A bifurcation and symmetry discussion of the Sommerfeld effect

The Arnold Sommerfeld effect is an intriguing resonance capture and release series of events originally demonstrated in 1902. A single event is studied using a two degree of freedom mathematical model of a motor with imbalance mounted to laterally restricted spring connected cart. For a certain power supplied, in general the motor rotates at a speed consistent with a motor on a rigid base. However at speeds close to the natural frequency of the cart, it seemingly takes on extra oscillations where for a single rotation it both speeds up and then slows down. Therefore in a standard experimental demonstration of the effect, as the supplied torque force is increased or decreased, this may give the illusion that the stable operation of the motor is losing and gaining stability. This is not strictly the case, instead small oscillations always present in the system solution are amplified near the resonant frequency. The imbalance in the motor causes a single resonance curve to fold back on itself forming two fold bifurcations which leads to hysteresis and an asymmetry between increasing and decreasing the motor speed. Although as outlined the basic mechanism is due the interplay between two stable and one unstable limit cycles, a more complicated bifurcation scenario is observed for higher imbalances in the motor. The presence of a Z2 phase space symmetry tempers the dynamics and bifurcation picture.Comment: 14 pages, 8 figure

Multi-stabilities and symmetry-broken one-colour and two-colour states in closely coupled single-mode lasers

We theoretically investigate the dynamics of two mutually coupled identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-colour states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150~GHz. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour and two-colour states. Several of these states give rise to multi-stabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.Comment: 12 pages, 15 figure

Two closely coupled lasers, dynamics & applications

The dynamics of two mutually coupled identical single-mode semi-conductor lasers are theoretically investigated. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities whilst at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable two-colour states, where both single-mode lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. For low coupling but possibly large separation, the frequency of the relaxation oscillations of the freerunning lasers defines the dynamics. Chaotic and quasi-periodic states are identified and shown to be stable. For weak coupling undamped relaxation oscillations dominate where each laser is locked to three or more odd number of colours spaced by the relaxation oscillation frequency. It is shown that the instabilities that lead to these states are directly connected to the two colour mechanism where the change in the number of optical colours due to a change in the plane of oscillation. At initial coupling, in-phase and anti-phase one colour states are shown to emerge from “on” uncoupled lasers using a perturbation method. Similarly symmetry-broken one-colour states come from considering one free-running laser initially “on” and the other laser initially “off”. The mechanism that leads to a bi-stability between in-phase and anti-phase one-colour states is understood. Due to an equivariant phase space symmetry of being able to exchange the identical lasers, a symmetric and symmetry-broken variant of all states mentioned above exists and is shown to be stable. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour, symmetric and symmetry-broken two-colour, symmetric and symmetry-broken undamped relaxation oscillations, symmetric and symmetry-broken quasi-periodic, and symmetric and symmetry-broken chaotic states. As symmetry-broken states always exist in pairs, they naturally give rise to bi-stability. Several of these states show multistabilities between symmetric and symmetry-broken variants and among states. Three memory elements on the basis of bi-stabilities in one and two colour states for two coupled single-mode lasers are proposed. The switching performance of selected designs of optical memory elements is studied numerically

A 2MASS study of candidate precursors to UCHII regions

There has been two major efforts in the past 7 years to study UCHII regions (Molinari et al. 1996; Sridharan et al., 2002). They compiled a list of 217 best candidates of the precursors to UCHII regions. We conducted a near IR study into these sources using the 2MASS all sky survey. A method of Nyquist bining stellar counts around these sources revealed the presence of embedded clusters in at least 63 (30%) of the sample. More than 50 of these were previously unknown groupings, 29 are classified as large clusters, 18 as small and the rest as stellar groups. This technique of detection provided stellar density contour maps which allowed us to discuss the morphology of the groupings. We estimated that the ratio of Hierarchical type to central condensed type cluster (H/C = 0.9 \approx 1) which possibly implies both a basic unity of gravity and turbulence but also maybe the decay of the turbulence with time. The positions of the candidate (pre) UCHII regions show a striking preference for the very centre of the clusters. We statistically calculate the number of cluster members detectable by the 2MASS telescope, and we extend this estimate and the mass to almost the deuterium burning limit with the use of an universal IMF from Muench et al. (2002). We observe a correlation between the relative age of the (pre) UCHII regions and the number of members in the clusters. With the use of cc-diagrams, we obtained the average dust extinction and we discussed the colours of massive protostars. The mass of the dust cloud was available for 15 clusters from Beuther et al. (2002) and so, we estimated the local star formation efficiency

Robust Damping in Self-Excited Mechanical Systems

A technique to optimize the stability of a general mechanical system is outlined. The method relies on decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance. An optimization problem can then be formulated where the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, we define a system to be more stable if its eigenvalue with largest real part is as negative as possible. The technique is demonstrated by applying it to an introduced non-dimensionalized variant of a known minimal wobbling disc brake model. In this case, it is shown to be beneficial to shift some damping from the disc to the pins for a system optimized for stability

A programmable nonlinear acoustic metamaterial

Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic “editing” capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor

Spatiotemporally Resolved Heat Dissipation in 3D Patterned Magnetically Responsive Hydrogels

Multifunctional nanocomposites that exhibit well-defined physical properties and encode spatiotemporally controlled responses are emerging as components for advanced responsive systems, for example, in soft robotics or drug delivery. Here an example of such a system, based on simple magnetic hydrogels composed of iron oxide magnetic nanoflowers and Pluronic F127 that generates heat upon alternating magnetic field irradiation is described. Rules for heat-induction in bulk hydrogels and the heat-dependence on particle concentration, gel volume, and gel exposed surface area are established, and the dependence on external environmental conditions in “closed” as compared to “open” (cell culture) system, with controllable heat jumps, of ∆T 0–12°C, achieved within ≤10 min and maintained described. Furthermore the use of extrusion-based 3D printing for manipulating the spatial distribution of heat in well-defined printed features with spatial resolution <150 µm, sufficiently fine to be of relevance to tissue engineering, is presented. Finally, localized heat induction in printed magnetic hydrogels is demonstrated through spatiotemporally-controlled release of molecules (in this case the dye methylene blue). The study establishes hitherto unobserved control over combined spatial and temporal induction of heat, the applications of which in developing responsive scaffold remodeling and cargo release for applications in regenerative medicine are discussed.Enterprise IrelandScience Foundation Irelan