Investigation of tanpura string vibrations using a two-dimensional time-domain model incorporating coupling and bridge friction

Tanpura string vibrations have been investigated previously using numerical models based on energy conserving schemes derived from a Hamiltonian description in one-dimensional form. Such time-domain models have the property that, for the lossless case, the numerical Hamiltonian (representing total energy of the system) can be proven to be constant from one time step
to the next, irrespective of any of the system parameters; in practice the Hamiltonian can be shown to be conserved within machine precision. Models of this kind can reproduce a jvari effect, which results from the bridge-string interaction. However the one-dimensional formulation has recently been shown to fail to replicate the jvaris strong dependence on the thread placement. As a first step towards simulations which accurately emulate this sensitivity to the thread placement, a twodimensional model is proposed, incorporating coupling of controllable level between the two string polarisations at the string termination opposite from the barrier. In addition, a friction force acting when the string slides across the bridge in horizontal direction is introduced, thus effecting a further damping mechanism. In this preliminary study, the string is terminated at the position of the thread. As in the one-dimensional model, an implicit scheme has to be used to solve the system, employing Newton's method to calculate the updated positions and momentums of each string segment. The two-dimensional model is proven to be energy conserving when the loss parameters are set to zero, irrespective of the coupling constant. Both frequency-dependent and independent losses are then added to the string, so that the model can be compared to analogous instruments. The influence of coupling and the bridge friction are investigated.

Discrete-Time Conserved Quantities for Damped Oscillators

Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.

Improving the robustness of the iterative solver in state-space modelling of guitar distortion circuitry

Iterative solvers are required for the discrete-time simulation of nonlinear behaviour in analogue distortion circuits. Unfortunately,these methods are often computationally too expensive for realtime simulation. Two methods are presented which attempt to reduce the expense of iterative solvers. This is achieved by applying information that is derived from the specific form of the non linearity.The approach is first explained through the modelling of an asymmetrical diode clipper, and further exemplified by application to the Dallas Rangemaster Treble Booster guitar pedal, which provides an initial perspective of the performance on systems with multiple nonlinearities.

MRZ-99030 – a novel modulator of Aβ aggregation: II – reversal of Aβ oligomer-induced deficits in long-term potentiation (LTP) and cognitive performance in rats and mice.

β-amyloid1-42 (Aβ1-42) is a major endogenous pathogen underlying the aetiology of Alzheimer's disease (AD). Recent evidence indicates that soluble Aβ oligomers, rather than plaques, are the major cause of synaptic dysfunction and neurodegeneration. Small molecules that suppress Aβ aggregation, reduce oligomer stability or promote off-pathway non-toxic oligomerization represent a promising alternative strategy for neuroprotection in AD. MRZ-99030 was recently identified as a dipeptide that modulates Aβ1-42 aggregation by triggering a non-amyloidogenic aggregation pathway, thereby reducing the amount of intermediate toxic soluble oligomeric Aβ species. The present study evaluated the relevance of these promising results with MRZ-99030 under pathophysiological conditions i.e. against the synaptotoxic effects of Aβ oligomers on hippocampal long term potentiation (LTP) and two different memory tasks. Aβ1-42 interferes with the glutamatergic system and with neuronal Ca2+ signalling and abolishes the induction of LTP. Here we demonstrate that MRZ-99030 (100–500 nM) at a 10:1 stoichiometric excess to Aβ clearly reversed the synaptotoxic effects of Aβ1-42 oligomers on CA1-LTP in murine hippocampal slices. Co-application of MRZ-99030 also prevented the two-fold increase in resting Ca2+ levels in pyramidal neuron dendrites and spines triggered by Aβ1-42 oligomers. In anaesthetized rats, pre-administration of MRZ-99030 (50 mg/kg s.c.) protected against deficits in hippocampal LTP following i.c.v. injection of oligomeric Aβ1-42. Furthermore, similar treatment significantly ameliorated cognitive deficits in an object recognition task and under an alternating lever cyclic ratio schedule after the i.c.v. application of Aβ1-42 and 7PA2 conditioned medium, respectively. Altogether, these results demonstrate the potential therapeutic benefit of MRZ-99030 in AD.

