reasonably better.

Keywords:

Mickens’ Extended iteration procedure,Nonlinear oscillator with the fractional term,Nonlinearity,Fourier series,

Refference:

I. Ayub Hossain M.M. and Haque, B.M.I., 2019,” A solitary convergent periodic solution of the inverse truly nonlinear oscillator by modified Mickens’ extended iteration procedure”, J. Mech. Con t. & Math. Sci., Vol. – 16, No. – 8, pp 1 – 9.
II. Azami R, Ganji D D, Babazadeh H, Dvavodi A G, Ganji S S, 2009, “ He’s Max-min method for the relativistic oscillator and high order Duﬃng equation”, International journal of modern physics B, Vol. 23 (32), pp. 5915-5927.
III. Beléndez A, 2009, “Homotopy perturbation method for a conservative force nonlinear oscillator”, Computers and Mathematics with Applications, Vol. 58, pp. 2267–2273.
IV. Beléndez A, Hernamdez A, Beléndez T, Fernandez E, Alvarez M L and Neipp C, 2007, “Application of He’s homotopy perturbation method to Duffing-harmonic Oscillator”, Int. J. Nonlinear Sci. and Numer. Simul., Vol. 8(1), pp.79-88.
V. Beléndez, A., Pascual, C., Ortuno, M., Beléndez, T. and Gallego, S., 2009 “Application of a modified He’s homotopy perturbation method to obtain higher order approximations to a nonlinear oscillator with discontinuities” Nonlinear Anal. Real World Appl, Vol.10 (2), pp. 601-610.
VI. Chowdhury M S H, Alal Md Hosen, Kartini Ahmed, Ali M Y, Ismail A F, 2017, “ High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method”, Results in physics, Vol. 7, pp. 3962-3967.
VII. Daeichin, M., Ahmadpoor, M.A., Askari, H., Yildirim, A., 2013, “Rational energy balance method to nonlinear oscillators with cubic term”, Asian European Journal of Mathematics, Vol. 6 (02), pp. 13500-19.

VIII. Durmaz, S., Kaya, M.O., 2012, “High-order energy balance method to nonlinear oscillators”, Journal of Applied Mathematics.
IX. Elias-Zuniga A, Oscar Martinez-Romero, and Rene K, Cordoba-Diaz, 2012, “Approximate solution for the Duffing-harmonic oscillator by the Enhanced Cubication Method”, Mathematical problems in Engineering, Vol. 2012(10), pp 1155-66.
X. Ganji S. S., Ganji D. D. and Karimpour S., 2008, “Determination of the frequency-amplitude relation for nonlinear oscillators with fractional potential using He’s energy balance method” Progress in Electromagnetics Research C, Vol. 5, pp. 21–33.
XI. Haque B M I, Alam M S and Majedur Rahmam M, 2013, “Modified solutions of some oscillators by iteration procedure”, J. Egyptian Math. Soci., Vol.21, pp.68-73.
XII. Haque B M I, 2013, “A new approach of Mickens’ iteration method for solving some nonlinear jerk equations”, Global Journal of Sciences Frontier Research Mathematics And Decision Science, Vol.13 (11), pp. 87-98.
XIII. Haque B M I, Alam M S, Majedur Rahman M and Yeasmin I A, 2014, “Iterative technique of periodic solutions to a class of non-linear conservative systems”, Int. J. Conceptions on Computation and Information technology, Vol.2(1), pp.92-97.
XIV. Haque B M I, 2014, “A new approach of Mickens’ extended iteration method for solving some nonlinear jerk equations”, British journal of Mathematics & Computer Science, Vol.4(22), pp.3146-3162.
XV. Haque, B.M.I., Bayezid Bostami M., Ayub Hossain M.M., Hossain M.R. and Rahman M.M., 2015 “Mickens Iteration Like Method for Approximate Solution of the Inverse Cubic Nonlinear Oscillator” British journal of Mathematics & Computer Science, Vol. 13, pp.1-9.
XVI. Haque, B.M.I., Ayub Hossain M.M., Bayezid Bostami M. and Hossain M.R., 2016 “Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iteration Procedure” British journal of Mathematics & Computer Science, Vol. 14, pp.1-7.
XVII. Haque, B.M.I., Asifuzzaman M. and Kamrul Hasam M., 2017 “Improvement of analytical solution to the inverse truly nonlinear oscillator by extended iterative method” Communications in Computer and Information Science, Vol. 655, pp. 412-421.

