2 Note that in the approximation in which we are work-
ing, the shape of the Wilson line is irrelevant, and the fram- ing is entirely specified by its boundary endpoint(s).
∂χ(z) = j(z). TheOPE of χ with various op- erators can be derived fromthe known j OPEs. As explained at length in , while generically χ does not exist as an operator in the holographic dual CFT (since its zero mode is unphysical), it is nevertheless a useful computational tool. In terms of χ, the expression for the gauge-invariant bulk scalar reads
3.2. AC field applied perpendicularly to pre-existing magnetization
Now we investigate the results obtained in the “crossed field” configuration. A typical result of the decay of the c-axis average magnetic flux density against the transverse field AC field is plotted in figure 3. This graph shows how the average flux density (probed by the sensing coil) is affected drastically when cycles of transverse field are applied to the single domain. This behaviour is in excellent agreement with other results of crossed field experiments carried out on other superconducting materials [27-31]. It should be emphasized that the DC signal plotted in figure 3 is the average flux density, which may differ fromthe true magnetization due to finite-size effects, as shown clearly in ref. . On figure 4, the results of similar experiments are displayed, but what is plotted is the central flux density against the surface of the sample, as recorded by a miniature Hall probe stuck against the sample surface. Two experiments were carried out in order to investigate the influence of parameters of the experimental system on the measured data. On figure 4(a), the Hall probe was intentionally misoriented by a small angle (4 degrees) while in figure 4(b) the Hall probe was purposefully placed near the edge of the sample. The results are always compared to those obtained with a correctly placed Hall probe. The two set of curves plotted in figure 4(b) are very close to each other, showing that the exact positioning of the Hall probe against the surface is not a critical parameter of the experiment. Figure 4(a), however, shows that a correct Hall probe angular orientation is essential. Following similar sets of experiments carried out at different angles, it was determined in practice that the (unavoidable) experimental misorientation that can be tolerated should be 0.5° or less.
displacement used as boundary conditions is thus picked up from nodes in thebulk of the DIC mesh. The displacement fields measured by DIC and MIC using the mesh in Figure 9(a) for the last loading step are depicted in Figure 11 . The scatter between the two displacements is difficult to observe by the naked eyes. For assessing the accuracy of the displacement field obtained by MIC, the correlation error map are plotted for the two analyses in Figure 12 . These two error maps are again difficult to distinguish what confirms that the MIC displacement leads to a registration of the images of the same accuracy as the DIC analysis. To further assess this point, the average correlation error for DIC and MIC is plotted as a function of the steps in Figure 13 . The error level is slightly higher for MIC, what is expected because only 500 modes are used to measure the displacement instead of 2 × N . The search of the optimal solution in terms of grey level conservation is thus more constraint and the minimum error level reached with the reduced parametrization is higher. These results ensure that the displacement parametrization adopted for MIC leads to measured fields globally as accurate as thoses obtained for a DIC analysis.
As expected, the transverse field reduces the -axis induction but perceptible differences appear between the and direc- tions. First we examine the field distribution along the axis (Fig. 4). The plots are slightly tilted as indicated by the arrows in Fig. 4. This behavior can be understood qualita- tively by considering demagnetization effects and by taking into account that the Hall probe is located at a finite distance fromthe sample top surface. After the first sweep, the sample is per- manently magnetized along the -axis. Since the induction lines are necessarily closed, they find a return path in the free space, in particular above the top-surface of the disk. This produces an additional -component of the induction measured by the Hall probe. This component is positive for and negative for , resulting in a distorted flux profile. Measurements with fields directed toward (not shown here) yield the oppo- site phenomenon. Therefore the behavior depicted in Fig. 4 is merely a geometric effect caused by the trapped induction in the transverse field direction.
