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Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.
Eric Minor
The Parallelization and Optimization of the N-Body Problem using OpenMP and Cuda
The Parallelization and Optimization of the N-Body Problem using OpenMP and Cuda
This research paper aims at exploiting efficient ways of implementing the N-Body problem. The N-Body problem, in the field of physics, predicts the movements and planets and their gravitational interactions. In this paper, the efficient execution of heavy computational work through usage of different cores in CPU and GPU is looked into; achieved by integrating the OpenMP parallelization API and the Nvidia CUDA into the code. The paper also aims at performance analysis of various algorithms used to solve the same problem. This research not only aids as an alternative to complex simulations but also for bigger data that requires work distribution and computationally expensive procedures.
Tushaar Gangarapu
Estudio del proceso termodinámico en una máquina de expreso
Estudio del proceso termodinámico en una máquina de expreso
Estudio de los procesos termodinámicos que conllevan una máquina de expreso. Se utiliza solo agua, sin el filtro de café para utilizar solo la densidad del agua. Se encuentra que es similar a un proceso de Carnot, pero como un ciclo abierto.
Luis Alberto González José
FSU-MATH2400-Project3-IncludesSampleSolution
FSU-MATH2400-Project3-IncludesSampleSolution
In this project, students create a two-dimensional shape with nonuniform density, finds its center of mass, and hang it from a mobile. The various portion of the project address the differences and relationships between computing the center of mass of a discrete set of point masses and a lamina. Included here is also a sample solution to help students formulate their own well-written solutions. Also, in the LaTeX code are a few comments to address some of the basics of LaTeX and Overleaf.
Sarah Wright
The Chaos of Damped-driven Pendulum System
The Chaos of Damped-driven Pendulum System
We will study some aspects of the damped driven pendulum. We will see that the trajectory of damped driven pendulum is unpredictable under certain ranges of parameters. Under some conditions, the trajectory behaves like random. A perturbation of initial condition will lead to different result. Several mathematical tools will be introduced in this study.
zev
Proof of function's representation with Taylor Series
Proof of function's representation with Taylor Series
Proof of a function's representation with Taylor Series
Adrian D'Costa
On the quantum differentiation of smooth real-valued functions
On the quantum differentiation of smooth real-valued functions
Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.
Kolosov Petro
Random Fibonacci Sequences
Random Fibonacci Sequences
This paper will be looking at the development of random Fibonacci sequences throughout history and investigating the various mathematical methods used by many mathematicians to determine important qualities about the sequence, which all lead to the growth rate.
samkoper
E6 Übungsblatt 11
E6 Übungsblatt 11
Experimentalphysik 6: Festkörperphysik
Jean Amadeus Elsner

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