| 1. |
- Alho, A., et al.
(författare)
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A stellar model with diffusion in general relativity
- 2017
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 120, s. 62-72
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Tidskriftsartikel (refereegranskat)abstract
- We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self similar solution. (C) 2017 Elsevier B.V. All rights reserved.
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| 2. |
- Alho, Artur, et al.
(författare)
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Dynamics of Robertson-Walker spacetimes with diffusion
- 2015
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Ingår i: Annals of Physics. - : Elsevier BV. - 0003-4916 .- 1096-035X. ; 354, s. 475-488
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Tidskriftsartikel (refereegranskat)abstract
- We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.
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| 3. |
- Alho, Artur, et al.
(författare)
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Multi-body Spherically Symmetric Steady States of Newtonian Self-Gravitating Elastic Matter
- 2019
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 371:3, s. 975-1004
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Tidskriftsartikel (refereegranskat)abstract
- We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e. in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.
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| 4. |
- Alho, Artur, et al.
(författare)
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Self-gravitating static balls of power-law elastic matter
- 2022
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0753 .- 1095-0761. ; 26:9, s. 2885-2908
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of power-law stored energy functions for spher-ically symmetric elastic bodies that includes well-known material models, such as the Saint Venant-Kirchhoff, Hadamard, Signorini and John models. We identify a finite subclass of these stored en-ergy functions, which we call Lamé type, that depend on no more material parameters than the bulk modulus k > 0 and the Pois-son ratio —1 < v < 1/2. A general theorem proving the existence of static self-gravitating elastic balls for some power-law materials has been given elsewhere. In this paper numerical evidence is pro-vided that some hypotheses in this theorem are necessary, while others are not.
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| 5. |
- Alho, A., et al.
(författare)
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Static Self-gravitating Newtonian Elastic Balls
- 2020
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Ingår i: Archive for Rational Mechanics and Analysis. - : Springer Science and Business Media LLC. - 0003-9527 .- 1432-0673. ; 238, s. 639-669
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Tidskriftsartikel (refereegranskat)abstract
- The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and the Euler formulation of elasticity theory for spherically symmetric bodies introduced recently by the authors. Examples of elastic materials covered by the results of this paper are Saint Venant-Kirchhoff, John and Hadamard materials.
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| 6. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Spherically symmetric steady states of John elastic bodies in general relativity
- 2014
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:16
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Tidskriftsartikel (refereegranskat)abstract
- We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large (z approximate to 2.8) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
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| 7. |
- Ben-Artzi, J., et al.
(författare)
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Arbitrarily Large Solutions of the Vlasov-Poisson System
- 2018
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1410 .- 1095-7154. ; 50:4, s. 4311-4326
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Tidskriftsartikel (refereegranskat)abstract
- We study smooth, global-in-time solutions of the Vlasov--Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class consists of spherically symmetric solutions that initially possess arbitrarily small density and field values but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time.
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| 8. |
- Ben-Artzi, Jonathan, et al.
(författare)
-
Arbitrarily Large Solutions of the Vlasov-Poisson System
- 2018
-
Ingår i: SIAM Journal on Mathematical Analysis. - 1095-7154 .- 0036-1410. ; 50:4, s. 4311-4326
-
Tidskriftsartikel (refereegranskat)abstract
- We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class consists of spherically symmetric solutions that initially possess arbitrarily small density and field values but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time.
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| 9. |
- Ben-Artzi, J., et al.
(författare)
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CONCENTRATING SOLUTIONS OF THE RELATIVISTIC VLASOV-MAXWELL SYSTEM
- 2019
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Ingår i: Communications in Mathematical Sciences. - 1539-6746 .- 1945-0796. ; 17:2, s. 377-392
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Tidskriftsartikel (refereegranskat)abstract
- We study smooth, global-in-time, spherically-symmetric solutions of the relativistic Vlasov-Poisson system that possess arbitrarily large charge densities and electric fields. In particular, we construct solutions that describe a thin shell of equally charged particles concentrating arbitrarily close to the origin and which give rise to charge densities and electric fields as large as one desires at some finite time. We show that these solutions exist even for arbitrarily small initial data or any desired mass. In the latter case, the time at which solutions concentrate can also be made arbitrarily large. As the constructed solutions are spherically-symmetric, they also satisfy the relativistic Vlasov-Maxwell system and thus our results apply to the latter system as well.
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| 10. |
- Calogero, Simone, 1974
(författare)
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A First Course in Options Pricing Theory
- 2023
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Among the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions, making it indispensable to practitioners. The emergence of artificial intelligence in the financial industry has led to further interest in mathematical finance and has increased the demand for literature on this subject that is accessible to a large audience. This book presents a self-contained introduction to options pricing theory and includes • a complete discussion of the required concepts in finance and probability theory; • an introduction to basic models, emphasizing both critical thinking and practical applications • over 200 exercises, several Python codes for the analysis and application of the options pricing models, and numerical projects intended to help close the gap between theory and practice.
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