Bulk melt-processed Y-Ba-Cu-O (YBCO) has significant potential for a variety of high-field permanent-magnet- like applications, such as the rotor of a brushless motor. When used in rotating devices of this kind, however, the YBCO can be subjected to both transient and alternating magnetic fields that are not parallel to the direction of magnetization and which have a detrimental effect on the trapped field. These effects may lead to long-term decay of the magnetization of thebulk sample. In the present work, we analyze both experimentally and numerically the remagnetization process of a melt-processed YBCO single domain that has been partially demagnetized by a magnetic field applied orthogonal to the initial direction of trapped flux. Magnetic torque measurements are used as a tool to probe changes in the remanent magnetization during various sequences of applied field. The application of a small magnetic field between the transverse cycles parallel to the direction of original magnetization results in partial remagnetization of the sample. Rotating the applied field, however, is found to be much more efficient at remagnetizing thebulk material than applying a magnetizing field pulse of the same amplitude. The principal features of the experimental data can be reproduced qualitatively using a two- dimensional finite-element numerical model based on an E-J power law. Finally, the remagnetization process is shown to result fromthe complex modification of current distribution within the cross-section of thebulk sample.
As expected, these results are completely different fromthe transport properties of the same model in the absence of bulk dephasing , where the quantum coherence of thebulk dynamics maintains the localized character via a step-magnetization profile and an exponentially decaying current with the system size .
 “50 years of Anderson Localization”, E. Abrahams Ed, World Scientific (2010).  R. Nandkishore and D. A. Huse, Ann. Review of Cond. Mat. Phys. 6, 15 (2015).  E. Altman and R. Vosk, Ann. Review of Cond. Mat. Phys. 6, 383 (2015).  S. A. Parameswaran, A. C. Potter and R. Vasseur, arXiv:1610.03078.  J. Z. Imbrie, V. Ros and A. Scardicchio, arXiv:1609.08076.
In this chapter, we have given a brief survey of active contours in segmentation as well as techniques for road and hydrographic network extraction from images. Active contour methods are categorized into two different classes: edge-based and region-based. The for- mer has many limitations because it considers local information around theboundary of the object in question. Between the two types of edge-based active contours, geometric active contours have many advantages over parametric active contours, such as computational simplicity and the ability to change curve topology during evolution. The introduction of region-based methods tends to give better segmentation results because they use global in- formation about the object. The corresponding energy functionals tends to have fewer local minima which makes reasonable the use of local optimization algorithms. Moreover, we have mentioned a family of active contour methods which incorporates specific knowledge about the shape of the object: the so-called shape priors. Our interest fits this family of methods because we aim to model network-like regions which have complex shapes and need specific and sophisticated shape priors for automatic (or semi-automatic) solution of the problem of extraction.
Crossed-magnetic-field effects on bulk high-temperature superconductors have been studied both experi- mentally and numerically. The sample geometry investigated involves finite-size effects along both 共crossed-兲 magnetic-field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O single domains that had been premagnetized with the applied field parallel to their shortest direction 共i.e., the c axis兲 and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample ab plane. The magnetic properties were measured using orthogonal pickup coils, a Hall probe placed against the sample surface, and magneto-optical imaging. We show that all principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E-J power law and in which the current density flows perpendicularly to the plane within which the two components of magnetic field are varied. The results of this study suggest that the suppression of the magnetic moment under the action of a transverse field can be predicted successfully by ignoring the existence of flux-free configura- tions or flux-cutting effects. These investigations show that the observed decay in magnetization results fromthe intricate modification of current distribution within the sample cross section. The current amplitude is altered significantly only if a field-dependent critical current density J c 共B兲 is assumed. Our model is shown to be quite appropriate to describe the cross-flow effects in bulk superconductors. It is also shown that this model does not predict any saturation of the magnetic induction, even after a large number 共⬃100兲 of transverse field cycles. These features are shown to be consistent with the experimental data.
where G = (H − iω) −1 and ~ k = (k x , k y ) is the momen-
tum. This can be implemented numerically, and some examples are given in Fig. 1 . The Chern number can be as large as -5, which is unusually high for such a model. The phase diagrams in Fig. 1 show changes in Chern numbers away fromthe analytically calculated bulk gap closing lines for the Γ and Dirac points. To be certain that this is not a numerical error we track thebulk gap across some of these transitions, see Fig. 2 . For all the changes in the Chern number we can see that the gap does close at some point in the BZ as required. One can also explicitly check that thebulk-boundary correspon- dence holds, demonstrating that these regions are not caused by numerical errors. However, as we shall see in what follows, these high Chern numbers do not necessar- ily lead to large numbers of protected MBS.
