Search results for "bound"

Two -methods to generate Bézier surfaces from the boundary

2009

Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.

Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique

2006

Dupin cyclides were introduced in 1822 by the French mathematician C-P. Dupin. They are algebraic surfaces of degree 3 or 4. The set of geometric properties of these surfaces has encouraged an increasing interest in using them for geometric modeling. A couple of algorithmes is already developed to convert a Dupin cyclide patch into a rational biquadratic Bezier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bezier patch into a Dupin cyclide one, and we present a conversion algorithm to compute the parameters of a Dupin cyclide with the boundary of the patch that corresponds to the given Bezier patch.

A third order partial differential equation for isotropic boundary based triangular Bézier surface generation

2011

Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.

Tectonic retreat of a segment of the Triassic paleomargin of the Saccense Carbonate Platform around the T/J boundary: the seismic-scale section of Mo…

2010

Basic Notions of the Theory of Heat

2016

This chapter summarizes some basic notions of thermodynamics and defines the empirical variables which are needed for the description of thermodynamic systems in equilibrium. Empirical temperature and several scales used to measure temperature are defined. The so-called “zeroth law of thermodynamics” is formulated which says that systems which are in mutual equilibrium have the same temperature. Thermodynamic ensembles corresponding to different macroscopic boundary conditions are introduced and are illustrated by simple models such as the ideal gas. Also, entropy appears on the scene for a first time, both in its statistical and its thermodynamical interpretation. Gibb’s fundamental form i…

Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin-film geometry: A Monte Carlo simulation

1997

The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte-Carlo simulations of the bond fluctuation model of symmetric polymer mixtures. Both the canonical and semi-grand-canonical ensemble are studied. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the intrinsic profile) like sqrt{D}, before a crossover to a saturation value w_max (w_max^2 proport…

SMOS REFLEX 2003: L-band emissivity characterization of vineyards

2005

The goal of the Soil Moisture and Ocean Salinity mission over land is to infer surface soil moisture from multiangular L-band radiometric measurements. As the canopy affects the microwave emission of land, it is necessary to characterize different vegetation layers. This paper presents the Reference Pixel L-Band Experiment (REFLEX), carried out in June-July 2003 at the Vale/spl grave/ncia Anchor Station, Spain, to study the effects of grapevines on the soil emission and on the soil moisture retrieval. A wide range of soil moisture (SM), from saturated to completely dry soil, was measured with the Universitat Polite/spl grave/cnica de Catalunya's L-band Automatic Radiometer (LAURA). Concurre…

Surface to boundary layer coupling in the urban area of Lisbon comparing different urban canopy models in WRF

2019

Abstract This work presents a sensitivity study to evaluate different Urban Canopy Models (UCM) existing within the Weather Research and Forecasting Model (WRF) in the urban area of Lisbon, Portugal. Several hind-cast simulations were carried out for a selected period in July 2010, in which synoptic conditions favoured urban heat island formation. We aim to gain knowledge on the feedback of modified urban canopy representation in WRF on local scale meteorology and the boundary-layer dynamics over the urban area, by comparing a single layer urban canopy model (SLUCM) and a more sophisticated multi-layer building effect parametrisation (BEP). We find significant differences in the characteris…

Boundary elements analysis of adhesively bonded piezoelectric active repair

2009

Abstract This paper presents the analysis of active piezoelectric patches for cracked structures by the boundary element method. A two-dimensional boundary integral formulation based on the multidomain technique is used to model cracks and to assemble the multi-layered piezoelectric patches to the host damaged structures. The fracture mechanics behavior of the repaired structures is analyzed for both perfect and imperfect interface between patches and host beams. The imperfect interface, representing the adhesive between two different layers, is modeled by using a “spring model” that involves linear relationships between the interface tractions, in normal and tangential directions, and the …

Quasi-Stationary Distribution and Gibbs Measure of Expanding Systems

1996

Let T be an expanding transformation defined on A —(J A{, i= 1being a finite collection of connected open bounded subsets of 2Rn,such that T Acontains strictly Aand Tis Markovian. We prove the existence of a quasi-stationary distrition for T. We show that the T-invariant probability on the limit Cantor set is Gibbsian with potential Log|_DT|. Using the Hilbert projective metric we prove that both distributions are weak limits of conditional laws of probabilities, the speed of convergence being exponential. These results develop a previous work by G. Pianigiani and J.A. Yorke.