| 3401. |
- Khesin, B., et al.
(författare)
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Geometric hydrodynamics via Madelung transform
- 2018
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 115:24, s. 6165-6170
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important partial differential equations of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schrodinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a Kahler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results.
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| 3402. |
- Khesin, B., et al.
(författare)
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Geometry of the Madelung Transform
- 2019
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Ingår i: Archive for Rational Mechanics and Analysis. - : Springer Science and Business Media LLC. - 0003-9527 .- 1432-0673. ; 234:2, s. 549-573
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Tidskriftsartikel (refereegranskat)abstract
- The Madelung transform is known to relate Schrodinger-type equations in quantum mechanics and the Euler equations for barotropic-type fluids. We prove that, more generally, the Madelung transform is a Kahler map (that is a symplectomorphism and an isometry) between the space of wave functions and the cotangent bundle to the density space equipped with the Fubini-Study metric and the Fisher-Rao information metric, respectively. We also show that Fusca's momentum map property of the Madelung transform is a manifestation of the general approach via reduction for semi-direct product groups. Furthermore, the Hasimoto transform for the binormal equation turns out to be the 1D case of the Madelung transform, while its higher-dimensional version is related to the Willmore energy in binormal flows.
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| 3403. |
- Khesin, Boris, et al.
(författare)
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Simple Unbalanced Optimal Transport
- 2024
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Ingår i: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - 1073-7928 .- 1687-0247.
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphisms with a natural metric, which allows a Riemannian submersion to the space of volume forms of arbitrary total mass. We describe its finite-dimensional version and present a concise comparison study of the geometry, Hamiltonian features, and geodesics for this and other extensions. One of the corollaries of this approach is that along any geodesic the total mass evolves with constant acceleration, as an object's height in a constant buoyancy field.
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| 3404. |
- Khesin, B., et al.
(författare)
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The Toda Flow as a Porous Medium Equation
- 2023
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 401, s. 1879-98
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Tidskriftsartikel (refereegranskat)abstract
- We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its similarities and differences with the dispersionless Toda system. The Toda flow describes an integrable interaction of several particles on a line with an exponential potential between neighbours, while its continuous version is an integrable PDE, whose physical meaning was obscure. Here we show that this continuous Toda flow can be naturally regarded as a special IPM equation, while the key double-bracket property of Toda is shared by all equations of the IPM type, thus manifesting their gradient and non-autonomous Hamiltonian origin. Finally, we comment on Toda and IPM modifications of the QR diagonalization algorithm, as well as describe double-bracket flows in an invariant setting of general Lie groups with arbitrary inertia operators.
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| 3405. |
- Khoomrung, Sakda, 1978, et al.
(författare)
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Metabolic Profiling and Compound-Class Identification Reveal Alterations in Serum Triglyceride Levels in Mice Immunized with Human Vaccine Adjuvant Alum
- 2020
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Ingår i: Journal of Proteome Research. - : American Chemical Society (ACS). - 1535-3907 .- 1535-3893. ; 19:1, s. 269-278
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Tidskriftsartikel (refereegranskat)abstract
- Alum has been widely used as an adjuvant for human vaccines; however, the impact of Alum on host metabolism remains largely unknown. Herein, we applied mass spectrometry (MS) (liquid chromatography-MS)-based metabolic and lipid profiling to monitor the effects of the Alum adjuvant on mouse serum at 6, 24, 72, and 168 h post-vaccination. We propose a new strategy termed subclass identification and annotation for metabolomics for class-wise identification of untargeted metabolomics data generated from high-resolution MS. Using this approach, we identified and validated the levels of several lipids in mouse serum that were significantly altered following Alum administration. These lipids showed a biphasic response even 168 h after vaccination. The majority of the lipids were triglycerides (TAGs), where TAGs with long-chain unsaturated fatty acids (FAs) decreased at 24 h and TAGs with short-chain FAs decreased at 168 h. To our knowledge, this is the first report on the impact of human vaccine adjuvant Alum on the host metabolome, which may provide new insights into the mechanism of action of Alum. ©
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| 3406. |
- Khoomrung, Sakda, 1978, et al.
