1,134 research outputs found
sj-docx-1-wmr-10.1177_0734242X221139170 – Supplemental material for Mini-review of inventory data for the dewatering and drying of sewage sludge
No full textSupplemental material, sj-docx-1-wmr-10.1177_0734242X221139170 for Mini-review of inventory data for the dewatering and drying of sewage sludge by Huimin Chang, Yan Zhao, Ankun Xu, Anders Damgaard and Thomas H Christensen in Waste Management & Research</p
The solution of a chiral random matrix model with complex eigenvalues
No full textWe describe in detail the solution of the extension of the chiral Gaussian unitary ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. We briefly discuss applications to the Dirac operator eigenvalue spectrum in quantum chromodynamics with non-vanishing chemical potential
Determination of F_pi from Distributions of Dirac Operator Eigenvalues with Imaginary Density
No full textIn the epsilon-regime of lattice QCD one can get an accurate measurement of the pion decay constant F_pi by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources. Because we choose imaginary chemical potentials our Dirac eigenvalues remain real. Based on the relevant chiral Random Two-Matrix Theory we derive individual eigenvalue distributions in terms of density correlations functions to leading order in the finite-volume epsilon-expansion. As a simple byproduct we also show how the associated individual Dirac eigenvalue distributions and their correlations can be computed directly from the effective chiral Lagrangian
Individual eigenvalue distributions of chiral random two-matrix theory and the determination of F_pi
No full textDirac operator eigenvalues split into two when subjected to two different external vector sources. In a specific finite-volume scaling regime of gauge theories with fermions, this problem can be mapped to a chiral Random Two-Matrix Theory. We derive analytical expressions to leading order in the associated finite-volume expansion, showing how
individual Dirac eigenvalue distributions and their correlations equivalently can be computed directly from the effective chiral Lagrangian in the epsilon-regime. Because of its equivalence to chiral Random Two-Matrix Theory, we use the latter for all explicit computations. On the mathematical side, we define and determine gap probabilities and individual eigenvalue distributions in that theory at finite N, and also derive the relevant scaling limit as N is taken to infinity. In particular, the gap probability for one Dirac eigenvalue is given in terms of a new kernel that depends on the external vector source. This expression may give a new and simple way of determining the pion decay
constant F_pi from lattice gauge theory simulations
The effect of competition between two spatially separated markets - An investigation of two interlinked Bak-Sneppen models
No full textThis paper investigates the effect of competition in a market consisting of interlinked economic agents. In particular, the effect of increased competition from the surrounding markets is demonstrated. The presented work is an extension of the Bak-Sneppen model (Bak and Sneppen 1993). Here are two Bak-Sneppen models interlinked such that if the lowest fitness value of one market exceeds the fitness values of the other market minus transportation cost, all cells lower than this band will receive a new random value. The model shows that interdependency between markets has a strong effect on the competitiveness of the least competitive market. The external competition is able to make the least competitive market perform better as well as worse than on its own.Bak-Sneppen model, interdependency, competition, Marketing,
Vector and axial-vector propagators in the epsilon-regime of QCD
No full textDamgaard PH, Hernandez P, Jansen K, Lellouch L, Laine M. Vector and axial-vector propagators in the epsilon-regime of QCD. NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS. 2004;129:754-756.Using quenched and unquenched chiral perturbation theory we compute axial and vector current two-point functions at finite volume and fixed gauge field topology in the c-regime of QCD
On finite-volume gauge theory partition functions
No full textWe prove a Mahoux–Mehta-type theorem for finite-volume partition functions of SU(Nc≥3) gauge theories coupled to fermions in the fundamental representation. The large-volume limit is taken with the constraint V1/mπ4. The theorem allows one to express any k-point correlation function of the microscopic Dirac operator spectrum entirely in terms of the 2-point function. The sum over topological charges of the gauge fields can be explicitly performed for these k-point correlation functions. A connection to an integrable KP hierarchy, for which the finite-volume partition function is a τ-function, is pointed out. Relations between the effective partition functions for these theories in 3 and 4 dimensions are derived. We also compute analytically, and entirely from finite-volume partition functions, the microscopic spectral density of the Dirac operator in SU(Nc) gauge theories coupled to quenched fermions in the adjoint representation. The result coincides exactly with earlier results based on Random Matrix Theory
Stochastic and parastochastic aspects of supersymmetric functional measures
No full textThis collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form
A new chiral two-matrix theory for dirac spectra with imaginary chemical potential
No full textWe solve a new chiral Random Two-Matrix Theory by means of biorthogonal polynomials for any matrix size . By deriving the relevant kernels we find explicit formulas for all -point spectral (mixed or unmixed) correlation functions. In the microscopic limit we find the corresponding scaling functions, and thus derive all spectral correlators in this limit as well. We extend these results to the ordinary (non-chiral) ensembles, and also there provide explicit solutions for any finite size , and in the microscopic scaling limit. Our results give the general analytical expressions for the microscopic correlation functions of the Dirac operator eigenvalues in theories with imaginary baryon and isospin chemical potential, and can be used to extract the tree-level pion decay constant from lattice gauge theory configurations. We find exact agreement with previous computations based on the low-energy effective field theory in the two special cases where comparisons are possible
Finite-size scaling of vector and axial current correlators
No full textDamgaard PH, Hernandez P, Jansen K, Laine M, Lellouch L. Finite-size scaling of vector and axial current correlators. Nuclear Physics B. 2003;656(1-2):226-238.Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching. (C) 2003 Elsevier Science B.V. All rights reserved
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