Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap

The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.Comment: 16 pp., 1 figure. v2: a few paragraphs and one appendix added, title and abstract slightly changed, essential results unchange

PRELIMINARY GEOTHERMAL INVESTIGATION IN THE BASIN OF KATERINI (NORTHERN GREECE)

Η παρούσα εργασία περιγράφει τα αποτελέσματα της προκαταρκτικής γεωθερμικής έρευνας που διενεργήθηκε από το ΙΓΜΕ στην λεκάνη της Κατερίνης (Β. Ελλάδα). Οι ερευνητικές εργασίες κατά κύριο λόγο περιελάμβαναν θερμομετρήσεις στην κεφαλή 73 υπαρχουσών υδρογεωτρήσεων, μέτρηση της θερμοκρασίας σε συνάρτηση με το βάθος στο εσωτερικό πέντε (5) γεωτρήσεων και χημικές αναλύσεις 18 δειγμάτων από επιλεγμένες θέσεις. Με βάση τα στοιχεία που προέκυψαν από την κατανομή των θερμοκρασιών, διακρίνονται τρεις επιμέρους περιοχές γεωθερμικού ενδιαφέροντος. Ως σημαντικότερη κρίνεται αυτή του Κάτω Αγίου Ιωάννη (νότια τμήμα της λεκάνης), όπου μετρήθηκαν θερμοκρασίες της τάξης των 27oC σε βάθος 340m. Εν τούτοις, για τη λεπτομερή διερεύνηση των γεωθερμικών συνθηκών στη λεκάνη Κατερίνης, απαιτείται περαιτέρω συστηματική έρευνα και κατασκευή τουλάχιστον μίας ερευνητικής γεωθερμικής γεώτρησης μεγάλου βάθους.This paper describes the results of the preliminary surface geothermal exploration conducted by IGME in the basin of Katerini (Northern Greece). It mainly regards temperature measurements at the wellhead of 73 wells and in the interior of five boreholes, as well as sampling and chemical analyses from 18 selected sites. Based on the collected data, three sub-regions of geothermal interest can be distinguished, the most important of which is the area of Kato Agios Ioannis (to the south of the basin), with temperatures around 27oC at the depth of 340m. Nonetheless, the detailed geothermal investigation of this basin requires further systematic research as well as the drilling of at least one deep geothermal exploration borehole

Optimized Perturbation Theory for Wave Functions of Quantum Systems

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure

A NEW APPROACH TO TEACHING NATURAL RESOURCE SAMPLING

A basic undergraduate course in statistics is often not adequate for students in renewable natural resource programs such as wildlife, forestry, fisheries, and related subjects. A strong foundation in the basics of sampling in time and space of forest, vegetation, wildlife and fish populations is needed. A brief account of our experience in teaching such a course over the last three years along with progress on developing course-related material and activities is reported. This includes the development of: 1) computer-based simulations; 2) in-class participation simulations to illustrate the basic concepts of sampling in space and time; 3) exercises to introduce students to basic field sampling methods (quadrat, line and point sample units, mark/recapture, radio telemetry, etc.); and 4) an associated hypermedia text. From the beginning, emphasis is placed on cost-effectiveness and on the importance of sampling in the decision-making process. Students are required to develop their own sampling project, implement the project, present the results in an open forum, and prepare an associated report in the format of a scientific paper

Variational solution of the Gross-Neveu model; 2, finite-N and renormalization

We show how to perform systematically improvable variational calculations in the O(2N) Gross-Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the renormalization group. The final point is a general framework for the calculation of non-perturbative quantities like condensates, masses, etc..., in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a "two-loop" variational calculation are in very good agreement with exact quantities down to low values of N

Element specific characterization of heterogeneous magnetism in (Ga,Fe)N films

We employ x-ray spectroscopy to characterize the distribution and magnetism of particular alloy constituents in (Ga,Fe)N films grown by metal organic vapor phase epitaxy. Furthermore, photoelectron microscopy gives direct evidence for the aggregation of Fe ions, leading to the formation of Fe-rich nanoregions adjacent to the samples surface. A sizable x-ray magnetic circular dichroism (XMCD) signal at the Fe L-edges in remanence and at moderate magnetic fields at 300 K links the high temperature ferromagnetism with the Fe(3d) states. The XMCD response at the N K-edge highlights that the N(2p) states carry considerable spin polarization. We conclude that FeN{\delta} nanocrystals, with \delta > 0.25, stabilize the ferromagnetic response of the films.Comment: 4 pages, 3 figures, 1 tabl

A novel hierarchical template matching model for cardiac motion estimation

Cardiovascular disease diagnosis and prognosis can be improved by measuring patient-specific in-vivo local myocardial strain using Magnetic Resonance Imaging. Local myocardial strain can be determined by tracking the movement of sample muscles points during cardiac cycle using cardiac motion estimation model. The tracking accuracy of the benchmark Free Form Deformation (FFD) model is greatly affected due to its dependency on tunable parameters and regularisation function. Therefore, Hierarchical Template Matching (HTM) model, which is independent of tunable parameters, regularisation function, and image-specific features, is proposed in this article. HTM has dense and uniform points correspondence that provides HTM with the ability to estimate local muscular deformation with a promising accuracy of less than half a millimetre of cardiac wall muscle. As a result, the muscles tracking accuracy has been significantly (p<0.001) improved (30%) compared to the benchmark model. Such merits of HTM provide reliably calculated clinical measures which can be incorporated into the decision-making process of cardiac disease diagnosis and prognosis

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure