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This paper proposes a simple and accurate monomial-like equation for estimating the inductance of Multilayer Rectangle-shaped Planar Windings (MLRPWs) for high-frequency, high-power applications. The equation consists of the power product…
We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to…
The winding of a single polymer in thermal equilibrium around a repulsive cylindrical obstacle is perhaps the simplest example of statistical mechanics in a multiply connected geometry. As shown by S.F. Edwards, this problem is closely…
Determination of polymer molecular weight distribution (MWD) from rheological measurements is desirable due to the ease and low cost of rheometry compared to other methods such as gel permeation chromatography. However, relating MWD to…
The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
Several heuristic procedures to estimate the rotor position of permanent magnet synchronous motors (PMSM) via signal injection have been reported in the literature. Using averaging theory, a framework to analyse such schemes has been…
We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (\Delta…
Estimating a vector $\mathbf{x}$ from noisy linear measurements $\mathbf{Ax}+\mathbf{w}$ often requires use of prior knowledge or structural constraints on $\mathbf{x}$ for accurate reconstruction. Several recent works have considered…
We discuss the appropriate techniques for modelling the geometry of open ended elastic polymer molecules. The molecule is assumed to have fixed endpoints on a boundary surface. In particular we discuss the concept of the winding number, a…
Let $M^m$ be an oriented manifold, let $N^{m-1}$ be an oriented closed manifold, and let $p$ be a point in $M^m$. For a smooth map $f:N^{m-1} \to M^m, p \not\in Im f,$ we introduce an invariant $awin_p(f)$ that can be regarded as a…
For designing high-field electromagnets, the Lorentz force on coils must be computed to ensure a support structure is feasible, and the inductance should be computed to evaluate the stored energy. Also, the magnetic field and its variation…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity…
This paper compares two actuator line methodologies for modelling wind turbines employing high-order h/p solvers and large-eddy simulations. The methods combine the accuracy of high-order solvers (in this work the maximum order is 6) with…
This paper presents analytical results on longitudinal power profile estimation (PPE) methods, which visualize signal power evolution in optical fibers at a coherent receiver. The PPE can be formulated as an inverse problem of the nonlinear…
We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending…
The most commonly used weighted least square state estimator in power industry is nonlinear and formulated by using conventional measurements such as line flow and injection measurements. PMUs (Phasor Measurement Units) are gradually adding…
The Immersion and Invariance (I&I) wind speed estimator is a powerful and widely-used technique to estimate the rotor effective wind speed on horizontal axis wind turbines. Anyway, its global convergence proof is rather cumbersome, which…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…