XVIII. Haque, B.M.I., Selim Reza A.K.M. and Mominur Rahman M., 2019 “On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method” Journal of Advances in Mathematics and Computer Science, Vol. 33, pp. 1-9.
XIX. Haque, B.M.I. and Ayub Hossain M.M., 2019 “A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure” Journal of Advances in Mathematics and Computer Science, Vol. 34, pp.1-9.
XX. Haque B M I and Afrin Flora S, 2020 “On the analytical approximation of the quadratic nonlinear oscillator by modified extended iteration Method”, Applied Mathematics and Nonlinear Sciences, June 15th, pp. 1-10.
XXI. Haque B M I, Zaidur Rahman M and Iqbal Hossain M, 2020 “Periodic solution of the nonlinear jerk oscillator containing velocity times acceleration-squared: an iteration approach”, journal of Mechanics of Continua and Mathematical Sciences, Vol. 15(6), pp. 419-433.
XXII. Haque B M I and Iqbal Hossain M, 2021 “An Analytical Approach for Solving the Nonlinear Jerk Oscillator Containing Velocity Times Acceleration-Squared by An Extended Iteration Method”, journal of Mechanics of Continua and Mathematical Sciences, Vol. 16(2), pp. 35-47.
XXIII. Hosen MA, Chowdhury MSH, Ali MY, Ismail AF, 2016, “A new analytic approximation technique for highly nonlinear oscillations based on energy balanced method”, Results Phys., Vol. 6, pp. 496-504.
XIV. Hosen MA, Chowdhury MSH, 2015, “A new reliable analytic solution for strongly nonlinear oscillator with cubic and harmonic restoring force”, Results Phys., Vol. 5, pp. 111-4.
XXV. Lai SK, Lim CW, Wu BS, Wang C, Zeng QC, He XF, 2008, “Newton-harmonic balanced approach for accurate solutions to nonlinear cubic-quintic Duffing oscillator”, Appl Math Model, Vol. 33(2), pp. 852-66.
XXVI. Mickens R E, 1984, “Comments on the method of harmonic balance”, J. Sound Vib., Vol. 94, pp.456- 460.
XXVII. Mickens R E, 1987, “Iteration Procedure for determining approximate solutions to nonlinear oscillator equation”, J. Sound Vib., Vol. 116, pp.185-188.

XXVIII. Mickens R E, 2005, “A general procedure for calculating approximation to periodic solutions of truly nonlinear oscillators”, J. Sound Vib., Vol. 287, pp.1045-1051.
XXIX. Mickens R E, 2010, “Truly Nonlinear Oscillations, World Scientific, Singapore”.
XXX. Nayfeh A H, 1973, “Perturbation Method”, John Wiley & sons, New York.
XXXI. Nayfeh A H Mook D T, 1979, “Nonlinear Oscillations”, John Wiley & sons, New York.

AN EFFICIENT NUMERICAL SCHEME FOR STATIC TORQUE PROFILING OF SWITCHED RELUCTANCE MACHINE WITH EXPERIMENTAL VALIDATION

Authors:

Sanam Rehman Mahar, Muhammad Mujtaba Shaikh, Ali Asghar Memon

DOI NO:

https://doi.org/10.26782/jmcms.2022.01.00008

Abstract:

In AC and DC drives, the use of switched reluctance machine (SRM) is becoming popular as it has a few preferences over AC and DC drives in a simple and robust construction without brushes, low inertia, and high torque to weight ratio, without rotor windings, simple circuit power converter, etc. SRM is widely used in variable speed and servo drives. Because of the double saliency structure and the high nonlinearity of magnetic material, it is difficult to represent the flux-linkage and static torque characteristic of the SRM. This work promotes the use of an improved numerical integration scheme for the static characteristics of SRM. The static torque function that depends on the rotor position and the phase current of the flux linkage features family (for different rotor positions) is improved in the proposed work. Firstly, we use an experimental setup for the electromagnetic characteristic of SRM. Then, we use the improved scheme to develop an efficient mathematical model for static characteristics and finally simulate the static characteristic of SRM through MATLAB code. In the last step, we compare the performance of the proposed integrator model with an existing approach for better efficiency of the static characteristic of SRM with experimental validation.

