A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Growth and Melting of Metallic Nanoclusters in Glass: A Review of Recent Investigations

The mechanisms of nucleation and growth and the solid-to-liquid transition of metallic nanoclusters embedded in sodium borate glass were recently studied in situ via small-angle X-ray scattering (SAXS) and wide-an-le X-ray scattering (WAXS). SAXS results indicate that, under isothermal annealing conditions, the formation and growth of Bi or Ag nanoclusters embedded in sodium borate glass occurs through two successive stages after a short incubation period. The first stage is characterized by the nucleation and growth of spherical metal clusters promoted by the diffusion of Bi or Ag atoms through the initially supersaturated glass phase. The second stage is named the coarsening stage and occurs when the (Bi- or Ag-) doping level of the vitreous matrix is close to the equilibrium value. The experimental results demonstrated that, at advanced stages of the growth process, the time dependence of the average radius and density number of the clusters is in agreement with the classical Lifshitz-Slyozov-Waoner (LSW) theory. However, the radius distribution function is better described by a lognormal function than by the function derived from the theoretical LSW model. From the results of SAXS measurements at different temperatures, the activation energies for the diffusion of Ag and Bi through sodium borate glass were determined. In addition, via combination of the results of simultaneous WAXS and SAXS measurements at different temperatures, the crystallographic structure and the dependence of melting temperature T(m) on crystal radius R of Bi nanocrystals were established. The experimental results indicate that T(m) is a linear and decreasing function of nanocrystal reciprocal radius 1/R, in agreement with the Couchman and Jesser theoretical model. Finally, a weak contraction in the lattice parameters of Bi nanocrystals with respect to bulk crystals was established.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Loops, Chains, Sheets, and Networks from Variable Coordination of Cu(hfac)(2) with a Flexibly Hinged Aminoxyl Radical Ligand

One pair of reactants, Cu(hfac)(2) = M and the hinge-flexible radical ligand 5-(3-N-tert-butyl-N-aminoxylphenyl)pyrimidine (3PPN = L), yields a diverse set of five coordination complexes: a cyclic loop M(2)L(1) dimer; a 1:1 cocrystal between an M(2)L(2) loop and an ML(2) fragment; a ID chain of M(2)L(2) loops linked by M; two 2D M(3)L(2) networks of (M-L)(n) chains crosslinked by M with different repeat length pitches; a 3D M(3)L(2) network of M(2)L(2) loops cross-linking (M-L)(n)-type chains with connectivity different from those in the 2D networks. Most of the higher dimensional complexes exhibit reversible, temperature-dependent spin-state conversion of high-temperature paramagnetic states to lower magnetic moment states having antiferromagnetic exchange within Cu-ON bonds upon cooling, with accompanying bond contraction. The 3D complex also exhibited antiferromagnetic exchange between Cu(II) ions linked in chains through pyrimidine rings.

Mastication effort study using photorefractive holographic interferometry technique

The purpose of this work was the force-displacement response analysis of the masticatory process in a dried human skull by Double-Exposure Photorefractive Holographic Interferometry Technique (2E-PRHI). The load concentration and dissipation of the forces from dried human skull were analysed at applied loading stands as a Simulation of Isolated Contraction (SIC) of some mastication muscles. The 2EHI and Fringe Analysis Method were used to obtain the quantitative results of this force-displacement response. These results document quantitatively the real biomechanical response from dried human skull under applied loading and it can be used for complementary study by finite element model and others analysis type. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.

Influence of different light sources and photo-activation methods on degree of conversion and polymerization shrinkage of a nanocomposite resin

The purpose of this study was to evaluate the influence of different light sources and photo-activation methods on degree of conversion (DC%) and polymerization shrinkage (PS) of a nanocomposite resin (Filtek (TM) Supreme XT, 3M/ESPE). Two light-curing units (LCUs), one halogen-lamp (QTH) and one light-emitting-diode (LED), and two different photo-activation methods (continuous and gradual) were investigated in this study. The specimens were divided in four groups: group 1-power density (PD) of 570 mW/cm(2) for 20 s (QTH); group 2-PD 0 at 570 mW/cm(2) for 10 s + 10 s at 570 mW/cm(2) (QTH); group 3-PD 860 mW/cm(2) for 20 s (LED), and group 4-PD 125 mW/cm(2) for 10 s + 10 s at 860 mW/cm(2) (LED). A testing machine EMIC with rectangular steel bases (6 x 1 x 2 mm) was used to record the polymerization shrinkage forces (MPa) for a period that started with the photo-activation and ended after two minutes of measurement. For each group, ten repetitions (n = 40) were performed. For DC% measurements, five specimens (n = 20) for each group were made in a metallic mold (2 mm thickness and 4 mm diameter, ISO 4049) and them pulverized, pressed with bromide potassium (KBr) and analyzed with FT-IR spectroscopy. The data of PS were analyzed by Analysis of Variance (ANOVA) with Welch`s correction and Tamhane`s test. The PS means (MPa) were: 0.60 (G1); 0.47 (G2); 0.52 (G3) and 0.45 (G4), showing significant differences between two photo-activation methods, regardless of the light source used. The continuous method provided the highest values for PS. The data of DC% were analyzed by Analysis of Variance (ANOVA) and shows significant differences for QTH LCUs, regardless of the photo-activation method used. The QTH provided the lowest values for DC%. The gradual method provides lower polymerization contraction, either with halogen lamp or LED. Degree of conversion (%) for continuous or gradual photo-activation method was influenced by the LCUs. Thus, the presented results suggest that gradual method photo-activation with LED LCU would suffice to ensure adequate degree of conversion and minimum polymerization shrinkage.

