This chapter draws attention to a specific feature of a NEG model that uses linear (and not iso-elastic) demand functions, namely its ability to account for zero trade. Thus, it represents a suitable framework to study how changes in parameters that are typical for NEG models, such as trade costs and regional market size, not only shape the regional distribution of economic activity, but at the same time determine the emergence of additional trade links between formerly autarkic regions. We survey some related papers and present a three-region framework that potentially nests many possible trade patterns. To focus the analysis, we study in more detail three specific trade patterns frequently found in the EU trade network. We start with three autarkic regions; then we introduce the possibility that two regions trade with each other; and, finally, we allow for one region trading with the other two, but the latter are still not trading with each other. We find a surprising plethora of long-run equilibria each involving a specific regional distribution of economic activity and a specific pattern of trade links. We show how a reduction in trade costs shapes simultaneously industry location and the configuration of the trade network.

Ces travaux de thèse sont basés principalement sur le phénomène de multistabilité des structures minces de type plaques et coques ainsi que quelques applications associées. Les travaux sont divisés en deux parties. La première partie a pour objet l’étude théorique, numérique et expérimentale de la multistabilité des coques minces orthotropes peu profondes à courbures uniformes. On montre notamment qu’une telle coque, lorsqu’elle est soumise à la combinaison d’une courbure initiale et d’une précontrainte suffisamment élevées, possède jusqu’à trois configurations stables vis-à-vis des propriétés matériaux. Dans un premier temps, nous proposons des critères de conception et fabrication de coques multistables allant jusqu’à la tristabilité, validés numériquement et expérimentalement. Ensuite, nous appliquons ces critères à la conception et à la fabrication de coques multistables cylindriques dont la différence de niveau énergétique entre les deux états stables est minime. Sur ce support, la deuxième partie est consacrée à des applications exploitant la bistabilité des coques cylindriques minces à faible différence énergétique. Nous effectuons tout d’abord une application au contrôle de forme via l’utilisation de matériaux actifs que l’on attache à la structure. Cela comprend une première phase théorique de conception de la structure et de la loi d’actionnement, et une seconde phase de mise en œuvre expérimentale. Ensuite, nous étudions théoriquement et expérimentalement les propriétés de dynamique non-linéaire de ce type de coques dans le but de mettre en évidence les modes d’oscillations intrinsèques à une source d’excitation externe. Enfin, nous proposons une application à la récupération d’énergie vibratoire non-linéaire de coques multistables cylindriques métalliques par voie piézoélectrique. / This work is essentially based on the phenomenon of multistability of thin structures as plates and shells and some associated applications. The work is divided in two parts. The first part aims to study theoretically, numerically and experimentally the multistability of thin orthotropic shallow shells with uniform curvature. We show notably that such a shell, when submitted to the combination of initial curvature and pre-stresses sufficiently high, possesses up to three stable states towards the choice of the material. First, we propose criteria to design and manufacture multistable shells up to tristability ; this work is validated by finit element simulations and experiments. After, we apply those criteria to the design and manufacture ofcylindrical multistable shells for which the energetic gap between stable states is minimal. The second part is dedicated to direct applications of bistability of thin cylindrical bistable shells with low energetic gap. We first propose an application on shape control via the use of active materials which we bond on the structure. This includes a first phase of theoretical design of both the structure and the actuation law, and a second phase of experimental demonstration. After, we study both theoretically and experimentally the non-linear dynamic properties of such structures with the aim to highlight the different modes of oscillations intrinsic to an external excitation source. Finally, we propose an application to non-linear broadband energy harvesting from vibrations based on multistable piezoelectric excited shells.

Magnetic shape memory alloys are active materials which deform under the application of a magnetic field or an external stress. Due to their internal friction, recognizable from the strain-stress hysteresis, this new material technology allows the design of multistable actuators. This paper describes and characterizes an innovative airflow control valve whose aperture is proportional to the deformation of the active material and thus controllable by the input voltage. The multistability of the material is partially exploited within an airflow control loop to reduce the energy losses of the valve when a specific airflow value must be hold.

