Theoretical limit of the minimal magnetization switching field and the optimal field pulse for Stoner particles

The theoretical limit of the minimal magnetization switching field and the optimal field pulse design for uniaxial Stoner particles are investigated. Two results are obtained. One is the existence of a theoretical limit of the smallest magnetic field out of all possible designs. It is shown that the limit is proportional to the damping constant in the weak damping regime and approaches the Stoner-Wohlfarth (SW) limit at large damping. For a realistic damping constant, this limit is more than ten times smaller than that of so-called precessional magnetization reversal under a non-collinear static field. The other is on the optimal field pulse design: If the magnitude of a magnetic field does not change, but its direction can vary during a reversal process, there is an optimal design that gives the shortest switching time. The switching time depends on the field magnitude, damping constant, and magnetic anisotropy. However, the optimal pulse shape depends only on the damping constant.Comment: 4 pages, 4 figure

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Critical current under an optimal time-dependent polarization direction for Stoner particles in spin-transfer torque induced fast magnetization reversal

Fast magnetization reversal of uniaxial Stoner particles by spin-transfer torque due to the spin-polarized electric current is investigated. It is found that a current with a properly designed time-dependent polarization direction can dramatically reduce the critical current density required to reverse a magnetization. Under the condition that the magnitude and the polarization degree of the current do not vary with time, the shape of the optimal time-dependent polarization direction is obtained such that the magnetization reversal is the fastest.Comment: 4 pages, 3 figure

Discussion on `Characterization of 1-3 piezoelectric polymer composites - a numerical and analytical evaluation procedure for thickness mode vibrations' by C.V. Madhusudhana Rao, G. Prasad, Condens. Matter Phys., 2010, Vol.13, No.1, 13703

In the paper entitled "Characterization of 1-3 piezoelectric polymer composites - a numerical and analytical evaluation procedure for thickness mode vibrations", the dependence of the thickness electromechanical coupling coefficient on the aspect ratio of piezoceramic fibers is studied by finite element simulation for various volume fractions of piezoceramic fibers in a 1-3 composite. The accuracy of the results is questionable because the boundary condition claiming that `predefined displacements are applied perpendicularly on $C^+$ plane on all nodes' is not suitable for the analysis of 1-3 composite with comparatively large aspect ratio from 0.2 to 1. A discussion regarding this problem and the suggested corrections are presented in this paper.Comment: 4 pages, 3 figure

Floquet spin states in graphene under ac driven spin-orbit interaction

We study the role of periodically driven time-dependent Rashba spin-orbit coupling (RSOC) on a monolayer graphene sample. After recasting the originally $4\times 4$ system of dynamical equations as two time-reversal related two-level problems, the quasi-energy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case the system is a gapped at the Dirac point. The rotating wave approximation (RWA) applied to the driven system unphysically preserves this feature, while the Magnus-Floquet approach as well as a numerically exact evaluation of the Floquet equation show that this gap is dynamically closed. In addition, a sizable oscillating pattern of the out-of-plane spin polarization is found in the driven case for states which completely unpolarized in the static limit. Evaluation of the autocorrelation function shows that the original uniform interference pattern corresponding to time-independent RSOC gets distorted. The resulting structure can be qualitatively explained as a consequence of the transitions induced by the ac driving among the static eigenstates, i.e., these transitions modulate the relative phases that add up to give the quantum revivals of the autocorrelation function. Contrary to the static case, in the driven scenario, quantum revivals (suppresions) are correlated to spin up (down) phases.Comment: 10 pages, 8 figures. Typos corrected. Accepted for publication in PR

Vision-based hand gesture interaction using particle filter, principle component analysis and transition network

Vision-based human-computer interaction is becoming important nowadays. It offers natural interaction with computers and frees users from mechanical interaction devices, which is favourable especially for wearable computers. This paper presents a human-computer interaction system based on a conventional webcam and hand gesture recognition. This interaction system works in real time and enables users to control a computer cursor with hand motions and gestures instead of a mouse. Five hand gestures are designed on behalf of five mouse operations: moving, left click, left-double click, right click and no-action. An algorithm based on Particle Filter is used for tracking the hand position. PCA-based feature selection is used for recognizing the hand gestures. A transition network is also employed for improving the accuracy and reliability of the interaction system. This interaction system shows good performance in the recognition and interaction test

Fast domain wall propagation under an optimal field pulse in magnetic nanowires

We investigate field-driven domain wall (DW) propagation in magnetic nanowires in the framework of the Landau-Lifshitz-Gilbert equation. We propose a new strategy to speed up the DW motion in a uniaxial magnetic nanowire by using an optimal space-dependent field pulse synchronized with the DW propagation. Depending on the damping parameter, the DW velocity can be increased by about two orders of magnitude compared the standard case of a static uniform field. Moreover, under the optimal field pulse, the change in total magnetic energy in the nanowire is proportional to the DW velocity, implying that rapid energy release is essential for fast DW propagation.Comment: 4 pages, 3 figures; updated version replace