217 research outputs found

### 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

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