Keywords:

Numerical scheme,Switched Reluctance machine,Static Torque,Numerical Integration,Experimental Validation,

Refference:

I. A. A. Memon (2012). Prediction of compound losses in a switched reluctance machine and inverter (Doctoral dissertation) University of Leeds (School of Electronic and Electrical Engineering), http://lib.leeds.ac.uk/record=b3231863.
II. Ahmad, S. S., & Narayanan, G. (2016). A simplified flux linkage characteristics model of switched reluctance machine. In 2016 IEEE International Conference Power Electronics, Drives and Energy Systems (PEDES) (pp. 1-6). IEEE.
III. Arias, A., Rain, X., & Hilairet, M. (2013). Enhancing the flux estimation. Electric power systems research, 104, 62-70.
IV. Charles V. Jones, “The Unified Theory of Electrical Machines”, London, 1967.
V. Cheok, A. D., & Ertugrul, N. (2001). Computer-based automated test measurement system for determining magnetization characteristics of switched reluctance motors. IEEE Transactions on Instrumentation and Measurement, 50(3), 690-696.
VI. Corda J. (1979). PhD thesis, University of Leeds 1979.
VII. Dahlquist, G., & Björck, Å. (2008). Numerical methods in scientific computing, volume i. Society for Industrial and Applied Mathematics.
VIII. Ganji, B. and Askari, M.H., (2016). Analysis and modeling of different topologies for linear switched reluctance motor using finite element method. Alexandria Engineering Journal, 55(3), pp.2531-2538.
IX. Malik K., M. M. Shaikh, M. Saleem Chandio, A. W. Shaikh (2020). “Some New And Efficient Derivative-Based Schemes For Numerical Cubature”, J. Mech. Cont. & Math. Sci., Vol.-15, No.-10, Pp 67-78.
X. Memon A. A., R. A. Talani, A. A. Memon (2016) Selecting best interpolation technique for simulation modelling of switched reluctance machine, Indian j.Sci Technol. 9 (16).
XI. Memon K., M. M. Shaikh, M. S. Chandio, A. W. Shaikh (2020). “A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral”, Sindh Univ. Res. Jour. (Sci. Ser.) Vol. 52 (01) 37-40.
XII. Memon, A. A., and Shaikh, M. M. (2017). Input data for mathematical modeling and numerical simulation of switched reluctance machines. Data in brief, 14,138-142.
XIII. Memon, A. A., Shah, S. A. A., Shah, W., Baloch, M. H., Kaloi, G. S., & Mirjat, N. H. (2018). A flexible mathematical model for dissimilar operating modes of a switched reluctance machine. IEEE Access, 6: 9643-9649.
XIV. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. (2020). Look- up data tables-based modeling of switched reluctance machine and experimental validation of the static torque with statistical analysis. Journal of Magnetics, 25(2), 233-244.
XV. Qing, Z. (2003). Modeling of switched reluctance motors for torque control.
XVI. Saha, N., Panda, A. K., & Panda, S. (2018). Speed control with torque ripple reduction of switched reluctance motor by many optimizing liaison technique. Journal of Electrical Systems and Information Technology, 5(3), 829-842.
XVII. Saxena, R., Singh, B., & Pahariya, Y. (2010). Measurement of Flux Linkage and Inductance Profile of SRM International Journal of Computer and Electrical Engineering, 2(2), 389.
XVIII. Shaikh, M. M., & Mujtaba, M. (2019). Analysis of polynomial collocation and uniformly spaced quadrature methods for second kind linear Fredholm integral equations – a comparison. Turkish Journal of Analysis and Number Theory, 7(4), 91-97.
XIX. Shaikh, M. M., Chandio, M. S., & Soomro, A. S. (2016). A modified four-point closed mid-point derivative based quadrature rule for numerical integration. Sindh University Research Journal-SURJ (Science Series), 48(2).
XX. Shaikh, M. M., Massan, S.-u-R. and Wagan, A. I. (2015). A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases. International Journal of Heat and Mass Transfer, 88, 538-543.
XXI. Shaikh, M. M., Massan, S.-u-R. and Wagan, A. I. (2019). A sixteen decimal places’ accurate Darcy friction factor database using non-linear Colebrook’s equation with a million nodes: A way forward to the soft computing techniques. Data in brief, 27, 104733.
XXII. Shehata, A. M., El-Wakeel, A. S., Abdalla, Y. S., & Mostafa, R. M. (2018). Flux linkage and inductance measurement of a fault tolerant switched reluctance motor drive. In 2018 Twentieth International Middle East Power Systems Conference (MEPCON) (pp. 322-327). IEEE.
XXIII. Talani, R. A., Bhutto, G. M., Mangi, F. H., & Keerio, M. U. Comparative study of static torque characteristic of switched reluctance motor using spline and linear data interpolation techniques. Engineering, Science & Technology, 51.
XXIV. Uma, S., Kamalakannan, C., & Karthikeyan, R. (2013). Static and dynamic characteristics of 8/6, 400W switched reluctance motor. International Journal of Computer Applications, 66 (12), 1-8.