<p dir="ltr">The ability to change the shape of aerodynamic surfaces is necessary for modern aircraft, both to provide control while performing maneuvers and to meet the conflicting requirements of various flight conditions such as takeoff/landing and level cruise. These shape changes have traditionally been accomplished through the use of various mechanical devices actuating discrete aerodynamic surfaces, for example ailerons and flaps. Such control surfaces and high-lift devices are generally limited to their specific functionality and create surface discontinuities which increase drag and aircraft noise. Broadly speaking, the design and study of morphing wings typically seeks to improve the performance of aircraft by completing one or more of the following objectives: reducing the drag from discontinuities in the aerodynamic surface of the wing by closing hinge gaps and creating smooth transitions, reducing weight and/or mechanical complexity by integrating mechanism functionality into compliant structures that can bear aerodynamic load and maintain shape adaptability, and providing unique or optimal functionality to the aircraft by allowing it to adjust its aerodynamic shape to meet the needs of various flight conditions with conflicting objectives and constraints.</p><p dir="ltr">The concepts proposed in this work represent potential methods for addressing these objectives. In each case, a compliant structure with multiple stable states is embedded into the wing. Exploiting elastic structural instabilities in this way provides the advantage that a structure can be made relatively stiff while still allowing for large deformations. In the first case, the development of a 3D-printable rib with an embedded bistable element creates a truss-like 2D structure that allows for modification of the airfoil. Switching states of the elements changes their local stiffness, and therefore the global stiffness of the system. By optimizing the topology of the airfoil, a passive deflection of the trailing edge can be leveraged to change the camber to leverage different lift characteristics for varying operating conditions. Primary work on this concept has included the construction of multiple experimental demonstrators for validating the concept through static structural and wind tunnel testing. In the second case, a cellular material has been investigated incorporating a bistable unit cell with a sinusoidal arch. This provides a metamaterial that can exhibit large, reversible deformations with as many stable configurations as there are rows in the honeycomb. This metamaterial is incorporated into a beam-like structure which can serve as a spar for a spanwise morphing wing, providing sufficient bending and torsional stiffness, particularly when utilized at the wing tip. Extending and retracting the wing by switching the states of the honeycomb rows provides a significant change to the wing’s induced drag and wing loading, making it ideal for optimal flight in both loitering and cruising conditions. Contributions to this concept have been the development and characterization of the bistable unit cell and honeycomb, as well as the design and analysis of the metabeam and morphing wing concept.</p>

Die vorliegende Arbeit umfasst die Entwicklung eines Rahmens zur Bewertung der Stabilität von (multistabilen) komplexen (vernetzten) dynamischen Systemen. Als ersten Beitrag schlagen wir die multiple-node basin stability (MNBS) vor, um die Stabilität vernetzter dynamischer Systeme als Reaktion auf nicht-infinitesimale Störungen zu messen, die gleichzeitig mehrere Knoten des Systems beeinflussen. Weiterhin beziehen wir uns auf das Konzept der Resilienz zur Charakterisierung von Multistabilität. Inspiriert vom Konzept der ökologischen Resilienz schlussfolgern wir, dass die Stabilität der verschiedenen Attraktoren eines multistabilen Systems von der Gesamtstruktur ihrer jeweiligen Einzugsgebiet bestimmt wird. Insbesondere identifizieren wir sowohl die lokale Dynamik des Systems im Zustandsraum als auch die relative Position des Attraktors im Einzugsgebiet zusätzlich zum dessen Volumen als entscheidende Aspekte, welche die Gesamtstabilität eines Attraktors charakterisieren. Die genannten Aspekte werden im Maß der integral stability (IS) für die ganzheitliche Quantifizierung von Multistabilität zusammengeführt. Komplementär lässt sich auch das Konzept der technischen Resilienz betrachten, welches sich auf die Rückkehrgeschwindigkeit eines Systems zu seinem Gleichgewicht, in Folge einer Störung, bezieht. Im spezifischen Kontext von vernetzten dynamischen Systemen definieren wir die single-node recovery time (SNRT). Diese stellt ein neues Maß zur Schätzung der relativen Zeitskalen dar, die der transienten Knotendynamik eines Netzwerks zugrunde liegen, welches nach einer nicht-infinitesimalen Störung an einem Knoten in seinen gewünschten Betriebszustand zurückkehrt. Schliesslich befassen wir uns mit der Untersuchung der Synchronisationsstabilität in speziellen komplexen Netzwerken, welche entweder die Kleine-Welt-Eigenschaft aufweisen oder eine Kombination aus skalenfreier Knotengradverteilung und hierarchischer Organisation zeigen. / The present endeavour comprises the development of a framework for the assessment of the stability of (multistable) complex (networked) dynamical systems. As a first contribution, we propose the framework of multiple-node basin stability (MNBS) for gauging the stability of networked dynamical systems in response to non-infinitesimal perturbations simultaneously affecting multiple nodes of the system. We then turn to the theoretical framework of resilience in identifying the different aspects characterizing multistability. Inspired by the concept of ecological resilience, we assert that the stability of the different attractors of a multistable system is determined by the overall structure of their respective basins of attraction. In particular, we identify the local dynamics of the system in the state space and the relative position of the attractor within the basin, in addition to the volume of the basin of attraction as crucial aspects determining overall stability of an attractor. We combine the aforementioned aspects in proposing the measure of integral stability (IS) for holistically quantifying multistability. We also draw inspiration from the concept of engineering resilience, which relates to the speed of return of the system to its equilibrium, following a perturbation. In the specific context of networked dynamical systems, we propose the framework of single-node recovery time (SNRT) for obtaining an estimate of the relative time scales underlying the transient dynamics of the nodes of a network returning to its desired operational state, following a non-infinitesimal perturbation to any specific node. Finally, we delve into the explicit investigation of the stability of synchronization on complex dynamical networks exhibiting small-world properties and of those, simultaneously displaying scale-free behaviour and hierarchical organization.

