Magnetic fields around radio galaxies from Faraday rotation measure analysis

The purpose of this thesis is to investigate the strength and structure of the magnetized medium surrounding radio galaxies via observations of the Faraday effect. This study is based on an analysis of the polarization properties of radio galaxies selected to have a range of morphologies (elongated tails, or lobes with small axial ratios) and to be located in a variety of environments (from rich cluster core to small group). The targets include famous objects like M84 and M87. A key aspect of this work is the combination of accurate radio imaging with high-quality X-ray data for the gas surrounding the sources. Although the focus of this thesis is primarily observational, I developed analytical models and performed two- and three-dimensional numerical simulations of magnetic fields. The steps of the thesis are: (a) to analyze new and archival observations of Faraday rotation measure (RM) across radio galaxies and (b) to interpret these and existing RM images using sophisticated two and three-dimensional Monte Carlo simulations. The approach has been to select a few bright, very extended and highly polarized radio galaxies. This is essential to have high signal-to-noise in polarization over large enough areas to allow computation of spatial statistics such as the structure function (and hence the power spectrum) of rotation measure, which requires a large number of independent measurements. New and archival Very Large Array observations of the target sources have been analyzed in combination with high-quality X-ray data from the Chandra, XMM-Newton and ROSAT satellites. The work has been carried out by making use of: 1) Analytical predictions of the RM structure functions to quantify the RM statistics and to constrain the power spectra of the RM and magnetic field. 2) Two-dimensional Monte Carlo simulations to address the effect of an incomplete sampling of RM distribution and so to determine errors for the power spectra. 3) Methods to combine measurements of RM and depolarization in order to constrain the magnetic-field power spectrum on small scales. 4) Three-dimensional models of the group/cluster environments, including different magnetic field power spectra and gas density distributions. This thesis has shown that the magnetized medium surrounding radio galaxies appears more complicated than was apparent from earlier work. Three distinct types of magnetic-field structure are identified: an isotropic component with large-scale fluctuations, plausibly associated with the intergalactic medium not affected by the presence of a radio source; a well-ordered field draped around the front ends of the radio lobes and a field with small-scale fluctuations in rims of compressed gas surrounding the inner lobes, perhaps associated with a mixing layer.

Vector Fields in a Rindler Space

In questo lavoro ci si propone di studiare la quantizzazione del campo vettoriale, massivo e non massivo, in uno spazio-tempo di Rindler, considerando in particolare i gauge di Feynman e assiale. Le equazioni del moto vengono risolte esplicitamente in entrambi i casi; sotto opportune condizioni, è stato inoltre possibile trovare una base completa e ortonormale di soluzioni delle equazioni di campo in termini di modi normali di Fulling. Si è poi analizzata la quantizzazione dei campi vettoriali espressi in questa base.

Influence of Electromagnetic Fields On Biological Signalling: An Experimental and Theoretical Approach

The primary goals of this study were to develop a cell-free in vitro assay for the assessment of nonthermal electromagnetic (EMF) bioeffects and to develop theoretical models in accord with current experimental observations. Based upon the hypothesis that EMF effects operate by modulating Ca2+/CaM binding, an in vitro nitric oxide (NO) synthesis assay was developed to assess the effects of a pulsed radiofrequency (PRF) signal used for treatment of postoperative pain and edema. No effects of PRF on NO synthesis were observed. Effects of PRF on Ca2+/CaM binding were also assessed using a Ca2+-selective electrode, also yielding no EMF Ca2+/CaM binding. However, a PRF effect was observed on the interaction of hemoglobin (Hb) with tetrahydrobiopterin, leading to the development of an in vitro Hb deoxygenation assay, showing a reduction in the rate of Hb deoxygenation for exposures to both PRF and a static magnetic field (SMF). Structural studies using pyranine fluorescence, Gd3+ vibronic sideband luminescence and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy were conducted in order to ascertain the mechanism of this EMF effect on Hb. Also, the effect of SMF on Hb oxygen saturation (SO2) was assessed under gas-controlled conditions. These studies showed no definitive changes in protein/solvation structure or SO2 under equilibrium conditions, suggesting the need for real-time instrumentation or other means of observing out-of-equilibrium Hb dynamics. Theoretical models were developed for EMF transduction, effects on ion binding, neuronal spike timing, and dynamics of Hb deoxygenation. The EMF sensitivity and simplicity of the Hb deoxygenation assay suggest a new tool to further establish basic biophysical EMF transduction mechanisms. If an EMF-induced increase in the rate of deoxygenation can be demonstrated in vivo, then enhancement of oxygen delivery may be a new therapeutic method by which clinically relevant EMF-mediated enhancement of growth and repair processes can occur.

