Bridging The Divide Between The Modulus Of Elasticity Obtained From Direct Test And Flextural Test Methods: Paper 1 Central Point Load

The modulus of elasticity E is a fundamental material constant which is usually determined from experimentation and is an index of the stiffness of the material. The Direct Tensile or compressive test method is usually used for the determination of this constant, while the flexural test method is an indirect test method. Three samples of each of Glass, Mahogany timber, Massonia timber, Cotton timber, Iroko timber, Y16 steel, Y12 steel, Y10 steel and R12 steel were tested in flexure with a central point load in a simply supported arrangement. The respective deflections were recorded via dial gauges for each incremental load and repeated when unloading. The average load and deflection are back substituted into the deflection equation of a point loaded simply supported beam and the circular beam theory equation from where E1 and E2 are obtained respectively. For all the materials tested           (Glass, Timber and Steel), It was discovered that the ratio E2/E1 was 1.5. This raises the question of which of the two equations is correct. However the surprising constant of E2/E1 = 1.5 informed the need to get the average of E1 and E2 as the required E. This way the average E so obtained compares with quoted E from the direct Tensile or compressive test methods for the various Engineering materials tested. Therefore within the limits of experimental errors, EDirect = 1.25 EFlexure. Keywords: Young’s Modulus, Tensile Test, Flexural Test, Deflection, Moment, Circular Bending Theor

Universality in the Screening Cloud of Dislocations Surrounding a Disclination

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by S. Seung and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own and allows to compute the energy for an {\em arbitrary} distribution of defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy} with very minor additional computational effort. Some implications for recent experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file

Gluino Pair Production at Linear e^+e^- Colliders

We study the potential of high-energy linear $e^+e^-$ colliders for the production of gluino pairs within the Minimal Supersymmetric Standard Model (MSSM). In this model, the process $e^+e^-\to\tilde{g}\tilde{g}$ is mediated by quark/squark loops, dominantly of the third generation, where the mixing of left- and right-handed states can become large. Taking into account realistic beam polarization effects, photon and $Z^0$-boson exchange, and current mass exclusion limits, we scan the MSSM parameter space for various $e^+e^-$ center-of-mass energies to determine the regions, where gluino production should be visible.Comment: 22 pages, 9 figure

Dynamic renormalization group study of a generalized continuum model of crystalline surfaces

We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential favoring discrete values of the height variable. The model thus interpolates between the overdamped sine-Gordon model and a related continuum model of crystalline tensionless surfaces. The RG flow predicts the existence of an equilibrium roughening transition only for d = 2 dimensional surfaces, between a flat low-temperature phase and a rough high-temperature phase in the Edwards-Wilkinson (EW) universality class. The surface is always in the flat phase for any other substrate dimensions d > 2. For any value of d, the linear surface diffusion mechanism is an irrelevant perturbation of the linear surface tension mechanism, but may induce long crossovers within which the scaling properties of the linear molecular-beam epitaxy equation are observed, thus increasing the value of the sine-Gordon roughening temperature. This phenomenon originates in the non-linear lattice potential, and is seen to occur even in the absence of a bare surface tension term. An important consequence of this is that a crystalline tensionless surface is asymptotically described at high temperatures by the EW universality class.Comment: 22 pages, 5 figures. Accepted for publication in Physical Review

Vortex dynamics and states of artificially layered superconducting films with correlated defects

Linear resistances and $IV$-characteristics have been measured over a wide range in the parameter space of the mixed phase of multilayered a-TaGe/Ge films. Three films with varying interlayer coupling and correlated defects oriented at an angle $\approx 25$ from the film normal were investigated. Experimental data were analyzed within vortex glass models and a second order phase transition from a resistive vortex liquid to a pinned glass phase. Various vortex phases including changes from three to two dimensional behavior depending on anisotropy have been identified. Careful analysis of $IV$-characteristics in the glass phases revealed a distinctive $T$ and $H$-dependence of the glass exponent $\mu$. The vortex dynamics in the Bose-glass phase does not follow the predicted behavior for excitations of vortex kinks or loops.Comment: 16 pages, 10 figures, 3 table

Precision measurement of solar neutrino oscillation parameters by a long-baseline reactor neutrino experiment in Europe

We consider the determination of the solar neutrino oscillation parameters $\Delta m^2_{21}$ and $\theta_{12}$ by studying oscillations of reactor anti-neutrinos emitted by nuclear power plants (located mainly in France) with a detector installed in the Frejus underground laboratory. The performances of a water Cerenkov detector of 147 kt fiducial mass doped with 0.1% of Gadolinium (MEMPHYS-Gd) and of a 50 kt scale liquid scintillator detector (LENA) are compared. In both cases 3$\sigma$ uncertainties below 3% on $\Delta m^2_{21}$ and of about 20% on $\sin^2\theta_{12}$ can be obtained after one year of data taking. The Gadolinium doped Super-Kamiokande detector (SK-Gd) in Japan can reach a similar precision if the SK/MEMPHYS fiducial mass ratio of 1 to 7 is compensated by a longer SK-Gd data taking time. Several years of reactor neutrino data collected by MEMPHYS-Gd or LENA would allow a determination of $\Delta m^2_{21}$ and $\sin^2\theta_{12}$ with uncertainties of approximately 1% and 10% at 3$\sigma$, respectively. These accuracies are comparable to those that can be reached in the measurement of the atmospheric neutrino oscillation parameters $\Delta m^2_{31}$ and $\sin^2\theta_{23}$ in long-baseline superbeam experiments.Comment: 16 pages, 6 figure

Symmetries and Elasticity of Nematic Gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these novel materials.Comment: 21 pages, 4 eps figure

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review

Possible implications of the channeling effect in NaI(Tl) crystals

The channeling effect of low energy ions along the crystallographic axes and planes of NaI(Tl) crystals is discussed in the framework of corollary investigations on WIMP Dark Matter candidates. In fact, the modeling of this existing effect implies a more complex evaluation of the luminosity yield for low energy recoiling Na and I ions. In the present paper related phenomenological arguments are developed and possible implications are discussed at some extent.Comment: 16 pages, 10 figures, preprint ROM2F/2007/15, submitted for publicatio