| 1. |
- Ivanenko, Yevhen, et al.
(author)
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Passive Approximation and Optimization Using B-Splines
- 2019
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In: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
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Journal article (peer-reviewed)abstract
- A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
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| 2. |
- Altmann, Robert, et al.
(author)
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Localization And Delocalization Of Ground States Of Bose-Einstein Condensates Under Disorder
- 2022
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 82:1, s. 330-358
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Journal article (peer-reviewed)abstract
- This paper studies the localization behavior of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify exponential localization of the ground state, depending on statistical parameters and the strength of the potential. Numerical studies further show delocalization if we leave the identified parameter range, which is in agreement with experimental data. These mathematical and numerical findings allow the prediction of physically relevant regimes where localization of ground states may be observed experimentally.
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| 3. |
- Appelö, Daniel, et al.
(author)
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Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability
- 2006
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 67:1, s. 1-23
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Journal article (peer-reviewed)abstract
- Since its introduction the perfectly matched layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limited to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters, which is applicable to all hyperbolic systems and which we prove is well-posed and perfectly matched. We also introduce an automatic method for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell's equations, the linearized Euler equations, and arbitrary 2 x 2 systems in (2 + 1) dimensions.
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| 4. |
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| 5. |
- Engström, Christian
(author)
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Inverse bounds of two-component composites
- 2007
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:3, s. 666-679
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Journal article (peer-reviewed)abstract
- A method is presented for estimating microstructural parameters from permittivity measurements of two-component composites. This structural information is described by a particular positive measure in the Stieltjes integral representation of the effective permittivity. The dependence on the geometrical structure can be reduced to the problem of calculating the moments of the measure. We present a method that uses measurement data at a set of distinct frequencies or temperatures to calculate bounds on several moments. These inverse bounds are improved when the volume fraction is known or the material is isotropic. Composites with known geometrical structure illustrate the method.
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| 6. |
- Engström, Christian, et al.
(author)
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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
- 2009
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:1, s. 231-247
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Journal article (peer-reviewed)abstract
- We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.
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| 7. |
- Lindström, Torsten, 1965-, et al.
(author)
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Destabilization, Stabilization, and Multiple Attractors in Saturated Mixotrophic Environments
- 2020
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In: SIAM Journal on Applied Mathematics. - United States : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 80:6, s. 2338-2364
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Journal article (peer-reviewed)abstract
- The ability of mixotrophs to combine phototrophy and phagotrophy is now well recognized and found to have important implications for ecosystem dynamics. In this paper, we examine the dynamical consequences of the invasion of mixotrophs in a system that is a limiting case of the chemostat. The model is a hybrid of a competition model describing the competition between autotroph and mixotroph populations for a limiting resource, and a predator--prey-type model describing the interaction between autotroph and herbivore populations. Our results show that mixotrophs are able to invade in both autotrophic environments and environments described by interactions between autotrophs and herbivores. The interaction between autotrophs and herbivores might be in equilibrium or cycle. We find that invading mixotrophs have the ability to both stabilize and destabilize autotroph-herbivore dynamics depending on the competitive ability of mixotrophs. The invasion of mixotrophs can also result in multiple attractors.
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| 8. |
- Pramanik, Satyajit, et al.
(author)
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Confinement- induced control of similarity solutions in premelting dynamics and other thin film problems
- 2019
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In: SIAM Journal on Applied Mathematics. - : Siam Publications. - 0036-1399 .- 1095-712X. ; 79:3, s. 938-958
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Journal article (peer-reviewed)abstract
- We study the combined effects of nonlocal elasticity and confinement-induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement-induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement-induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an in finite sequence of oscillations. However, when the confinement-induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations and similarity solutions vanish. Implications of our results for general thermomechanical dynamics, frost heave observations, and cryogenic cell preservation are discussed. Finally, through its influence on the viscosity, the confinement effect implicitly introduces a new universal length scale into the volume flux. Thus, there are a host of thin film problems, from droplet breakup to wetting/dewetting dynamics, whose properties (similarity solutions, regularization, and compact support) will change under the action of the confinement effect. Therefore, our study suggests revisiting the mathematical structure and experimental implications of a wide range of problems within the framework of the confinement effect.
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| 9. |
- Wittsten, Jens, et al.
(author)
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Perturbations of time shifts in signal apparition
- 2018
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In: SIAM Journal on Applied Mathematics. - 0036-1399 .- 1095-712X. ; 78:5, s. 2840-2864
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Journal article (peer-reviewed)abstract
- In the field of exploration geophysics, the method known as "signal apparition" offers a different perspective on how to separate signals acquired from simultaneously fired seismic sources. The method uses a periodic sequence of small time shift variations to encode the different sources, and this choice leads to exact separation of signals in diamond-shaped regions of the frequencywavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the signal apparition method's sensitivity to perturbations of the periodic time shift sequence. We model (measured or unknown) perturbations in a stochastic fashion and prove that the resulting inverse problem of separating the data is still well-posed, and we demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.
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| 10. |
- Dao, Tuan Anh, et al.
(author)
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Viscous Regularization of the MHD Equations
- 2024
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 84:4, s. 1439-1459
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Journal article (peer-reviewed)abstract
- Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this paper, we present a new viscous flux to regularize the MHD equations that holds many attractive properties. In particular, we prove that the proposed viscous flux preserves positivity of density and internal energy, satisfies the minimum entropy principle, is consistent with all generalized entropies, and is Galilean and rotationally invariant. We also provide a variation of the viscous flux that conserves angular momentum. To make the analysis more useful for numerical schemes, the divergence of the magnetic field is not assumed to be zero. Using continuous finite elements, we show several numerical experiments, including contact waves and magnetic reconnection.
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