1.3. Outline of the paper: In Section 2 we give the precise definition of our micro- scopic dynamics and its invariant measures, we also introduce all the spaces of test functions where the microscopic fluctuation fields, namely the density and the height, will be defined and we give the proper definition of these fields. Section 3 contains all the rigorous definitions of solutions to the SPDEs that we obtain, namely the OU /SBE with Dirichlet boundary conditions, the KPZ equation with Neumann boundary condi- tions and the SBE with linear Robin boundary conditions, and we explain how these equations are linked. In Section 4 we prove the convergence of the microscopic fields to the solutions of the respective SPDEs, namely Theorems 3.17 and 3.20 . In Section 5 we prove the second order Boltzmann-Gibbs principle, which is the main technical result that we need at the microscopic level in order to recognize the macroscopic limit of the density fluctuation field as an energy solution to the SBE. Finally, in Section 6 we give the proof of the uniqueness of solutions to the aforementioned SPDEs. The appendices contain some important aside results that are needed along the paper, but to facilitate the reading flow we removed them fromthe main body of the text. In particular, Ap- pendix E sketches how one could prove that the microscopic Cole-Hopf transformation of the microscopic density fluctuation field converges to the SHE, and in particular we show that already at the microscopic level the Cole-Hopf transformation changes theboundary conditions from Neumann to Robin’s type.
The spontaneous or magnetic field-induced reversal of the magnetisation direction in materials and nanostruc- tures has been the subject of intensive studies since many decades. The use of magnetic materials in applications ranging from compass needles to electrical motors, truck brakes, cellular phones and personal computers has triggered the search for materials with particular properties concerning both their static and dynamic behaviour. Materials used e.g. in transformers need to switch their magnetisation direction under very small values of applied magnetic fields to minimise losses; these are so-called soft magnetic materials. On the other hand, permanent magnets used in electrical motors and generators need their magnetisation to be as stable as possible against both magnetic fields and thermal effects; these are so-called hard magnetic materials. Consider however information written on magnetic storage media in the form of small magnetic grains. In this case, a compromise must be found for the grains need to be stable for years, but on the other hand their magnetisation direction should respond quickly to moderate magnetic field values to allow information to be written fast. Thus for each particular case an understanding of how magnetisation reversal proceeds is needed. Magnetisation reversal can take place in different ways, depending on the size of the object and physical parameters like the exchange interaction and magnetic anisotropy. In the atomic case, a magnetic field along a direction other than the initial magnetisation will cause a torque on the magnetisation given by M × H ef f , where H ef f is the local effective field. This torque will induce a
tical transitions which can be brought into resonance with electromagnetic fields in plasmonic nanostructures and microcavities 15–18 ; v) in monolayer TMDs, electron-
hole (e-h) interactions are much stronger than in con- ventional semiconductors, due to the reduced effective screening 19,20 and carrier confinement in a single atomic layer - common features of all the 2D systems- in combi- nation with large carrier effective masses (see Ref. 21 and references therein); that leads to the impossibility to use the standard hydrogenic model in 2D limit and makes meaningless the usual classification of strong and weak exciton based on the binding energy. On the contrary, the investigation of the exciton dispersion as a function of momentum q, which can be experimentally accessed by electron energy loss spectroscopy 22 , is capable to reveal
top of this, we cannot exclude that the object obtained by braid translation of the open boundary conditions for the gl(1|1) is not some sort of version of symplectic fermions with topological defects: this requires further study .
