We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε, ε2}. The homogenization is performed by means of evolution multiscale convergence, a generalization of the concept of two-scale convergence to include any number of scales in both space and time. In particular we apply a compactness result for gradients. The outcome of the homogenization procedure is that we obtain a homogenized problem of hyperbolic-parabolic type together with two elliptic local problems, one for each rapid scale.

During Sweden’s commitment in the international intervention in Afghanistan the policymaking regarding the civil-military coordination measures failed. The Swedish government stated and emphasized in their appropriations and strategies that their intent – cooperation and synergies – were a crucial point for mission success. Even so, the government didn´t take any actions clarifying how their intent should be met. Who, how and why were questions left unanswered from the government to the authorities and personnel on the field level in Afghanistan. The research question guiding us through this thesis is: Why did the government fail in the implementation process of the civil-military cooperation on the field level in Afghanistan? To narrow down the extent of the thesis the author has chosen three management theories – decentralization, legitimacy and implementation – incorporated in three hypotheses. After using these three hypotheses as an analytic tool the author has come to the following conclusions: Because of traditional Swedish governance and the lack of an appointed process manager, the questions who, how and why could only be answered by authorities and field personnel from their own perspective. Because of these circumstances there never was a coherent Swedish contribution regarding civil-military cooperation. (Less)

This paper concerns the homogenization of nonlinear dissipative hyperbolicproblems\begin{gather*}\partial _{tt}u^{\varepsilon }\left( x,t\right) -\nabla \cdot \left( a\left(\frac{x}{\varepsilon ^{q_{1}}},\ldots ,\frac{x}{\varepsilon ^{q_{n}}},\frac{t}{\varepsilon ^{r_{1}}},\ldots ,\frac{t}{\varepsilon ^{r_{m}}}\right) \nablau^{\varepsilon }\left( x,t\right) \right) \\+g\left( \frac{x}{\varepsilon ^{q_{1}}},\ldots ,\frac{x}{\varepsilon ^{q_{n}}},\frac{t}{\varepsilon ^{r_{1}}},\ldots ,\frac{t}{\varepsilon ^{r_{m}}},u^{\varepsilon }\left( x,t\right) ,\nabla u^{\varepsilon }\left( x,t\right)\right) =f(x,t)\end{gather*}where both the elliptic coefficient $a$ and the dissipative term $g$ areperiodic in the $n+m$ first arguments where $n$ and $m$ may attain anynon-negative integer value. The homogenization procedure is performed withinthe framework of evolution multiscale convergence which is a generalizationof two-scale convergence to include several spatial and temporal scales. Inorder to derive the local problems, one for each spatial scale, the crucialconcept of very weak evolution multiscale convergence is utilized since itallows less benign sequences to attain a limit. It turns out that the localproblems do not involve the dissipative term $g$ even though the homogenizedproblem does and, due to the nonlinearity property, an important part of thework is to determine the effective dissipative term. A brief illustration ofhow to use the main homogenization result is provided by applying it to anexample problem exhibiting six spatial and eight temporal scales in such away that $a$ and $g$ have disparate oscillation patterns.

Reconstructing the homogenized coefficient, which is also called the G-limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G-limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G-limit from the weak L-2-limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.

The main contribution of this paper is the homogenization of the linear parabolic equation ∂tuε(x,t)-∇·(a(x/εq1,...,x/εqn,t/εr1,...,t/εrm)∇uε(x,t))=f(x,t) exhibiting an arbitrary finite number of both spatial and temporal scales. We briefly recall some fundamentals of multiscale convergence and provide a characterization of multiscale limits for gradients, in an evolution setting adapted to a quite general class of well-separated scales, which we name by jointly well-separated scales (see appendix for the proof). We proceed with a weaker version of this concept called very weak multiscale convergence. We prove a compactness result with respect to this latter type for jointly well-separated scales. This is a key result for performing the homogenization of parabolic problems combining rapid spatial and temporal oscillations such as the problem above. Applying this compactness result together with a characterization of multiscale limits of sequences of gradients we carry out the homogenization procedure, where we together with the homogenized problem obtain n local problems, that is, one for each spatial microscale. To illustrate the use of the obtained result, we apply it to a case with three spatial and three temporal scales with q1=1, q2=2, and 0

Fin clipping has been used for decades as a marking method for sea-ranched salmonids but there are concerns about the method such as reduced survival and other animal welfare aspects. In this study sea migrating hatchery-reared brown trout juveniles (20–21 months old) were marked in four groups by removing either the adipose fin, left pelvic fin, both pelvic fins or the adipose fin + the left pelvic fin. All groups, together with an unmarked control group, were tagged with coded wire tags and released into the River Dalälven (Sweden). This was repeated over four years and on average the return rate was < 1%. Brown trout marked by removing both pelvic fins had ca 30% lower adult return rate compared with the other four groups. The other three fin clipping groups did not differ from the unclipped control group. These results, in combination with earlier studies, indicate that adipose fin removal is least detrimental to the fish and removal of a single paired fin may be used in exceptional cases. We advise against multiple fin removal.