In dieser Arbeit werden zwei nichtlineare Phänomene untersucht, Multistabilität durch verzögerte Rückkopplung und Synchronisation von quasiperiodischen Oszillationen. Dies geschieht mit Hilfe von Halbleiterlasern und auf dem selben Chip wie der Laser integrierter ultrakurzer optischer Rückkopplung. Verzögerte Rückkopplung ist unter anderem die Ursache für das Phänomen der Faltung von Lasermoden, und damit für das Auftreten von mehreren möglichen Laserzuständen für die selben Parameter. Ein tristabiles Regime von Dauerstrichzuständen kann im Experiment für mehrere breite Parameterbereiche der Rückkopplung beobachtet werden. Sehr nahe der Laserschwelle wird einer der Laserzustände durch den stabilen ``aus''''-Zustand ersetzt. Theoretische Betrachtungen im Rahmen des paradigmatischen Lang-Kobayashi Models verzögerter Rückkopplung ermöglichen eine in sich konsistente Interpretation der experimentellen Ergebnisse. Neben der Beeinflussung des stationären Verhaltens eines Halbleiterlasers kann verzögerte Rückkopplung Instabilitäten in der Laseremission hervorrufen. Abhängig von Rückkoppelstärke und -phase werden zwei verschiedene Intensitätspulsationen des emittierten Lichtes beobachtet. Synchronisationsprozesse solcher Pulsationen wurden von mir in einem System von zwei verschiedenen gekoppelten Multisektionslasern untersucht. Periodische Selbstpulsationen von Laser 1 werden hierfür in Laser 2 injiziert, welcher sich in einem Regime quasiperiodischer Intentensitätspulsationen mit zwei fundamentalen Frequenzen befindet. Das Experiment zeigt eine neue Art von Übergang zu synchronem Verhalten, welche kürzlich mit Hilfe von gekoppelten generischen Phasen- und van der Pol Oszillatormodellen aufgedeckt wurde. Desweiteren konnten bislang unerforschte Prozesse des Kohärenzübertrags auch zu nichtsynchronisierten Oszillationen beobachtet werden. / In this work two nonlinear phenomena are investigated, multistability due to delayed feedback and synchronization of quasiperiodic oscillations. The experimental devices are semiconductor lasers with ultra-short optical feedback, which is integrated on the same chip as the laser. Delayed feedback causes the folding of lasing modes, leading to hysteresis effects and even the coexistence of several laser states for the same parameters. A regime of tristability of continuous-wave (cw) states is found for multiple ranges of applied currents. Very close to threshold, one of the lasing states may be replaced by the stable ``off''''-state. Theoretical investigations in the framework of the paradigmatic Lang-Kobayashi model provide a consistent understanding of the experimental findings. Besides modifying the stationary behavior of a semiconductor laser, delayed feedback can cause instabilities of the laser output. Depending on strength and phase of the feedback, two types of self-sustaining pulsations of the emitted light intensity are found in our devices. Synchronization processes of such pulsations are studied in a system of two coupled multisection lasers. Periodic self-pulsations of laser 1 are injected into laser 2, which is operating in a regime with two-frequency quasiperiodic self-pulsations. The experimental system demonstrates the new type of transitions to synchrony between three frequencies which has been recently revealed using generic coupled phase and van der Pol oscillator models. Moreover, carefully determining the coherence of the noisy oscillations, so far unexplored processes of coherence transfer to nonsynchronized oscillations are revealed.

