Search results for "scale invariance"
showing 10 items of 29 documents
Primordial power spectrum features in phenomenological descriptions of inflation
2016
We extend an alternative, phenomenological approach to inflation by means of an equation of state and a sound speed, both of them functions of the number of $e$-folds and four phenomenological parameters. This approach captures a number of possible inflationary models, including those with non-canonical kinetic terms or scale-dependent non-gaussianities. We perform Markov Chain Monte Carlo analyses using the latest cosmological publicly available measurements, which include Cosmic Microwave Background (CMB) data from the Planck satellite. Within this parametrization, we discard scale invariance with a significance of about $10\sigma$, and the running of the spectral index is constrained as …
Shift- and scale-invariant recognition of contour objects with logarithmic radial harmonic filters.
2008
The phase-only logarithmic radial harmonic (LRH) filter has been shown to be suitable for scale-invariant block object recognition. However, an important set of objects is the collection of contour functions that results from a digital edge extraction of the original block objects. These contour functions have a constant width that is independent of the scale of the original object. Therefore, since the energy of the contour objects decreases more slowly with the scale factor than does the energy of the block objects, the phase-only LRH filter has difficulties in the recognition tasks when these contour objects are used. We propose a modified LRH filter that permits the realization of a shi…
Operator mixing and scaling deviations in asymptotically free field theories
1976
Predictions of asymptotically free field theories for scaling deviations of the structure functions are compared with recent SLAC and Fermilab data on deep-inelastic lepton-hadron scattering. Contributions of nonsinglet as well as singlet Wilson operators are taken into account. The latter contributions are found to be non-negligible; specifically it is observed, in agreement with neutrino data, that about 60% of the proton's momentum is due to gluons. The expected quantitative pattern of scaling violations is given for a large range of ..omega.. and Q/sup 2/. (AIP)
Universal Dynamic Fragmentation inDDimensions
2004
A generic model is introduced for brittle fragmentation in $D$ dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for $D=2$. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for $D=3$. In the experiments the nonzero grain size of rock causes deviation from th…
Charge and current distributions in elastic electron scattering by 1P shell nuclei
1974
The authors study the charge and magnetic form factors appearing in elastic electron scattering by 1p shell nuclei. The question that the form factors may be obtained from simple nuclear models by simply introducing a scaling factor has been examined using the j-j coupling, the L-S coupling and the intermediate coupling of Cohen-Kurath (CK) resulting from effective interactions. Results for /sup 6/Li, /sup 7 /Li, /sup 9/Be and /sup 13/C are given and the q/sup 2/ dependences of their form factors are compared in the three models and with experiment. The CK scheme gives similar results to the L-S coupling for /sup 6/Li and /sup 7/Li in agreement with experiment, whereas it is intermediate be…
Unconstrained periodic boundary conditions for solid state elasticity
2004
We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.
On the renormalization of ultraviolet divergences in the inflationary angular power spectrum
2015
We revise the role of ultraviolet divergences of cosmological observables and the corresponding renormalization from a space-time perspective. We employ the two-point function of primordial perturbations generated during inflation to derive an analytic expression for the multipole coefficients Cl in the Sachs-Wolfe regime. We analyzethe ultraviolet behaviorand stress the fact that the standard result in the literature is equivalent to a renormalization of the two-point function at zeroth adiabatic order. We also argue that renormalization at second adiabatic order seems to be more appropriate from a physical point of view. This may change significantly the predictions for Cl, while maintain…
Multidimensional Analysis of the Distribution of Galaxies with Different Luminosity
1989
We have used the multidimensional or multifractal formalism to study the large scale luminosity segregation of the CfA catalogue. In every sample we have analyzed, it has been found that the spectrum of scaling indices is scale invariant and that bright galaxies are more clustered than faint galaxies.
Measure dependence of 2D simplicial quantum gravity
1995
We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.
Mapping acoustical activity in 3D chiral mechanical metamaterials onto micropolar continuum elasticity
2020
Abstract We compare the phonon band structures and chiral phonon eigenmodes of a recently experimentally realized three-dimensional (3D) cubic chiral metamaterial architecture to results from linear micropolar elasticity, an established generalization of classical linear Cauchy elasticity. We achieve very good qualitative agreement concerning the anisotropies of the eigenfrequencies, the anisotropies of the eigenmode properties of the acoustic branches, as well as with respect to the observed pronounced sample-size dependence of acoustical activity and of the static push-to-twist conversion effects. The size dependence of certain properties, that is, the loss of scale invariance, is a finge…