Sound radiation of 3 MHz driven gas bubbles

The sound radiation of 3 MHz acoustically driven air bubbles in liquid is analysed with respect to possible applications in second harmonic ultrasound diagnostics devices, which have recently come into clinical use. In the forcing pressure amplitude P_a = 1-10 atm and ambient radius R_0 = 0.5-5 \mu m parameter domain a narrow regime around the resonance radius R_0 \sim 1-1.5 \mu m and relatively modest P_a \sim 2-2.5 atm is identified in which optimal sound yield in the second harmonic is achieved while maintaining spherical stability of the bubble. For smaller P_a and larger R_0 hardly any sound is radiated; for larger P_a bubbles become unstable towards non-spherical shape oscillations of their surface. The computation of these instabilities is essential for the evaluation of the optimal parameter regime. A region of slightly smaller R_0 and P_a \sim 1-3 atm is best suited to achieve large ratios of the second harmonic to the fundamental intensity. Spherical stability is guaranteed in the suggested regimes for liquids with an enhanced viscosity compared to water, such as blood.Comment: 19 pages, 10 low resolution ps-figures; higher resolution figures can be retrieved from http://staff-www.uni-marburg.de/~hilgenfe/hires.htm

Topological charge pumping with ultracold bosonic atoms in optical superlattices

Elektrische Ströme werden üblicherweise durch eine externe Spannung hervorgerufen, die zu einem dissipativen Ladungstransport in Richtung des Gradienten führt. Schon in der Antike war jedoch bekannt, dass eine gerichtete Bewegung auch durch periodische Modulation eines Systems erzeugt werden kann wie etwa bei der Archimedes-Schraube. Ein quantenmechanisches Analogon wurde 1983 von David Thouless vorgeschlagen - die topologische Ladungspumpe. In einem solchen 1D System werden Teilchen durch eine adiabatische, zyklische Änderung des Hamilton-Operators gezielt in eine Richtung bewegt. Erstaunlicherweise können damit selbst in normalerweise isolierenden Medien Ströme erzeugt werden. Darüber hinaus ist die Bewegung für homogen besetzte Bänder in periodischen Potentialen quantisiert. Diese Quantisierung kann auf eine höherdimensionale topologische Invariante, die erste Chern-Zahl, zurückgeführt werden. Eine 1D topologische Ladungspumpe kann daher als eine dynamische Version des 2D Quanten-Hall-Effekts aufgefasst werden. Dies eröffnet die Möglichkeit, Quanten-Hall-Physik auch in höherdimensionalen Räumen experimentell zu untersuchen. Für 4D Systeme wurde ein neuartiger Quanten-Hall-Effekt vorhergesagt, bei dem ein quantisierter nichtlinearer Hall-Strom auftritt, der 4D topologische Eigenschaften aufweist. Dieser 4D Quanten-Hall-Effekt stellt das fundamentale Modell dar, auf dem die meisten niederdimensionalen topologischen Isolatoren basieren, und weist faszinierende Randeffekte wie isolierte Weyl-Punkte auf. Diese Arbeit befasst sich mit der experimentellen Realisierung von 1D und 2D topologischen Ladungspumpen für ultrakalte bosonische Atome in optischen Übergittern. Durch die periodische Modulation eines 1D Übergitters wird eine Bewegung von Atomen in einem fraktionellen Mott-Isolator induziert. Diese wird mit Hilfe von in-situ Abbildungen und sogenanntem site-resolved band mapping quantitativ vermessen. Damit wird zum ersten Mal für eine topologische Ladungspumpe ein quantisierter Transport in einem ausgedehnten System beobachtet. Daneben werden die Transporteigenschaften des ersten angeregten Bandes untersucht, in dem die Bewegung in die entgegengesetzte Richtung erfolgt. Dieses anomale Verhalten belegt unzweifelhaft den quantenmechanischen Ursprung dieses Transports. Des Weiteren kann in diesem Band die Existenz eines topologischen Übergangs in Abhängigkeit der Gittertiefen nachgewiesen werden. Mit Hilfe einer 2D topologischen Ladungspumpe wird eine dynamische Version des 4D Quanten-Hall-Effekt realisiert. Dessen Hauptmerkmal, der nichtlineare Hall-Strom, wird in einem zeitabhängigen, gewinkelten 2D Übergitter in-situ beobachtet - der erste Nachweis einer Bewegung mit intrinsischer 4D Symmetrie. Mit einer kleinen Atomwolke werden die geometrischen Eigenschaften dieser Bewegung lokal bestimmt und daraus das Verhalten eines unendlich großen Systems rekonstruiert. Die Quantisierung des Transports kann durch die Bestimmung der damit verknüpften 4D topologischen Invarianten, der zweiten