To muddy the waters some more, a crucial point in our discussion is that we have insisted on braid translating models with open, local boundary conditions. In the RSOS case, this was all that was needed to understand the periodic models. It turns out, however, that the relationship between representations of the periodic Temperley–Lieb algebra and the blob algebra is much more general . One can, for instance, imagine starting fromthe representation of the affine TL algebra in the periodic gl(1|1) spin chain, and try to “invert” the braid translation (we provide details for this in App. E) in order to obtain a representation of the blob algebra on the open spin chain, with much more complicated modules than the ones encountered so far. This representation would then be one that, like in the RSOS case, becomes relevant to the understanding of the periodic model. But in doing so one would get a very non-local expression for the blob generator, see the derivation in App. E.2:
We first introduce the concept of regularized curvature lines that model the lines designers draw over curved surfaces, encompassing curvature lines and their extension as geodesics over flat or umbilical regions. We build on this concept to define the orthogonal cross field that assigns two regularized curvature lines to each point of a 3D surface. Our algorithm first estimates the projection of this cross field in the drawing, which is non-orthogonal due to foreshortening. We formulate this estimation as a scattered interpo- lation of the strokes drawn in the sketch, which makes our method robust to sketchy lines that are typical for design sketches. Our interpolation relies on a novel smoothness energy that we derive from our definition of regular- ized curvature lines. Optimizing this energy subject to the stroke constraints produces a dense non-orthogonal 2D cross field, which we then lift to 3D by imposing orthogonality. Thus, one central concept of our approach is the generalization of existing cross field algorithms to the non-orthogonal case. We demonstrate our algorithm on a variety of concept sketches with vari- ous levels of sketchiness. We also compare our approach with existing work that takes clean vector drawings as input.
Figure 6: Histograms for the ε xx , ε yy and ε xy distributions, calculated pixelwise as a function
procedure described in . They were slightly inclined to avoid aliasing in the corresponding images, as justified in  and illustrated in Figure 7. As in the preceding case, the distance between camera and specimens was adjusted in such a way that 6 pixels were used to sample one grid and checkerboard period. The two specimens were fixed in turn in a grip and a translation was applied to each of them according to the procedure described in Section 3.4 above. The light intensity was adjusted in such a way that the highest dynamic range of the camera sensor was used, but without saturating any pixel. Interestingly, the optimal lighting conditions are not the same for the two types of specimens. Indeed the bright spots in a 2D grid image are darker than their counterparts in a checkerboard image if exactly the same lighting conditions and camera settings (aperture, shutter time) are used in both cases, although the size of these spots is exactly the same. This is probably a consequence of the point spread function (PSF) of the lens of the camera. Indeed, white boxes are completely surrounded by black lines in 2D grid images, which is not the case for the checkerboard. The aperture of the lens was therefore changed and the distance between specimen and lighting sources was adjusted from one case to each other, in order to have a gray level distribution, which covers the widest range without reaching saturation at any pixel.
Let us also mention the following. An acylindrically hyperbolic group Γ may admit various non-elementary acylindrical actions on hyperbolic spaces. A fruitful line of research initiated by Abbott  is to find the best possible one. Such an action Γ y X is called universal if for any element g of Γ such that there exists an acylindrical action of Γ for which g is loxodromic, the action of g on X also is loxodromic. One can also introduce a partial order on cobounded acylindrical actions, see . When existing, a maximal action for this partial order is called a largest acylindrical action. Any largest action is necessarily a universal action and is unique. Abbott, Behrstock and Durham  proved that any non-elementary hierarchically hyperbolic group admits a largest acylindrical action. More precisely, they proposed a way to modify the hierarchical structure of the group so that the action of Γ on CS is a largest acylindrical action, where S ∈ S is the maximal domain. We will use this modified hierarchical structure in the following, see in particular the discussion after Proposition 3.9.
(Figure S2a). This test showed that the cold/warm difference was significant for some parameters (for example, EBC, EBC bb ), however, for EBC ff no differences between cold and warm properties
Figure 3 shows the variations of EBC concentration and Table S1 reports the seasonal medians of this parameter. EBC median concentrations are significantly higher in autumn and winter (0.34 µg m −3 (25th percentile: 0.21 µg m −3 ; 75th percentile: 0.54 µg m −3 ) and 0.32 µg m −3 (0.18 µg m −3 ; 0.56 µg m −3 )) compared to spring and summer (0.24 µg m −3 (0.16 µg m −3 ; 0.41 µg m −3 ) and 0.25 µg m −3 (0.17 µg m −3 ; 0.37 µgm −3 )), respectively. This might be a result of higher contributions of sources from combustion linked to conventional heating devices often observed during this time of the year. This may also be related to different combustion sources emitted all year long (i.e., traffic) but influenced by the seasonal variation of theboundary layer dynamics (represented for each season in Figure S1) trapping surface-emission during the cold season in a thinner layer than during summer. This is in agreement with Cesari et al., (2018) [ 33 ] at the Environmental-Climate Observatory of Lecce in Italy, who reported the highest concentrations of EBC during winter due to a possible influence of combustion sources like biomass burning and boundary layer dynamics. The hypotheses in this study will be further investigated in Section 2.2 . The atmospheric BL heights presented in this study were extracted fromthe reanalysis ERA-Interim of the European Center for Medium-Range Weather Forecasts (ECMWF) model with a resolution of 0.25 ◦ . During the day, the development of the BL is associated with enhanced vertical mixing, and therefore, a dilution of surface emitted pollutants. At night, on the contrary, the emitted particles accumulate in a thinner boundary layer with reduced vertical mixing leading to higher surface concentrations.
