3.3. Case 3: Simple model of a **diffuse** **interface** In practice, sharp interfaces are not expected in real spintronic devices since the sputtering process generally builds **diffuse** interfaces. As previously mentioned, it is of extreme complexity to perform DFT calculations of these real systems because of the simulation supercell size and hence the large amount of atoms involved. One step forward, compared to the previously studied cases 1 and 2, is the construction of a simple rough **interface**, where only one atom of one material is replaced by one of the other (see figure 1–A2). In doing so, we take the first step to understand more realistic **diffuse** inter- faces. As in case 2, the rough **interface** was optimized by means of CG method followed by the self-consistent calculation of the layer resolved DOS. Subsequently m k (∞) is determined. In order to compare the present case with previous ones the layer resolved m k (∞) values are shown in Fig. 3 (d). It reveals that the polarization extends further into the Cu due to an enhancement of the magnetic moment, and that the rough Co/Cu inter- face, considerably damps out the oscillations of m k (∞) present in the atomically sharp **interface**. The physical explanation of the reduction in the oscillatory behavior of m k (∞) in the present case compared to cases 1 and 2 is lies in the smooth chemical transition between both materials which favors the gradual charge transfer be- tween Co and Cu at the mixed Co/Cu plane.

Many methods exist for accounting for different classes of surfactants. For insoluble surfac- tants, which are modelled with no bulk presence, one can describe their evolution and be- haviour purely from their interfacial concentrations. Here, research directions are directed to methods which accurately and efficiently predict the **interface** evolution. In particular techniques that exploit the fact that the **interface** dimension is one less than the bulk, and treat the surfactant efficiently with a surface partial differential equation. One popular idea is that the **interface** can be tracked explicitly with marker particles (Lagrangian points [45]), that is, the computational mesh tracks the **interface**. These may be coupled with a Navier- Stokes solver, such as an embedded boundary method [84]. One may also use tracking for the **interface** but solve for the surfactant using a finite volume method [68, 88]. Another field of investigation is for solving problems over a fixed grid and employ techniques to cap- ture or reconstruct the **interface**, such as volume of fluid methods [73] (relying on volume conservation to construct the **interface**), level set methods [138] (a level set of a function represents the **interface** [101, 102]) or novel fixed grid methods such as segment projection methods [79] (the **interface** is segmented and parametrised by simple functions on chosen coordinate planes). Finally, one may use a carefully chosen smoothing function that pre- serves key mathematical structure, and replaces the (sharp) hypersurface with a (**diffuse**) thin interfacial region. This technique is known as a phase field model or **diffuse** **interface** model [92], with a more general discussion in [8]. One particular benefit of this method over any others mentioned (including the level set formulation), is that the approximation it provides to the free boundary problem is more mathematically grounded. In particular there is much stronger notion of convergence as our interfacial region shrinks to a hypersur- face, and this allows for the recovery of the equations for the entire free boundary problem. We shall utilize this latter method in this thesis, and the corresponding asymptotic analysis which characterises the recovery will be presented in a forthcoming article [42].

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These difficulties have led to the development of **diffuse** **interface** (or phase field) models to provide an alternative description of fluid/fluid interfaces. At the core of these models, it is assumed that there is some microscale mixing of the macroscopically immiscible fluids and the sharp **interface** is replaced by an interfacial layer of finite width. Within this region the two fluids are mixed and the model has to account for certain mixing energies. An order parameter is introduced to distinguish between the fluids within the interfacial layer, where it takes distinct constant values in each of the bulk regions and varies smoothly across the narrow interfacial layer (see Figure 1.2). The original sharp **interface** can then be represented as the zero level set of the order parameter, which draws on ideas of the front-capturing method, thus allowing different level sets to exhibit different topologies. We mention the work of Lowengrub et al. [1999]; Lowengrub and Truskinovsky [1998] on the investigation of phase field models near topological transitions in the context of two-phase flows. We remark that, in contrast to the front-capturing method where the inter- face is represented as a level set of an artificial function, the order parameter in the phase field model can have physical meaning. For example, one can choose the order parameter to be the difference in volume fraction, the difference in mass concentra- tion or the density difference (see [Abels et al., 2011; Lowengrub and Truskinovsky, 1998]).