Chern-Zahl, nachgewiesen werden. Die Nichtlinearität dieser Bewegung wird aufgezeigt, indem ihre Abhängigkeit von den verantwortlichen externen Störungen untersucht wird. Die hier zusammengefassten Ergebnisse stellen den ersten Schritt der Erforschung topologisch nichttrivialer Phasen in höherdimensionalen Systemen dar.Electric currents are usually generated by applying a voltage, leading to a dissipative transport of charge in the direction of the external bias. Yet, already in ancient times it was known that a motion can also be induced by a periodic modulation in absence of any bias as exemplified by the Archimedes screw. A quantum mechanical analogue of this was proposed by David Thouless in 1983 - the topological charge pump. In such a device, an adiabatic cyclic variation of the Hamiltonian of a one-dimensional (1D) system gives rise to a unidirectional motion of particles. Remarkably, this scheme enables the generation of currents even in otherwise insulating media. Moreover, the resulting transport is quantized for uniformly occupied bands in periodic potentials. This quantization can be related to a higher-dimensional topological invariant, the first Chern number. A 1D topological charge pump can thus be interpreted as a dynamical version of the 2D quantum Hall effect. As such, topological charge pumping provides a unique tool to study higher-dimensional quantum Hall physics, which is otherwise inaccessible to experiments. In 4D, a novel quantum Hall effect was predicted, whose characteristic feature is a quantized non-linear Hall response with 4D topology. Furthermore, 4D quantum Hall systems form the fundamental model for many lower-dimensional topological insulators and exhibit intriguing boundary effects such as isolated Weyl points. This thesis reports on the experimental implementation of 1D and 2D topological charge pumps for ultracold bosonic atoms in dynamically controlled optical superlattices. By periodically modulating a 1D superlattice, atoms forming a fractional Mott insulator are displaced by a quantized distance per cycle. This motion is studied quantitatively using in-situ imaging and site-resolved band mapping. A quantized bulk transport by a topological charge pump is observed for the first time. In addition, the transport properties of the first excited band are probed. This reveals an anomalous pumping response in the direction opposite to the one for ground-state atoms, thereby unambiguously demonstrating the transport's quantum mechanical origin. Additionally, a topological transition is detected in the excited band as a function of the lattice depths. The concept of topological charge pumping is extended to 2D systems to implement a dynamical version of the 4D integer quantum Hall effect. Its key signature, the non-linear Hall response, is observed in-situ in a time-dependent, angled 2D superlattice. This constitutes the first observation of a bulk response with intrinsic 4D symmetries in any physical system. By locally probing the geometric properties of the non-linear response with a small atom cloud, the response of an infinite system is reconstructed. Its quantization is demonstrated by determining the associated 4D topological invariant, the second Chern number. Furthermore, the non-linear character of the response is revealed by studying its dependence on the external perturbations that generate the response. The results presented here serve as the first step towards the exploration of topologically non-trivial phases in higher-dimensional systems

Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.Comment: 41 pages, 21 eps and ps figures; LaTeX stylefiles replaced because the PostScript file produced at the archive had misplaced and misscaled figure

Dynamic equilibrium Mechanism for Surface Nanobubble Stabilization

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls (Dammer & Lohse, PRL96, 206101 (2006); Zhang {\it et al.}, PRL98, 136101 (2007); Mezger {\it et al.}, J.\ Chem. Phys. 128, 244705 (2008)). This influx balances the outflux and allows for a meta-stable equilibrium, which however vanishes in thermodynamic equilibrium. Our theory predicts the equilibrium radius of the surface nanobubbles, as well as the threshold for surface nanobubble formation as a function of hydrophobicity and gas concentration.Comment: 4 pages, 3 figures. Phys. Rev. Lett. 101, in press (2008

