A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

Reply to comment by A. G. J. Hilberts and P. A. Troch on "Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling"

We thank Hilberts and Troch [2006] for their comment on our paper [Cartwright et al, 2005]. Before proceeding with our specific replies to the comments we would first like to clarify the definitions and meanings of equations (1)-(3) as presented by Hilberts and Troch [2006]. First, equation (1) is the fundamental definition of the (complex) effective porosity as derived by Nielsen and Perrochet [2000]. Equations (2) and (3), however, represent the linear frequency response function of the water table in the sand column responding to simple harmonic forcing. This function, which was validated by Nielsen and Perrochet [2000], provides an alternative method for estimating the complex effective porosity from the experimental sand column data in the absence of direct measurements of h_(tot) (which are required if equation (1) is to be used).

Bandwidth considerations for multilevel converters

Multilevel converters can achieve an overall effective switch frequency multiplication and consequent ripple reduction through the cancellation of the lowest order switch frequency terms. This paper investigates the harmonic content and the frequency response of these multimodulator converters. It is shown that the transfer function of uniformly sampled modulators is a bessel function associated with the inherent sampling process. Naturally sampled modulators have a flat transfer function, but multiple switchings per switch cycle will occur unless the input is slew-rate limited. Lower sideband harmonics of the effective carrier frequency and, in uniform converters, harmonics of the input signal also limit the useful bandwidth. Observations about the effect of the number of converters, their type (naturally or uniformly sampled), and the ratio of modulating frequency and switch frequency are made.

Superior electric double layer capacitors using ordered mesoporous carbons

This paper reports for the first time superior electric double layer capacitive properties of ordered mesoporous carbon (OMCs) with varying ordered pore symmetries and mesopore structure. Compared to commercially used activated carbon electrode, Maxsorb, these OMC carbons have superior capacitive behavior, power output and high-frequency performance in EDLCs due to the unique structure of their mesopore network, which is more favorable for fast ionic transport than the pore networks in disordered microporous carbons. As evidenced by N-2 sorption, cyclic voltammetry and frequency response measurements, OMC carbons with large mesopores, and especially with 2-D pore symmetry, show superior capacitive behaviors (exhibiting a high capacitance of over 180 F/g even at very high sweep rate of 50 mV/s, as compared to much reduced capacitance of 73 F/g for Maxsorb at the same sweep rate). OMC carbons can provide much higher power density while still maintaining good energy density. OMC carbons demonstrate excellent high-frequency performances due to its higher surface area in pores larger than 3 nm. Such ordered mesoporous carbons (OMCs) offer a great potential in EDLC capacitors, particularly for applications where high power output and good high-frequency capacitive performances are required. (C) 2005 Elsevier Ltd. All rights reserved.

Analysis of Piezoelectric sensor to detect flexural waves

The electromechanical transfer characteristics of adhesively bonded piezoelectric sensors are investigated. By the use of dynamic piezoelectricity theory, Mindlin plate theory for flexural wave propagation, and a multiple integral transform method, the frequency-response functions of piezoelectric sensors with and without backing materials are developed and the pressure-voltage transduction functions of the sensors calculated. The corresponding simulation results show that the sensitivity of the sensors is not only dependent on the sensors' inherent features, such as piezoelectric properties and geometry, but also on local characteristics of the tested structures and the admittance and impedance of the attached electrical circuit. It is also demonstrated that the simplified rigid mass sensor model can be used to analyze successfully the sensitivity of the sensor at low frequencies, but that the dynamic piezoelectric continuum model has to be used for higher frequencies, especially around the resonance frequency of the coupled sensor-structure vibration system.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

The functional roles of passive electroreception in non-electric fishes

Passive electroreception is a complex and specialised sense found in a large range of aquatic vertebrates primarily designed for the detection of weak bioelectric fields. Particular attention has traditionally focused on cartilaginous fishes, but a range of teleost and non-teleost fishes from a diversity of habitats have also been examined. As more species are investigated, it has become apparent that the role of electroreception in fishes is not restricted to locating prey, but is utilised in other complex behaviours. This paper presents the various functional roles of passive electroreception in non-electric fishes, by reviewing much of the recent research on the detection of prey in the context of differences in species' habitat (shallow water, deep-sea, freshwater and saltwater). A special case study on the distribution and neural groupings of ampullary organs in the omnihaline bull shark, Carcharhinus leucas, is also presented and reveals that prey-capture, rather than navigation, may be an important determinant of pore distribution. The discrimination between potential predators and conspecifics and the role of bioelectric stimuli in social behaviour is discussed, as is the ability to migrate over short or long distances in order to locate environmentally favourable conditions. The various theories proposed regarding the importance and mediation of geomagnetic orientation by either an electroreceptive and/or a magnetite-based sensory system receives particular attention. The importance of electroreception to many species is emphasised by highlighting what still remains to be investigated, especially with respect to the physical, biochemical and neural properties of the ampullary organs and the signals that give rise to the large range of observed behaviours.

The influence of joint position on the dynamics of perception-action coupling

Six right-handed subjects performed rhythmic flexion and extension movements of the index finger in time with an auditory metronome. On each block of trials, the wrist of the response hand was placed in a extended, neutral or flexed position. In the flex-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger flexion with each beat of the metronome. In the extend-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger extension with each beat of the metronome. The frequency of the metronome was increased from 2.00 Hz to 3.75 Hz in 8 steps (8 s epochs) of 0.25 Hz. During trials prepared in the extend-on-the-beat pattern, all subjects exhibited transitions to either a flex-on-the-beat pattern or to phase wandering as the frequency of pacing was increased. The time at which these transitions occurred was reliably influenced by the position of the wrist. Four subjects exhibited qualitative departures from the flex-on-the-beat pattern at pacing frequencies that were greater than those at which the extend-on-the-beat pattern could be maintained. The lime at which these departures occurred was not influenced by the position of the wrist. These results are discussed with reference to the constraints imposed on the coordination dynamics by the intrinsic properties of the neuromuscular-skeletal system.

Influence of hysteresis on tidal capillary fringe dynamics in a well-sorted sand

Nielsen and Perrochet [Adv. Water Resour. 23 (2000) 503] presented experimental data for cyclic water movement in the vadose zone above an oscillating watertable. The response of the watertable to cyclic forcing was characterised by the ratios of the forcing head to watertable amplitudes and their associated phase lag. They found that their non-hysteretic Richards' equation model failed to represent the observed behaviour of these parameters. This paper explores the effect on the simulated capillary fringe dynamics (in terms of these parameters) of including varying degrees of hysteresis in the moisture retention curve used in a numerical model of their experiment. It is clear that hysteresis can indeed account for observed discrepancies between simulation and experiment and that the effect of hysteresis varies with the frequency of oscillation. The use of a single-valued mean retention curve, as advocated by some authors, fails to provide a match between the simulated and observed behaviour of the Nielsen and Perrochet parameters, but is shown to be adequate for predicting time-averaged soil moisture profiles. (C) 2003 Elsevier Ltd. All rights reserved.