168 research outputs found

    Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: Application to Navier-Stokes equations with model order reduction

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    This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution configurations can arise from the same parametric instance. We thus aim at describing how optimal control allows to change the solution profile and the stability of state solution branches. First of all, a general framework for nonlinear optimal control problem is presented in order to reconstruct each branch of optimal solutions, discussing in detail the stability properties of the obtained controlled solutions. Then, we apply the proposed framework to several optimal control problems governed by bifurcating Navier-Stokes equations in a sudden-expansion channel, describing the qualitative and quantitative effect of the control over a pitchfork bifurcation, and commenting in detail the stability eigenvalue analysis of the controlled state. Finally, we propose reduced order modeling as a tool to efficiently and reliably solve parametric stability analysis of such optimal control systems, which can be challenging to perform with standard discretization techniques such as Finite Element Method

    Optical coherence tomography diagnostic signs in posterior uveitis.

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    A diagnostic sign refers to a quantifiable biological parameter that is measured and evaluated as an indicator of normal biological, pathogenic, or pharmacologic responses to a therapeutic intervention. When used in translational research discussions, the term itself often alludes to a signs used to accelerate or aid in diagnosis or monitoring and provide insight into "personalized" medicine. Many new diagnostic signs are being developed that involve imaging technology. Optical coherence tomography is an imaging technique that provides in vivo quasi-histological images of the ocular tissues and as such it's able to capture the structural and functional modifications that accompany inflammation and infection of the posterior part of the eye. From the hyperreflective inflammatory cells and deposits in the vitreous and on the hialoid, to the swollen photoreceptors bodies in multiple evanescent white dots syndrome, and from optical difference of the subretinal fluid compartments in Vogt-Koyanagi-Harada disease to the hyporeflective granulomas in the choroid, these tomographical signs can be validate to reach the status of biomarkers. Non-invasive imaging diagnostic signs of inflammation can be very useful to clinicians seeking to make a diagnosis and can represent a dataset for machine learning to offer a more empirical approach to the detection of posterior uveitis

    Model order reduction for bifurcating phenomena in fluid-structure interaction problems

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    This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid

    Diplazium humbertii Pichi Sermolli 1973

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    <i>Diplazium humbertii</i> (C.Chr.) Pichi Sermolli (1973: 444) (Figs. 4 E–F, 6–7). <p> <i>Athyrium humbertii</i> Christensen (1937: 54)</p> <p> <b>Lectotype</b> (designated by Pichi Sermolli 1973):— D.R. CONGO. North Kivu: Montagnes à l’Ouest du Lac Kivu (Congo Belge). Forêt, 2000–2400 m, February–March 1929, <i>H. Humbert 7497</i> (BM000918405!; isolectotype BM000918404!)</p> <p> <b>Specimens seen:</b> — RWANDA. Western Province: Nyungwe National Park, route Astrida (= Huye) – Bukavu, vers km 93, forêt de Rugege (= Nyungwe) près d’Uwinka, Territ. Shangugu (= Rusizi), 24 September 1956, <i>G. Troupin 2598</i> (BR0000013688578); a sud-est del lago Kivu a 45 km da Bukavu lungo la strada per Astrida (= Huye), 15 August 1956, <i>R. Pichi Sermolli 5323</i> (BR0000013688585); Forêt de Nyungwe, environs de Kamiranzovu, Préfecture Cyangugu (= Rusizi), September 1971, <i>G. Bouxin 1211</i> (BR0000013688462); Kamiranzovu, 11 August 2007, <i>E. Fischer s.n.</i> (KOBL); Cyamudongo Forest, 4 April 2021, <i>E. Fischer s.n.</i> (KOBL).</p> <p> <b>Distribution in Rwanda:</b> —Western Province, Nyungwe National Park.</p> <p> <b>Distribution in Africa:</b> Eastern D.R. Congo, Western Uganda, Western Rwanda, Western Burundi, Western Tanzania. Albertine Rift endemic.</p> <p> <b>Habitat:</b> —Montane rainforest, elev. 1900–2400 m.</p> <p> <b>Note:</b> —The spores (Fig. 4 E, F) resemble those of <i>Diplazium cyamudongoense sp. nov.</i> (Fig, 4 A–D) and have a cristate perispore, 54.3–57.2 × 28.6–37.1 µm, the alae are 5.7–7.15 µm high and 1.5–2.86 µm wide. The remaining perispore bears up to 1.4–1.6 µm long spine-like scattered projections.</p>Published as part of <i>Fischer, Eberhard & Lobin, Wolfram, 2023, Synoptic Revision of Diplazium (Athyriaceae) in Rwanda with description of Diplazium cyamudongoense sp. nov., pp. 169-183 in Phytotaxa 600 (3)</i> on page 175, DOI: 10.11646/phytotaxa.600.3.4, <a href="http://zenodo.org/record/8080860">http://zenodo.org/record/8080860</a&gt

    Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method

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    The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.Comment: 26 pages, 30 figure

    Disease of the Year : Differential Diagnosis of Uveitic Macular Edema

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    Uveitic cystoid macular edema (UME) is an important cause of visual morbidity among patients with both infectious and non-infectious uveitis. UME may be associated in more than 30% cases of active uveitis. However, even patients with minimal features of intraocular inflammation may develop recurrent or chronic UME. Therefore, the evaluation and management of UME in patients with uveitis may be challenging. A number of vitreoretinal pathologies may result in UME and accumulation of fluid in the intra- or subretinal space. These need to be carefully distinguished from each other so that appropriate management can be initiated. All types of uveitis, including anterior uveitis (where the primary site of inflammation is not in the posterior segment) can present with UME. Other conditions such as diabetes, and surgery, can present with macular edema. This index review highlights various differential diagnoses of UME and provides illustrative case examples with multimodal imaging evaluation

    Wide-field spectral domain-optical coherence tomography in central serous chorioretinopathy

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    The aim the study was to describe wide-field spectral-domain optical coherence tomography morphologic relationships of the vitreous, retina, and choroid in central serous chorioretinopathy (CSCR) eyes. Standardized horizontal, vertical, and two oblique (supertemporal to inferonasal and supranasal to inferotemporal) SD-OCT sections were collected for 40 patient with CSCR. For extramacular imaging, images were obtained from eight locations: (1) nasal to the optic disk, (2) extreme nasal periphery, (3) superior to the superotemporal vascular arcade, (4) extreme superior periphery, (5) inferior to the inferotemporal vascular arcade, (6) extreme inferior periphery, (7) temporal to the macula, and (8) extreme temporal periphery. Wide-angle montage images of OCT from equator to equator were composed with a montaging software. Average subfoveal choroidal thickness was 478 ± 114 μm (range 232–695 μm) at the macular level, 367 ± 94 μm in the superior periphery, 257 ± 103 μm in the inferior periphery, 431 ± 121 and 280 ± 88 μm in the nasal and in the temporal periphery, respectively. Wide-field EDI-OCT revealed a relative thinning of the inner choroidal layer in the periphery, including the small and medium large vessels, which ranged from 86 μm nasally to 120.1 μm superiorly, with a mean of 98.8 ± 13.6 μm. Beneath the thinned inner choroidal layer, hyporeflective lumina, corresponding to the outer choroidal layer, were identified in the periphery of all eyes. The outer choroidal layer thickness ranged from 175.5 μm temporally to 235.5 μm superiorly, with a mean of 217.8 ± 41.4 μm. The novel approach of montaging SD-OCT images to examine relationships between the choroid, retina, and associated structures adjacent to and outside of the macula may have a number of relevant applications in the study of pathologic features of central serous chorioretinopathy
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