Den har uppsatsen handlar om hur pussel och skr ack kan kombineras i ett och samma digitala spel. Hur man som utvecklare kan f a en j amn balans mellan skr acken och pusslen som presenteras f or spelaren i spelet. Den typ av skr ack som den h ar uppsatsen har fokus pa ar genren 'Survival-Horror' och anv ander sig av den typ av skr ack som i digital spel kategoriserats som 'Survival-Horror'-spel. Den har uppsatsen visar en analys av 'Survival-Horror', samlar information om pussel och skr ack f or att utforma en hypotes hur dessa kan kombineras. F or att kontrollera om hypotesen st ammer utf ordes en intervju innan pussel- och skr ackmomenten implementerades i ett digitalt spel. Efter implementationerna genomf ordes det speltester i tv a omg angar f or att analysera resultatet mellan de tv a omg angarna.

We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.

We first study the fundamental ideas behind two-scale convergence to enhance an intuitive understanding of this notion. The classical definitions and ideas are motivated with geometrical arguments illustrated by illuminating figures. Then a version of this concept, very weak two-scale convergence, is discussed both independently and briefly in the context of homogenization. The main features of this variant are that it works also for certain sequences of functions which are not bounded in L-2 (Omega) and at the same time is suited to detect rapid oscillations in some sequences which are strongly convergent in L-2 (Omega). In particular, we show how very weak two-scale convergence explains in a more transparent way how the oscillations of the governing coefficient of the PDE to be homogenized causes the deviation of the G-limit from the weak L-2 (Omega)(NxN)-limit for the sequence of coefficients. Finally, we investigate very weak multiscale convergence and prove a compactness result for separated scales which extends a previous result which required well-separated scales.

In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the “rapid” self-similar case), respectively.

We apply a new version of multiscale convergence named very weak multiscale convergence to find possible frequencies of oscillation in an unknown coecient of a partial dierential equation from its solution. We also use this notion to study homogenization of a certain linear parabolic problem with multiple spatial and temporal scales.

In this paper we homogenise monotone parabolic problems with two spatial scales and finitely many temporal scales. Under a certain well-separatedness assumption on the spatial and temporal scales as explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the "slow" self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the "rapid" self-similar case), respectively.

The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. ...

Detta arbete behandlar amnet stamningsbelysning for hemmiljo. Projektets huvudfragestallning ar; hur utformar man en belysning som ger anvandaren mojlighet att skapa onskad stamning i rummet? For att ta reda pa detta samlades kunskap kring ljusets effekter pa manniska och rum. Vidare samlades en fokusgrupp som for att ge sin input om sina vanor, onskemal och behov angaende belysning. Forslag pa en produkt arbetades fram via en process bestaende idegenerering, skissning, modellering och slutligen prototypbygge. Resultatet ar en golvbaserad stamningsbelysning som kan dimras genom att skarmen oppnas upp respektive stangs med handkraft.

We briefly recall the concept of multiscale convergence, which is a generalization of two-scale convergence. Then we investigate a related concept, called very weak multiscale convergence, and prove a compactness result with respect to this type of convergence. Finally we illustrate how this result can be used to study homogenization problems with several scales of oscillations.

In this contribution we study the homogenization of non-periodic stationary heat conduction problems with homogeneous Dirichlet boundary data by applying the recently developed λ-scale convergence technique developed by Holmbom and Silfver. λ-scale convergence can be seen as either being a special case of scale convergence (developed by Mascarenhas and Toader) or of “generalized” two-scale convergence (developed by Holmbom, Silfver, Svanstedt and Wellander). From either viewpoint, it is a possibly powerful generalization of Nguetseng’s classical, periodic two-scale convergence method. We give a definition of the concept of λ-scale convergence, which is then used to claim a main theorem on homogenization of certain non-periodic stationary heat conduction problems. The original part of the contribution starts by defining a two-dimensional “toy model”. We show that the “toy model” satisfies the right conditions such that the aforementioned main theorem on the homogenization can be employed. In this way we derive the homogenized problem, i.e. the homogenized thermal conductivity matrix, and the local problem. The contribution is concluded by giving a numerical example where we explicitly compute the homogenized thermal conductivity matrix.

The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.

Abstract In this thesis we investigate aspects of the phantom,energy,defined by having an equation of state parameter w < −1, which recently has at- tained interest from cosmologists,since WMAP probe measurements,have shown,that the dark energy of the Universe may,be of this kind. We begin by making,a survey over fundamental,principles of comsology and general relativity. Then we investigate the evolution of the Universe having,a constant,supernegative,w where,we,see that there will be a future “Big Rip”. After this, we define a plausible scalar field model for the phantom energy. Nevertheless, we continue by speculating whether the phantom,is really an axion. We then go in to a stability analysis of the phantom,energy which renders that the defined scalar field model perhaps needs a cut-off at ∼ 100 MeV. We then look into the thermodynamics of the phantom fluid, and come to the conclusion that the Generalized Second Law of Thermodynamics,is violated for arbitrarily small “phantom impulses”. We also show that black holes’ masses decrease due to phantom accretion, and an analogous analysis tells us that the same may be said for the domain,beyond,the cosmological,event horizon,of the de Sitter universe leading to the conjecture,that all event horizons change,in size due to the one-way passage of different kind of energies — DEC violating