Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Investigation Into Harmful Patterns Over Multitrack Shingled Magnetic Detection Using the Voronoi Model

Two-dimensional magnetic recording 2-D (TDMR) is a promising technology for next generation magnetic storage systems based on a systems-level framework involving sophisticated signal processing at the core. The TDMR channel suffers from severe jitter noise along with electronic noise that needs to be mitigated during signal detection and recovery. Recently, we developed noise prediction-based techniques coupled with advanced signal detectors to work with these systems. However, it is important to understand the role of harmful patterns that can be avoided during the encoding process. In this paper, we investigate the Voronoi-based media model to study the harmful patterns over multitrack shingled recording systems. Through realistic quasi-micromagnetic simulation studies, we identify 2-D data patterns that contribute to high media noise. We look into the generic Voronoi model and present our analysis on multitrack detection with constrained coded data. We show that the 2-D constraints imposed on input patterns result in an order of magnitude improvement in the bit-error rate for the TDMR systems. The use of constrained codes can reduce the complexity of 2-D intersymbol interference (ISI) signal detection, since the lesser 2-D ISI span can be accommodated at the cost of a nominal code rate loss. However, a system must be designed carefully so that the rate loss incurred by a 2-D constraint does not offset the detector performance gain due to more distinguishable readback signals.