(författare)
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Rapid Quantification of Yeast Lipid using Microwave-Assisted Total Lipid Extraction and HPLC-CAD
- 2013
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Ingår i: Analytical Chemistry. - : American Chemical Society (ACS). - 0003-2700 .- 1520-6882. ; 85:10, s. 4912-4919
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Tidskriftsartikel (refereegranskat)abstract
- We here present simple and rapid methods for fast screening of yeast lipids in Saccharomyces cerevisiae. First we introduced a microwave-assisted technique for fast lipid extraction that allows the extraction of lipids within 10 min. The new method enhances extraction rate by 27 times, while maintaining product yields comparable to conventional methods (n = 14, P > 0.05). The recovery (n = 3) from spiking of synthetic standards were 92 +/- 6% for cholesterol, 95 +/- 4% for triacylglycerol, and 92 +/- 4% for free fatty acids. Additionally, the new extraction method combines cell disruption and extraction in one step, and the approach, therefore, not only greatly simplifies sample handling but also reduces analysis time and minimizes sample loss during sample preparation. Second, we developed a chromatographic separation that allowed separation of neutral and polar lipids from the extracted samples within a single run. The separation was performed based on a three gradient solvent system combined with hydrophilic interaction liquid chromatography-HPLC followed by detection using a charged aerosol detector. The method was shown to be highly reproducible in terms of retention time of the analytes (intraday; 0.002-0.034% RSD; n = 10, interday; 0.04-1.35% RSD; n = 5) and peak area (intraday; 0.63-6% RSD; n = 10, interday; 4-12% RSD; n = 5).
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| 3407. |
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| 3408. |
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| 3409. |
- Kiejna, Adam, et al.
(författare)
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The energetics and structure of rutile TiO2(110)
- 2006
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Ingår i: JOURNAL OF PHYSICS-CONDENSED MATTER. ; 18:(17), s. 4207-4217
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Tidskriftsartikel (refereegranskat)abstract
- Density functional theory and a pseudopotential plane wave method are applied to study electronic and structural properties of the defect-free TiO2(110) surface. The variations of the surface energy, work function, and atomic displacements are examined for partially and fully relaxed slabs modelling the rutile (110) surface, and consisting of up to 33 atomic layers. Relatively small relaxations of atomic positions in the outermost layers have a strong influence on the calculated surface energies and work functions. The effect of nonequivalence of the odd-even layer terminations is explored. A simple method is proposed which allows one to estimate accurate surface energies for relaxed systems from calculations for partially relaxed slabs.
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| 3410. |
- Kilde Löfgren, Sebastian, 1991, et al.
(författare)
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Rolling balls or trapping ions? How students relate models to real-world phenomena in the physics laboratory
- 2023
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Ingår i: Science Education. - 0036-8326 .- 1098-237X. ; 107:5, s. 1215-37
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Tidskriftsartikel (refereegranskat)abstract
- The creation and use of models in science is of great importance for knowledge production and communication. For example, toy models are often used as idealized explanatory models in physics education. Models can be a powerful tool for exploring phenomena in ways that facilitate learning. However, careful consideration of instruction and explanations needs to be considered to guide how students relate models to real-world phenomena in subject-correct ways. A design experiment was conducted to investigate how upper secondary school students can use models for learning in the physics laboratory. The intervention used in the study was a laboratory exercise developed over three phases where students worked with a mechanical Paul trap and a simulation to understand the principle behind a real Paul trap. Each phase of the study consisted of three to five laboratory sessions. The data were analyzed using thematic analysis and the learning process was understood using the theoretical framework of variation theory. From the results, it was possible to identify patterns of variation for successful lab groups and critical aspects and features students need to discern to effectively modelize the mechanical Paul trap. The findings also indicate that having students work with models can be a meaningful clarificatory process to develop a deeper understanding of the use and limitations of models in science.
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