A natural auditory scene contains many sound sources each of which produces complex sounds. These sounds overlap and reach our ears at the same time, but they also change constantly. To still be able to follow the sound source of interest, the auditory system must decide where each individual tone belongs to and integrate this information over time. For well-controlled investigations on the mechanisms behind this challenging task, sound sources need to be simulated in the lab. This is mostly done with sine tones arranged in certain spectrotemporal patterns. The vast majority of studies simply interleave two sub-sequences of sine tones. Participants report how they perceive these sequences or they perform a task whose performance measure allows hints on how the scene was perceived. While many important insights have been gained with this procedure, the questions that can be addressed with it are limited and the commonly used response methods are partly susceptible to distortions or only indirect measures. The present thesis enlarged the complexity of the tone sequences and the diversity of perceptual measures used for investigations on auditory scene analysis. These changes are intended to open up new questions and give new perspectives on our knowledge about auditory scene analysis. In detail, the thesis established three-tone sequences as a tool for specific investigations on the perceptual foreground and background processing in complex auditory scenes. In addition, it modifies an already established approach for indirect measures of auditory perception in a way that enables detailed and univocal investigations on background processing. Finally, a new response method, namely a no-report method for auditory perception that might also serve as a method to validate subjective report measures, was developed. This new methodological approach uses eye movements as a measurement tool for auditory perception. With the aid of all these methodological improvements, the current thesis shows that auditory foreground formation is actually more complex than previously assumed since listeners hold more than one auditory source in the foreground without being forced to do so. In addition, it shows that the auditory system prefers a limited number of specific source configurations probably to avoid combinatorial explosion. Finally, the thesis indicates that the formation of the perceptual background is also quite complex since the auditory system holds perceptual organization alternatives in parallel that were basically assumed to be mutually exclusive. Thus, both the foreground and the background follow different rules than expected based on two-tone sequences. However, one finding seems to be true for both kinds of sequences: the impact of the tone pattern on the subjective perception is marginal, be it in two- or three-tone sequences. Regarding the no-report method for auditory perception, the thesis shows that eye movements and the reported auditory foreground formations were in good agreement and it seems like this approach indeed has the potential to become a first no-report measure for auditory perception.:Abstract 3 Acknowledgments 5 List of Figures 8 List of Tables 9 Collaborations 11 1 General Introduction 13 1.1 The auditory foreground 13 1.1.1 Attention and auditory scene analysis 13 1.1.2 Investigating auditory scene analysis with two-tone sequences 16 1.1.3 Multistability 18 1.2 The auditory background 21 1.2.1 Investigating auditory background processing 22 1.3 Measures of auditory perception 23 1.3.1 Report procedures 23 1.3.2 Performance-based measures 26 1.3.3 Psychophysiological measures 27 1.4 Summary and goals of the thesis 30 2 The auditory foreground 33 2.1 Study 1: Foreground formation in three-tone sequences 33 2.1.1 Abstract 33 2.1.2 Introduction 33 2.1.3 Methods 37 2.1.4 Results 43 2.1.5 Discussion 48 2.2 Study 2: Pattern effects in three-tone sequences 53 2.2.1 Abstract 53 2.2.2 Methods 53 2.2.3 Results 54 2.2.4 Discussion 58 2.3 Study 3: Pattern effects in two-tone sequences 59 2.3.1 Abstract 59 2.3.2 Introduction 59 2.3.3 General Methods 63 2.3.4 Experiment 1 – Methods and Results 65 2.3.5 Experiment 2 – Methods and Results 67 2.3.6 Experiment 3 – Methods and Results 70 2.3.7 Discussion 72 3 The auditory background 74 3.1 Study 4: Background formation in three-tone sequences 74 3.1.1 Abstract 74 3.1.2 Introduction 74 3.1.3 Methods 77 3.1.4 Results 82 3.1.5 Discussion 86 4 Audio-visual coupling for investigations on auditory perception 90 4.1 Study 5: Using Binocular Rivalry to tag auditory perception 90 4.1.1 Abstract 90 4.1.2 Introduction 90 4.1.3 Methods 92 4.1.4 Results 100 4.1.5 Discussion 108 5 General Discussion 113 5.1 Short review of the findings 113 5.2 The auditory foreground 114 5.2.1 Auditory foreground formation and attention theories 114 5.2.2 The role of tone pattern in foreground formation 116 5.2.3 Methodological considerations and continuation 117 5.3 The auditory background 118 5.3.1 Auditory object formation without attention 120 5.3.2 Multistability without attention 121 5.3.3 Methodological considerations and continuation 122 5.4 Auditory scene analysis by audio-visual coupling 124 5.4.1 Methodological considerations and continuation 124 5.5 Artificial listening situations and conclusions on natural hearing 126 6 Conclusions 128 References 130