ALL-OPTICAL N-BIT BINARY TO TWO’S COMPLEMENT CONVERTER WITH THE HELP OF SEMICONDUCTOR OPTICAL AMPLIFIER-ASSISTED SAGNAC SWITCH

Authors:

Arunava Bhattachryya, Dilip Kumar Gayen

DOI NO:

https://doi.org/10.26782/jmcms.2022.01.00009

Abstract:

All-optical n-bit paired to 2's complement converter has been planned with the assistance of Terahertz optical unbalanced demultiplexer (TOAD) switches. The paper depicts all-optical transformation conspire to utilize a bunch of every single optical switch. PC framework ordinarily utilizes 2's complement for paired deduction and intelligent control. By embracing a definite mathematical reproduction the impact of these critical boundaries on the measurements that decide the nature of exchange is completely examined and diverse plan rules are extricated for their legitimate determination to guarantee ideal activity.

Keywords:

Terahertz optical asymmetric demultiplexer,semiconductor optical amplifier,2’s complement operation,optical logic,

Refference:

I. A. Bhattacharyya, D. K. Gayen, and T. Chattopadhyay, “All-optical 4-bit Binary to Binary Coded Decimal Converter with the help of Semiconductor Optical Amplifier -assisted Sagnac Switch”, Optics Communications, Elsevier, 293, 31–42 (2013).
II. B. C. Wang, V. Baby, W. Tong, L. Xu, M. Friedman, R. J. Runster, I. Glesk, and P. Prucnal, “A novel fast optical switch based on two Cascaded Terahertz optical asymmetric demultiplexers (TOAD),” Opt. Express, vol.10, pp. 15-23, Jan. 2002.
III. D. K. Gayen, T. Chattopadhyay, M. K. Das, J. N. Roy, and R. K. Pal, “All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier -assisted sagnac switch”, IET Circuits, Devices & Systems, 5(2), 123-131 (2011)
IV. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE Quantum Electronics, vol. 25, pp. 2297-2306, 1989.
V. H. Le-Minh, Z. Ghassemlooy, W. P. Ng., R. Ngah, “TOAD Switch with symmetric switching window”, LCS2004 conf., London, UK, pp. 89-93, 2004.
VI. H. Le-Minh, Z. Ghassemlooy, and W. P. Ng, “Ultrafast all-optical self clock extraction based on two inline symmetric Mach-Zehnder Switches,” in Proc. ICTON 2006, vol. 4, pp. 64-67, Nottingham, UK, 2006.
VII. Hoa Le Minh, Zabih Ghassemlooy, Wai Pang Ng,” Characterization and Performance Analysis of a TOAD Switch Employing a Dual Control Pulse Scheme in. High-speed OTDM Demultiplexer”, IEEE Communications Letters, vol. 12, 4, APRIL 2008.
VIII. J. P. Sokoloff, I. Glesk, P. R. Prucnal, “Performance of a 50Gb/s Optical Time Domain Multiplexed System using a TOAD”, IEEE Pho. Tech. Lett., 6(1), pp. 98-100, 1994.

IX. K. E. Zoiros, J. Vardakas, T. Houbavlis, and M. Moyssidis, “Investigation of SOA-assisted Sagnac recirculating shift register switching characteristics”, International Journal for Light and Electron Optics, 116(11), 527-541 (2005).
X. M. Eiselt, W. Pieper, H. G. Weber, LALOM: Semiconductor Laser Amplifier in a Loop Mirror”, IEEE Light. Tech., 13(10), pp. 2099-2112.
XI. W. Hong, D. Huang, and G. Zhu, “Switching window of an SOA loop mirror with SOA sped-up by a CW assist light at transparency wavelength”, Optics Communications, 238(1-3), 151-156 (2004).