Topological charge pumping with ultracold bosonic atoms in optical superlattices

Elektrische Ströme werden üblicherweise durch eine externe Spannung hervorgerufen, die zu einem dissipativen Ladungstransport in Richtung des Gradienten führt. Schon in der Antike war jedoch bekannt, dass eine gerichtete Bewegung auch durch periodische Modulation eines Systems erzeugt werden kann wie etwa bei der Archimedes-Schraube. Ein quantenmechanisches Analogon wurde 1983 von David Thouless vorgeschlagen - die topologische Ladungspumpe. In einem solchen 1D System werden Teilchen durch eine adiabatische, zyklische Änderung des Hamilton-Operators gezielt in eine Richtung bewegt. Erstaunlicherweise können damit selbst in normalerweise isolierenden Medien Ströme erzeugt werden. Darüber hinaus ist die Bewegung für homogen besetzte Bänder in periodischen Potentialen quantisiert. Diese Quantisierung kann auf eine höherdimensionale topologische Invariante, die erste Chern-Zahl, zurückgeführt werden. Eine 1D topologische Ladungspumpe kann daher als eine dynamische Version des 2D Quanten-Hall-Effekts aufgefasst werden. Dies eröffnet die Möglichkeit, Quanten-Hall-Physik auch in höherdimensionalen Räumen experimentell zu untersuchen. Für 4D Systeme wurde ein neuartiger Quanten-Hall-Effekt vorhergesagt, bei dem ein quantisierter nichtlinearer Hall-Strom auftritt, der 4D topologische Eigenschaften aufweist. Dieser 4D Quanten-Hall-Effekt stellt das fundamentale Modell dar, auf dem die meisten niederdimensionalen topologischen Isolatoren basieren, und weist faszinierende Randeffekte wie isolierte Weyl-Punkte auf. Diese Arbeit befasst sich mit der experimentellen Realisierung von 1D und 2D topologischen Ladungspumpen für ultrakalte bosonische Atome in optischen Übergittern. Durch die periodische Modulation eines 1D Übergitters wird eine Bewegung von Atomen in einem fraktionellen Mott-Isolator induziert. Diese wird mit Hilfe von in-situ Abbildungen und sogenanntem site-resolved band mapping quantitativ vermessen. Damit wird zum ersten Mal für eine topologische Ladungspumpe ein quantisierter Transport in einem ausgedehnten System beobachtet. Daneben werden die Transporteigenschaften des ersten angeregten Bandes untersucht, in dem die Bewegung in die entgegengesetzte Richtung erfolgt. Dieses anomale Verhalten belegt unzweifelhaft den quantenmechanischen Ursprung dieses Transports. Des Weiteren kann in diesem Band die Existenz eines topologischen Übergangs in Abhängigkeit der Gittertiefen nachgewiesen werden. Mit Hilfe einer 2D topologischen Ladungspumpe wird eine dynamische Version des 4D Quanten-Hall-Effekt realisiert. Dessen Hauptmerkmal, der nichtlineare Hall-Strom, wird in einem zeitabhängigen, gewinkelten 2D Übergitter in-situ beobachtet - der erste Nachweis einer Bewegung mit intrinsischer 4D Symmetrie. Mit einer kleinen Atomwolke werden die geometrischen Eigenschaften dieser Bewegung lokal bestimmt und daraus das Verhalten eines unendlich großen Systems rekonstruiert. Die Quantisierung des Transports kann durch die Bestimmung der damit verknüpften 4D topologischen Invarianten, der zweiten Chern-Zahl, nachgewiesen werden. Die Nichtlinearität dieser Bewegung wird aufgezeigt, indem ihre Abhängigkeit von den verantwortlichen externen Störungen untersucht wird. Die hier zusammengefassten Ergebnisse stellen den ersten Schritt der Erforschung topologisch nichttrivialer Phasen in höherdimensionalen Systemen dar.Electric currents are usually generated by applying a voltage, leading to a dissipative transport of charge in the direction of the external bias. Yet, already in ancient times it was known that a motion can also be induced by a periodic modulation in absence of any bias as exemplified by the Archimedes screw. A quantum mechanical analogue of this was proposed by David Thouless in 1983 - the topological charge pump. In such a device, an adiabatic cyclic variation of the Hamiltonian of a one-dimensional (1D) system gives rise to a unidirectional motion of particles. Remarkably, this scheme enables the generation of currents even in otherwise insulating media. Moreover, the resulting transport is quantized for uniformly occupied bands in periodic potentials. This quantization can be related to a higher-dimensional topological invariant, the first Chern number. A 1D topological charge pump can thus be interpreted as a dynamical version of the 2D quantum Hall effect. As such, topological charge pumping provides a unique tool to study higher-dimensional quantum Hall physics, which is otherwise inaccessible to experiments. In 4D, a novel quantum Hall effect was predicted, whose characteristic feature is a quantized non-linear Hall response with 4D topology. Furthermore, 4D quantum Hall systems form the fundamental model for many lower-dimensional topological insulators and exhibit intriguing boundary effects such as isolated Weyl points. This thesis reports on the experimental implementation of 1D and 2D topological charge pumps for ultracold bosonic atoms in dynamically controlled optical superlattices. By periodically modulating a 1D superlattice, atoms forming a fractional Mott insulator are displaced by a quantized distance per cycle. This motion is studied quantitatively using in-situ imaging and site-resolved band mapping. A quantized bulk transport by a topological charge pump is observed for the first time. In addition, the transport properties of the first excited band are probed. This reveals an anomalous pumping response in the direction opposite to the one for ground-state atoms, thereby unambiguously demonstrating the transport's quantum mechanical origin. Additionally, a topological transition is detected in the excited band as a function of the lattice depths. The concept of topological charge pumping is extended to 2D systems to implement a dynamical version of the 4D integer quantum Hall effect. Its key signature, the non-linear Hall response, is observed in-situ in a time-dependent, angled 2D superlattice. This constitutes the first observation of a bulk response with intrinsic 4D symmetries in any physical system. By locally probing the geometric properties of the non-linear response with a small atom cloud, the response of an infinite system is reconstructed. Its quantization is demonstrated by determining the associated 4D topological invariant, the second Chern number. Furthermore, the non-linear character of the response is revealed by studying its dependence on the external perturbations that generate the response. The results presented here serve as the first step towards the exploration of topologically non-trivial phases in higher-dimensional systems