Evaluation of Human Exposure to Magnetic Fields Generated by Electric Power Systems in Complex Configurations

The international growing concern for the human exposure to magnetic fields generated by electric power lines has unavoidably led to imposing legal limits. Respecting these limits, implies being able to calculate easily and accurately the generated magnetic field also in complex configurations. Twisting of phase conductors is such a case. The consolidated exact and approximated theory regarding a single-circuit twisted three-phase power cable line has been reported along with the proposal of an innovative simplified formula obtained by means of an heuristic procedure. This formula, although being dramatically simpler, is proven to be a good approximation of the analytical formula and at the same time much more accurate than the approximated formula found in literature. The double-circuit twisted three-phase power cable line case has been studied following different approaches of increasing complexity and accuracy. In this framework, the effectiveness of the above-mentioned innovative formula is also examined. The experimental verification of the correctness of the twisted double-circuit theoretical analysis has permitted its extension to multiple-circuit twisted three-phase power cable lines. In addition, appropriate 2D and, in particularly, 3D numerical codes for simulating real existing overhead power lines for the calculation of the magnetic field in their vicinity have been created. Finally, an innovative ‘smart’ measurement and evaluation system of the magnetic field is being proposed, described and validated, which deals with the experimentally-based evaluation of the total magnetic field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the three Cartesian field components and their correlation with the field currents via multilinear regression techniques. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.

Using national FADN database to describe Italian farms and arable fields. A comparison of sustainability level between organic versus conventional regimes.

The study defines a new farm classification and identifies the arable land management. These aspects and several indicators are taken into account to estimate the sustainability level of farms, for organic and conventional regimes. The data source is Italian Farm Account Data Network (RICA) for years 2007-2011, which samples structural and economical information. An environmental data has been added to the previous one to better describe the farm context. The new farm classification describes holding by general informations and farm structure. The general information are: adopted regime and farm location in terms of administrative region, slope and phyto-climatic zone. The farm structures describe the presence of main productive processes and land covers, which are recorded by FADN database. The farms, grouped by homogeneous farm structure or farm typology, are evaluated in terms of sustainability. The farm model MAD has been used to estimate a list of indicators. They describe especially environmental and economical areas of sustainability. Finally arable lands are taken into account to identify arable land managements and crop rotations. Each arable land has been classified by crop pattern. Then crop rotation management has been analysed by spatial and temporal approaches. The analysis reports a high variability inside regimes. The farm structure influences indicators level more than regimes, and it is not always possible to compare the two regimes. However some differences between organic and conventional agriculture have been found. Organic farm structures report different frequency and geographical location than conventional ones. Also different connections among arable lands and farm structures have been identified.

Characterization of electromagnetic fields in the aSPECT spectrometer and reduction of systematic errors

Das aSPECT Spektrometer wurde entworfen, um das Spektrum der Protonen beimrnZerfall freier Neutronen mit hoher Präzision zu messen. Aus diesem Spektrum kann dann der Elektron-Antineutrino Winkelkorrelationskoeffizient "a" mit hoher Genauigkeit bestimmt werden. Das Ziel dieses Experiments ist es, diesen Koeffizienten mit einem absoluten relativen Fehler von weniger als 0.3% zu ermitteln, d.h. deutlich unter dem aktuellen Literaturwert von 5%.rnrnErste Messungen mit dem aSPECT Spektrometer wurden an der Forschungsneutronenquelle Heinz Maier-Leibnitz in München durchgeführt. Jedoch verhinderten zeitabhängige Instabilitäten des Meßhintergrunds eine neue Bestimmung von "a".rnrnDie vorliegende Arbeit basiert hingegen auf den letzten Messungen mit dem aSPECTrnSpektrometer am Institut Laue-Langevin (ILL) in Grenoble, Frankreich. Bei diesen Messungen konnten die Instabilitäten des Meßhintergrunds bereits deutlich reduziert werden. Weiterhin wurden verschiedene Veränderungen vorgenommen, um systematische Fehler zu minimieren und um einen zuverlässigeren Betrieb des Experiments sicherzustellen. Leider konnte aber wegen zu hohen Sättigungseffekten der Empfängerelektronik kein brauchbares Ergebnis gemessen werden. Trotzdem konnten diese und weitere systematische Fehler identifiziert und verringert, bzw. sogar teilweise eliminiert werden, wovon zukünftigernStrahlzeiten an aSPECT profitieren werden.rnrnDer wesentliche Teil der vorliegenden Arbeit befasst sich mit der Analyse und Verbesserung der systematischen Fehler, die durch das elektromagnetische Feld aSPECTs hervorgerufen werden. Hieraus ergaben sich vielerlei Verbesserungen, insbesondere konnten die systematischen Fehler durch das elektrische Feld verringert werden. Die durch das Magnetfeld verursachten Fehler konnten sogar soweit minimiert werden, dass nun eine Verbesserung des aktuellen Literaturwerts von "a" möglich ist. Darüber hinaus wurde in dieser Arbeit ein für den Versuch maßgeschneidertes NMR-Magnetometer entwickelt und soweit verbessert, dass nun Unsicherheiten bei der Charakterisierung des Magnetfeldes soweit reduziert wurden, dass sie für die Bestimmung von "a" mit einer Genauigkeit von mindestens 0.3% vernachlässigbar sind.