This thesis is about expanded narrative, a new field of experimental narrative practices that are not represented by single subjects or by categories such as ‘interactive’. It is defined by works that present a challenge to the form, fiction or nonfiction, in terms of the content, structure, style of writing or audience engagement. Extending the cognitive term ‘perceptual multistability’, that refers to switching between interpretations experienced when we look at an ambiguous figures, such as, the Necker cube, this thesis develops the position that expanded narrative practices and specifically locative narrative, a genera of expanded narrative, hold the potential to prompt the experiential effects of multi-stability. The metaphor of multi-stability introduced here stands in for three aspects of experience: language, perception and belief. While ambiguity and misperceptions have been recognised in the literature of experiential narrative practices, further exposition is required. The thesis asks what are the conditions in which the qualities of the metaphor of multi-stability may be prompted and what framework usefully articulates the parameters of experience? Drawing upon the writings of the philosopher William James, subsequent pragmatists, cognitive neuroscience and narratology, it explores how a radical empiricist perspective can form the basis of a non-foundational experiential framework that questions the status of knowledge and the problems of translation between experience and narrative interpretation. It suggests that the subjective classification of imagined and perceptual objects can be affected by the relations between the narrative form, the environment and the participant’s beliefs. The major contributions of the thesis are (1) the development of the Jamesian experiential framework that sets up cross-disciplinary parameters for the thematics of experience to engage with the ontological and epistemological challenges of evaluating and designing for multistability presents; (2) a relational approach to interpretation and coding participants’ feedback of locative narratives; (3) that is employed in the development of a collection of speculative strategies for evoking the effect of the metaphor of multi-stability, based on the development of four published locative narrative apps and ten prototypes. While highly contingent, participant introspective accounts of experience are central here to the methodology, the process of serial hypothesis forming and the iterative development of prototypes and locative narrative case studies. This research does not attempt to draw causal connections from science to that of narrative experience or vice versa. The thesis first considers the field of expanded narrative and the semantic and pragmatic framings of the term narrative and narratological framings of language as multi-stable. It goes on to examine the antecedent and coexistent practices of locative narrative. The epistemological implications for misperception, the function of representation and intentionality in perception are examined in relation to the environmentally situated perceptual, interpretative, aesthetic and emotional dimensions of experience. This research contributes to research in narrative and creative practices. It extends the form of locative narrative with the concept of multi-stability that has a wider application with the field of expanded narrative, creative practice and narratology.

Perceptual multistability is a phenomenon that is mostly studied in all modalities separately. The phenomenon reveals fundamental principles of the perceptual system in the formation of an emerging cognitive representation in the consciousness. The momentary perceptual organizations evoked during the stimulation with ambiguous stimuli switches between several perceptual organizations or percepts: The auditory streaming stimulus in audition and the moving plaids stimulus in vision, elicit different at least two percepts that dominate awareness exclusively for a random phase or dominance duration before an inevitable switch to another percept occurs. The similarity in the perceptual experience has led to propose a global mechanism contributing to the perceptual multistability phenomena crossmodally. Contrary, the difference in the perceptual experience has led to propose a distributed mechanism that is modality-specific. The development of a hybrid model has synergized both approaches. We accumulate empirical evidence for the contribution of a global mechanism, albeit distributed mechanisms play an indispensable role in this cross-modal interplay. The overt report of the perceptual experience in our experiments is accompanied by the recording of objective, cognitive markers of the consciousness: Reflexive movements of the eyes, namely the dilation of the pupil and the optokinetic nystagmus, correlate with the unobservable perceptual switches and perceptual states respectively and have their neuronal rooting in the brainstem. We complement earlier