A new diffuse-interface approximation of the Willmore flow

Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that includes a rather simple but efficient penalization of the deviation from a quasi-one dimensional structure of the phase fields. We justify the approximation property by a Gamma convergence result for the energies and a matched asymptotic expansion for the flow. Ground states of the energy are shown to be one-dimensional, in contrast to the presence of saddle solutions for the usual diffuse approximation. Finally we present numerical simulations that illustrate the approximation property and apply our new approach to problems where the usual approach leads to an undesired behavior.

Diffuse approximation for identification of the mechanical properties of microcapsules

A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes at steady state when it flows through a microfluidic microchannel of comparable cross-sectional size. From the mid-plane capsule profile, we deduce two characteristic geometric quantities that uniquely characterize the shape taken by the microcapsule under external hydrodynamic stresses. To identify the values of the unknown rigidity of the membrane and of the size of the capsule, we compare the geometric quantities with the values predicted numerically using a fluid-structure-interaction model by solving the three-dimensional capsule-flow interactions. The complete numerical data set is obtained off-line by systematically varying the governing parameters of the problem, i.e. the capsule-to-tube confinement ratio, and the capillary number, which is the ratio of the viscous to elastic forces. We show that diffuse approximation efficiently estimates the unknown mechanical resistance of the capsule membrane. We validate the data-driven procedure by applying it to the geometric and mechanical characterization of ovalbumin microcapsules (diameter of the order of a few tens of microns). As soon as the capsule is sufficiently deformed to exhibit a parachute shape at the rear, the capsule size and surface shear modulus are determined with an accuracy of 0.2% and 2.7%, respectively, as compared with 2–3% and 25% without it, in the best cases (Hu et al. Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law. Phys Rev E 2013; 87(6): 063008). Diffuse approximation thus allows the capsule size and membrane elastic resistance to be provided quasi-instantly with very high precision. This opens interesting perspectives for industrial applications that require tight control of the capsule mechanical properties in order to secure their behavior when they transport active material.

El negocio jurídico, la declaración de voluntad y el ordenamiento jurídico

Uwe Wesel, professor of law at the Free University of Berlin, expressed in several of his writings an interesting thought: more than the law of obligations (Schuldrecht) the law of contracts (Vertragsrecht) is a better metadiscourse to reread and interpret the spectrum of The legal, which could even give an accurate account of the history of Western law. From the origins of the Greek civilization and to the Lisbon agreement, the contract was the institute that most connected the legal with the reasonableness, fairness, proportionality, justice and the conservative and protective sense of the community; of course also with the market economy and globalization. For this reason, this diffuse approximation of the contract and the legal business within western juridicity provides interesting inputs, such as inadvertent responses to how certain constitutional principles emerged? Or why do freedom and equality rights always entail obligations? under many others perspectives.

Diffuse approximation to the kinetic theory in a Fermi system

We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the distorted Fermi surface. Using the finite range interaction, we show that the momentum dependence of the diffuse coefficient Dp(p) has a maximum at Fermi momentum p = pF whereas the drift coefficient Kp(p) is negative and reaches a minimum at p ≈ pF. For a cold Fermi system the diffusion coefficient takes the nonzero value which is caused by the relaxation on the distorted Fermi surface at temperature T = 0. The numerical solution of the diffusion equation was performed for the particle-hole excitation in a nucleus with A = 16. The evaluated relaxation time τr ≈ 8.3 ⋅ 10-23 s is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.

Comparing Diffuse Approximation and Kriging Method for Predicting the Tool Life when Milling Ultrahigh Strength Steel

Tool wear can affect surface quality of the work-piece and frequent tool changing leads to low machining efficiency. Tool life of milling ultrahigh strength steel is thus an important indicator in manufacturing. In this study, we compare Diffuse Approximation (DA) and Kriging method for predicting tool life of milling ultrahigh strength steel. Latin hypercube method is employed as design of experiments after comparing three different designs of experiments (full factorial design, Latin Hypercube Sampling (LHS) and random design). An example with LHS is taken to investigate accuracy of approximation of DA and Kriging method. The results show that the DA provides significant improvement in accuracy of prediction compared with Kriging method. Tool life of milling ultrahigh strength steel predicted by DA is almost close to ‘exact’ values, especial for big mutation of adjacent measured values. The most errors with DA are less than ones with Kriging method.