| 1. |
- Bergemann, Maria, et al.
(författare)
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The Gaia-ESO Survey : Hydrogen lines in red giants directly trace stellar mass
- 2016
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 594
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Tidskriftsartikel (refereegranskat)abstract
- Red giant stars are perhaps the most important type of stars for Galactic and extra-galactic archaeology: they are luminous, occur in all stellar populations, and their surface temperatures allow precise abundance determinations for many different chemical elements. Yet, the full star formation and enrichment history of a galaxy can be traced directly only if two key observables can be determined for large stellar samples: age and chemical composition. While spectroscopy is a powerful method to analyse the detailed abundances of stars, stellar ages are the missing link in the chain, since they are not a direct observable. However, spectroscopy should be able to estimate stellar masses, which for red giants directly infer ages provided their chemical composition is known. Here we establish a new empirical relation between the shape of the hydrogen line in the observed spectra of red giants and stellar mass determined from asteroseismology. The relation allows determining stellar masses and ages with an accuracy of 10-15%. The method can be used with confidence for stars in the following range of stellar parameters: 4000 < T-eff < 5000 K, 0.5 < log g < 3.5, -2.0 < [ Fe/H] < 0.3, and luminosities log L/L-Sun < 2.5. Our analysis provides observational evidence that the H-alpha spectral characteristics of red giant stars are tightly correlated with their mass and therefore their age. We also show that the method samples well all stellar populations with ages above 1 Gyr. Targeting bright giants, the method allows obtaining simultaneous age and chemical abundance information far deeper than would be possible with asteroseismology, extending the possible survey volume to remote regions of the Milky Way and even to neighbouring galaxies such as Andromeda or the Magellanic Clouds even with current instrumentation, such as the VLT and Keck facilities.
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| 2. |
- Grigoriev, Yurii, et al.
(författare)
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Delay differential equations
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 251-292
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Tidskriftsartikel (refereegranskat)abstract
- In this chapter, applications of group analysis to delay differential equations are considered. Many mathematical models in biology, physics and engineering, where there is a time lag or aftereffect, are described by delay differential equations. These equations are similar to ordinary differential equations, but their evolution involves past values of the state variable. For the sake of completeness the chapter is started with a short introduction into the theory of delay differential equations. The mathematical background of these equations is followed by the section which deals with the definition of an admitted Lie group for them and some examples. The purpose of the next section is to give a complete group classification with respect to admitted Lie groups of a second-order delay ordinary differential equation. The reasonable generalization of the definition of an equivalence Lie group for delay differential equations is considered in the next section. The last section of the chapter is devoted to application of the developed theory to the reaction-diffusion equation with a delay.
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| 3. |
- Grigoriev, Yurii, et al.
(författare)
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Introduction to group analysis and invariant solutions of integro-differential equations
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 57-111
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Tidskriftsartikel (refereegranskat)abstract
- In this chapter an introduction into applications of group analysis to equations with nonlocal operators, in particular, to integro-differential equations is given. The most known integro-differential equations are kinetic equations which form a mathematical basis in the kinetic theories of rarefied gases, plasma, radiation transfer, coagulation. Since these equations are directly associated with fundamental physical laws, there is special interest in studies of their solutions. The first section of this chapter contains a retrospective survey of different methods for constructing symmetries and finding invariant solutions of such equations. The presentation of the methods is carried out using simple model equations of small dimensionality, allowing the reader to follow the calculations in detail. In the next section, the classical scheme of the construction of determining equations of an admitted Lie group is generalized for equations with nonlocal operators. In the concluding sections of this chapter, the developed regular method of obtaining admitted Lie groups is illustrated by applications to some known integro-differential equations.
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| 4. |
- Grigoriev, Yurii, et al.
(författare)
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Introduction to group analysis of differential equations
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 1-55
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Tidskriftsartikel (refereegranskat)abstract
- The first chapter is a brief, but a sufficiently comprehensive introduction to the methods of Lie group analysis of ordinary and partial differential equations. The chapter presents basic concepts from the theory: continuous transformation groups, their generators, Lie equations, groups admitted by differential equations, integration of ordinary differential equations using their symmetries, group classification and invariant solutions of partial differential equations. New trends in modern group analysis such as the theory of Lie-Bäcklund transformations groups and approximate groups are also reflected. The intention of the chapter is to give the basic ideas of classical and modern group analysis to beginner readers and provide useful materials for advanced specialists
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| 5. |
- Grigoriev, Yurii, et al.