Directly Printable Flexible Strain Sensors for Bending and Contact Feedback of Soft Actuators

This paper presents a fully printable sensorized bending actuator that can be calibrated to provide reliable bending feedback and simple contact detection. A soft bending actuator following a pleated morphology, as well as a flexible resistive strain sensor, were directly 3D printed using easily accessible FDM printer hardware with a dual-extrusion tool head. The flexible sensor was directly welded to the bending actuator’s body and systematically tested to characterize and evaluate its response under variable input pressure. A signal conditioning circuit was developed to enhance the quality of the sensory feedback, and flexible conductive threads were used for wiring. The sensorized actuator’s response was then calibrated using a vision system to convert the sensory readings to real bending angle values. The empirical relationship was derived using linear regression and validated at untrained input conditions to evaluate its accuracy. Furthermore, the sensorized actuator was tested in a constrained setup that prevents bending, to evaluate the potential of using the same sensor for simple contact detection by comparing the constrained and free-bending responses at the same input pressures. The results of this work demonstrated how a dual-extrusion FDM printing process can be tuned to directly print highly customizable flexible strain sensors that were able to provide reliable bending feedback and basic contact detection. The addition of such sensing capability to bending actuators enhances their functionality and reliability for applications such as controlled soft grasping, flexible wearables, and haptic devices

Breakup of diminutive Rayleigh jets

Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $\tau_\mathrm{c} = \sqrt{\rho r^3 / \gamma}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary integral (BI) calculation, showing deviations at the final moment of the pinch-off. Inspite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results

A numerical model investigation of the effects of proposed confined disposal facilities on New Bedford harbor, Massachusetts

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (p. 142-147).by R. Michael Lohse.M.S