Parameter Optimisation for Woodwind Single-Reed Models

Time-domain modelling of single-reed woodwind instruments usually involves a lumped model of the excitation mechanism. The parameters of this lumped model have to be estimated for use in numerical simulations. Several attempts have been made to estimate these parameters, including observations of the mechanics of isolated reeds, measurements under artificial or real playing conditions and estimations based on numerical simulations. In this study an optimisation routine is presented, that can estimate reed-model parameters, given the pressure and flow signals in the mouthpiece. The method is validated, tested on a series of numerically synthesised data. In order to incorporate the actions of the player in the parameter estimation process, the optimisation routine has to be applied to signals obtained under real playing conditions. The estimated parameters can then be used to resynthesise the pressure and flow signals in the mouthpiece. In the case of measured data, as opposed to numerically synthesised data, special care needs to be taken while modelling the bore of the instrument. In fact, a careful study of various experimental datasets revealed that for resynthesis to work, the bore termination impedance should be known very precisely from theory. An example is given, where the above requirement is satisfied, and the resynthesised signals closely match the original signals generated by the player.

SATCOM Retrodirective Array

We present an in depth look at the challenges involved in using analogue retrodirective arrays for satellite communications. The main technical issues surrounding the development of a retrodirective (self-steering) Satellite Communications (SATCOM) system are given and techniques for mitigating these issues provided. Detailed results are given for a prototype high performance circularly polarized retrodirective array architecture suitable for mounting on an un-stabilized mobile platform. The paper concludes with practical retrodirective L-band array results with the array used to acquire actual broadband satellite data signals from a commercial L-band satellite system. Received satellite signals as low as -130dBm at the antenna elements are tracked. Accurate self-tracking occurs over the azimuth range of up to +/- 40 degrees.

Lake Kumphawapi revisited – The complex climatic and environmental record of a tropical wetland in NE Thailand

Kumphawapi, which is Thailand’s largest natural freshwater lake, contains a >10,000-year-long climatic and environmental archive. New data sets (stratigraphy, chronology, hydrogen isotopes, plant macrofossil and charcoal records) for two sedimentary sequences are here combined with earlier multi-proxy studies to provide a comprehensive reconstruction of past climatic and environmental changes for Northeast Thailand. Gradually higher moisture availability due to a strengthening of the summer monsoon led to the formation of a large shallow lake in the Kumphawapi basin between >10,700 and c. 7000 cal. BP. The marked increase in moisture availability and lower evaporation between c. 7000 and 6400 cal. BP favoured the growth and expansion of vegetation in and around the shallow lake. The increase in biomass led to gradual overgrowing and infilling, to an apparent lake level lowering and to the development of a wetland. Multiple hiatuses are apparent in all investigated sequences between c. 6500 and 1400 cal. BP and are explained by periodic desiccation events of the wetland and erosion due to the subsequent lake level rise. The rise in lake level, which started c. 2000 cal. BP and reached shallower parts c. 1400 cal. BP, is attributed to an increase in effective moisture availability. The timing of hydroclimatic conditions during the past 2000 years cannot be resolved because of chronological limitations.

Extended Energy Vector Prediction of Ambisonically Reproduced Image Direction at Off-Centre Listening Positions

This paper presents an extension to the energy vector, well known in the Ambisonics literature, to improve its predictions of localisation at off-centre listening positions. In determining the source direction, a perceptual weight is assigned to each loudspeaker gain, taking into account the relative arrival times, levels, and directions of the loudspeaker signals. The proposed model is evaluated alongside the original energy vector and two binaural models through comparison with the results of recent perceptual studies. The extended version was found to provide results that were at least 50% more accurate than the second best predictor for two experiments involving off-centre listeners with first- and third-order Ambisonics systems.

Interannual and (multi-)decadal variability in the sedimentary BIT index of Lake Challa, East Africa, over the past 2200 years: assessment of the precipitation proxy

The branched vs. isoprenoid tetraether (BIT) index is based on the relative abundance of branched tetraether lipids (brGDGTs) and the isoprenoidal GDGT crenarchaeol. In Lake Challa sediments the BIT index has been applied as a proxy for local monsoon precipitation on the assumption that the primary source of brGDGTs is soil washed in from the lake's catchment. Since then, microbial production within the water column has been identified as the primary source of brGDGTs in Lake Challa sediments, meaning that either an alternative mechanism links BIT index variation with rainfall or that the proxy's application must be reconsidered. We investigated GDGT concentrations and BIT index variation in Lake Challa sediments at a decadal resolution over the past 2200 years, in combination with GDGT time-series data from 45 monthly sediment-trap samples and a chronosequence of profundal surface sediments.

