Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1110194
Ola A. Jarab’ah
Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.
{"title":"Path Integral Quantization of Non-Natural Lagrangian","authors":"Ola A. Jarab’ah","doi":"10.4236/jamp.2023.1110194","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110194","url":null,"abstract":"Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1110191
Grégoire Lutanda Panga
The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.
{"title":"2D Curves in Conformal Hyperquaternion Algebras H<sup>⊗2<i>m</i></sup>","authors":"Grégoire Lutanda Panga","doi":"10.4236/jamp.2023.1110191","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110191","url":null,"abstract":"The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.119171
Koshun Suto
In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phenomena. However, relativity is not taken into account in this Rydberg formula for wavelength. If the special theory of relativity is taken into account, R∞ can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.
{"title":"The Physical Constant Called the Rydberg Constant Does Not Exist","authors":"Koshun Suto","doi":"10.4236/jamp.2023.119171","DOIUrl":"https://doi.org/10.4236/jamp.2023.119171","url":null,"abstract":"In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phenomena. However, relativity is not taken into account in this Rydberg formula for wavelength. If the special theory of relativity is taken into account, R∞ can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1110198
Abdelrahman Mahdy
The tunneling ionization (TI) is the most dominated ionization process in the production of terahertz radiation by two femtosecond lasers, although its validity above the ionization threshold of some gases is uncertain. In the present research, we employ a 1D fluid code to simulate the efficiency of the produced terahertz radiation by two femtosecond laser beams in air plasma. Two ionization models in the context of the TI process which are the Ammosov-Delone-Krainov (ADK) for noble gases and its developed molecular ADK (MO-ADK) model for molecular gases are intrinsically used to conduct this study. The main target of the present research is to examine the validity of these models Above-Threshold-Ionization (ATI) of these gases. For this purpose, we simulated the ionization rate and the power spectrum of the produced radiation, in addition we numerically evaluated the efficiency of the produced radiation as function of the input beams intensity at particular energy fraction factor, relative phase and initial pulse duration of these beams. These calculations conducted for a selected noble gas at varying energy levels and a chosen molecular air plasma gas at different quantum numbers. Numerical results near and above the ionization threshold of the selected gases have clarified that the ADK and MO-ADK model are successful valid to study the efficiency of the produced THz radiation at low energy levels and small quantum numbers of the selected gases, meanwhile, with any further increase in the energy level and the quantum number values of these gases, both of the ADK and MO-ADK are failed to correctly analyze the efficiency process and estimate its fundamental parameters.
{"title":"Numerical Simulation for the Efficiency of the Produced Terahertz Radiation by Two Femtosecond Laser Pulses: Above-Threshold-Ionization","authors":"Abdelrahman Mahdy","doi":"10.4236/jamp.2023.1110198","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110198","url":null,"abstract":"The tunneling ionization (TI) is the most dominated ionization process in the production of terahertz radiation by two femtosecond lasers, although its validity above the ionization threshold of some gases is uncertain. In the present research, we employ a 1D fluid code to simulate the efficiency of the produced terahertz radiation by two femtosecond laser beams in air plasma. Two ionization models in the context of the TI process which are the Ammosov-Delone-Krainov (ADK) for noble gases and its developed molecular ADK (MO-ADK) model for molecular gases are intrinsically used to conduct this study. The main target of the present research is to examine the validity of these models Above-Threshold-Ionization (ATI) of these gases. For this purpose, we simulated the ionization rate and the power spectrum of the produced radiation, in addition we numerically evaluated the efficiency of the produced radiation as function of the input beams intensity at particular energy fraction factor, relative phase and initial pulse duration of these beams. These calculations conducted for a selected noble gas at varying energy levels and a chosen molecular air plasma gas at different quantum numbers. Numerical results near and above the ionization threshold of the selected gases have clarified that the ADK and MO-ADK model are successful valid to study the efficiency of the produced THz radiation at low energy levels and small quantum numbers of the selected gases, meanwhile, with any further increase in the energy level and the quantum number values of these gases, both of the ADK and MO-ADK are failed to correctly analyze the efficiency process and estimate its fundamental parameters.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135211879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.118150
Glenn Xavier Vaz, Zeinab El-Sayegh
This research paper aims to identify the effect of tire size on the handling characteristics of a trailer attached to a vehicle. In various stability tests, different models with different tires from the market were tested. A successful outcome of this research would generate an efficient tire selection process and improve the handling of a trailer attached to a vehicle while maximizing fuel efficiency. In this study, different accurate tire models using the magic formula were developed in vehicle dynamics modelling and simulation software. These models were then simulated on on-road conditions to predict vehicle and trailer behaviour under different conditions within the software. Two distinct tests were conducted, the J-Turn test and the Double Lane change test. The results of these tests were used to evaluate the handling characteristics and decide on a better tire size for the trailer attached to the vehicle.