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The review [4] provides an overview on diﬀuse **interface** methods in the context of ﬂuid ﬂows. In [26, 27] it was already proposed to combine a Cahn-Hilliard equation for distinguishing the two phases with a Navier-Stokes system. An additional term was included in the momentum equation to model the surface contributions to forces. In the case of diﬀerent densities, Lowengrub and Truskinovsky [41] derived quasi- incompressible models, where the ﬂuid velocity is not divergence free. On the other hand, Abels, Garcke, and Gr¨ un [1] derived a thermodynamically consistent diﬀuse **interface** model for two-phase ﬂow with diﬀerent densities and with solenoidal ﬂuid velocities. Following the derivation in [1], we will derive three diﬀuse **interface** models, which approximate the sharp **interface** models in the diﬀuse-limited regime.

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While various phase-field models have recently appeared for two-phase fluids with dif- ferent densities, only some are known to be thermodynamically consistent, and practi- cal stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible **diffuse**-**interface** Navier– Stokes Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of ther- modynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the de- rived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with nonsolenoidal ve- locity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and break-up dynamics of droplets including pinching due to gravity.

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The moving boundary problem (1.9) may be simplified by setting some param- eters to zero or infinity (formally). In particular, two interesting simplifications are possible. The first one is when (t) propagates because of nonzero at (t), and satisfies a steady **interface** problem. This is a so-called tumor-front propagation with quasi-steady nutrient evolution. The second one is when (t) propagates sim- ply because of a constant nonzero = 0 . These two simplifications allow for direct

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Abstract. We analyse a **diffuse** **interface** type approximation, known as the **diffuse** domain approach, of a linear coupled bulk-surface elliptic PDE system. The well-posedness of the **diffuse** domain approximation is shown using weighted Sobolev spaces and we prove that the solution to the **diffuse** domain approximation converges weakly to the solution of the coupled bulk-surface elliptic system as the approximation parameter tends to zero. Moreover, we can show strong convergence for the bulk quantity, while for the surface quantity, we can show norm convergence and strong convergence in a weighted Sobolev space.

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is to use phase field model (**interface** capturing, **diffuse** **interface** theory) to simulate multiphase and multi-component flows [1, 2, 12, 13, 35, 40], which is an increasingly popular choice for modeling the motion of multiphase and multi-component fluids. In the phase field model, a conserved order parameter such as a mass concentration that varies continuously over thin interfacial layers is introduced, and the order parameter is mostly uniform in the bulk phases. Based on this idea, sharp fluid interfaces are replaced by thin but nonzero thickness transition regions where the interfacial forces are smoothly distributed. The free **interface** can be automatically tracked without imposing any mathematical conditions on the moving **interface**. One advantage of the phase field model is that the governing system of equations in the model can be derived from the variational principle. Moreover, the phase field model usually leads to well-posed nonlinear systems that satisfy the energy dissipation law. Therefore, this model has become a well-known simulation tool to resolve the motion of free interfaces in multiple components, and has also been successfully applied to many problems in the fields of science and industry [5, 21, 24, 25, 49, 51, 52].

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Burkina Faso, like the countries of Africa south of the Sahara, has a solar field in abundance. Development policies in energy matters are therefore oriented towards this form of energy. In the field of research applied to renewable energies, the knowledge of the solar energy potential in a given site is a paramount parameter for the designers of systems having solar as a source of energy. There are relatively few sites for measuring solar radiation over the entire territory of Burkina Faso (E. Ouedraogo and O. C. A. Ouedraogo,2012). As a result, the necessary complete meteorological data are most often missing. In addition, we found that some semi-empirical formulas often do not allow to evaluate the solar radiation of certain localities of the country. Numerous studies exist in the literature on solar potential estimation models. We can cite the first steps led by Liu and Jordan (B. Y. H. Liu and R. C. Jordan, 1960), which gave a relation between **diffuse** daily solar irradiation and global one on a horizontal surface. We can also mention the work of (J. F. Orgill and K.G.T. Hollands, 1977) as well as the work of (Beriot NICOLAS, 1985) which correlated the **diffuse** fraction of solar radiation with the clarity index. Markovian approaches have contributed to the modeling of random fluctuations in solar radiation (S. HARROUNI et A. MAAFI, 2002) and have enabled the development of solar radiation calculation models. More recent studies have focused on modeling the randomness of solar radiation using neural networks (A. MAAFI et S. HARROUNI, 2000) and fractal analysis (A. SFETSOS et A. H. COONICK, 2000, S. BARBARO, G. CANNATA, S. COPPOLINO, C. LEONE and SINAGRA, 1981). Some authors have used insolation (J. Canada, 1988, C. Gueymard, 1993) and others, the daily average of the relative humidity, the maximum and the minimum of the temperature (I. Supit and R.R. Van Kappel, 1998, J. C. Ododo et al, 1995). In this work, we will first map the thermal zones of Burkina Faso. On the basis of this map study the theoretical modeling of solar radiation, then proceed to its validation. Finally , a comparative study of the evolutions of the solar radiation of the climatic zones will be carried out, an approach which has not been realized in the previous works. *Corresponding author: GUENGANE Hassime 1,2,*,