Geomorphological and statistical analysis on Ravenna dune fields changes, based on Terrestrial Laser Technology

Coastal sand dunes represent a richness first of all in terms of defense from the sea storms waves and the saltwater ingression; moreover these morphological elements constitute an unique ecosystem of transition between the sea and the land environment. The research about dune system is a strong part of the coastal sciences, since the last century. Nowadays this branch have assumed even more importance for two reasons: on one side the born of brand new technologies, especially related to the Remote Sensing, have increased the researcher possibilities; on the other side the intense urbanization of these days have strongly limited the dune possibilities of development and fragmented what was remaining from the last century. This is particularly true in the Ravenna area, where the industrialization united to the touristic economy and an intense subsidence, have left only few dune ridges residual still active. In this work three different foredune ridges, along the Ravenna coast, have been studied with Laser Scanner technology. This research didn’t limit to analyze volume or spatial difference, but try also to find new ways and new features to monitor this environment. Moreover the author planned a series of test to validate data from Terrestrial Laser Scanner (TLS), with the additional aim of finalize a methodology to test 3D survey accuracy. Data acquired by TLS were then applied on one hand to test some brand new applications, such as Digital Shore Line Analysis System (DSAS) and Computational Fluid Dynamics (CFD), to prove their efficacy in this field; on the other hand the author used TLS data to find any correlation with meteorological indexes (Forcing Factors), linked to sea and wind (Fryberger's method) applying statistical tools, such as the Principal Component Analysis (PCA).

Computer simulations of slowly relaxing systems in external fields

Eine der offenen Fragen der aktuellen Physik ist das Verständnis von Systemen im Nichtgleichgewicht. Im Gegensatz zu der Gleichgewichtsphysik ist in diesem Bereich aktuell kein Formalismus bekannt der ein systematisches Beschreiben der unterschiedlichen Systeme ermöglicht. Um das Verständnis über diese Systeme zu vergrößern werden in dieser Arbeit zwei unterschiedliche Systeme studiert, die unter einem externen Feld ein starkes nichtlineares Verhalten zeigen. Hierbei handelt es sich zum einen um das Verhalten von Teilchen unter dem Einfluss einer extern angelegten Kraft und zum anderen um das Verhalten eines Systems in der Nähe des kritischen Punktes unter Scherung. Das Modellsystem in dem ersten Teil der Arbeit ist eine binäre Yukawa Mischung, die bei tiefen Temperaturen einen Glassübergang zeigt. Dies führt zu einer stark ansteigenden Relaxationszeit des Systems, so dass man auch bei kleinen Kräften relativ schnell ein nichtlineares Verhalten beobachtet. In Abhängigkeit der angelegten konstanten Kraft können in dieser Arbeit drei Regime, mit stark unterschiedlichem Teilchenverhalten, identifiziert werden. In dem zweiten Teil der Arbeit wird das Ising-Modell unter Scherung betrachtet. In der Nähe des kritischen Punkts kommt es in diesem Modell zu einer Beeinflussung der Fluktuationen in dem System durch das angelegte Scherfeld. Dies hat zur Folge, dass das System stark anisotrop wird und man zwei unterschiedliche Korrelationslängen vorfindet, die mit unterschiedlichen Exponenten divergieren. Infolgedessen lässt sich der normale isotrope Formalismus des "finite-size scaling" nicht mehr auf dieses System anwenden. In dieser Arbeit wird gezeigt, wie dieser auf den anisotropen Fall zu verallgemeinern ist und wie damit die kritischen Punkte, sowie die dazu gehörenden kritischen Exponenten berechnet werden können.

