Direct and inverse scattering problems for quasi-linear biharmonic operator in 3D

Abstract. We consider direct and inverse scattering problems for three-dimensional biharmonic operator $Hu = ∆^2u + Vu$, where $∆$ is the Laplacian and $V$ is a scalar valued perturbation. The scattering problem for this operator is given as a partial differential equation $Hu = k^4u$, with a parameter $k$. In the direct scattering problem, our goal is to find the solution $u$ while the perturbation (V\) is known. We also assume that the solution $u$ can be written as a sum of two functions $u_{0}$ and $u_{sc}$, where $u_{0}$ is a plane wave and $u_{sc}$ is an outgoing wave in the sense that it satisfies to the Sommerfeld radiation conditions at the infinity. Our approach in this text is to first modify the partial differential equation into an integral equation by using the fundamental solution. Next, we show that this integral equation is solvable, and it has a unique solution. Finally, we prove two main results of this text; an asymptotic formula for the solution with large values of $x ∈ \mathbb{R}^3$ and Saito’s formula. The asymptotic behaviour of the solution leads us to defining the scattering amplitude. In the inverse scattering problem, the goal is to gather some information about the unknown perturbation V while the behaviour of the function u is known. With Saito’s formula we obtain two corollaries regarding the inverse scattering problem, namely uniqueness and a representation formula for the function $V(x, 1)$, when the scattering amplitude is known. We end the text by first defining the inverse Born approximation for both full scattering data and backscattering data. We also discuss some results that have been obtained previously with this approach

Multidimensional scattering for biharmonic operator with quasi-linear perturbations

Abstract This dissertation consists of an introduction part and four articles, where scattering problems for biharmonic operator with non-linear perturbations are considered. First three of these articles have been published in peer-reviewed journals, and the fourth article is made publicly available on arXiv service. In first two articles, we focus on the direct scattering problems in dimensions two and three, respectively. As the main result, the Saito’s formula is proven and uniqueness for the inverse scattering problem is therefore obtained. Last two articles concern with limited scattering data problems. In the third article, we prove that the main singularities of a combination of perturbations can be reconstructed from the backscattering data by using Born approximation. Finally, in the last article we consider fixed incident angle scattering and prove the reconstruction of the main singularities of zero-order perturbation from this dataset.Tiivistelmä Tämä väitöskirjatyö koostuu johdannosta ja neljästä artikkelista, joissa tutkitaan sirontaongelmia biharmoniselle operaattorille, joka sisältää epälineaarisia häiriöitä johtotermille. Ensimmäiset kolme artikkelia on julkaistu vertaisarvioiduissa julkaisuissa ja neljäs on saatavilla arXiv-järjestelmässä. Ensimmäiset kaksi artikkelia käsittelee suoraa sirontaongelmaa kaksi- ja kolmeulotteisissa reaaliavaruuksissa. Molempien artikkeleiden päätuloksena todistamme Saiton kaavan, jonka seurauksena saadaan, että käänteisellä sirontaongelmalla on yksikäsitteinen ratkaisu. Seuraavissa kahdessa artikkelissa keskitymme osittaisen sirontadatan ongelmiin. Kolmannessa artikkelissa osoitamme, että takaisinsirontadatan perusteella, Bornin approksimaatiota käyttämällä, voidaan kerätä tietoa eräästä häiriöfunktioiden yhdistelmästä

Jamography: How to document and reference design jams in academia

In this chapter, we propose that academic papers on ephemeral development events, such as game jams and hackathons, pay more attention when providing identifiable details of the events, or have a dedicated reference section (‘jamography’) detailing the referenced events in an identifiable manner in order to improve transparency and sustainability of the publications. Game jams are organised in a global context, and depite the similarities of jams, important differences can be noted in terms of how jams are implemented, what their formats are, and what culture and context are surrounding them. Furthermore, game jam names are not always unique. This means that, when identifying game jams in an academic study, one can find it impossible to tell two events apart. Since the game jams topic is an emerging and still poorly documented area in research, it is hard to know what kind of game jams are being discussed. Apart from this, whereas game jams are ephemeral, vanishing as soon as they are completed, documentation is key - website references do not always suffice. In this chapter, we propose and argue the key information and format.Peer reviewe

Inverse scattering for three-dimensional quasi-linear biharmonic operator

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude

Playful furniture: breaching a serious setting with interactive seats

Are shaggy seats which make cute noises playful or disruptive in a conference setting? This article pushes the limits of game scholars’ lusory attitude by breaching an academic seminar with a playful experiment. Five MurMur Moderator seats, interactive and interruptive furniture prototypes, were set up at a game research seminar where they were used as ambient elements during the presentations. The experience was evaluated by observation, accompanied with seminar tweets, and by conducting a small survey after the seminar. The experiences of the participants varied from enthusiastically positive to strong negative feelings. Through this experiment, we were able to explore the important issue of polarized attitudes of adults toward play and provide some food for thought for the future design of adult play