{"title":"Analysis of the Effect of Trailer Tire Size on the Articulated Vehicle’s Stability","authors":"Glenn Xavier Vaz, Zeinab El-Sayegh","doi":"10.4236/jamp.2023.118150","DOIUrl":"https://doi.org/10.4236/jamp.2023.118150","url":null,"abstract":"This research paper aims to identify the effect of tire size on the handling characteristics of a trailer attached to a vehicle. In various stability tests, different models with different tires from the market were tested. A successful outcome of this research would generate an efficient tire selection process and improve the handling of a trailer attached to a vehicle while maximizing fuel efficiency. In this study, different accurate tire models using the magic formula were developed in vehicle dynamics modelling and simulation software. These models were then simulated on on-road conditions to predict vehicle and trailer behaviour under different conditions within the software. Two distinct tests were conducted, the J-Turn test and the Double Lane change test. The results of these tests were used to evaluate the handling characteristics and decide on a better tire size for the trailer attached to the vehicle.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"270 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136217399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1111215
Xueji Jiu
{"title":"The Minimum Hosoya Index of a Kind of Tetracyclic Graph","authors":"Xueji Jiu","doi":"10.4236/jamp.2023.1111215","DOIUrl":"https://doi.org/10.4236/jamp.2023.1111215","url":null,"abstract":"","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135507764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1111211
Victor Kaigalula, Jeconia Okelo, Samuel Mutua, Onesmus Muvengei
The aim of this study is to examine unsteady incompressible Magnetohydrodynamic fluid flow together with soret and dufour effects on mass and heat transfer through a collapsible elastic tube. The governing equations are continuity equation, momentum equation, energy equation and concentration equation. The velocity, temperature and concentration profiles together with heat and mass transfer rate were determined. The system of nonlinear partial differential equations governing the flow solved numerically by applying collocation method and implemented in MATLAB. The numerical solution of the profiles displayed both by graphically and numerically for different values of the physical parameters entering into the problem. The effects of varying various parameters such as Reynolds number, Hartmann number, Soret number, Dufour number and Prandtl number on velocity, temperature and concentration profiles also the rate of heat and mass transfer are discussed. The study is significant because heat and mass transfer mechanisms with the soret and dufour effects considerations play an important role due to its wide range of application including but not limited to medical fields, biological sciences and other physical sciences where collapsible tubes are applied.
{"title":"Magneto-Hydrodynamic Flow of an Incompressible Fluid in a Collapsible Elastic Tube with Mass and Heat Transfer","authors":"Victor Kaigalula, Jeconia Okelo, Samuel Mutua, Onesmus Muvengei","doi":"10.4236/jamp.2023.1111211","DOIUrl":"https://doi.org/10.4236/jamp.2023.1111211","url":null,"abstract":"The aim of this study is to examine unsteady incompressible Magnetohydrodynamic fluid flow together with soret and dufour effects on mass and heat transfer through a collapsible elastic tube. The governing equations are continuity equation, momentum equation, energy equation and concentration equation. The velocity, temperature and concentration profiles together with heat and mass transfer rate were determined. The system of nonlinear partial differential equations governing the flow solved numerically by applying collocation method and implemented in MATLAB. The numerical solution of the profiles displayed both by graphically and numerically for different values of the physical parameters entering into the problem. The effects of varying various parameters such as Reynolds number, Hartmann number, Soret number, Dufour number and Prandtl number on velocity, temperature and concentration profiles also the rate of heat and mass transfer are discussed. The study is significant because heat and mass transfer mechanisms with the soret and dufour effects considerations play an important role due to its wide range of application including but not limited to medical fields, biological sciences and other physical sciences where collapsible tubes are applied.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"293 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135446641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1111212
Feng Liu, Feng Gao, Xiaojun Ding
Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.
{"title":"Optimizing Designed Variable Speed Control Moment Gyroscopes with Variable Skew Angle","authors":"Feng Liu, Feng Gao, Xiaojun Ding","doi":"10.4236/jamp.2023.1111212","DOIUrl":"https://doi.org/10.4236/jamp.2023.1111212","url":null,"abstract":"Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.118141
Alexander Soiguine
Geometric Algebra formalism opens the door to developing a theory deeper than conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, unambiguous definition of states, observables, measurements, Maxwell equations solution in those terms, bring into reality a kind of physical fields spreading through the whole three-dimensional space and values of the time parameter. The fields can be modified instantly in all points of space and time values, thus eliminating the concept of cause and effect, and perceiving of one-directional time. In the suggested theory all measured observable values get available all together, not through looking one by one. In this way quantum computer appeared to be a kind of analog computer keeping and instantly processing information by and on sets of objects possessing an infinite number of degrees of freedom. As practical implementation, the multithread GPUs bearing the CUDA language functionality allow to simultaneously calculate observable measurement values at a number of space/time discrete points only restricted by the GPU threads capacity.
{"title":"Quantum Computer on Nvidia GPU","authors":"Alexander Soiguine","doi":"10.4236/jamp.2023.118141","DOIUrl":"https://doi.org/10.4236/jamp.2023.118141","url":null,"abstract":"Geometric Algebra formalism opens the door to developing a theory deeper than conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, unambiguous definition of states, observables, measurements, Maxwell equations solution in those terms, bring into reality a kind of physical fields spreading through the whole three-dimensional space and values of the time parameter. The fields can be modified instantly in all points of space and time values, thus eliminating the concept of cause and effect, and perceiving of one-directional time. In the suggested theory all measured observable values get available all together, not through looking one by one. In this way quantum computer appeared to be a kind of analog computer keeping and instantly processing information by and on sets of objects possessing an infinite number of degrees of freedom. As practical implementation, the multithread GPUs bearing the CUDA language functionality allow to simultaneously calculate observable measurement values at a number of space/time discrete points only restricted by the GPU threads capacity.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.1110204
Md. Shahadat Hossain Mojumder, Md. Nazmul Haque, Md. Joni Alam
In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.
{"title":"Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation","authors":"Md. Shahadat Hossain Mojumder, Md. Nazmul Haque, Md. Joni Alam","doi":"10.4236/jamp.2023.1110204","DOIUrl":"https://doi.org/10.4236/jamp.2023.1110204","url":null,"abstract":"In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.","PeriodicalId":15035,"journal":{"name":"Journal of Applied Mathematics and Physics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135263688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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