ANALYSIS OF RACETRACK RESONATOR USING SIGNAL PROCESSING TECHNIQUE

Authors:

Sabitabrata Dey

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00001

Abstract:

Optical double racetrack resonator (ODRR) and optical quadruple racetrack resonator (OQRR) made of Silicon-on-insulator (SOI) with their effective refractive indices changing with respect to frequency have been analyzed for obtaining optical filter with wider ranges of free spectral range (FSR). FSR expansion is based on the Vernier principle. Delay line signal processing in Z- domain and Mason’s gain formula is being used for analyzing these ODRR and OQRR. A free spectral range of 4.87THz is obtained for the drop port. Further, the change in the dimensions of the racetrack resonators produced an enhanced FSR of 5.77THz for ODRR. Combining both this model of ODRR we obtained an OQRR model that produces FSR as much as 6.86THz. Apart from obtaining wider FSR, this architecture exhibits interstitial spurious transmission of almost -50dB with negligible resonance loss. Group delay, dispersion characteristics, and finesse have also been determined for the architecture.

Keywords:

Racetrack resonator,Mason’s gain formula,free spectral range,Vernier principle,Resonance loss,Group delay,Dispersion,

Refference:

I. A. Wirth L, M.G da Silva, D.M.C Neves, A.S.B Sombra, “Nanophotonicgraphene-basedracetrack- resonatoradd/drop filter”, Optics Communications, 366(2016) 210-220, Elsevier.
II. A. Oppenheim, R. Schafer, “Digital Signal Processing”, 2nd edition Prentice-Hall, IncEnglewood, NJ, 1975.
III. Christi K.Madsen, Jian H Zhao, “Optical filter design and analysis, A signal processing approach”, John Wiley & sons, Inc, New York, 1999.
IV. D. Marcuse, “Bending losses of the asymmetric slab waveguide,” Bell System Tech. J. 50 (8), 2551–2563 (1971).
V. Fengnian Xia, Lidija Sekaric and Yurii A. Vlasov,” Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators”, 1 May 2006, Vol. 14, No. 9, Optics Express.3872.
VI. H. Liu, C. F. Lam, and C. Johnson, “Scaling Optical Interconnects in Data center Networks Opportunities and Challenges for WDM,” 2010 18th IEEE Symp. High Perf. Interconnects, pp. 113–16.
VII. Intel Silicon Innovation: Fueling New Solutions for the Digital Planet, www.intel.com/technology/silicon.
VIII. J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express, vol. 16, pp. 4296–4301, March 2008.
IX. Landobasa Y.M. Tobing, Dumon Pieter, “Fundamental principles of operation and notes on fabrication of photonic microresonators, Photonic Microring Research and Application”, 156, Springer, 2010 chap-1.
X. Otto Schwelb, „Transmission, Group Delay, and Dispersion in Single-Ring Optical Resonators and Add/Drop Filters- A Tutorial Overview‟, IEEE journal of Lightwave technology 22 (5) (2004).
XI. P. W. Coteus J. U. Knickerbocker, C. H. Lam, Y. A. Vlasov, “Technologies for exascale systems”, IBM J. Res. & Dev. Vol. 55 No. 5 Paper 14 September/October 2011.
XII. R. Boeck, W. Shi, L. Chrostowski, N.A.F Jaeger, “FSR-Eliminated Vernier racetrack Resonators using Grating-Assisted Couplers”, IEEE Photonics journal, DOI: 10.1109/JPHOT.2013.2280342, IEEE.
XIII. Robi Boeck, Nicolas A. F. Jaeger, Nicolas Rouger, Lukas Chrostowski “Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement” Optics Express (2010). OCIS codes: (130.0130) Integrated optics; (130.7408) Wavelength filtering devices; (230.5750) Resonators.
XIV. Robi Boeck, Jonas Flueckiger, Nicolas Rouger, Lukas Chrostowski ” Experimental performance of DWDM quadruple Vernier racetrack resonators ” OSA (2013) OCIS codes (230.7408) Wavelength filtering devices; (230.5750) Resonators.
XV. S.J Mason, “Feedback Properties of Signal Flow Graphs,” Proc. IRE, Vol. 44, no. 7, pp. 920-926, July 1975.
XVI. S. Dey, S. Mandal, “Modeling and analysis of quadruple optical ring resonator performance as optical filter using Vernier principle”, Optics Communications 285 (2012) 439–446.
XVII. Sabitabrata Dey, S.Mandal, “ Wide free-spectral-range triple ring resonator as optical filter,” Optical Engineering, SPIE,Vol. 50(8),pp 084601-(1-9), August, 2011.
XVIII. Yurii A. Vlasov, “Silicon CMOS-Integrated Nano-Photonics for Computer and Data Communications Beyond 100G”, IEEE Communications Magazine, February 2012.

