Dependable Digitally-Assisted Mixed-Signal IPs Based on Integrated Self-Test & Self-Calibration

Heterogeneous SoC devices, including sensors, analogue and mixed-signal front-end circuits and the availability of massive digital processing capability, are being increasingly used in safety-critical applications like in the automotive, medical, and the security arena. Already a significant amount of attention has been paid in literature with respect to the dependability of the digital parts in heterogeneous SoCs. This is in contrast to especially the sensors and front-end mixed-signal electronics; these are however particular sensitive to external influences over time and hence determining their dependability. This paper provides an integrated SoC/IP approach to enhance the dependability. It will give an example of a digitally-assisted mixed-signal front-end IP which is being evaluated under its mission profile of an automotive tyre pressure monitoring system. It will be shown how internal monitoring and digitally-controlled adaptation by using embedded processors can help in terms of improving the dependability of this mixed-signal part under harsh conditions for a long time

Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models

In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form $$\sum_{j=0}^{n} \sum_{i=0}^j \frac{\binom{f_1(n)}{i}}{\binom{f_2(n)}{j}}\,c^{i-j},$$ where $f_1, f_2$ are functions of $n$. Such sums appear in the analyses of the Mabinogion urn and the Ehrenfest urn in probability. Using hypergeometric functions, we are able to simplify these sums, and in some cases express them in terms of the harmonic numbers

Calculation of the quark condensate through Schwinger-Dyson equation

In this letter, we clarify the algebra expression for calculating the quark condensate based on the non-perturbative quark propagator calculated through Schwinger-Dyson equation. The quark condensates, which characterize the low energy QCD vacuum, should not get a divergent quantity at large energy scale; the re-normalization group evolution behaviour at large energy scale therefore should be interpreted as "smeared collective effects" for it contains both perturbative and non-perturbative parts. We prefer the integral expression and get a quantity which is both convergent and scale dependent.Comment: 6 page

Counting points on varieties over finite fields of small characteristic

We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this result is an efficient method for computing the order of the group of rational points on the Jacobian of a smooth geometrically connected projective curve over a finite field of small characteristic.Comment: To appear in: "Algorithmic number theory: lattices, number fields, curves and cryptography", J.P. Buhler and P. Stevenhagen (ed.), Math. Sci. Res. Inst. Publ. 44. (Submitted July 2001; Accepted October 2002.

Integrals of KK and EE from Lattice Sums

We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals $K$ and $E$. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced

Holonomic alchemy and series for 1/π1/\pi

We adopt the "translation" as well as other techniques to express several identities conjectured by Z.-W. Sun in arXiv:1102.5649v47 by means of known formulas for $1/\pi$ involving Domb and other Ap\'ery-like sequences.Comment: 23 page

Propagation of Solar Energetic Particles in Three-dimensional Interplanetary Magnetic Fields: Radial Dependence of Peak Intensities

A functional form I_{max}(R)=kR^{-\alpha}, where R is the radial distance of spacecraft, was usually used to model the radial dependence of peak intensities I_{max}(R) of solar energetic particles (SEPs). In this work, the five-dimensional Fokker-Planck transport equation incorporating perpendicular diffusion is numerically solved to investigate the radial dependence of SEP peak intensities. We consider two different scenarios for the distribution of spacecraft fleet: (1) along the radial direction line, (2) along the Parker magnetic field line. We find that the index \alpha in the above expression varies in a wide range, primarily depending on the properties (e.g., location, coverage) of SEP sources and on the longitudinal/latitudinal separations between the sources and the magnetic footpoints of the observers. Particularly, the situation that whether the magnetic footpoint of the observer is located inside or outside of the SEP source is a crucial factor determining the values of index \alpha. A two-phase phenomenon is found in the radial dependence of peak intensities. The "position" of the breakpoint (transition point/critical point) is determined by the magnetic connection status of the observers. This finding suggests that a very careful examination of magnetic connection between SEP source and each spacecraft should be taken in the observational studies. We obtain a lower limit of R^{-1.7\pm0.1} for empirically modelling the radial dependence of SEP peak intensities. Our findings in this work can be used to explain the majority of the previous multispacecraft survey results, and especially to reconcile the different/conflicting empirical values of index \alpha in the literature.Comment: Published in Ap

Spinon walk in quantum spin ice

We study a minimal model for the dynamics of spinons in quantum spin ice. The model captures the essential strong coupling between the spinon and the disordered background spins. We demonstrate that the spinon motion can be mapped to a random walk with an entropy-induced memory in imaginary time. Our numerical simulation of the spinon walk indicates that the spinon propagates as a massive quasiparticle at low energy despite its strong coupling to the spin background at the microscopic energy scale. We discuss the experimental implications of our findings.Comment: 12 pages, 10 figure

Cleavage Tendency of Anisotropic Two Dimensional Materials: ReX2 (X=S, Se) and WTe2

With unique distorted 1T structure and the associated in-plane anisotropic properties, mono- and few-layer ReX2 (X=S, Se) have recently attracted particular interest. Based on experiment and first-principles calculations, we investigate the fracture behavior of ReX2. We find that the cleaved edges of ReX2 flakes usually form an angle of ~120{\deg} or ~60{\deg}. In order to understand such phenomenon, we perform comprehensive investigations on the uniaxial tensile stress-strain relation of monolayer and multi-layer ReX2 sheets. Our numerical calculation shows that the particular cleaved edges of ReX2 flakes are caused by unique anisotropic ultimate tensile strengths and critical strains. We also calculate the stress-strain relation of WTe2, which explains why their cleaved edges are not corresponding to the principle axes. Our proposed mechanism about the fracture angle has also been supported by the calculated cleavage energies and surface energies for different edge surfaces

Nonlinear ER effects in an ac applied field

The electric field used in most electrorheological (ER) experiments is usually quite high, and nonlinear ER effects have been theoretically predicted and experimentally measured recently. A direct method of measuring the nonlinear ER effects is to examine the frequency dependence of the same effects. For a sinusoidal applied field, we calculate the ac response which generally includes higher harmonics. In is work, we develop a multiple image formula, and calculate the total dipole moments of a pair of dielectric spheres, embedded in a nonlinear host. The higher harmonics due to the nonlinearity are calculated systematically.Comment: Presented at Conference on Computational Physics (CCP2000), held at Gold Coast, Australia from 3-8, December 200