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A survey on sunglasses has shown that the sunglasses lenses reduce the UV irradiances to the lens and retina. 33 Standards organisations in Australia and other countries have established minimal standards for sunglasses, for example AS, 1990. 34 These are based on the ocular protection provided by the lens and provide no information of the ocular UV exposure around the lens and frame. Lenses opaque to UV radiation reduce UV exposures through the lenses, however **diffuse** UV is still possible to reach the eye around the side of the lenses. 35 For sunglasses, side shields and overhead protection or alternatively tightly fitting wrap around sunglasses are essential to reduce the ocular exposures due to the high relative proportions of **diffuse** UV radiation. 2,35

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Recent studies performed by computed tomography (CT) evaluation in family members of patients with familial idiopathic pulmonary fibrosis (IPF) [1], in healthy elderly patients [2] and, more recently, in large longitudinal cohorts for cardiovascular disease and lung cancer screening, provide proof of evidence for the early identification of subclinical interstitial lung abnormalities (ILAs) and set the conceptual basis for a possible screening strategy in **diffuse** parenchymal lung diseases (DPLDs). These advances have become possible by integrating the wide-scale use of high-resolution computed tomography (HRCT) in large longitudinal studies and due to the more recent advances in molecular medicine, particularly in relation to genetics. The MUC5B genotype, well known to be associated with a mild form of IPF, has been shown recently to be associated with the serial progression of ILAs, thus providing strong indirect support for the view that screening for ILAs might eventually provide a means for the early identification of IPF. Further molecular studies will elucidate the molecular profile of IPF, and eventually of ILAs, and this may lead in the future to the identification of different subtypes of pulmonary fibrosis for which the identification and treatment of early subclinical forms might become a reality.

There has been a growing interest in the simulation of sounds in interactive worlds, using physical models that are stimulated according to dynamical interactions in the world. This can be traced back to the work of Hahn [1], in which impacts between graphically rendered objects were modelled with modal resonators. Modal resonators themselves have a long history predating digital computers. Van den Doel [2, 3] expanded this to continuous contact excitations, still using modal resonators. The continuous excitations depend on the dynamics of the points of contact between resonating objects. Modal resonators are useful for simulating a variety of objects but they are not suitable for objects with **diffuse** resonance. These form a broad and important class, and an audio-enabled interactive world simulator should be expected to deal with them competently. Other digital linear structures exist for handling **diffuse** resonances, but the computational expense is considerably greater per object for similar quality. This paper investigates the nature of the **diffuse** resonance, reviews techniques that have been previously been applied and then proposes a new resonator paradigm that combines physical modelling with perceptual modelling. Some examples are described, but no assessment is made in terms of listener tests or objective perceptual comparison. It is suggested that the effectiveness of the technique will be quite obvious to most listeners.

**Diffuse** anterior retinoblastoma is a rare variant of **diffuse** infiltrating retinoblastoma that occurs unilaterally in children between the ages of 3 and 9 years. The majority of cases are nonhereditary; however, there is one reported case in a child with a germline mutation of the RB1 gene. FNAB should only be performed at highly specialized centers with experienced ophthalmologists and ophthalmic pathologists as a last resort to narrow the differential diagnosis due to the risk of tumor dissemination. Simultaneously, exploring the particular clini- cal hint presentation and seeking diagnostic tools other than FNAB that could confirm the diagnosis without amplifying the tumor dissemination are of importance. Additionally, making adjustment of management such as selecting the appropriate adjuvant therapy methods is crucial for the survival rate and living quality of the patients. Detailed, long-term case reports following diagnosed children are still lacking.

In daily life, architects work with drawings. Therefore they like to work with images. That is why when choosing user **interface**, they like a user **interface** which uses images. They do not like a textual user **interface**. This may be the reason why most respondents choose user **interface** 2 as their favourite. Based on the statement above, user **interface** 3 may be the respondents‘ favourite if the list of material is presented in the form of list of images instead of list of texts. In here, the users can drag and drop the pictures in the list as in user **interface** 2. However, architects do not really understand technical detail like construction materials. Therefore, one of the respondents suggests a user **interface** without inputting materials. Another reason for the popularity of user **interface** 2 is the use of, although not exactly, principle of direct manipulation. In here, after the users input a value by dragging and dropping into the container, they can see the values they inputted in the same window. By having this, they can check whether the value they inputted is correct or not. The principle of direct manipulation is supported by the use of tabbed navigation since the users do not need to move to different window to fill all parameters. This allows users to make fewer errors and complete tasks in less time, because they can see the results of an action before completing the action, thus evaluating the output and compensating for mistakes [34]. The advantages of direct manipulation interfaces include their intuitiveness, simplicity, and flexibility. Novice users find this type of **interface** easier to learn than an equivalent command-based or menu-based **interface** [35]. Although different from existing user **interface**, user **interface** 2 is still easy to use. This is because the use

