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| 2. |
- Mustafa, Dawan, 1985, et al.
(author)
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The BGK Equation as the Limit of anN-Particle System
- 2020
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In: Journal of Statistical Physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 181, s. 715-737
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Journal article (peer-reviewed)abstract
- The spatially homogeneous BGK equation is obtained as the limit of a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.
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| 3. |
- Anderson, Dan, 1943, et al.
(author)
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Introduction to direct variational and moment methods and an application to the Child-Langmuir law
- 2015
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In: European Journal of Physics. - : IOP Publishing. - 1361-6404 .- 0143-0807. ; 2015:36, s. 065032-
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Journal article (peer-reviewed)abstract
- A short introduction is given of direct variational methods and its relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions of difficult physical equations. A pedagogicalapplication of moment methods is given to the physically and technically important Child–Langmuir law in electron physics. The analysis is shown to provide simple, yet accurate, approximate solutions of the two-dimensionalproblem (a problem which does not allow an exact analytical solution)and illustrates the usefulness and the power of moment methods.
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| 4. |
- Carlsson, Marcus, et al.
(author)
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A Note on holomorphic functions and the fourier-laplace transform
- 2017
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In: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 120:2, s. 225-248
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Journal article (peer-reviewed)abstract
- We revisit the classical problem of when a given function, which is analytic in the upper half plane ℂ+, can be written as the Fourier transform of a function or distribution with support on a half axis (-∞, b], b∈ℝ.We derive slight improvements of the classical Paley-Wiener-Schwartz Theorem, as well as softer conditions for verifying membership in classical function spaces such as Hp(ℂ+).
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| 5. |
- Carlsson, Marcus, et al.
(author)
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The Dirichlet problem for standard weighted Laplacians in the upper half plane
- 2016
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In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X. ; 436:2, s. 868-889
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Journal article (peer-reviewed)abstract
- In this paper the Dirichlet problem for a class of standard weighted Laplace operators in the upper half plane is solved by means of a counterpart of the classical Poisson integral formula. Boundary limits and representations of the associated solutions are studied within a framework of weighted spaces of distributions. Special attention is given to the development of a, suitable uniqueness theory for the Dirichlet problem under appropriate growth constraints at infinity. (C) 2015 Elsevier Inc. All rights reserved.
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| 6. |
- Carlsson, Marcus, et al.
(author)
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A note on variable susceptibility, the herd-immunity threshold and modeling of infectious diseases
- 2023
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In: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 18
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Journal article (peer-reviewed)abstract
- The unfolding of the COVID-19 pandemic has been very difficult to predict using mathematical models for infectious diseases. While it has been demonstrated that variations in susceptibility have a damping effect on key quantities such as the incidence peak, the herd-immunity threshold and the final size of the pandemic, this complex phenomenon is almost impossible to measure or quantify, and it remains unclear how to incorporate it for modeling and prediction. In this work we show that, from a modeling perspective, variability in susceptibility on an individual level is equivalent with a fraction θ of the population having an “artificial” sterilizing immunity. We also derive novel formulas for the herd-immunity threshold and the final size of the pandemic, and show that these values are substantially lower than predicted by the classical formulas, in the presence of variable susceptibility. In the particular case of SARS-CoV-2, there is by now undoubtedly variable susceptibility due to waning immunity from both vaccines and previous infections, and our findings may be used to greatly simplify models. If such variations were also present prior to the first wave, as indicated by a number of studies, these findings can help explain why the magnitude of the initial waves of SARS-CoV-2 was relatively low, compared to what one may have expected based on standard models.
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| 7. |
- Johansson, Petter, 1981-
(author)
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Some results on amoebas and coamoebas of affine spaces
- 2017. - 1
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In: Analysis Meets Geometry. - Cham, Switzerland : Birkhäuser Verlag. - 9783319524719 ; , s. 261-285
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Book chapter (peer-reviewed)abstract
- We give some topological characteristics of the coamoeba of a generic k-dimensional affine space and two stronger versions, specific for the affine case, of a result by Nisse, Sottile and the author. We also give topological and partly algebraical characterizations of the amoeba and coamoeba in some special cases: k=n-1, k=1 and, when n is even, k=n/2, in the last case with a certain emphasis on the example n=4.
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| 8. |
- Anderson, Dan, 1943, et al.
(author)
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The least uncomfortable journey from A to B
- 2016
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In: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 84:9, s. 690-695
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Journal article (peer-reviewed)abstract
- A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.
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| 9. |
- Chung, Yong Moo, et al.
(author)
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Quenched limit theorems for random U(1) extensions of expanding maps
- 2023
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In: Discrete and Continuous Dynamical Systems. - : American Institute of Mathematical Sciences. - 1078-0947 .- 1553-5231. ; 43:1, s. 338-377
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Journal article (peer-reviewed)abstract
- In this paper we provide quenched central limit theorems, large deviation principles and local central limit theorems for random U(1) extensions of expanding maps on the torus. The results are obtained as special cases of corresponding theorems that we establish for abstract random dynamical systems. We do so by extending a recent spectral approach developed for quenched limit theorems for expanding and hyperbolic maps to be applicable also to partially hyperbolic dynamics.
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| 10. |
- Anderson, D., et al.
(author)
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The optimal journey from A to B
- 2008
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In: American Journal of Physics. - : American Association of Physics Teachers. - 0002-9505 .- 1943-2909. ; 76:9, s. 863-866
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Journal article (peer-reviewed)abstract
- How fast can you comfortably travel between two points A and B? This question is formulated as a minimization problem of a functional where the discomfort is quantified in terms of the integral of the square of the acceleration between A and B. The problem is solved in terms of the corresponding Euler-Lagrange equation and approximately using a direct variational approach based on trial functions and Ritz optimization. The main purpose of the analysis is to introduce undergraduate students to variational calculus in an interesting and pedagogical way.
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