Equation of state near the endpoint of the critical line

We discuss first order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about the short distance physics can therefore be extracted from the precise location of the endpoint and non-universal amplitudes. Our method is based on non-perturbative flow equations and yields directly the universal features of the equation of state, without additional theoretical assumptions of scaling or resummations of perturbative series. The universal results compare well with other methods.Comment: LaTeX, 22 pages with 7 figures, uses epsf.sty and rotate.st

Stress Concentration in a Stretched Cylindrical Shell With Two Equal Circular Holes 1

In this investigation, the stress distribution due to uniaxial tension of an infinitely lon

Exploring <em>Musa paradisiaca</em> Peel Extract as a Green Corrosion Inhibitor for Mild Steel Using Factorial Design Method

The suitability ofMusa paradisiaca (banana) peel extract as a green corrosion inhibitor for mild steel in acidic medium (1 M HCl) was investigated using factorial method of the design of experiment. The effects of two independent variables (concentration of banana peel extract and temperature) on the corrosion inhibition efficiency were investigated. The physicochemical properties of the extract such as surface tension, viscosity, flash point, and specific gravity were determined using standardized methods provided by the American System of Testing Materials (D-971). The relationship between the independent variables and the inhibitor efficiency was modeled by gasometric and thermometric methods. The statistical analysis of the inhibition efficiency was carried out using the “Fit Regression Model” of Minitab® 17.0, while the fitness of the models was assessed by the coefficient of determination (R2) and the analysis of variance (ANOVA). From the results obtained, gasometric method achieved a maximum inhibition efficiency of 66.83%, with an R2 of 90.76%, whereas thermometric method gave a maximum inhibition efficiency of 65.70%, with an R2 of 95.56%. This study shows that banana peel extract has the capacity to prevent the corrosion of mild steel in acidic medium

Phase transition and critical behaviour of the d=3 Gross-Neveu model

A second order phase transition for the three dimensional Gross-Neveu model is established for one fermion species N=1. This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent \nu = 0.63 and scalar and fermionic anomalous dimension \eta_\sigma = 0.31 and \eta_\psi = 0.11, respectively. We also compute critical exponents for other N. Our results are based on exact renormalization group equations.Comment: 4 pages, 1 figure; v4 corresponds to the published articl

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

Nonperturbative renormalization group approach to frustrated magnets

This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach - the effective average action method - that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated - O(N) - case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.Comment: 58 pages, 15 PS figure

Axial forces and bending moments in the loaded rabbit tibia in vivo

<p>Abstract</p> <p>Background</p> <p>Different animal models are used as fracture models in orthopaedic research prior to implant use in humans, although biomechanical forces can differ to a great extend between species due to variable anatomic conditions, particularly with regard to the gait. The rabbit is an often used fracture model, but biomechanical data are very rare. The objective of the present study was to measure axial forces, bending moments, and bending axis directly in the rabbit tibia <it>in vivo</it>. The following hypothesis was tested: Axial forces and bending moments in the mid-diaphysis of rabbit tibia differ from other experimental animals or indirectly calculated data.</p> <p>Methods</p> <p>A minifixateur system with 4 force sensors was developed and attached to rabbit tibia (<it>n </it>= 4), which were subsequently ostectomised. Axial forces, bending moments and bending angles were calculated telemetrically during weight bearing in motion between 6 and 42 days post operation.</p> <p>Results</p> <p>Highest single values were 201% body weight [% bw] for axial forces and 409% bw cm for bending moments. Whereas there was a continous decrease in axial forces over time after day 10 (<it>P </it>= 0.03 on day 15), a decrease in bending moments was inconsistent (<it>P </it>= 0.03 on day 27). High values for bending moments were frequently, but not consistently, associated with high values for axial forces.</p> <p>Conclusion</p> <p>Axial forces in rabbit tibia exceeded axial forces in sheep, and differed from indirectly calculated data. The rabbit is an appropriate fracture model because axial loads and bending moments in rabbit tibia were more closely to human conditions than in sheep tibia as an animal model.</p