| 41. |
- Arnlind, Joakim, et al.
(author)
-
Eigenvalue Dynamics off the Calogero-Moser system
- 2004
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In: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 68:2, s. 121-129
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Journal article (peer-reviewed)abstract
- By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.
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| 42. |
- Arnlind, Joakim, et al.
(author)
-
Spinning Membranes
- 2004
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In: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 599:1-2, s. 118-128
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Journal article (peer-reviewed)abstract
- We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdS(p) X S-q, as well as in flat space-time. Nontrivial reductions of the BMN matrix model equations are also given.
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| 43. |
- Arnlind, Joakim, et al.
(author)
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Trace Extensions, Determinant Bundles, and Gauge Group Cocycles
- 2002
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In: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 62:2, s. 101-110
-
Journal article (peer-reviewed)abstract
- We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.
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| 44. |
- Asekritova, Irina, et al.
(author)
-
Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
- 2009
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In: Mathematical modelling of wave phenomena. - Melville, New York : American Institute of Physics. ; , s. 224-232, s. 224-232
-
Conference paper (peer-reviewed)abstract
- Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.
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| 45. |
- Bensow, Rickard, 1972, et al.
(author)
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Residual Based VMS Subgrid Modeling for Vortex Flows
- 2009
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In: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 199:13-16, s. 802-809
-
Journal article (peer-reviewed)abstract
- This paper presents a residual based subgrid modeling approach for Large Eddy Simulations (LES) based on the variational multiscale method as a cure for the problem of preservation of vortices in numerical flow simulation. This approach combines a splitting of the non-linear term in the Navier–Stokes equations into strain and vorticity with a residual based modeling of the subgrid problems. The benefit is that certain driving phenomena, normally not present in subgrid modeling, e.g. vortex stretching, can be seen in the equations.Here, we focus on two of the subgrid terms arising from the subgrid scale problem. The effect of the two terms are illustrated in an LES of a three dimensional flow around a wing where the main feature is the formation and preservation of a tip vortex, an important phenomenon in many aerodynamic and hydrodynamical applications. We see that the addition of the new subgrid terms correctly counteracts the dissipative effect, arising from numerics and turbulence modeling, on the vortex and thus strongly improves prediction of the tip vortex.
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| 46. |
- Bergman Ärlebäck, Jonas, 1972-
(author)
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Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
- 2009
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Reports (other academic/artistic)abstract
- This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.
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| 47. |
- Bergman Ärlebäck, Jonas, 1972-
(author)
-
Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
-
Reports (other academic/artistic)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
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| 48. |
- Berntsson, Fredrik, 1971-, et al.
(author)
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Numerical Solution of Cauchy Problems for Elliptic Equations in "Rectangle-like" Geometries
- 2005
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In: FEMLAB Conference,2005. - Stockholm : Comsol AB.
-
Conference paper (other academic/artistic)abstract
- We consider two dimensional inverse steady state heat conduction problems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on one part of the boundary and we want to find the solution in the whole domain. The problem is ill--posed in the sense that the solution does not depend continuously on the data. Using an orthogonal coordinate transformation the domain is mapped onto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in the least squares sense. This particular approximation of the derivative is computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions. This inverse problem arises in iron production, where the walls of a melting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples located inside the walls. The shape of the interface between the molten iron and the walls can then be determined by solving an inverse heat conduction problem. In our work we make extensive use of Femlab for creating test problems. By using Femlab we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.
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| 49. |
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| 50. |
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