MINIMIZATION OF TORQUE RIPPLES IN A SWITCHED RELUCTANCE MACHINE BY AN OPTIMAL SWITCHING ANGLE WITHIN A LOW INDUCTANCE REGION

Authors:

Sadam Hussain Lashari, Ali Asghar Memon

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00002

Abstract:

Because of its high starting torque and improved performance in a variety of operating situations, the switched reluctance machine (SRM) has emerged as a potential challenger in the family of electrical machines. SRM has been a new addition to the industrial market in recent years. Drawbacks of SRMs are the torque ripple and acoustic noise. This research focuses on the minimization of torque ripples in a Switched Reluctance Machine by optimal switching angle in a low inductance region for a range of speed. For this, simulation is performed with the aim that SRM operation in a low inductance region will take place with low torque ripples. The finding of this research will help in better performance of the machine when operated at the desired angle.

Keywords:

Experimental Validation,Switched Reluctance Machine,Static Torque,Torque Ripples,

Refference:

I. A. A. Memon (2012). Prediction of compound losses in a switched reluctance machine and inverter (Doctoral dissertation) University of Leeds (School of Electronic and Electrical Engineering)
II. Ghousia, Syeda Fatima. “Impact analysis of dwell angles on current shape and torque in switched reluctance motors.” International journal of power electronics and drive systems 2, no. 2 (2012): 160.
III. Xu, Y.Z., Zhong, R., Chen, L. and Lu, S.L., 2012. Analytical method to optimise turn-on angle and turn-off angle for switched reluctance motor drives. IET Electric Power Applications, 6(9), pp.593-603.
IV. Suryadevara, R. and Fernandes, B.G., 2013, December. Control techniques for torque ripple minimization in switched reluctance motor: An overview. In 2013 IEEE 8th International Conference on Industrial and Information Systems (pp. 24-29).
V. Nashed, M.N., Mahmoud, S.M., El-Sherif, M.Z. and Abdel-Aliem, E.S., 2014. Optimum change of switching angles on switched reluctance motor performance. International Journal of Current Engineering and Technology, 4(2).
VI. Wei, Ye, Ma Qishuang, Zhang Poming, and Guo Yangyang. “Torque ripple reduction in switched reluctance motor using a novel torque sharing function.” In 2016 IEEE International Conference on Aircraft Utility Systems (AUS), pp. 177-182. IEEE, 2016.
VII. Memon, Ali Asghar, Syed Asif Ali Shah, Wajiha Shah, Mazhar Hussain Baloch, Ghulam Sarwar Kaloi, and Nayyar Hussain Mirjat. “A Flexible Mathematical Model for Dissimilar Operating Modes of a Switched Reluctance Machine.” IEEE Access 6 (2018): 9643-9649.
VIII. Üstün, O. and Önder, M., 2020. An Improved Torque Sharing Function to Minimize Torque Ripple and Increase Average Torque for Switched Reluctance Motor Drives. Electric Power Components and Systems, 48 (6-7), pp.667-681.
IX. Keerthana, C. and Sundaram, M., 2020, June. State of Art of Control Techniques adopted for Torque Ripple Minimization in Switched Reluctance Motor Drives. In 2020 4th International Conference on Trends in Electronics and Informatics (ICOEI) (48184) (pp. 105-110).
X. Touati, Z., Mahmoud, I. and Khedher, A., 2021, March. Torque Ripple Minimization Approach of a 3-phase Switched Reluctance Motor. In 2021 18th International Multi-Conference on Systems, Signals & Devices (SSD) (pp. 533-538).
XI. Ren, P., Zhu, J., Jing, Z., Guo, Z. and Xu, A., 2021. Minimization of torque ripple in switched reluctance motor based on MPC and TSF. IEEJ Transactions on Electrical and Electronic Engineering, 16(11), pp.1535-1543.

