We generate a basis of the space of bicubic and biquartic C1-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R2. The basis functions are obtained by suitably ...combining C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. 18). They are described by simple explicit formulas for their spline coefficients.
These C1-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.
•Construction of a basis for bicubic and biquartic C1-smooth isogeometric functions on planar bilinear multi-patch domains.•The basis functions are described by simple explicit formulas for their spline coefficients.•Numerical experiments (e.g. solving the biharmonic equation) showed optimal rates of convergence.
Purpose: To introduce guidelines in selecting the particle size distribution (n0, cm−1) that will guarantee optimal oral absorption for drugs with low solubility.
Methods: Unlike other ...multi-compartmental models the gastrointestinal tract is modeled as a continuous tube with spatially varying properties. The transport through the intestinal lumen is described using the dispersion model. The model accounts for the dissolution of poly-dispersed powders.
Results: The model was used to examine the sensitivity of the absorption on permeability (P) and water solubility (Cs) following administration in different log-normal powders. The absorption exhibits inverse sigmoidal dependence on the mean particle size (rm, µm) regardless of the administrated dose or drug properties. Thus, there is an optimal rm that maximizes the benefit-cost ratio of the formulation; finer particles do not improve the absorption while coarser particles decrease it. Using the model we find that the optimal rm depends mainly on the drug Cs and on the geometrical standard deviation (gSTD).
Conclusions: The results of this work provide the formulator with guidelines to select both rm and gSTD that guarantee optimal absorption.
In 1 Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in 16 is that it can handle both ...approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control over the knot vectors of non-uniform B-Splines. Violation of Schoenberg-Whitney condition is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well. PUBLICATION ABSTRACT
Predicting the time course of in vivo biodegradation is a key issue in the design of an increasing number of biomedical applications such as sutures, tissue analogs and drug-delivery devices. The ...design of such biodegradable devices is hampered by the absence of quantitative models for the enzymatic erosion of solid protein matrices. In this work, we derive and simulate a reaction diffusion model for the enzymatic erosion of fibrillar gels that successfully reproduces the main qualitative features of this process. A key aspect of the proposed model is the incorporation of steric hindrance into the standard Michaelis–Menten scheme for enzyme kinetics. In the limit of instantaneous diffusion, the model equations are analogous to the standard equations for enzymatic degradation in solution. Invoking this analogy, the total quasi-steady-state approximation is used to derive approximate analytical solutions that are valid for a wide range of in vitro conditions. Using these analytical approximations, an experimental–theoretical method is derived to unambiguously estimate all the kinetic model parameters. Moreover, the analytical approximations correctly describe the characteristic hyperbolic dependence of the erosion rate on enzyme concentration and the zero-order erosion of thin fibers. For definiteness, the analysis of published experimental results of enzymatic degradation of fibrillar collagen is demonstrated, and the role of diffusion in these experiments is elucidated.
We solve the following problem: given a polynomial of order \(n\) and the corresponding \(Bézier\) tensor product patches over an unstructured regular quadrilateral mesh of any valence, find a ...solution to the \(G^{1}1\) or \(C^{1}1\) approximation (resp. interpolation) problem ! Constraints defining regularity conditions across patches have to be satisfied. The resulting number of free degrees of freedom must be such that for instance the interpolation problem has a solution. This is similar to studying the minimal determining set (MDS) for a \(C^{1}\) continuity construction. The givenunstructured quadrilateral mesh can include a cubic boundary curve. The final surface approximation or PDE solution is obtained by energy methods. We completely solve the problem and show that there is always a solution for \(n\ge 5\) and under some mesh restrictions for \(n=4\). From a practical point of view, the present paper provides a way to build first order smooth interpolation/approximation and solutions to partial differential equations for arbitrary structures of quadrilateral meshes.
Volume-preserving free-form solids Rappoport, A.; Sheffer, A.; Bercovier, M.
IEEE transactions on visualization and computer graphics,
03/1996, Letnik:
2, Številka:
1
Journal Article
Recenzirano
Some important trends in geometric modeling are the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models, by using free-form objects in ...addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper, we integrate all of these requirements into a single geometric primitive by endowing the tri-variate tensor-product free-form solid with several important physical properties, including volume and internal deformation energy. Volume preservation is of benefit in several application areas of geometric modeling, including computer animation, industrial design and mechanical engineering. However, previous physics-based methods, which have usually used some form of "energy", have neglected the issue of volume (or area) preservation. We present a novel method for modeling an object composed of several tensor-product solids while preserving the desired volume of each primitive and ensuring high-order continuity constraints between the primitives. The method utilizes the Uzawa algorithm for non-linear optimization, with objective functions based on deformation energy or least squares. We show how the algorithm can be used in an interactive environment by relaxing exactness requirements while the user interactively manipulates free-form solid primitives. On current workstations, the algorithm runs in real-time for tri-quadratic volumes and close to real-time for tri-cubic volumes.
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