Search results for "Dimension"

Three-dimensional level-curve scanning based on intersection of laser lines

2005

A dimensional measurement system that also tracks object movements is presented here. The method directly yields the level curves of an object. It is an extension of collimation methods, coupled with the use of structured lighting with features formed from several luminous planes intersecting in a single line. This line defines a set of points of the space at a fixed distance Z 0 from the measuring head. The locus of the points of the object where the lighting is reduced to a single line is the level curve sought. The introduction of an asymmetry into the lighting structure permits one to determine the direction as well as an approximate value of the value of the distance to the level curve…

Target localization in the three-dimensional space by wavelength multiplexing.

2002

A method to localize a target in the three-dimensional space is presented. Each different position of the target on the depth axis produces, when captured with a CCD camera, an image of a different size on its sensor plane. The size of this image depends only on the distance between the target and the camera. The use of a white light optical correlator that gives us a different response depending on the scale of the input image permits us to know the depth position of the particular target. The obtained results demonstrate the utility of the newly proposed method.

A lumped model for a seismic source

1993

A lumped mechanical model is proposed and solved. This model is dynamically equivalent, in the mean field approximation, to a faulted lithosphere. The transition from the continuous system (modelled according to W. H. Prescott and A. Nur) to the lumped one, has been made by preserving all the relevant features exhibited by the continuous system. In particular the coupling between different components of the stress and strain tensors is suitably taken into account. The dynamics of the lumped system depends on six control parameters fixed by the physical properties of the continuous system. Three of the control parameters are dimensionless and describe: the seismic wave quality factor of the…

Non-equilibrium temperature of well-developed quantum turbulence

2009

Abstract A non-equilibrium effective temperature of quantum vortex tangles is defined as the average energy of closed vortex loops. The resulting thermodynamic expressions for the entropy and the energy in terms of the temperature of the tangle are confirmed by a microscopic analysis based on a potential distribution function for the length of vortex loops. Furthermore, these expressions for the entropy and energy in terms of temperature are analogous to those of black holes: this may be of interest for establishing further connections between topological defects in superfluids and cosmology.

Fractal dimension of superfluid turbulence : A random-walk toy model

2021

This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf 43}, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent pr…

Quantum Einstein Gravity: Towards an Asymptotically Safe Field Theory of Gravity

2007

Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.

1990

For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.

Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field

1992

In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.

Thermal deformations of inhomogeneous elastic plates

1995

We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear was well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Karman equations are formulated. Its is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Karman equations

WENO Schemes for Multi-Dimensional Porous Media Flow Without Capillarity

2016

In this work we derive a numerical technique based on finite-difference WENO schemes for the simulation of multi-dimensional multiphase flows in a homogeneous porous medium. The key idea is to define a compatible discretization for the fluxes of the convective term in order to maintain their divergence-free character not only in the continuous setting but also in the discrete setting, ensuring the conservation of the sum of the saturations through time evolution. The one-dimensional numerical technique is derived in detail for the case of neglected capillarity effects. Numerical results obtained with one-dimensional and two-dimensional standard tests of multiphase flow in a homogeneous poro…