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This chapter discusses analysis of data acquired using optical imaging techniques, which have the potential to combine good spatial and temporal resolution. Topics covered include noise sources, differential and ratio maps, and multivariate methods.

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's calculus lemma. The transform of the Langevin equation obeys the ordinary calculus rule, hence can be easily performed and some misleadings can be avoided. The origin of the difference between this approach and that using Ito's lemma comes from the different definitions of the stochastic integral. This chapter also discusses drift velocity, an example with an exact solution, use of Langevin equation for a general random variable, extension of this equation to the multiple dimensional case, and means of products of random variables and noise source.

Magnetic information storage has evolved rapidly, with advances in materials, either by scaling or by incorporating newly discovered phenomena, contributing significantly in their evolution from tapes, to HDDs in both longitudinal and perpendicular geometries, to solid-state memory devices. This chapter presents a comprehensive overview, covering in detail the principles of the recording process and a qualitative description of current and emerging technologies. In general, the width of a recorded transition is proportional to the magnetization–thickness product (M_rδ) of the medium; this should be as small as possible. Noise in the recorded signal is dominated by the physical microstructure of the medium and high recording densities require smallest grain sizes (D_g). There are two time scales of interest in recording: short (10⁻⁹ s), governed by the switching of the medium within the short write pulse, and long (~10 years), defined by the required stability of the recorded information for subsequent retrieval. The trade-offs between three competing requirements to achieve high signal to noise, long-term thermal stability of the written bits, and writeability within the limits of maximally generated write fields, provide an ongoing challenge in HDD media design and development. Different approaches to increasing areal densities in magnetic recording are presented, with heat-assisted magnetic recording (HAMR) and bit-patterned media (BPM) currently being favored; in addition, solid-state magnetic memory architectures, such as STT-MRAM and devices using current-induced domain wall motion, appear promising.