Climatological analysis of temperature and salinity fields in the Mediterranean sea

A climatological field is a mean gridded field that represents the monthly or seasonal trend of an ocean parameter. This instrument allows to understand the physical conditions and physical processes of the ocean water and their impact on the world climate. To construct a climatological field, it is necessary to perform a climatological analysis on an historical dataset. In this dissertation, we have constructed the temperature and salinity fields on the Mediterranean Sea using the SeaDataNet 2 dataset. The dataset contains about 140000 CTD, bottles, XBT and MBT profiles, covering the period from 1900 to 2013. The temperature and salinity climatological fields are produced by the DIVA software using a Variational Inverse Method and a Finite Element numerical technique to interpolate data on a regular grid. Our results are also compared with a previous version of climatological fields and the goodness of our climatologies is assessed, according to the goodness criteria suggested by Murphy (1993). Finally the temperature and salinity seasonal cycle for the Mediterranean Sea is described.

Revealing atomic-scale details in the force fields above carbonate surfaces

Diese Arbeit stellt eine ausführliche Studie fundamentaler Eigenschaften der Kalzit CaCO3(10.4) und verwandter Mineraloberflächen dar, welche nicht nur durch die Verwendung von Nichtkontakt Rasterkraftmikroskopie, sondern hauptsächlich durch die Messung von Kraftfeldern ermöglicht wurde. Die absolute Oberflächenorientierung sowie der hierfür zugrundeliegende Prozess auf atomarer Skala konnten erfolgreich für die Kalzit (10.4) Oberfläche identifiziert werden.rnDie Adsorption chiraler Moleküle auf Kalzit ist relevant im Bereich der Biomineralisation, was ein Verständnis der Oberflächensymmetrie unumgänglich macht. Die Messung des Oberflächenkraftfeldes auf atomarer Ebene ist hierfür ein zentraler Aspekt. Eine solche Kraftkarte beleuchtet nicht nur die für die Biomineralisation wichtige Wechselwirkung der Oberfläche mit Molekülen, sondern enthält auch die Möglichkeit, Prozesse auf atomarer Skala und damit Oberflächeneigenschaften zu identifizieren.rnDie Einführung eines höchst flexiblen Messprotokolls gewährleistet die zuverlässige und kommerziell nicht erhältliche Messung des Oberflächenkraftfeldes. Die Konversion der rohen ∆f Daten in die vertikale Kraft Fz ist jedoch kein trivialer Vorgang, insbesondere wenn Glätten der Daten in Frage kommt. Diese Arbeit beschreibt detailreich, wie Fz korrekt für die experimentellen Bedingungen dieser Arbeit berechnet werden können. Weiterhin ist beschrieben, wie Lateralkräfte Fy und Dissipation Γ erhalten wurden, um das volle Potential dieser Messmethode auszureizen.rnUm Prozesse auf atomarer Skala auf Oberflächen zu verstehen sind die kurzreichweitigen, chemischen Kräfte Fz,SR von größter Wichtigkeit. Langreichweitige Beiträge müssen hierzu an Fz angefittet und davon abgezogen werden. Dies ist jedoch eine fehleranfällige Aufgabe, die in dieser Arbeit dadurch gemeistert werden konnte, dass drei unabhängige Kriterien gefunden wurden, die den Beginn zcut von Fz,SR bestimmen, was für diese Aufgabe von zentraler Bedeutung ist. Eine ausführliche Fehleranalyse zeigt, dass als Kriterium die Abweichung der lateralen Kräfte voneinander vertrauenswürdige Fz,SR liefert. Dies ist das erste Mal, dass in einer Studie ein Kriterium für die Bestimmung von zcut gegeben werden konnte, vervollständigt mit einer detailreichen Fehleranalyse.rnMit der Kenntniss von Fz,SR und Fy war es möglich, eine der fundamentalen Eigenschaften der CaCO3(10.4) Oberfläche zu identifizieren: die absolute Oberflächenorientierung. Eine starke Verkippung der abgebildeten Objekte

