Journal of Applied Mathematics and Physics

Journal Information
ISSN / EISSN : 2327-4352 / 2327-4379
Current Publisher: Hans Publishers (10.4236)
Former Publisher: Scientific Research Publishing, Inc, (10.4236)
Total articles ≅ 1,581
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Latest articles in this journal

Haolu Zhang, Lianwang Chen, Lei Fu
Journal of Applied Mathematics and Physics, Volume 09, pp 594-605; doi:10.4236/jamp.2021.94043

Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.
Wonsang Chung, Yeounju Kim, Seohyeon Kim, Jeongmin Kwon
Journal of Applied Mathematics and Physics, Volume 09, pp 648-660; doi:10.4236/jamp.2021.94047

In this paper, we will consider the simplest pseudo-addition where pseudo-multiplication and pseudo-division are the same as the ordinary ones and distributivity hold. Using this we consider a special type of the non-uniform discrete times with the pseudo-translation symmetry. Besides, we demand that the displacement should be invariant under the pseudo-translation. From these, we obtain the new definition of the instantaneous velocity which is pseudo-translation symmetry in both time and position and formulate the mechanics which are pseudo-linear and pseudo-translation invariant.
Samo Liu
Journal of Applied Mathematics and Physics, Volume 09, pp 556-564; doi:10.4236/jamp.2021.94039

Since their publications, theories in classical and modern physics have thoroughly studied the essence of matters. However, modern physical models only examined the change on the appearance of substances within its surrounding space, and it has never involved the study of absolute space as models in modern physics did not endorse the existence of absolute space. This work put in question the theories of higher-dimensional Universe accepted in mainstream physics. In order to reignite discussions in the Essence of the Universe, the author proposed the hypothesis that the Essence of the Universe is the zero-dimensional space and that it does not change accordingly with the change in substances, and that space is only and solely space. This work explored the topic of a zero-dimensional Universe using Western and Eastern philosophical concepts and their derivatives. This work concluded that zero-dimensional space could be a possibility that should be further studied, that the cause and information of Intelligent Energy proposed by the author influenced the motion and change of substances, and that time and force were merely parameters that describe the state of matters.
Hongyun Wang, Wesley A. Burgei, Hong Zhou
Journal of Applied Mathematics and Physics, Volume 09, pp 427-440; doi:10.4236/jamp.2021.93030

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power; then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.
Moh A. Hassan, Tarig M. Elzaki
Journal of Applied Mathematics and Physics, Volume 09, pp 21-30; doi:10.4236/jamp.2021.91003

In this study, we used Double Elzaki Transform (DET) coupled with Adomian polynomial to produce a new method to solve Third Order Korteweg-De Vries Equations (KdV) equations. We will provide the necessary explanation for this method with addition some examples to demonstrate the effectiveness of this method.
Huaxiong Chen, Yanyan Wang
Journal of Applied Mathematics and Physics, Volume 09, pp 31-40; doi:10.4236/jamp.2021.91004

In this paper, the homotopy analysis method is applied to deduce the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to u1/3. By introducing the auxiliary linear operator and the initial guess of solution, the homotopy analysis solving is set up. By choosing the suitable convergence-control parameter, the accurate high-order approximations of solution and frequency for the whole range of initial amplitudes can easily be obtained. Comparison of the results obtained using this method with those obtained by different methods reveals that the former is more accurate, effective and convenient for these types of nonlinear oscillators.
K. M. Abualnaja, M. S. Elgendy, F. S. Ibrahim
Journal of Applied Mathematics and Physics, Volume 09, pp 101-126; doi:10.4236/jamp.2021.91008

Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past asymmetric wedge with variable surface temperature embedded in a porous medium saturated with a nanofluid has been studied. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The velocity in the potential flow is assumed to vary arbitrary with time. The non-Darcy effects including convective, boundary and inertial effects will be included in the analysis. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations are solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. To validating the method used, we compared our results with previous results in earlier papers on special cases of the problem and are found to be in agreement. Effects of various parameters on velocity, temperature and nanoparticle volume fraction profiles are graphically presented.
Mengqin Yang, Hedong Xu, Cong Li, Suohai Fan
Journal of Applied Mathematics and Physics, Volume 09, pp 295-305; doi:10.4236/jamp.2021.92021

We investigate the effect of strategy-homogeneity on the prisoner’s dilemma game in a square lattice. Strategy-homogeneity means that the population contains at least one connected group in which individuals maintain the same strategy at each iteration and may update according to updating rule at next iteration. The simulation results show that the introduction of strategy-homogeneity increases the cooperation in the evolutionary stable state. For any value of temptation to defect, the density of cooperators in equilibrium state increases firstly and then decreases as the level of strategy-homogeneity increases constantly, and there exists an appropriate level of strategy-homogeneity, maximizing the density of cooperators. The results may be favorable for comprehending cooperative behaviors in societies composed of connected groups with coherent strategy.
M. Vubangsi, F. B. Migueu, B. F. Kamsu, L. S. Yonya Tchapda, M. Tchoffo, L. C. Fai
Journal of Applied Mathematics and Physics, Volume 09, pp 306-316; doi:10.4236/jamp.2021.92022

Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.
Dan Liu
Journal of Applied Mathematics and Physics, Volume 09, pp 370-378; doi:10.4236/jamp.2021.92025

In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.
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