findings on the sensitivity of the pupil to visual multistability: It was shown in two independent experiments that the pupil dilates at the time of reported perceptual switches in auditory multistability. A control condition on confounding effects from the reporting process confines the results. Endogenous, evoked internally by the unchanged stimulus ambiguity, and exogenous, evoked externally by the changes in the physical properties of the stimulus, perceptual switches could be discriminated based on the maximal amplitude of the dilation. The effect of exogenous perceptual has on the pupil were captured in a report and no-report task to detect confounding perceptual effects. In two additional studies, the moment-by-moment coupling and coupling properties of percepts between concurrent multistable processes in audition, evoked by auditory streaming, and in vision, evoked by moving plaids, were found crossmodally. In the last study, the externally induced percept in the visual multistable process was not relayed to the simultaneous auditory multistable process: Still, the observed general coupling is fragile but existent. The requirement for the investigation of a moment-by-moment coupling of the multistable perceptual processes was the application of a no-report paradigm in vision: The visual stimulus evokes an optokinetic nystagmus that has machine learnable different properties when following either of the two percepts. In combination with the manually reported auditory percept, attentional bottlenecks due to a parallel report were circumvented. The two main findings, the dilation of the pupil along reported auditory perceptual switches and the crossmodal coupling of percepts in bimodal audiovisual multistability, speak in favor of a partly global mechanism being involved in control of perceptual multistability; the global mechanism is incarcerated by the, partly independent, distributed competition of percepts on modality level. Potentially, supramodal attention-related modulations consolidate the outcome of locally distributed perceptual competition in all modalities.:COVER 1 BIBLIOGRAPHISCHE BESCHREIBUNG 2 ACKNOWLEDGEMENTS 3 CONTENTS 4 CHAPTER 1: Introduction 6 C1.1: Stability and uncertainty in perception 6 C1.2: Auditory, visual and audio-visual multistability 14 C1.3: Capturing the subjective perceptual experience 25 C1.4: Limitations of preceding studies, objectives, and outline of the Thesis 33 CHAPTER 2: Study 1 “Pupillometry in auditory multistability” 36 C2.1.1 Experiment 1: Introduction 36 C2.1.2 Experiment 1: Material and Methods 38 C2.1.3 Experiment 1: Data analysis 44 C2.1.4 Experiment 1: Results 48 C2.1.5 Experiment 1: Discussion 52 C2.2.1 Experiment 2: Introduction 54 C2.2.2 Experiment 2: Material and Methods 54 C2.2.3 Experiment 2: Data analysis 56 C2.2.4 Experiment 2: Results 57 C2.3 Experiment 1 & 2: Discussion 61 C2.4 Supplement Study 1 65 CHAPTER 3: Study 2 “Multimodal moment-by-moment coupling in perceptual bistability” 71 C3.1.1 Experiment 1: Introduction 71 C3.1.2 Experiment 1: Results 74 C3.1.3 Experiment 1: Discussion 80 C3.1.4 Experiment 1: Material and Methods 84 C3.1.5 Experiment 1: Data analysis 87 C3.2 Supplement Study 2 92 CHAPTER 4: Study 3 “Boundaries of bimodal coupling in perceptual bistability” 93 C4.1.1 Experiment 1: Introduction 93 C4.1.2 Experiment 1: Material and Methods 98 C4.1.3 Experiment 1: Data analysis 102 C4.1.4 Experiment 1: Results 108 C4.1.5 Experiment 1: Discussion 114 C4.2.1 Experiment 2: Introduction 116 C4.2.2 Experiment 2: Material and Methods 119 C4.2.3 Experiment 2: Data analysis 125 C4.2.4 Experiment 2: Results 133 C4.3 Experiment 1 & 2: Discussion 144 C4.4 Supplement Study 3 151 CHAPTER 5: General Discussion 154 C5.1 Significance for models of multistability and implications for the perceptual architecture 162 C5.2 Recommendations for future research 166 C5.3 Conclusion 168 REFERENCES 170 APPENDIX 186 A1: List of Figures 186 A2: List of Tables 188 A3: List of Abbreviations and Symbols 189

Magnetic Shape Memory (MSM) alloys show a superelastic behaviour with possible deformation rates up to 6% until 12% and a sufficient lifetime performance [1, 2]. In this paper, a passive application for a superelastic Ni-Mn-Ga-alloy is presented by using the MSM element as an accurately defined inner friction in a system of a multistable actuator, in particular a multistable proportional valve. The multistable valve is characterized by a currentless holding of the valve displacement in any position of the stroke. This circumstance makes the concept a very low energy consumption valve, compared to conventional proportional valves with solenoid actuators. The new aspect of a rigid connection of MSM Materials enables an absorption of tension as well as compressive forces. To realize an applicable controlling valve, a simple and effective controlling strategy has been implemented. Due to the stabilizing effect of the MSM element, an accurate controlling of the valve stroke and the usage for example as a pressure-, mass-flow or temperature-controlling valve was made possible. Furthermore, some potential applications in pneumatics as well as in hydraulics are presented.