(författare)
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Plasma kinetic theory : Vlasov-maxwell and related equations
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 145-208
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Tidskriftsartikel (refereegranskat)abstract
- This chapter is devoted to a group analysis of the Vlasov-Maxwell and related type equations. The equations form the basis of the collisionless plasma kinetic theory, and are also applied in gravitational astrophysics, in shallow-water theory, etc. Nonlocal operators in these equations appear in the form of the functionals defined by integrals of the distribution functions over momenta of particles. In the beginning sections the plasma kinetic theory equations are introduced and the way of looking at the symmetries of nonlocal equations is described. Much of the importance of the approach used in this chapter for calculating symmetries stems from the procedure of solving determining equations using variational differentiation. The set of symmetries obtained in the sections that follow comprises symmetries for the Vlasov-Maxwell equations of the non-relativistic and relativistic electron and electron-ion plasmas in both one- and three-dimensional cases, and symmetries for Benney equations. In the concluding sections of this chapter the procedure for symmetry calculation and the renormalization group algorithm go hand in hand to present illustrations from plasma kinetic theory, plasma dynamics, and nonlinear optics, which demonstrate the potentialities of the method in construction of analytic solutions to nonlocal problems of nonlinear physics.
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| 6. |
- Grigoriev, Yurii, et al.
(författare)
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Symmetries of stochastic differential equations
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 209-250
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Tidskriftsartikel (refereegranskat)abstract
- This chapter deals with applications of the group analysis method to stochastic differential equations. These equations are often obtained by including random fluctuations in differential equations, which have been deduced from phenomenological or physical view. In contrast to deterministic differential equations, only few attempts to apply group analysis to stochastic differential equations can be found in the literature. It is worth to note that this theory is still developing. Before defining an admitted symmetry for stochastic differential equations an introduction into the theory of this type of equations is given. The introduction includes the discussion of a stochastic integration, a stochastic differential and a change of the variables (Itô formula) in stochastic differential equations. Applications of the Itô formula are considered in the next section which deals with the linearization problem. The Itô formula and the change of time in stochastic differential equations are the main tools of defining admitted transformations for them. After introducing an admitted Lie group and supporting material of the introduced definition, some examples of applications of the given definition are studied.
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| 7. |
- Grigoriev, Yurii, et al.
(författare)
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The Boltzmann kinetic equation and various models
- 2010
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Ingår i: Lecture Notes in Physics. - Dordrecht : Springer. - 0075-8450. ; 806, s. 113-144
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Tidskriftsartikel (refereegranskat)abstract
- The chapter deals with applications of the group analysis method to the full Boltzmann kinetic equation and some similar equations. These equations form the foundation of the kinetic theory of rarefied gas and coagulation. They typically include special integral operators with quadratic nonlinearity and multiple kernels which are called collision integrals. Calculations of the 11-parameter Lie group G 11 admitted by the full Boltzmann equation with arbitrary intermolecular potential and its extensions for power potentials are presented. The found isomorphism of these Lie groups with the Lie groups admitted by the ideal gas dynamics equations allowed one to obtain an optimal system of admitted subalgebras and to classify all invariant solutions of the full Boltzmann equation. For equations similar to the full Boltzmann equation complete admitted Lie groups are derived by solving determining equations. The corresponding optimal systems of admitted subalgebras are constructed and representations of all invariant solutions are obtained.
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| 8. |
- Meleshko, Sergey, et al.
(författare)
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Symmetries of Integro-Differential Equations : with applications in mechanics and plasma physics
- 2010
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.
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| 9. |
- Neeraj, Kumar, et al.
(författare)
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Inertial spin dynamics in ferromagnets
- 2021
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Ingår i: Nature Physics. - : Springer Science and Business Media LLC. - 1745-2473 .- 1745-2481. ; 17, s. 245-250
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Tidskriftsartikel (refereegranskat)abstract
- The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.
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| 10. |
- Salikhov, Ruslan, et al.
(författare)
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Coupling of terahertz light with nanometre-wavelength magnon modes via spin-orbit torque
- 2023
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Ingår i: Nature Physics. - : Springer Science and Business Media LLC. - 1745-2473 .- 1745-2481. ; 19:4, s. 529-535
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Tidskriftsartikel (refereegranskat)abstract
- Spin-based technologies can operate at terahertz frequencies but require manipulation techniques that work at ultrafast timescales to become practical. For instance, devices based on spin waves, also known as magnons, require efficient generation of high-energy exchange spin waves at nanometre wavelengths. To achieve this, a substantial coupling is needed between the magnon modes and an electro-magnetic stimulus such as a coherent terahertz field pulse. However, it has been difficult to excite non-uniform spin waves efficiently using terahertz light because of the large momentum mismatch between the submillimetre-wave radiation and the nanometre-sized spin waves. Here we improve the light–matter interaction by engineering thin films to exploit relativistic spin–orbit torques that are confined to the interfaces of heavy metal/ferromagnet heterostructures. We are able to excite spin-wave modes with frequencies of up to 0.6 THz and wavelengths as short as 6 nm using broadband terahertz radiation. Numerical simulations demonstrate that the coupling of terahertz light to exchange-dominated magnons originates solely from interfacial spin–orbit torques. Our results are of general applicability to other magnetic multilayered structures, and offer the prospect of nanoscale control of high-frequency signals.
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