Brownian motion: A classroom demonstration and student experiment

Kirksey, H. Graden

doi:10.1021/ed065p1091

Cited by 7 publications

(7 citation statements)

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“…Upon application of magnetic field, the particles experience additional optical force and torque associated with PPHC and PTPS. While the average motional energies of particles remain constant at thermal equilibrium (~k T 1 2 B by equipartition law), the additional forces and torques lead to preferential changes in their mean positions and angular orientations which can be detected using a microscope [55,56]. In the following, we estimate these changes with simplifying approximations.…”

Section: Experimental Proposalmentioning

confidence: 99%

Thermal spin photonics in the near-field of nonreciprocal media

Khandekar

Jacob

2019

New J. Phys.

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The interplay of spin angular momentum and thermal radiation is a frontier area of interest to nanophotonics as well as topological physics. Here, we show that a thick planar slab of a nonreciprocal material, despite being at thermal equilibrium with its environment, can exhibit nonzero photon spin angular momentum and nonzero radiative heat flux in its vicinity. We identify them as the persistent thermal photon spin and the persistent planar heat current respectively. With a practical example system, we reveal that the fundamental origin of these phenomena is connected to the spinmomentum locking of thermally excited evanescent waves. We also discover spin magnetic moment of surface polaritons that further clarifies these features. We then propose an imaging experiment based on Brownian motion that allows one to witness these surprising features by directly looking at them using a lab microscope. We further demonstrate the universal behavior of these near-field thermal radiation phenomena through a comprehensive analysis of gyroelectric, gyromagnetic and magneto-electric nonreciprocal materials. Together, these results expose a surprisingly little explored research area of thermal spin photonics with prospects for new avenues related to non-Hermitian topological photonics and radiative heat transport.

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Section: Experimental Proposalmentioning

confidence: 99%

Thermal spin photonics in the near-field of nonreciprocal media

Khandekar

Jacob

2019

New J. Phys.

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“…The random movement of gas particles can be simulated using a method called a random walk which involves stochastically simulating a series of random molecular movements . During every step of the simulation, a random variable, positive or negative, is added to the position of the particle causing it to move.…”

Section: Simulation Examplesmentioning

confidence: 99%

“…Despite the prevalence, there is a paucity of introductory material on the subject appropriate for undergraduate chemistry courses. Many current examples that are at an undergraduate level use software that obscures the underlying stochastic process or employ dice/random value tables. − This article serves as an introduction to basic stochastic simulations for undergraduates and demonstrates how randomness guides physical and chemical processes with methods that can be implemented using computer software.…”

Section: Introductionmentioning

confidence: 99%

“…The first portion of this article provides the reader with an introduction to using random variables in simulations. The remainder of this article is devoted to detailed examples of stochastic simulations which include Brownian motion, diffusion, chemical kinetics, and chain-growth polymerization . Jupyter notebooks with the simulations coded in Python and NumPy are also provided in the Supporting Information for readers interested in experimenting with the simulations or for use in undergraduate courses.…”

Section: Introductionmentioning

confidence: 99%

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Introduction to Stochastic Simulations for Chemical and Physical Processes: Principles and Applications

Weiss

2017

J. Chem. Educ.

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An introduction to digital stochastic simulations for modeling a variety of physical and chemical processes is presented. Despite the importance of stochastic simulations in chemistry, the prevalence of turn-key software solutions can impose a layer of abstraction between the user and the underlying approach obscuring the methodology being employed. This article introduces the use of random variable generators in simulating physical and chemical processes suitable for use in undergraduate chemistry courses through detailed illustrative examples which include DNA sequences, Brownian motion, diffusion, chemical kinetics, and chain-growth polymerization. The results of the stochastic simulations are also compared to theoretical models. Jupyter notebooks containing Python code for running these simulations are provided in the Supporting Information section.

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“…Brownian motion is an important concept in chemistry and in other fields of science and engineering, and has several times been a topic in this Journal (1)(2)(3)(4)(5)(6)(7)(8). Because the most popular application of Brownian motion is concerned with diffusion or transport phenomena, the theory of Brownian motion along with the relevant mathematics has usually been discussed in the context of deterministic models involving analytical solutions of ordinary or partial differential equations (ODEs or PDEs) such as the Fick's laws.…”

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confidence: 99%

Simulation of One-Dimensional Brownian Motion by Stochastic Differential Equations

Muranaka¹

1999

J. Chem. Educ.

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Diffusion and transport phenomena can be explained by deterministic models involving ordinary or partial differential equations, and Brownian motion has been a popular model for simulating random physical processes. The real dynamics of Brownian motion, however, can be better presented in terms of stochastic or probabilistic models. A Basic program named RWALK, which stands for "random walk", has been written to simulate diffusion processes by a simple yet powerful mathematical tool known as a stochastic differential equation. By entering the initial value, drift, standard deviation (which is related to diffusion coefficient), and periods to be simulated, a student can generate various sample paths or trajectories with this program. A simple and economical exercise to model a student's wrist pulse has been devised. All suggested activities can be done in one normal laboratory period, and the simulation exercises with RWALK should give students in physical chemistry a concrete command over an abstract topic like Brownian motion as well as some exposure to basic statistical concepts using a spreadsheet or a commercial statistical software.

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Brownian motion: A classroom demonstration and student experiment

Cited by 7 publications

References 0 publications

Thermal spin photonics in the near-field of nonreciprocal media

Thermal spin photonics in the near-field of nonreciprocal media

Introduction to Stochastic Simulations for Chemical and Physical Processes: Principles and Applications

Simulation of One-Dimensional Brownian Motion by Stochastic Differential Equations

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