Introduction to Conformal Invariance and its Applications to Critical Phenomena

This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their application to the Ising, Potts, Ashkin-Teller and XY models, tricritical behaviour, the Yang-Lee singularity and the XXZ chain are presented. Finite-size scaling techniques and their conformal extensions are treated in detail. The vicinity of the critical point is studied using the exact $S$-matrix approach, the truncation method, the thermodynamic Bethe ansatz and asymptotic finite-size scaling functions. The integrability of the two-dimensional Ising model in a magnetic field is also dealt with. Finally, the extension of conformal invariance to surface critical phenomena is described and an outlook towards possible applications in critical dynamics is given.Comment: xvi + 260 pages (here only the first xvi are given), Latex, UGVA-DPT 1992/11-79

A two-scale Stefan problem arising in a model for tree sap exudation

The study of tree sap exudation, in which a (leafless) tree generates elevated stem pressure in response to repeated daily freeze-thaw cycles, gives rise to an interesting multi-scale problem involving heat and multiphase liquid/gas transport. The pressure generation mechanism is a cellular-level process that is governed by differential equations for sap transport through porous cell membranes, phase change, heat transport, and generation of osmotic pressure. By assuming a periodic cellular structure based on an appropriate reference cell, we derive an homogenized heat equation governing the global temperature on the scale of the tree stem, with all the remaining physics relegated to equations defined on the reference cell. We derive a corresponding strong formulation of the limit problem and use it to design an efficient numerical solution algorithm. Numerical simulations are then performed to validate the results and draw conclusions regarding the phenomenon of sap exudation, which is of great importance in trees such as sugar maple and a few other related species. The particular form of our homogenized temperature equation is obtained using periodic homogenization techniques with two-scale convergence, which we investigate theoretically in the context of a simpler two-phase Stefan-type problem corresponding to a periodic array of melting cylindrical ice bars with a constant thermal diffusion coefficient. For this reduced model, we prove results on existence, uniqueness and convergence of the two-scale limit solution in the weak form, clearly identifying the missing pieces required to extend the proofs to the fully nonlinear sap exudation model. Numerical simulations of the reduced equations are then compared with results from the complete sap exudation model.Comment: 35 pages, 8 figures. arXiv admin note: text overlap with arXiv:1411.303

CZĘSTOTLIWOŚCIOWY KONWERTER PWM ZE STEROWANIEM W OTWARTEJ PĘTLI

An harmonic domain model is developed for open-loop controlled voltage source inverters, which provides the steady-state solution for integer multiples of the fundamental frequency. The convolution of the switching function spectrum with the converter currents and voltages is used to describe the coupling of the AC side and the DC side. The modeling is based on a single phase leg and is extended to a single-phase and a three-phase voltage source inverter, which results in a non-linear algebraic equation system. For open-loop control the switching function is independent of the converter currents and voltages and the model is simplified to a linear equation system. This straightforward and fast model is verified by time domain simulations and experimental results. The modeling can be adapted to systems of coupled converters, which is presented for a back-to-back converter system showing the harmonic interaction of the connected subsystems.Opracowano model w domenie częstotliwości dla falowników napięcia sterowanych w otwartej pętli, który zapewnia rozwiązanie w stanie ustalonym dla całkowitych wielokrotności częstotliwości podstawowej. Splot spektrum funkcyjnego przełączania z prądami i napięciami przemiennika służy do opisania sprzężenia strony prądu przemiennego i prądu stałego. Modelowanie opiera się na pojedynczej fazie i jest rozszerzone na falownik jednofazowy i trójfazowy, co skutkuje nieliniowym układem równań algebraicznych. W przypadku sterowania w otwartej pętli funkcja przełączania jest niezależna od prądów i napięć przekształtnika, a model jest uproszczony do układu równań liniowych. Ten prosty i szybki model jest weryfikowany przez symulacje w dziedzinie czasu i wyniki eksperymentalne. Modelowanie może być dostosowane do systemów przekształtników sprzężonych, które przedstawiono dla systemu konwertera równoległego pokazującego harmoniczne oddziaływanie połączonych podsystemów

Frequency-Domain Modeling of Harmonic Interactions in Voltage-Source Inverters with Closed-Loop Control

Power electronic converters, together with their loads, sources, and controls, form a coupled system that includes many nonlinear interactions, for instance due to pulse-width modulation (PWM) and feedback control. In this paper we develop a complete, nonlinear modeling approach for voltage-source inverters in the frequency domain, taking into account the harmonic components introduced into the system from the inputs and from the nonlinear digital PWM. The most important contribution is a method for analyzing how these harmonics propagate through the nonlinear system in steady state. To enable this, an analytic model of PWM with arbitrary, multiple-frequency input is necessary. A revised model of Asymmetrical regularly-sampled double-edge PWM (AD-PWM) is proposed and its incorporation into the system model regarding sampling effects is discussed. The resulting nonlinear equation system is numerically and simultaneously solved, yielding the spectra of all relevant signals in the converter. The results are validated with time-domain simulations and with measurements, proving the effectiveness of the proposed approach

Decorrelation using Optimal Transport

Being able to decorrelate a feature space from protected attributes is an area of active research and study in ethics, fairness, and also natural sciences. We introduce a novel decorrelation method using Convex Neural Optimal Transport Solvers (Cnots), that is able to decorrelate continuous feature space against protected attributes with optimal transport. We demonstrate how well it performs in the context of jet classification in high energy physics, where classifier scores are desired to be decorrelated from the mass of a jet. The decorrelation achieved in binary classification approaches the levels achieved by the state-of-the-art using conditional normalising flows. When moving to multiclass outputs the optimal transport approach performs significantly better than the state-of-the-art, suggesting substantial gains at decorrelating multidimensional feature spaces

Over-stimulation of insulin/IGF-1 signaling by western diet may promote diseases of civilization: lessons learnt from laron syndrome

The insulin/insulin-like growth factor-1 (IGF-1) pathway drives an evolutionarily conserved network that regulates lifespan and longevity. Individuals with Laron syndrome who carry mutations in the growth hormone receptor (GHR) gene that lead to severe congenital IGF-1 deficiency with decreased insulin/IGF-1 signaling (IIS) exhibit reduced prevalence rates of acne, diabetes and cancer. Western diet with high intake of hyperglycemic carbohydrates and insulinotropic dairy over-stimulates IIS. The reduction of IIS in Laron subjects unmasks the potential role of persistent hyperactive IIS mediated by Western diet in the development of diseases of civilization and offers a rational perspective for dietary adjustments with less insulinotropic diets like the Paleolithic diet