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Timothy J Davis - One of the best experts on this subject based on the ideXlab platform.

  • 2d magnetic traps for ultra cold atoms a simple theory using Complex Numbers
    European Physical Journal D, 2002
    Co-Authors: Timothy J Davis
    Abstract:

    The properties of two-dimensional magnetic traps for laser-cooled atoms are analysed using Complex functions. The two components of the magnetic field from a series of parallel, infinitely long, current-carrying wires are represented by a Single Complex Number. The regions of the field where paramagnetic atoms can be trapped occur where the magnetic field is zero. The locations of the zeroes of the field are obtained as the solution to a polynomial and the multiplicity m of the solution determines both the 2(m + 1)-pole nature of the trap and the field gradient through the centre. The zeroes of the field can be merged or split by varying the locations of the currents, their strengths or by applying a uniform magnetic field. The theory is applied to magnetic traps created from long thin wires or permanent magnets on a substrate. The properties of a Number of magnetic trap configurations used for atom guides are discussed.

John Semmlow - One of the best experts on this subject based on the ideXlab platform.

  • linear systems in the frequency domain the transfer function
    Signals and Systems for Bioengineers (Second Edition)#R##N#A MATLAB-Based Introduction, 2012
    Co-Authors: John Semmlow
    Abstract:

    Publisher Summary This chapter presents a discusion of linear systems in a frequency domain. Linear systems can be represented by differential equations and transfer functions that are combinations of four basic elements. If signals are restricted to steady-state sinusoids, then phasor techniques can be used to represent these elements by algebraic equations that are functions of only frequency. Phasor techniques represent steady-state sinusoids as a Single Complex Number. With this representation, the calculus operation of differentiation can be implemented in algebra simply as multiplication by jω, where j = √(−1) ω is frequency in radians. If all the elements in a system can be represented by algebraic operations, they can be combined into a Single equation termed the transfer function. The transfer function relates the output of a system to the input through a Single equation. The transfer function can only deal with signals that are sinusoidal or can be decomposed into sinusoids. The transfer function not only offers a succinct representation of the system, it also gives a direct link to the frequency spectrum of the system. The concepts of analog and system representations of linear processes are explained in the chapter. It explains linearity, time invariance, causality, and superposition. The response of system elements to sinusoidal inputs is also discussed in the chapter.