| 1. |
- Altmann, Robert, et al.
(författare)
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Localization And Delocalization Of Ground States Of Bose-Einstein Condensates Under Disorder
- 2022
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 82:1, s. 330-358
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Ammari, Habib, et al.
(författare)
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Subwavelength Localized Modes for Acoustic Waves in Bubbly Crystals With a Defect
- 2018
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 78:6, s. 3316-3335
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Tidskriftsartikel (refereegranskat)abstract
- The ability to control wave propagation is of fundamental interest in many areas of physics. Photonic and phononic crystals have proved very useful for this purpose but, because they are based on Bragg interferences, these artificial media require structures with large dimensions. In [Ammari et al., J. Differential Equations, 263 (2017), pp. 5610-5629], it has been proved that a subwavelength bandgap opening occurs in bubble phononic crystals. To demonstrate the opening of a subwavelength phononic bandgap, a periodic arrangement of bubbles is considered and their subwavelength Minnaert resonance is exploited. In this paper, this subwavelength bandgap is used to demonstrate cavities, very similar to those obtained in photonic and phononic crystals, albeit of deeply subwavelength dimensions. The key idea is to increase the size of a single bubble inside the crystal, thus creating a defect. The goal is then to analytically and numerically show that this crystal has a localized eigenmode close to the defect bubble.
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| 3. |
- Andersson, Fredrik
(författare)
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Fast inversion of the Radon transform using log-polar coordinates and partial back-projections
- 2005
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 65:3, s. 818-837
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform and its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, inversion can be performed by means of finite convolutions and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.
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| 4. |
- Andersson, Lars-Erik, et al.
(författare)
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Attractors in Frictional Systems Subjected to Periodic Loads
- 2013
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 73:3, s. 1097-1116
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Tidskriftsartikel (refereegranskat)abstract
- This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.
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| 5. |
- Appelö, Daniel, et al.
(författare)
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Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability
- 2006
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 67:1, s. 1-23
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Tidskriftsartikel (refereegranskat)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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| 6. |
- Aurell, Alexander, et al.
(författare)
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Behavior near walls in the mean-field approach to crowd dynamics
- 2020
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 80:3, s. 1153-1174
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Tidskriftsartikel (refereegranskat)abstract
- This paper introduces a system of SDEs of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at and move along walls by means of sticky boundaries and boundary diffusion. As an alternative to Neumann-type boundary conditions, sticky boundaries and boundary diffusion have a "smoothing" effect on pedestrian motion. When these effects are active, the pedestrian paths are semimartingales with the first-variation part absolutely continuous with respect to the Lebesgue measure dt rather than an increasing process (which in general induces a measure singular with respect to dt) as is the case under Neumann boundary conditions. We show that the proposed mean-field model for pedestrian motion admits a unique weak solution and that it is possible to control the system in the weak sense, using a Pontryagin-type maximum principle. We also relate the mean-field type control problem to the social cost minimization in an interacting particle system. We study the novel model features numerically, and we confirm empirical findings on pedestrian crowd motion in congested corridors.
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| 7. |
- Bamberger, A, et al.
(författare)
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Higher order paraxial wave equation approximations in heterogeneous media
- 1988
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 48, s. 129-154
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Tidskriftsartikel (refereegranskat)abstract
- A new family of paraxial wave equation approximations is derived. These approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computational problems, e.g., in seismology, underwater acoustics and as artificial boundary conditions. The equations are written as systems which simplify computations. The support and singular support are studied; energy estimates are given which prove the well-posedness. The reflection and transmission are shown to be continuously dependent on material interfaces in heterogeneous media
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| 8. |
- Bamberger, A, et al.
(författare)
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Parabolic wave equation approximations in heterogenous media
- 1988
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399 .- 1095-712X. ; 48, s. 99-128
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Tidskriftsartikel (refereegranskat)abstract
- The properties of different variants of parabolic approximations of scalar wave equations are analyzed. These equations are of general form which includes those used in seismology, underwater acoustics and other applications. A new version of the parabolic approximation is derived for heterogeneous media. It has optimal properties with respect to wave reflection at material interfaces. The amplitud of the reflected and transmitted waves depend continuously on the interface. Existence, uniqueness and energy estimates are proved.
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| 9. |
- Bürger, Raimund, et al.
(författare)
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Entropy solutions of a scalar conservation law modeling sedimentation in vessels with varying cross-sectional area
- 2017
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 77:2, s. 789-811
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Tidskriftsartikel (refereegranskat)abstract
- The sedimentation of an ideal suspension in a vessel with variable cross-sectional area can be described by an initial-boundary value problem for a scalar nonlinear hyperbolic conservation law with a nonconvex flux function and a weight function that depends on spatial position. The sought unknown is the local solids' volume fraction. For the most important cases of vessels with downward-decreasing cross-sectional area and flux functions with at most one infection point, entropy solutions of this problem are constructed by the method of characteristics. Solutions exhibit discontinuities that mostly travel at variable speed, i.e., they are curved in the space-time plane. These trajectories are given by ordinary differential equations that arise from the jump condition. It is shown that three qualitatively different solutions may occur in dependence of the initial concentration. The potential application of the findings is a new method of flux identification via settling tests in a suitably shaped vessel. Related models also arise in flows of vehicular traffic, pedestrians, in pipes with varying cross-sectional area, and on curved surfaces.
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| 10. |
- Choi, Doo Sung, et al.
(författare)
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Corner effects on the perturbation of an electric potential
- 2018
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 78:3, s. 1577-1601
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Tidskriftsartikel (refereegranskat)abstract
- We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coeffcients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, the Nystrom discretization, and recursively compressed inverse preconditioning.
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