Hartle's model within the general theory of perturbatiye matchings: the change in mass

Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged.

Low Effort L-i Nuclear Fusion Plasma Control Using Model Predictive Control Laws

One of the main problems of fusion energy is to achieve longer pulse duration by avoiding the premature reaction decay due to plasma instabilities. The control of the plasma inductance arises as an essential tool for the successful operation of tokamak fusion reactors in order to overcome stability issues as well as the new challenges specific to advanced scenarios operation. In this sense, given that advanced tokamaks will suffer from limited power available from noninductive current drive actuators, the transformer primary coil could assist in reducing the power requirements of the noninductive current drive sources needed for current profile control. Therefore, tokamak operation may benefit from advanced control laws beyond the traditionally used PID schemes by reducing instabilities while guaranteeing the tokamak integrity. In this paper, a novel model predictive control (MPC) scheme has been developed and successfully employed to optimize both current and internal inductance of the plasma, which influences the L-H transition timing, the density peaking, and pedestal pressure. Results show that the internal inductance and current profiles can be adequately controlled while maintaining the minimal control action required in tokamak operation.

Effects of El Niño events on energy demand and egg production of rockfish (Scorpaenidae: Sebastes): a bioenergetics approach

Fish bioenergetics models estimate relationships between energy budgets and environmental and physiological variables. This study presents a generic rockfish (Sebastes) bioenergetics model and estimates energy consumption by northern California blue rockf ish (S. mystinus) under average (baseline) and El Niño conditions. Compared to males, female S. mystinus required more energy because they were larger and had greater reproductive costs. When El Niño conditions (warmer temperatures; lower growth, condition, and fecundity) were experienced every 3−7 years, energy consumption decreased on an individual and a per-recruit basis in relation to baseline conditions, but the decrease was minor (<4% at the individual scale, <7% at the per-recruit scale) compared to decreases in female egg production (12−19% at the individual scale, 15−23% at the per-recruit scale). When mortality in per-recruit models was increased by adding fishing, energy consumption in El Niño models grew more similar to that seen in the baseline model. However, egg production decreased significantly — an effect exacerbated by the frequency of El Niño events. Sensitivity analyses showed that energy consumption estimates were most sensitive to respiration parameters, energy density, and female fecundity, and that estimated consumption increased as parameter uncertainty increased. This model provides a means of understanding rockfish trophic ecology in the context of community structure and environmental change by synthesizing metabolic, demographic, and environmental information. Future research should focus on acquiring such information so that models like the bioenergetics model can be used to estimate the effect of climate change, community shifts, and different harvesting strategies on rockfish energy demands.

Linking energy policy, electricity generation and transmission using strong sustainability and co-optimization

The design of a sustainable electricity generation and transmission system is based on the established science of anthropogenic climate change and the realization that depending on imported fossil-fuels is becoming a measure of energy insecurity of supply. A model is proposed which integrates generation fuel mix composition, assignment of plants and optimized power flow, using Portugal as a case study. The result of this co-optimized approach is an overall set of generator types/fuels which increases the diversity of Portuguese electricity supply, lowers its dependency on imported fuels by 14.62% and moves the country towards meeting its regional and international obligations of 31% energy from renewables by 2020 and a 27% reduction in greenhouse gas emissions by 2012, respectively. The quantity and composition of power generation at each bus is specified, with particular focus on quantifying the amount of distributed generation. Based on other works, the resultant, overall distributed capacity penetration of 19.02% of total installed generation is expected to yield positive network benefits. Thus, the model demonstrates that national energy policy and technical deployment can be linked through sustainability and, moreover, that the respective goals may be mutually achieved via holistic, integrated design. ©2009 IEEE.

Material model of lung parenchyma based on living precision-cut lung slice testing.

We describe a novel constitutive model of lung parenchyma, which can be used for continuum mechanics based predictive simulations. To develop this model, we experimentally determined the nonlinear material behavior of rat lung parenchyma. This was achieved via uni-axial tension tests on living precision-cut rat lung slices. The resulting force-displacement curves were then used as inputs for an inverse analysis. The Levenberg-Marquardt algorithm was utilized to optimize the material parameters of combinations and recombinations of established strain-energy density functions (SEFs). Comparing the best-fits of the tested SEFs we found Wpar = 4.1 kPa(I1-3)2 + 20.7 kPa(I1 - 3)3 + 4.1 kPa(-2 ln J + J2 - 1) to be the optimal constitutive model. This SEF consists of three summands: the first can be interpreted as the contribution of the elastin fibers and the ground substance, the second as the contribution of the collagen fibers while the third controls the volumetric change. The presented approach will help to model the behavior of the pulmonary parenchyma and to quantify the strains and stresses during ventilation.

Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.

Optimizing the energy output of vertical axis wind turbines for fluctuating wind conditions

The control of a wind turbine to the mean wind speed in a gusty wind results in very poor performance. Fluctuations in wind speed with time constants shorter than the response time of a wind turbine results in operation away from optimum design conditions. The effectiveness of a turbine operating in a gusty wind is shown though the use of an unsteady performance coefficient, C e. This performance coefficient is similar in form to a power coefficient. However in order to accommodate unsteady effects, Ce is defined as a ratio of energy extracted to the total wind energy available over a set time period. The turbine's response to real wind data is modelled, in the first instance, by assuming a constant rotational speed operation. It is shown that a significant increase in energy production can be realized by demanding a Tip Speed Ratio above the steady state optimum. The constant speed model is then further extended to incorporate inertial and controller effects. Parameters dictating how well a turbine can track a demand in Tip Speed Ratio have been identified and combined, to form a non-dimensional turbine response parameter. This parameter characterizes a turbine's ability to track a demand in Tip Speed Ratio dependent on an effective gust frequency. A significant increase in energy output of 42% and 245% is illustrated through the application of this over-speed control. This is for the constant rotational speed and Tip Speed Ratio feedback models respectively. The affect of airfoil choice on energy extraction within a gusty wind has been considered. The adaptive control logic developed enables the application of airfoils demonstrating high maximum L/D values but sharp stalling characteristics to be successfully used in a VAWT design.

TOPS (Task optimization in the presence of signal-dependent noise) model

This paper proposes a movement trajectory planning model, which is a maximum task achievement model in which signal-dependent noise is added to the movement command. In the proposed model, two optimization criteria are combined, maximum task achievement and minimum energy consumption. The proposed model has the feature that the end-point boundary conditions for position, velocity, and acceleration need not be prespecified. Consequently, the method can be applied not only to the simple point-to-point movement, but to any task. In the method in this paper, the hand trajectory is derived by a psychophysical experiment and a numerical experiment for the case in which the target is not stationary, but is a moving region. It is shown that the trajectory predicted from the minimum jerk model or the minimum torque change model differs considerably from the results of the psychophysical experiment. But the trajectory predicted from the maximum task achievement model shows good qualitative agreement with the hand trajectory obtained from the psychophysical experiment. © 2004 Wiley Periodicals, Inc.

Investigation of the effect of combustor cooling geometry on acoustic energy absorption

To control combustion instabilities occurring in LPP gas turbine combustors, several active and passive systems have been developed in recent years. The combustion chamber cooling geometry has the potential to influence instability feedback loops by absorbing acoustical energy inside the combustor. The design of the cooling liner and the geometry of the cooling plenum and the cooling air flow rate have a significant influence on the absorption characteristics of the system. This paper presents the results of a cold flow study which was carried out in the course of a comprehensive study on the influence of the cooling geometry on combustor thermoacoustics. Absorption characteristics of three different cooling liner geometries and non-perforated plates were determined over a frequency range from 50 Hz to 600 Hz for different cooling flow rates and different cooling plenum volumes. The experimental results compared well with results from a low order thermoacoustic network model. The acoustic energy absorption spectrum of a cooling liner with 90°-hole configuration was found to be strongly dependent on cooling flow rate and cooling plenum volume, whereas the absorption spectrum of cooling liners with 25°-holes were found to be strongly dependent on the cooling plenum volume, but less dependent on the cooling air flow rate. All cooling liner setups with perforations were capable of increased acoustic absorption over a broad band of frequencies compared to the case of non-perforated combustor walls. © 2010 by Johannes Schmidt.

Dynamics of in-plane arch rocking: An energy approach

This study employs an analytical model to describe the rocking response of a masonry arch to in-plane seismic loading. Through evaluation of the rate of energy input to the system, the model reveals the ground motions that cause maximum rocking amplification. An experimental investigation of small-scale masonry arches subjected to past earthquake time histories is used to evaluate the analytical model and to explore arch rocking behaviour. The results demonstrate that rocking amplification can occur, but is highly sensitive to slight variations in the ground motion. Thus, the accuracy to which the arch response can be predicted is brought into perspective. The concept that the primary impulse of an expected ground motion is fundamentally important in predicting arch collapse is evaluated in light of the developed energy approach. Finally, a statistical method is proposed for predicting the probability of arch collapse during seismic loading.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.