Radio relics and magnetic fields in galaxy clusters

Radio relics are diffuse synchrotron sources generally located in the peripheries of galaxy clusters in merging state. According to the current leading scenario, relics trace gigantic cosmological shock waves that cross the intra-cluster medium where particle acceleration occurs. The relic/shock connection is supported by several observational facts, including the spatial coincidence between relics and shocks found in the X-rays. Under the assumptions that particles are accelerated at the shock front and are subsequently deposited and then age downstream of the shock, Markevitch et al. (2005) proposed a method to constrain the magnetic field strength in radio relics. Measuring the thickness of radio relics at different frequencies allows to derive combined constraints on the velocity of the downstream flow and on the magnetic field, which in turns determines particle aging. We elaborate this idea to infer first constraints on magnetic fields in cluster outskirts. We consider three models of particle aging and develop a geometric model to take into account the contribution to the relic transverse size due to the projection of the shock-surface on the plane of the sky. We selected three well studied radio relics in the clusters A 521, CIZA J2242.8+5301 and 1RXS J0603.3+4214. These relics have been chosen primarily because they are almost seen edge-on and because the Mach number of the shock that is associated with these relics is measured by X-ray observations, thus allowing to break the degeneracy between magnetic field and downstream velocity in the method. For the first two clusters, our method is consistent with a pure radiative aging model allowing us to derive constraints on the relics magnetic field strength. In the case of 1RXS J0603.3+4214 we find that particle life-times are consistent with a pure radiative aging model under some conditions, however we also collect evidences for downstream particle re-acceleration in the relic W-region and for a magnetic field decaying downstream in its E-region. Our estimates of the magnetic field strength in the relics in A 521 and CIZA J2242.8+5301 provide unique information on the field properties in cluster outskirts. The constraints derived for these relics, together with the lower limits to the magnetic field that we derived from the lack of inverse Compton X-ray emission from the sources, have been combined with the constraints from Faraday rotation studies of the Coma cluster. Overall results suggest that the spatial profile of the magnetic field energy density is broader than that of the thermal gas, implying that the ε_th /ε_B ratio decreases with cluster radius. Alternatively, radio relics could trace dynamically active regions where the magnetic field strength is biased high with respect to the average value in the cluster volume.

Ricerca di AGN oscurati nei Chandra Deep Fields

La forma spettrale dell’X-ray background richiede l’esistenza di un grande numero di AGN mediamente oscurati, oltre alla presenza di AGN fortemente oscurati, la cui densità di colonna supera il limite Compton (Nh>10^24 cm^(-2)). A causa della loro natura, questi oggetti risultano di difficile osservazione, per cui è necessario adottare un approccio multi-banda per riuscire a rivelarli. In questo lavoro di tesi abbiamo studiato 29 sorgenti osservate nel CDF-S e 10 nel CDF-N a 0.0710^23, spettro piatto, riga del ferro): a seguito di questa analisi sono state individuate 9 sorgenti che presentano indicazioni di forte oscuramento. Dallo studio del rapporto tra la luminosità X (2-10 keV) e quella MIR (12.3um) dedotta dal SED-fitting, si è ottenuta una conferma della possibile presenza di forte oscuramento nelle 9 sorgenti selezionate a seguito dell’analisi spettrale. Abbiamo inoltre confrontato il tasso di formazione stellare dedotto dalla banda X (0.5-8 keV) e da quella IR (8-1000um) per identificare le sorgenti nelle quali l’emissione da AGN risulta essere dominante. A seguito di questa analisi abbiamo identificato 9 sorgenti (le stesse di cui sopra) con indicazione di forte oscuramento; di queste, 3 mostrano chiare indicazioni della presenza di un AGN Compton Thick (Nh>10^24 cm^(-2), riga del ferro intensa, basso rapporto LX/MIR).

