a numerical and experimental investigation on the subtle dynamics of Tibetan bowls

UID/EAT/00472/2013Tibetan bowls have been traditionally used for ceremonial or meditation purposes, but also in contemporary music-making. They are handcrafted and produce different tones depending on their shape, size, mass and their alloy composition. Most important is the sound producing technique by impacting and/or rubbing, as well as the excitation location, the hardness and friction characteristics of the excitation stick. In a previous paper, we developed a physically-based method for nonlinear time-domain simulation of Tibetan bowls. Our computational approach, based on a compact modal formulation, produces realistic dynamical responses. In the present paper we focus on an interesting feature of Tibetan bowls: in order to produce self-excited responses, the stick must rub the bowl against the external side of the rim, e.g. adially\pressing outwards the bowl center. Indeed, experimenting with many bowls showed that they do not sing when rubbed internally. We start documenting this claim with experimental results from representative bowls, and then exploit our computational model in order to reproduce the observed behavior qualitatively. Our results are in good agreement with experiments, thereby demonstrating that internally excited bowls are dissipative and hence unable to sing.publishersversionpublishe

Physical modelling techniques for the dynamical characterization and sound synthesis of historical bells

SFRH/BD/91435/2012 PTDC/ART-PER/32568/2017 UIDB/00472/2020 UIDP/00472/2020Capable of maintaining characteristics practically intact over the centuries, bells are musical instruments able to provide important and unique data for the study of musicology and archaeology essential to understand past manufacturing and tuning techniques. In this research we present a multidisciplinary approach based on both direct and reverse engineering processes for the dynamical characterization and sound synthesis of historical bells which proven particularly useful to extract and preserve important information for Cultural Heritage. It allows the assessment of the bell’s 3D morphology, sound properties and casting and tuning techniques over time. The accuracy and usefulness of the developed techniques are illustrated for three historical bells, including the oldest recognized bell in Portugal, dated 1287, and two eighteenth century bells from the Mafra National Palace carillons (Portugal). The proposed approach combines non-invasive up-to-date imaging technology with modelling and computational techniques from vibration analysis, and can be summarized in the following steps: (1) For the diagnosis of existing bells, a precise assessment of the bell geometry is achieved through 3D scanning technologies, used for the field measurement and reconstruction of a 3D geometry model of each bell; (2) To access the modal properties of the bells, for any given (at the design stage) or measured geometry, a finite element model is built to compute the significant frequencies of the bell partials, and the corresponding modal masses and modeshapes. In the case of existing bells, comparison of the computed modes with those obtained from vibrational data, through experimental modal identification, enables the validation (or otherwise correction) of the finite element model; (3) Using the computed or experimentally identified modes, time-domain dynamical responses can be synthesized for any conceivable bell, providing realistic sounds for any given clapper and impact location. Although this study primarily aimed to better understand the morphology and sounds of historical bells to inform their conservation/preservation, this technique can be also applied to modern instruments, either existing or at design stages. To a larger extent, it presents strong potential for applications in the bell industry, namely for restoration and re-tuning, as well as in virtual museology.publishersversionpublishe

Modelling And Experiments

UIDB/00472/2020 UIDP/00472/2020In some mallet percussion instruments, such as vibraphones and marimbas, tubular acoustic resonators areplaced beneath the tuned bars to enhance sound radiation. Although widely used in commercial instruments, thevibroacoustic interaction between the tuned bars and theirresonators has not been studied extensively, and previousmodelling attempts regularly neglect important aspects ofthe coupling dynamics. This work develops on a previousstudy, where a minimal model for the coupling between asingle bar mode and a single resonator mode was presented. Here, the same modelling principles are applied toa system composed of a 1-D beam and a 1-D cylindricalacoustic resonator, leading to a lumped-parameter modelincluding the coupling dynamics between several barmodes and several resonator acoustic modes. The dynamics of the lumped-parameter model are explored throughtime-domain simulations and eigenvalue analysis, revelinga number of interesting (and rarely mentioned) features, forexample: the role of the ratio of damping coefficients between a bar mode and a resonator mode, the placementof the resonator along the bar’s length as well as its proximity to the bar, etc. Additionally, experimental results arepresented to validate the model and demonstrate its capacity to emulate real instruments, both qualitative andquantitatively.publishersversionpublishe