On the basis of histological classification of CMT, 26 cases were carcinomas, 20 carcinosarcomas and 7 sarcomas. Carcinomas were further classified into simple carcinoma (6/26), complex carcinoma (17/26), squamous cell carcinoma (2/26) and malignant myoepithelioma (1/26). The twenty cases of carcinosarcomas consisted of varying degree of epithelial, connective tissue and metaplastic components. Whereas, sarcomas comprised of 5 cases of osteosarcoma and one each of hemangiosarcoma and fibrosarcoma. Positive immunoreactivity of BCRP was observed in all the 53 cases of CMT. **Diffuse** and variable membranous and cytoplasmic immunoreactivity of BCRP was observed in cancerous epithelial cells and stromal connective tissue cells (Figures 1-3). The immunoreactivity of BCRP was also observed in endothelium, blood vessel wall, ductular epithelium and tumor emboli. On the basis of staining intensity, 7 cases revealed weak (+) immunoreactivity, 30 cases moderate (++) immunoreactivity and 16 cases strong (+++) immunoreactivity.

The study was conducted to demonstrate the feasibility of **diffuse** correlation spectroscopy (DCS) for continuous monitoring of cerebral blood flow (CBF) in preterm infants and to compare measurements of DCS with transcranial Doppler ultrasound (TCD); the latter technique is used routinely for this population. A priori, the two modalities need not be strongly correlated since they measure different quantities: TCD measures flow in primary arteries, and DCS measures flow in tissue microvasculature. Our results show that a correlation exists between TCD measurements of peak systolic and mean velocities in the middle cerebral artery and DCS measurements of blood flow index, and that this correlation is statistically significant in this population. Furthermore, a weak but significant correlation exists between BFI and end diastolic velocity. The relative weakness of this correlation is due primarily to the low signal-to-noise ratio (SNR) of the EDV measurements for this population. Intuitively, one might expect BFI to correlate most strongly with MV, given that BFI is extracted from an autocorrelation curve which is averaged over three seconds (approximately 7 cardiac cycles). However, since MV is derived from EDV, it is strongly influenced by the low SNR of the EDV data.

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Although the type and number of TV services have changed significantly, few studies have addressed the TV user **interface** even though there are clear challenges in the use of TV by consumers. It seems that TV viewers are having difficulty adapting to the new TV paradigm, because they are used to the limited and one directional service of traditional TV. For example, Internet TV failed in the market soon after its release. Also, the buying cycle for TV sets is longer than that of mobile phones, so updating to newer systems and different user experiences is very slow. Furthermore, most TV manufacturers are in far-east Asia with no major

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Abstract. The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceano- graphic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A fi- nal simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a **diffuse** air- water **interface** is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.

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The degree of ionization is higher in the 30 Doradus Nebula; N ( 0 + 2 )/N(04 ) 9 4.5 (1•5 for Orion). This will mean that the concentration of 0 J may be somewhat greater than one per cent, and that of 0 ° somewhat less than eight per cent. It is difficult to imagine the 0 +^ contribution becoming very high in **diffuse** nebulae, however, in view of the large third ionization potential (55eV), and the two ions 0 and 0 will probably still contribute about 90 per cent of the total oxygen abundance. We may write,therefore,

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According to the previous autopsy reports of SFTS patients [18, 19], SFTS nucleoprotein antigens have been found mainly in the lymph nodes, liver, spleen, and bone marrow by an immunostaining method; therefore, it has been presumed that lymphatic organs are the main sites of SFTSV proliferation. However, recent autopsy report of an SFTS patient without myocarditis demonstrated that by new immunohistochemistry and immunofluores- cent staining methods, the least amount of SFTS nucleoprotein antigen was detected in the heart [20]. This suggested that SFTSV can directly infect the heart. Although severe SFTS cases could suffer myocardial dys- function [13, 21], **diffuse** ST elevation in electrocardio- gram or narrowing of LV cavity and **diffuse** LV wall thickness in echocardiogram were not evident in these cases, and thus these cases were not suspected of having myocarditis.