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  • 1. Ivanenko, Yevhen
    et al.
    Custafsson, Mats
    Jonsson, B. L. G.
    Luger, Annemarie
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Nilsson, Börje
    Nordebo, Sven
    Toft, Joachim
    Passive Approximation and Optimization Using B-splines2019Inngår i: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, nr 1, s. 436-458Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 2.
    Pramanik, Satyajit
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Wettlaufer, John S.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Yale University, USA; University of Oxford, England.
    CONFINEMENT-INDUCED CONTROL OF SIMILARITY SOLUTIONS IN PREMELTING DYNAMICS AND OTHER THIN FILM PROBLEMS2019Inngår i: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, nr 3, s. 938-958Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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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