Le thème de la diffusion volontaire d’informations a été largement étudié dans la littérature. La plupart des études cherchent à expliquer les différences de niveaux de publication volontaire dans les rapports annuels via une étude des déterminants (e.g. Firth 1979 ; Cooke 1989 ; Meek et al. 1995 ; Raffournier 1995 ; Depoers 1999). Plus récemment, les recherches se sont étendues à d’autres moyens de communication tels que les conférences téléphoniques (e.g. Tasker 1998 ; Frankel et al. 1999 ; Brown et al. 2004) ou les sites Web des entreprises (e.g. Ettredge et al. 2002 ; Trabelsi et al. 2008 ; Li 2010 ; Ledoux et Cormier 2011). De manière surprenante et malgré l’intérêt des régulateurs, on constate une quasi-absence de littérature sur la diffusion volontaire d’informations lors des OPA/OPE. Ceci conduit Sirower et Lipin (2003, p. 26) à parler à ce sujet « d’énorme erreur ». En effet, selon ces auteurs, une stratégie de diff usion d’informations bien conçue pourrait permettre d’obtenir le soutien des actionnaires et ainsi favoriser la réussite des opérations. Les OPA/OPE sont des évènements particuliers dans la vie d’une entreprise, pouvant conduire les dirigeants à adopter des comportements de diffusion d’informations différents de leurs comportements habituels (Brennan 1999). Pour preuve, lors d’opérations inamicales, il n’est pas rare de voir les entreprises acquéreuse et cible se livrer à une véritable bataille de communication 3 .
interpretability of all elements of the class C ′ in the class C. (So the effective interpretation
of G in F (G) is an outgrowth of the computable left inverse functor for F , not of F itself.) The results in [HKSS02] are proven largely by the construction of computable functors, al- though not described in that way. However, one could also ask the same questions about cat- egories known not to be complete. For example, there is a natural construction of a Boolean algebra F (L) from a linear order L, simply by taking the interval algebra of L, where the morphisms in each category are simply homomorphisms of the structures. On its face, this functor appears to be neither full nor faithful, based on known results, and it does not have a precise computable inverse functor on its image, although it may come close to doing so. It cannot have all of these properties, because there does exist a linear order whose spectrum is not realized by any Boolean algebra, as shown by Jockusch and Soare in [JS91, Theo- rem 1]. (Here we use a generalization of the result in this article, namely, that a computable equivalence of categories onto a strictly full subcategory allows one to transfer spectra from objects of the first category to objects of the second. This generalization appears to have a straightforward direct proof, and in any case it follows from effective bi-interpretability, hence from [HTMMM15, Theorem 12], using [Mon14, Lemma 5.3].) We suspect that similar results distinguishing the properties of various everyday classes of countable structures may yield further insights into effectiveness, fullness, faithfulness, and other properties of functors among these classes, especially the incomplete ones listed in Section 1.C.
Roundness is relevant to characterize these asperities. A value of 100% characterizes a perfect disc and will decrease when it moves away from this shape.
The imagery was carried out by ombroscopy. To accom- plish this, fertilizer particles dispersed on glass were placed in front of a diffuse source of light. The selected enlargement generated a digital representation of about 3500 pixels for a particle 2.5 mm in diameter which allows a good estimate of its morphometric properties. The binarisation of the image is carried out with a fixed threshold since the conditions of lighting are stable. The minimum number of particles mea- sured by batch is 2000, which makes it possible to sufficiently minimize the confidence interval around the average of the granulometric and morphometric distributions.