Our 2200-year geochemical record reveals high-frequency variability in GDGT concentrations, and therefore in the BIT index, superimposed on distinct lower-frequency fluctuations at multi-decadal to century timescales. These changes in BIT index are correlated with changes in the concentration of crenarchaeol but not with those of the brGDGTs. A clue for understanding the indirect link between rainfall and crenarchaeol concentration (and thus thaumarchaeotal abundance) was provided by the observation that surface sediments collected in January 2010 show a distinct shift in GDGT composition relative to sediments collected in August 2007. This shift is associated with increased bulk flux of settling mineral particles with high Ti / Al ratios during March–April 2008, reflecting an event of unusually high detrital input to Lake Challa concurrent with intense precipitation at the onset of the principal rain season that year. Although brGDGT distributions in the settling material are initially unaffected, this soil-erosion event is succeeded by a massive dry-season diatom bloom in July–September 2008 and a concurrent increase in the flux of GDGT-0. Complete absence of crenarchaeol in settling particles during the austral summer following this bloom indicates that no Thaumarchaeota bloom developed at that time. We suggest that increased nutrient availability, derived from the eroded soil washed into the lake, caused the massive bloom of diatoms and that the higher concentrations of ammonium (formed from breakdown of this algal matter) resulted in a replacement of nitrifying Thaumarchaeota, which in typical years prosper during the austral summer, by nitrifying bacteria. The decomposing dead diatoms passing through the suboxic zone of the water column probably also formed a substrate for GDGT-0-producing archaea. Hence, through a cascade of events, intensive rainfall affects thaumarchaeotal abundance, resulting in high BIT index values.

Decade-scale BIT index fluctuations in Lake Challa sediments exactly match the timing of three known episodes of prolonged regional drought within the past 250 years. Additionally, the principal trends of inferred rainfall variability over the past two millennia are consistent with the hydroclimatic history of equatorial East Africa, as has been documented from other (but less well dated) regional lake records. We therefore propose that variation in GDGT production originating from the episodic recurrence of strong soil-erosion events, when integrated over (multi-)decadal and longer timescales, generates a stable positive relationship between the sedimentary BIT index and monsoon rainfall at Lake Challa. Application of this paleoprecipitation proxy at other sites requires ascertaining the local processes which affect the productivity of crenarchaeol by Thaumarchaeota and brGDGTs.

Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

A Real-Time Synthesis Oriented Tanpura Model

Physics-based synthesis of tanpura drones requires accurate simulation of stiff, lossy string vibrations while incorporating sustained contact with the bridge and a cotton thread. Several challenges arise from this when seeking efficient and stable algorithms for real-time sound synthesis. The approach proposed here to address these combines modal expansion of the string dynamics with strategic simplifications regarding the string-bridge and string-thread contact, resulting in an efficient and provably stable time-stepping scheme with exact modal parameters. Attention is given also to the physical characterisation of the system, including string damping behaviour, body radiation characteristics, and determination of appropriate contact parameters. Simulation results are presented exemplifying the key features of the model.

Physical model parameter optimisation for calibrated emulation of the Dallas Rangemaster Treble Booster guitar pedal

In this work we explore optimising parameters of a physical circuit model relative to input/output measurements, using the Dallas Rangemaster Treble Booster as a case study. A hybrid metaheuristic/gradient descent algorithm is implemented, where the initial parameter sets for the optimisation are informed by nominal values from schematics and datasheets. Sensitivity analysis is used to screen parameters, which informs a study of the optimisation algorithm against model complexity by fixing parameters. The results of the optimisation show a significant increase in the accuracy of model behaviour, but also highlight several key issues regarding the recovery of parameters.

Towards a Virtual-Acoustic String Instrument

In acoustic instruments, the controller and the sound producing system often are one and the same object. If virtualacoustic instruments are to be designed to not only simulate the vibrational behaviour of a real-world counterpart but also to inherit much of its interface dynamics, it would make sense that the physical form of the controller is similar to that of the emulated instrument. The specific physical model configuration discussed here reconnects a (silent) string controller with a modal synthesis string resonator across the real and virtual domains by direct routing of excitation signals and model parameters. The excitation signals are estimated in their original force-like form via careful calibration of the sensor, making use of adaptive filtering techniques to design an appropriate inverse filter. In addition, the excitation position is estimated from sensors mounted under the legs of the bridges on either end of the prototype string controller. The proposed methodology is explained and exemplified with preliminary results obtained with a number of off-line experiments.