Power-Optimal Control of a Stirling Engine's Frictional Piston Motion.

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin's maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method.

Cooling Cycle Optimization for a Vuilleumier Refrigerator.

Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We find improvements of the cooling power of more than 15%.

Endoreversible Modeling of a Hydraulic Recuperation System.

Hybrid drive systems able to recover and reuse braking energy of the vehicle can reduce fuel consumption, air pollution and operating costs. Among them, hydraulic recuperation systems are particularly suitable for commercial vehicles, especially if they are already equipped with a hydraulic system. Thus far, the investigation of such systems has been limited to individual components or optimizing their control. In this paper, we focus on thermodynamic effects and their impact on the overall systems energy saving potential using endoreversible thermodynamics as the ideal framework for modeling. The dynamical behavior of the hydraulic recuperation system as well as energy savings are estimated using real data of a vehicle suitable for application. Here, energy savings accelerating the vehicle around 10% and a reduction in energy transferred to the conventional disc brakes around 58% are predicted. We further vary certain design and loss parameters-such as accumulator volume, displacement of the hydraulic unit, heat transfer coefficients or pipe diameter-and discuss their influence on the energy saving potential of the system. It turns out that heat transfer coefficients and pipe diameter are of less importance than accumulator volume and displacement of the hydraulic unit.

Optimized Piston Motion for an Alpha-Type Stirling Engine.

The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of dissipative processes. In order to ensure the possibility of a technical implementation and the simplicity of the optimization, we restrict the possible piston movements to a parametrized class of smooth piston motions. In this theoretical study the engine model is based on endoreversible thermodynamics, which allows us to incorporate non-equilibrium heat and mass transfer as well as the friction of the piston motion. The regenerator of the Stirling engine is modeled as ideal. An investigation of the impact of the individual loss mechanisms on the resulting optimized motion is carried out for a wide range of parameter values. We find that an optimization within our restricted piston motion class leads to a power gain of about 50% on average.

Modeling, Simulation, and Reconstruction of 2-Reservoir Heat-to-Power Processes in Finite-Time Thermodynamics.

The connection between endoreversible models of Finite-Time Thermodynamics and the corresponding real running irreversible processes is investigated by introducing two concepts which complement each other: Simulation and Reconstruction. In that context, the importance of particular machine diagrams for Simulation and (reconstruction) parameter diagrams for Reconstruction is emphasized. Additionally, the treatment of internal irreversibilities through the use of contact quantities like the contact temperature is introduced into the Finite-Time Thermodynamics description of thermal processes.

Performance Features of a Stationary Stochastic Novikov Engine.

In this article a Novikov engine with fluctuating hot heat bath temperature is presented. Based on this model, the performance measure maximum expected power as well as the corresponding efficiency and entropy production rate is investigated for four different stationary distributions: continuous uniform, normal, triangle, quadratic, and Pareto. It is found that the performance measures increase monotonously with increasing expectation value and increasing standard deviation of the distributions. Additionally, we show that the distribution has only little influence on the performance measures for small standard deviations. For larger values of the standard deviation, the performance measures in the case of the Pareto distribution are significantly different compared to the other distributions. These observations are explained by a comparison of the Taylor expansions in terms of the distributions' standard deviations. For the considered symmetric distributions, an extension of the well known Curzon-Ahlborn efficiency to a stochastic Novikov engine is given.

Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime.

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

Extending the parQ transition matrix method to grand canonical ensembles.

Phase coexistence properties as well as other thermodynamic features of fluids can be effectively determined from the grand canonical density of states (DOS). We present an extension of the parQ transition matrix method in combination with the efasTM method as a very fast approach for determining the grand canonical DOS from the transition matrix. The efasTM method minimizes the deviation from detailed balance in the transition matrix using a fast Krylov-based equation solver. The method allows a very effective use of state space transition data obtained by different exploration schemes. An application to a Lennard-Jones system produces phase coexistence properties of the same quality as reference data.

Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators.

We discuss fastest effectively adiabatic transitions (FEATs) for a collection of noninteracting harmonic oscillators with shared controllable real frequencies. The construction of such transitions is presented for given initial and final equilibrium states, and the dependence of the minimum time control on the interval of achievable frequencies is discussed. While the FEAT times and associated FEAT processes are important in their own right as optimal controls, the FEAT time is an added feature which provides a measure of the quality of a shortcut to adiabaticity (STA). The FEAT time is evaluated for a previously reported experiment, wherein a cloud of Rb atoms is cooled following a STA recipe that took about twice as long as the FEAT speed limit, a time efficiency of 50%.

A mathematical model for predicting lane changes using the steering wheel angle.

INTRODUCTION: Positive safety effects of advanced driver assistance systems can only become effective if drivers accept and use these systems. Early detection of driver's intention would allow for selective system activation and therefore reduce false alarms. METHOD: This driving simulator study aims at exploring early predictors of lane changes. In total, 3111 lane changes of 51 participants on a simulated highway track were analyzed. RESULTS: Results show that drivers stopped their engagement in a secondary task about 7s before crossing the lane, which indicates a first planning phase of the maneuver. Subsequently, drivers start moving toward the lane, marking a mean steering wheel angle of 2.5°. Steering wheel angle as a directly measurable vehicle parameter appears as a promising early predictor of a lane change. A mathematical model of the steering wheel angle is presented, which is supposed to contribute for predicting lane change maneuvers. PRACTICAL APPLICATIONS: The mathematical model will be part of a further predictor of lane changes. This predictor can be a new advanced driver assistance system able to recognize a driver's intention. With this knowledge, other systems can be activated or deactivated so drivers get no annoying and exhausting alarm signals. This is one way how we can increase the acceptance of assistance systems.

Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment.

Virtual deposition runs have been performed to estimate the production yield of selected oxide optical interference coatings when plasma ion-assisted deposition with an advanced plasma source is applied. Thereby, deposition of each layer can be terminated either by broadband optical monitoring or quartz crystal monitoring. Numerous deposition runs of single-layer coatings have been performed to investigate the reproducibility of coating properties and to quantify deposition errors for the simulation. Variations of the following parameters are considered in the simulation: refractive index, extinction coefficient, and film thickness. The refractive index and the extinction coefficient are simulated in terms of the oscillator model. The parameters are varied using an apodized normal distribution with known mean value and standard deviation. Simulation of variations in the film thickness is performed specific to the selected monitoring strategy. Several deposition runs of the selected oxide interference coatings have been performed to verify the simulation results by experimental data.

Threshold-selecting strategy for best possible ground state detection with genetic algorithms.

Genetic algorithms are a standard heuristic to find states of low energy in complex state spaces as given by physical systems such as spin glasses but also in combinatorial optimization. The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover. Many schemes have been considered in literature as possible crossover selection strategies. We show for a large class of quality measures that the best possible probability distribution for selecting individuals in each generation of the algorithm execution is a rectangular distribution over the individuals sorted by their energy values. This means uniform probabilities have to be assigned to a group of the individuals with lowest energy in the population but probabilities equal to zero to individuals which are corresponding to energy values higher than a fixed cutoff, which is equal to a certain rank in the vector sorted by the energy of the states in the current population. The considered strategy is dubbed threshold selecting. The proof applies basic arguments of Markov chains and linear optimization and makes only a few assumptions on the underlying principles and hence applies to a large class of algorithms.

Maximum work in minimum time from a conservative quantum system.

This paper considers the problem of obtaining maximum work from a conservative quantum system corresponding to a given change in an external parameter in the Hamiltonian. The example we present is a non-interacting collection of harmonic oscillators with a shared frequency omega which changes from a given initial to a given final value. The example is interesting for its role in experiments at ultra-low temperatures and for probing finite-time versions of the third law of thermodynamics. It is also the simplest system displaying quantum friction, which represents loss mechanisms in any reversible prelude to a thermal process. The example leads to a new type of availability. It is also the first example of a minimum time for transitions between thermal states of a thermodynamic system.

Power law rank-abundance models for marine phage communities.

Metagenomic analyses suggest that the rank-abundance curve for marine phage communities follows a power law distribution. A new type of power law dependence based on a simple model in which a modified version of Lotka-Volterra predator-prey dynamics is sampled uniformly in time is presented. Biologically, the model embodies a kill the winner hypothesis and a neutral evolution hypothesis. The model can match observed power law distributions and uses very few parameters that are readily identifiable and characterize phage ecosystems. The model makes new untested predictions: (1) it is unlikely that the most abundant phage genotype will be the same at different time points and (2) the long-term decay of isolated phage populations follows a power law.

Decreased plasma cholesterol levels during aging in transgenic mouse models of Alzheimer's disease.

A large number of studies deals with the association of cholesterol and Abeta levels, however, the results are so far controversial. Whereas some studies report on increased cholesterol levels, other authors refer to an association of decreased peripheral cholesterol and the incidence of Alzheimer's disease. It is also questionable whether plasma cholesterol levels could be used as a predictive biomarker for the incidence of Alzheimer's disease. In the present report, we studied the relationship between these two parameters during aging in different transgenic mouse models of Alzheimer's disease, expressing both mutant human amyloid precursor protein and mutant human presenilin-1. Measurements of plasma cholesterol levels revealed a significant reduction in aged APP/PS1 and APP/PS1ki mice, whereas plasma levels in young and aged control mice remained almost unchanged. Furthermore, statistical analysis revealed a significant negative correlation between plasma cholesterol and brain Abeta42 levels during aging in the mice expressing both APP and PS1.

Fitness threshold accepting over extremal optimization ranks.

We treat the problem of selecting the next degree of freedom for update in an extremal optimization algorithm designed to find the ground state of a system with a complex energy landscape. We show that there exists a best distribution for selecting the next degree of freedom in order to optimize any linear function of the state probabilities, e.g., the expected number of visits to the ground state. We dub the class of algorithms using this best distribution in conjunction with extremal optimization fitness threshold accepting. In addition, we construct an extended random walk and use it to show that fitness threshold accepting is optimal also for several other measures of algorithm performance, such as maximizing the expected probability of seeing the ground state and minimizing the expected value of the lowest energy seen.

Structure of best possible strategies for finding ground states.

Finding the ground state of a system with a complex energy landscape is important for many physical problems including protein folding, spin glasses, chemical clusters, and neural networks. Such problems are usually solved by heuristic search methods whose efficacy is judged by empirical performance on selected examples. We present a proof that for a wide range of objective functions threshold accepting is the best possible strategy within a large class of algorithms that simulate random walks on the landscape. In particular, it can perform better than simulated annealing, Tsallis and Glauber statistics.