Vortex tension as an order parameter in three-dimensional U(1)+Higgs theory

We use lattice Monte Carlo simulations to study non-perturbatively the tension, i.e. the free energy per unit length, of an infinitely long vortex in the three-dimensional U(1)+Higgs theory. This theory is the low-energy effective theory of high-temperature scalar electrodynamics, the standard framework for cosmic string studies. The vortex tension is measured as a function of the mass parameter at a large value of the Higgs self-coupling, where the transition between the phases is continuous. It is shown that the tension gives an order parameter that can distinguish between the two phases of the system. We argue that the vortex tension can describe the physics of long strings without lattice artifacts, unlike vortex network percolation.Comment: 18 pages, 7 figure

application to musical Instruments

UID/EAT/00472/2013 EAT/00472/2013Most musical instruments consist of dynamical subsystems connected at a number of constraining points through which energy flows. For physical sound synthesis, one important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, in this paper, a different approach is explored, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is surprisingly absent from the literature. Here, such a modeling strategy is developed and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instru- ments. Objectives are twofold: (1) Develop the U-K equation for constrained flexible systems with subsystems modelled through unconstrained modes; and (2) apply this framework to compute string/body coupled dynamics. This example complements previous work [Debut, Antunes, Marques, and Carvalho, Appl. Acoust. 108, 3–18 (2016)] on guitar modeling using penalty meth- ods. Simulations show that the proposed technique provides similar results with a significant improvement in computational efficiency. VC 2017 Acoustical Society of America.publishersversionpublishe

Numerical simulations of string networks in the Abelian-Higgs model

We present the results of a field theory simulation of networks of strings in the Abelian Higgs model. Starting from a random initial configuration we show that the resulting vortex tangle approaches a self-similar regime in which the length density of lines of zeros of $\phi$ reduces as $t^{-2}$. We demonstrate that the network loses energy directly into scalar and gauge radiation. These results support a recent claim that particle production, and not gravitational radiation, is the dominant energy loss mechanism for cosmic strings. This means that cosmic strings in Grand Unified Theories are severely constrained by high energy cosmic ray fluxes: either they are ruled out, or an implausibly small fraction of their energy ends up in quarks and leptons.Comment: 4pp RevTeX, 3 eps figures, clarifications and new results included, to be published in Phys. Rev. Let

The evolution of a network of cosmic string loops

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the `rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.Comment: LaTeX, 27 pages, 10 figures included as .eps file

Thermodynamics of Gauge-Invariant U(1) Vortices from Lattice Monte Carlo Simulations

We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We discretize the system and introduce a gauge-invariant definition of a vortex passing through a loop on the lattice. We then study with Monte Carlo simulations the total vortex density, extract the physically meaningful part thereof, and demonstrate that it has a well-defined continuum limit. The total vortex density behaves as a pseudo order parameter, having a discontinuity in the regime of first order transitions and behaving continuously in the regime of second order transitions. Finally, we discuss further gauge-invariant observables to be measured.Comment: 13 pages, 5 figures. Some references added; to appear in Phys.Lett.

Screening for Drought Tolerance in Thirty Three Taro Cultivars

Taro [Colocasia esculenta (L.) Schott] is a root crop which is an important staple food in many regions of the world, producing 10.5 million tonnes on 1.4 million hectares a year. The crop is cultivated in wet (rain fed) or irrigated conditions, requiring on average 2,500 mm water per year, and in many countries it is cultivated in flooded plots. It is estimated that taro production could decrease by 40% as a result of the increase in drought and other severe events. In this work, thirty three accessions, including local cultivars, selected and hybrid lines were submitted to long duration drought stress and screened for tolerance. Twelve physiological, morphological and agronomic traits were measured at harvest, and subject to multivariate analysis. Stress indices, Water Use Efficiency and Factorial Analysis were useful for discriminating accessions regarding drought tolerance and yield stability, and drought tolerant and susceptible cultivars were identified. Our results confirm that different taro cultivars have different drought avoidance and tolerance strategies to cope with water scarcity. Better yield performers minimised biomass and canopy loss, while tolerance was observed in cultivars that presented low potential yield, but efficiently transferred resources to enhance corm formation. Among the 33 accessions, two local cultivars showed high yield stability and could be considered as suitable parents for breeding programs, while two others are well adapted to drought, but with overall low yield potential