Measurement of shrinkage of composite resin by laser speckle contrast analysis

The aim of this study was to evaluate the shrinkage of a microhybrid dental composite resin photo-activated by one LED with different power densities by means of speckle technique. The dental composite resin Filtek (TM) Z-250 (3M/ESPE) at color A(2) was used for the samples preparation. Uncured composite was packed in a metallic mold and irradiated during 20 s from 100 to 1000 mW cm(-2). For the photo-activation of the samples, it was used a LED prototype (Light Emission Diode) with wavelength centered at 470 nm and adjustable power density until 1 W cm(-2). The speckle patterns obtained from the bottom composite surfaces were monitored using a CCD camera without lens. The speckle field is recorded in a digital picture and stored by CCD camera as the carrier of information on the displacement of the tested surface. The calculated values were obtained for each pair of adjacent patterns and the changes in speckle contrast as a function of time were obtained from six repeated measurements. The speckle contrasts obtained from the bottom surface with 100 mW cm(-1) were smaller than those than the other power densities. The higher power densities provided the higher shrinkage.

Continuous and gradual photo-activation methods: influence on degree of conversion and crosslink density of composite resins

Thermal properties and degree of conversion (DC%) of two composite resins (microhybrid and nanocomposite) and two photo-activation methods (continuous and gradual) displayed by the light-emitting diode (LED) light-curing units (LCUs) were investigated in this study. Differential scanning calorimetry (DSC) thermal analysis technique was used to investigate the glass transition temperature (T(g)) and degradation temperature. The DC% was determined by Fourier transform infrared spectroscopy (FT-IR). The results showed that the microhybrid composite resin presented the highest T(g) and degradation temperature values, i.e., the best thermal stability. Gradual photo-activation methods showed higher or similar T(g) and degradation temperature values when compared to continuous method. The Elipar Freelight 2 (TM) LCU showed the lowest T(g) values. With respect to the DC%, the photo-activation method did not influence the final conversion of composite resins. However, Elipar Freelight 2 (TM) LCU and microhybrid resin showed the lowest DC% values. Thus, the presented results suggest that gradual method photo-activation with LED LCUs provides adequate degree of conversion without promoting changes in the polymer chain of composite resins. However, the thermal properties and final conversion of composite resins can be influenced by the kind of composite resin and LCU.

Single Synapse Information Coding in Intraburst Spike Patterns of Central Pattern Generator Motor Neurons

Burst firing is ubiquitous in nervous systems and has been intensively studied in central pattern generators (CPGs). Previous works have described subtle intraburst spike patterns (IBSPs) that, despite being traditionally neglected for their lack of relation to CPG motor function, were shown to be cell-type specific and sensitive to CPG connectivity. Here we address this matter by investigating how a bursting motor neuron expresses information about other neurons in the network. We performed experiments on the crustacean stomatogastric pyloric CPG, both in control conditions and interacting in real-time with computer model neurons. The sensitivity of postsynaptic to presynaptic IBSPs was inferred by computing their average mutual information along each neuron burst. We found that details of input patterns are nonlinearly and inhomogeneously coded through a single synapse into the fine IBSPs structure of the postsynaptic neuron following burst. In this way, motor neurons are able to use different time scales to convey two types of information simultaneously: muscle contraction (related to bursting rhythm) and the behavior of other CPG neurons (at a much shorter timescale by using IBSPs as information carriers). Moreover, the analysis revealed that the coding mechanism described takes part in a previously unsuspected information pathway from a CPG motor neuron to a nerve that projects to sensory brain areas, thus providing evidence of the general physiological role of information coding through IBSPs in the regulation of neuronal firing patterns in remote circuits by the CNS.

Columnar joints in the Patino Formation sandstones, Eastern Paraguay: a dynamic interaction between dyke intrusion, quartz dissolution and cooling-induced fractures

The Patino Formation sandstones, which crop out in Aregua neighborhood in Eastern Paraguay and show columnar joints near the contact zone with a nephelinite dyke, have as their main characteristics the high proportion of syntaxial quartz overgrowth and a porosity originated from different processes, initially by dissolution and later by partial filling and fracturing. Features like the presence of floating grains in the syntaxial cement, the transitional interpenetrative contact between the silica-rich cement and grains as well as the intense fracture porosity are strong indications that the cement has been formed by dissolution and reprecipitation of quartz from the framework under the effect of thermal expansion followed by rapid contraction. The increase of the silica-rich cement towards the dyke in association with the orthogonal disposition of the columns relative to dyke walls are indicative that the igneous body may represent the main heat source for the interstitial aqueous solutions previously existing in the sediments. At macroscopic scale, the increasing of internal tensions in the sandstones is responsible for the nucleation of polygons, leading to the individualization of prisms, which are interconnected by a system of joints, formed firstly on isotherm surfaces of low temperature and later on successive adjacent planes towards the dyke heat source.

Base Revision for Ontology Debugging

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.