Studi proses gerak brown relativistik dengan pendekatan Hanggi-Klimontovich

Najmudin, Irham (2018) Studi proses gerak brown relativistik dengan pendekatan Hanggi-Klimontovich. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Teori Gerak Brown telah berkembang sejak 60 tahun terakhir ini, penelitian tidak hanya dilakukan dalam bidang ekonomi dan biologi, namun juga berbagai bidang yang lain terutama dalam bidang astrofisika. Kajian Astofisika mengenai gerak Brown sangat penting untuk dikembangkan karena pergerakan partikel disekitar bintang masif seperti bintang neutron dan lubang hitam mengikuti gerak Brown. Pada penelitian ini dibangun proses gerak Brown untuk kasus relativistik kemudian diperluas pada proses gerak Brown relativistik dalam ruang (1+3)-Dimensi. Perluasan ini dilakukan melalui persamaan Langevin yang menggambarkan dinamika partikel dan persamaan Fokker-Planck yang menggambarkan evolusi waktu dari proses gerak Brown. Solusi persamaan Fokker-Planck diselesaikan melalui pendekatan Hanggi-Klimontovich yang kemudian disimulasikan menggunakan program Python 2.7. Hasil penelitian diperoleh peluang menemukan partikel pada kecepatan tertentu melalui persamaan Fokker-Planck pendekatan Hanggi Klimontovich. Sedangkan simulasi menghasilkan grafik yang menunjukkan bahwa puncak grafik akan cenderung mendekati kelajuan cahaya jika kecepatan partikel mendekati kelajuan cahaya.

ENGLISH:

The theory of Brownian motion has grown in the last 60 years, research has not only done in economics and biology but also a variety of other fields, especially in the field of Astrophysics. Study of Astrophysics on the Brownian motion is very important to be developed due to the movement of the particles around the massive stars such as neutron stars and black holes follow the Brownian motion. It was built on the research of the process of Brownian motion for the relativistic case and then expanded in a process of Brownian motion of relativistic space (3 + 1)-dimensional. This is done through the expansion of the equations that describe the dynamics of a particle of Langevin and Fokker-Planck equations describing the evolution time of the process of Brownian motion. The Fokker Planck equation solution solved through approach Hanggi-Klimontovich which are then simulated using Python 2.7 program. The research results obtained odds of finding a particle at a particular speed through the Fokker-Planck equation with Hanggi-Klimontovich approach. While the simulation generates a graph that shows that the peak of the charts will tend to approach the speed of light if the particle speed approaches the speed of light.

Item Type: Thesis (Undergraduate)
Supervisor: Rani, Erika and Syarifah, Umaiyatus
Keywords: Gerak Brown; Proses Stokastik; Persamaan Langevin; Persamaan Fokker-Planck; proses gerak brown relativistik (1+3)-Dimensi. Pendekatan Hanggi-Klimontovich; Brownian Motion; Stochastic Process; Langevin Equation; Fokker-Planck Equation; Relativistic Brownian Motion Process (3+1)-Dimensional; Hanggi-Klimontovich Approach
Departement: Fakultas Sains dan Teknologi > Jurusan Fisika
Depositing User: Durrotun Nafisah
Date Deposited: 21 Aug 2018 01:42
Last Modified: 21 Aug 2018 01:44
URI: http://etheses.uin-malang.ac.id/id/eprint/12009

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