SPATIAL DYNAMICS IN A PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

Authors:

Dridhiti Roy, Paritosh Bhattacharya

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00003

Abstract:

The dynamical behavior between predator and prey has been a dominant theme in ecology and mathematical ecology for a long time. In this paper, we look into the dynamics of the Beddington-DeAngelis predator-prey model. We reduce the equations by nondimensionalizing them and combining the spatial factor. Then we incorporate a prey refuge into the system. The model system is then subjected to homogeneous Neumann boundary conditions and the homogeneous equilibria of the full spatial model are being found.

Keywords:

Beddington-DeAngelis functional response,Beddington-DeAngelis predator-prey model,prey refuge,stability,reaction-diffusion predator-prey model,

Refference:

I. B. Ermentrout, Stripes or spots? Nonlinear effects in bifurcation of reaction–diffusion equations on the square, Proc. Roy. Soc. London 434 (1991) 413–417.

II. E. Gonz ́alez-Olivares and R. Ramos-Jiliberto, Consequences of prey refuge use on the dynamics of some simple predator–prey models: Enhancing stability?, in Proc. Third Brazilian Symp. Mathematical and Computational Biology (E-Papers Servicos Editoriais, 2004), pp. 75–98.

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NEW CONCEPTS OF T₂ SEPARATION AXIOMS IN SUPRA FUZZY TOPOLOGICAL SPACE USING QUASI COINCIDENCE SENSE

Authors:

Lalin Chowdhury, Sudipto Kumar Shaha, Ruhul Amin

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00004

Abstract:

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems or constructing some counterexamples which show the interrelations between certain topological concepts or preserving some properties under fewer conditions of those on topology. To contribute to this research area, in this paper, we establish some notions of separation axioms in supra fuzzy topological space in a quasi-coincidence sense. Also, we investigate some of its properties and establish certain relationships among them and other such concepts. Moreover, some of their basic properties are examined. The concept of separation axioms is one of the most important parts of fuzzy mathematics, mainly modern topological mathematics, which plays an important role in modern networking systems.

Keywords:

Fuzzy Set,Fuzzy Topology,Supra Fuzzy Topology,Quasi-coincidence,Initial and Final Supra Fuzzy Topology,

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RSRW DATA, CSP AND CYCLONE TRACK PREDICTION

Authors:

Indrajit Ghosh, Sukhen Das, Nabajit Chakravarty

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00005

Abstract:

Tropical cyclones are gradually becoming an increasing menace to the coastal human civilization throughout the World. This is due to their increased frequency and intensity of occurrence nowadays. With the global increase of sea surface temperature a marked increase in the percentage of their formation from depression happening especially in the tropical oceans of the World. The Coromandel Coast of India is not an exception to these. To mitigate their devastation effect on mankind we need to study the details of their dynamics governing equations and hence develop suitable solutions. In this paper the numerical value of a stability parameter, viz. CSP is determined employing the RSRW data of one tropical cyclone that has hit the Coromandel Coast of India in 2010. CSP is a dimensionless parameter that we obtained from the analytic solution of cyclone dynamics governing equations.

Keywords:

CSP,Radial velocity,Cross-radial velocity,RSRW,Cyclone eye,Tropical cyclone,

Refference:

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TIME SERIES ANALYSIS MODELING AND FORECASTING OF GROSS DOMESTIC PRODUCT OF PAKISTAN

Authors:

Nasir Saleem, Atif Akbar, A. H. M. Rahmatullah Imon, Abu Sayed Md Al Mamun

DOI NO:

https://doi.org/10.26782/jmcms.2022.02.00006

Abstract:

The purpose of this study was to forecast the Gross Domestic Product (GDP) of Pakistan. GDP of Pakistan was observed and analyzed by using time series analysis techniques and Box-Jenkins methodology. These methods were used for analysis, estimation, and forecasting purposes. Data of GDP of Pakistan was collected from (1961-2020). The model selected had the lowest Akaike Information Criteria (AIC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Error (ME), Mean Percentage Error (MPE), Schwarz Bayesian Information Criteria (SBIC), Schwarz Bayesian Criteria (SBC), values and high R². It was used for forecasting the GDP of Pakistan for the next 55 years from 2021-to 2075. Data were analyzed by using SPSS-21, Eviews-3, and Statgraphics-16. We have found that the best model is the Linear trend model. Based on this selected model, we have found that the GDP of Pakistan would become 2.51199 in 2035 and would become less in 2075 as compared to 2025.

Keywords:

AIC,Linear Trend Model,Time Series Models,Gross,Domestic Product,Forecasting,

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