21. |
- Ivanenko, Yevhen, et al.
(författare)
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Passive Approximation and Optimization Using B-Splines
- 2019
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
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Tidskriftsartikel (refereegranskat)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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22. |
- Jonsson, B. Lars G., et al.
(författare)
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Retrofocusing of acoustic wave fields by iterated time reversal
- 2004
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 64:6, s. 1954-1986
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small.
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23. |
- Jonsson, B. Lars G., et al.
(författare)
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Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal
- 2004
-
Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 64:6, s. 1954-1986
-
Tidskriftsartikel (refereegranskat)abstract
- In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small.
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24. |
- Kailath, Thomas, et al.
(författare)
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The Factorization and Representation of Operators in the Algebra Generated by Toeplitz Operators
- 1979
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM. - 0036-1399 .- 1095-712X. ; 37:3, s. 467-484
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the factorization and the representation of Fredholm operators belonging to the algebra $\mathcal{R}$ generated by inversion and composition of Toeplitz integral operators. The operators in $\mathcal{R}$ have the interesting property of being close to Toeplitz (in a sense quantifiable by an integer-valued index $\alpha $) and, at the same time, of being dense in the space of arbitrary kernels. By using these properties, we derive a set of efficient algorithms (generalized fast-Cholesky and Levinson recursions) for the factorization and the inversion of arbitrary Fredholm operators. The computational burden of these algorithms depends on how close (as measured by the index $\alpha $) these operators are to being Toeplitz.We also obtain several important representation theorems for the decomposition of operators in $\mathcal{R}$ in terms of sums of products of lower times upper triangular Toeplitz operators. These results can be used to approximate operators corresponding to noncausal and time-variant systems in terms of operators representing causal and anticausal time-invariant systems, a property that has a large number of potential applications in signal processing problems.
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25. |
- Karlin, V, et al.
(författare)
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Numerical solution of nonlinear hypersingular integral equations of the Peierls type in dislocation theory
- 2000
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399 .- 1095-712X. ; 60:2, s. 664-678
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we analyze hypersingular integral equations of the Peierls type specified on the whole real axis. The method of "approximate approximations" [Maz'ya, Proceedings of the Eighth Conference on the Mathematics of Finite Elements and Applications, VIII, MAFELAP 1993, Brunel University, 1994, pp. 107-104] is employed in order to produce numerical solutions of high accuracy, and the results are applied to problems in the theory of dislocations. The critical Peierls stress is evaluated for different configurations of dislocations and for different types of the interatomic force law.
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26. |
- Lindström, Torsten, 1965-, et al.
(författare)
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Destabilization, Stabilization, and Multiple Attractors in Saturated Mixotrophic Environments
- 2020
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Ingår i: 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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Tidskriftsartikel (refereegranskat)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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27. |
- Liu, Hailiang, et al.
(författare)
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Gaussian beam methods for the helmholtz equation
- 2014
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 74:3, s. 771-793
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Tidskriftsartikel (refereegranskat)abstract
- In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of nontrapping rays we show error estimates between the exact outgoing solution and Gaussian beams in terms of the wave number k, both for single beams and superposition of beams. The main result is that the relative local L-2 error in the beam approximations decay as k(-N/2) independent of dimension and presence of caustics for Nth order beams.
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28. |
- Muntean, Adrian, 1974-, et al.
(författare)
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Colloidal Transport in Locally Periodic Evolving Porous Media : An Upscaling Exercise
- 2020
-
Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 80:1, s. 448-475
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Tidskriftsartikel (refereegranskat)abstract
- We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow, therefore reducing the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and, therefore, can provide estimates on the storage capacity of the porous matrix.
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29. |
- Pramanik, Satyajit, et al.
(författare)
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Confinement- induced control of similarity solutions in premelting dynamics and other thin film problems
- 2019
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Ingår i: SIAM Journal on Applied Mathematics. - : Siam Publications. - 0036-1399 .- 1095-712X. ; 79:3, s. 938-958
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Tidskriftsartikel (refereegranskat)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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30. |
- Rikte, Sten
(författare)
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Existence, Uniqueness, and Causality Theorems for Wave Propagation in Stratified, Temporally Dispersive, Complex Media
- 1997
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 57:5, s. 89-1373
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Tidskriftsartikel (refereegranskat)abstract
- A mixed initial-boundary value problem for a nonlocal, hyperbolic equation is analyzed with respect to unique solubility and causality. The regularity of the step response and impulse response (the Green functions) is investigated, and a wave front theorem is proved. The problem arises, e.g., at time-varying, electromagnetic, plane wave excitation of stratified, temporally dispersive, bi-isotropic or anisotropic slabs. Concluding, the problem is uniquely solvable, strict causality holds, and a well-defined wave front speed exists. This speed is independent of dispersion and excitation, and depends on the nondispersive properties of the medium only.
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