Aggregate Programming in Scala: a Core Library and Actor-Based Platform for Distributed Computational Fields

La programmazione aggregata è un paradigma che supporta la programmazione di sistemi di dispositivi, adattativi ed eventualmente a larga scala, nel loro insieme -- come aggregati. L'approccio prevalente in questo contesto è basato sul field calculus, un calcolo formale che consente di definire programmi aggregati attraverso la composizione funzionale di campi computazionali, creando i presupposti per la specifica di pattern di auto-organizzazione robusti. La programmazione aggregata è attualmente supportata, in modo più o meno parziale e principalmente per la simulazione, da DSL dedicati (cf., Protelis), ma non esistono framework per linguaggi mainstream finalizzati allo sviluppo di applicazioni. Eppure, un simile supporto sarebbe auspicabile per ridurre tempi e sforzi d'adozione e per semplificare l'accesso al paradigma nella costruzione di sistemi reali, nonché per favorire la ricerca stessa nel campo. Il presente lavoro consiste nello sviluppo, a partire da un prototipo della semantica operazionale del field calculus, di un framework per la programmazione aggregata in Scala. La scelta di Scala come linguaggio host nasce da motivi tecnici e pratici. Scala è un linguaggio moderno, interoperabile con Java, che ben integra i paradigmi ad oggetti e funzionale, ha un sistema di tipi espressivo, e fornisce funzionalità avanzate per lo sviluppo di librerie e DSL. Inoltre, la possibilità di appoggiarsi, su Scala, ad un framework ad attori solido come Akka, costituisce un altro fattore trainante, data la necessità di colmare l'abstraction gap inerente allo sviluppo di un middleware distribuito. Nell'elaborato di tesi si presenta un framework che raggiunge il triplice obiettivo: la costruzione di una libreria Scala che realizza la semantica del field calculus in modo corretto e completo, la realizzazione di una piattaforma distribuita Akka-based su cui sviluppare applicazioni, e l'esposizione di un'API generale e flessibile in grado di supportare diversi scenari.

The nociceptive withdrawal reflex: Normative values of thresholds and reflex receptive fields

Assessments of spinal nociceptive withdrawal reflexes can be used in human research both to evaluate the effect of analgesics and explore pain mechanisms related to sensitization. Before the reflex can be used as a clinical tool, normative values need to be determined in large scale studies. The aim of this study was to determine the reference values of spinal nociceptive reflexes and subjective pain thresholds (to single and repeated stimulation), and of the area of the reflex receptive fields (RRF) in 300 pain-free volunteers. The influences of gender, age, height, weight, body-mass index (BMI), body side of testing, depression, anxiety, catastrophizing and parameters of Short-Form 36 (SF-36) were analyzed by multiple regressions. The 95% confidence intervals were determined for all the tests as normative values. Age had a statistically and quantitatively significant impact on the subjective pain threshold to single stimuli. The reflex threshold to single stimulus was lower on the dominant compared to the non-dominant side. Depression had a negative impact on the subjective pain threshold to single stimuli. All the other analyses either did not reveal statistical significance or displayed quantitatively insignificant correlations. In conclusion, normative values of parameters related to the spinal nociceptive reflex were determined. This allows their clinical application for assessing central hyperexcitability in individual patients. The parameters investigated explore different aspects of sensitization processes that are largely independent of demographic characteristics, cognitive and affective factors.

Generalized expansion of nociceptive reflex receptive fields in chronic pain patients

Widespread central hypersensitivity is present in chronic pain and contributes to pain and disability. According to animal studies, expansion of receptive fields of spinal cord neurons is involved in central hypersensitivity. We recently developed a method to quantify nociceptive receptive fields in humans using spinal withdrawal reflexes. Here we hypothesized that patients with chronic pelvic pain display enlarged reflex receptive fields. Secondary endpoints were subjective pain thresholds and nociceptive withdrawal reflex thresholds after single and repeated (temporal summation) electrical stimulation. 20 patients and 25 pain-free subjects were tested. Electrical stimuli were applied to 10 sites on the foot sole for evoking reflexes in the tibialis anterior muscle. The reflex receptive field was defined as the area of the foot (fraction of the foot sole) from which a muscle contraction was evoked. For the secondary endpoints, the stimuli were applied to the cutaneous innervation area of the sural nerve. Medians (25-75 percentiles) of fraction of the foot sole in patients and controls were 0.48 (0.38-0.54) and 0.33 (0.27-0.39), respectively (P=0.008). Pain and reflex thresholds after sural nerve stimulation were significantly lower in patients than in controls (P<0.001 for all measurements). This study provides for the first time evidence for widespread expansion of reflex receptive fields in chronic pain patients. It thereby identifies a mechanism involved in central hypersensitivity in human chronic pain. Reverting the expansion of nociceptive receptive fields and exploring the prognostic meaning of this phenomenon may become future targets of clinical research.