Stochastic Engine Research Articles

Faster Uphill Relaxation in Thermodynamically Equidistant Temperature Quenches.

We uncover an unforeseen asymmetry in relaxation: for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in the case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth single-well potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines.

Systematic parameter space study for the UHECR origin from GRBs in models with multiple internal shocks

ABSTRACT We scrutinize the paradigm that conventional long-duration gamma-ray bursts (GRBs) are the dominant source of the ultrahigh energy cosmic rays (UHECRs) within the internal shock scenario by describing UHECR spectrum and composition and by studying the predicted (source and cosmogenic) neutrino fluxes. Since it has been demonstrated that the stacking searches for astrophysical GRB neutrinos strongly constrain the parameter space in single-zone models, we focus on the dynamics of multiple collisions for which different messengers are expected to come from different regions of the same object. We propose a model that can describe both stochastic and deterministic engines, which we study in a systematic way. We find that GRBs can indeed describe the UHECRs for a wide range of different model assumptions with comparable quality albeit with the previously known problematic energy requirements; the heavy mass fraction at injection is found to be larger than 70 per cent ($95 {{\ \rm per\ cent}}$ CL). We demonstrate that the post-dicted (from UHECR data) neutrino fluxes from sources and UHECR propagation are indeed below the current sensitivities but will be reached by the next generation of experiments. We finally critically review the required source energetics with the specific examples found in this study.

Fast-forward approach to stochastic heat engine.

The fast-forward (FF) scheme proposed by Masuda and Nakamura [Proc. R. Soc. A 466, 1135 (2010)1364-502110.1098/rspa.2009.0446] in the context of conservative quantum dynamics can reproduce a quasistatic dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high- (T_{h}) and low- (T_{c}) temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally adiabatic processes and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency η at the maximum power of this engine is found to be η^{*}=1/2{1+1/2(T_{c}/T_{h})^{1/2}-5/4T_{c}/T_{h}+O[(T_{c}/T_{h})^{3/2}]} and η^{*}=1-(T_{c}/T_{h})^{1/2}, respectively, in the cases of strong and weak dissipation. The result is justified for a wide family of time-scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.

Stochastic Floquet quantum heat engines and stochastic efficiencies.

Based on the notion of quantum trajectory, we present a stochastic theoretical framework for Floquet quantum heat engines. As an application, the large deviation functions of two types of stochastic efficiencies for a two-level Floquet quantum heat engine are investigated. We find that the statistics of one efficiency agree well with the predictions of the universal theory of efficiency fluctuations developed by Verley etal. [Phys. Rev. E 90, 052145 (2014)10.1103/PhysRevE.90.052145], whereas the statistics of the other efficiency do not. The reason for this discrepancy is attributed to the lack of fluctuation theorems for the latter type of efficiency.

Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition.

We study the efficiency fluctuations of a stochastic heat engine made of N interacting unicyclic machines and undergoing a phase transition in the macroscopic limit. Depending on N and on the observation time, the machine can explore its whole phase space or not. This affects the engine efficiency that either strongly fluctuates on a large interval of equiprobable efficiencies (ergodic case) or fluctuates close to several most likely values (nonergodic case). We also provide a proof that despite the phase transition, the decay rate of the efficiency distribution at the reversible efficiency remains largest one although other efficiencies can now decay equally fast.

Thermodynamic uncertainty relations under arbitrary control protocols

Thermodynamic uncertainty relations quantifying a trade-off between current fluctuation and entropy production have been found in various stochastic systems. Herein, we study the thermodynamic uncertainty relations for Langevin systems driven by an external control protocol. Using information-theoretic techniques, we derive the uncertainty relations for arbitrary observables satisfying a scaling condition in both overdamped and underdamped regimes. We prove that the observable fluctuation is constrained by both entropy production and a kinetic term. The derived bounds are applicable to both current and noncurrent observables, and hold for arbitrary time-dependent protocols, thus, providing a wide range of applicability. We illustrate our universal bounds with the help of three systems: a dragged Brownian particle, a Brownian gyrator, and a stochastic underdamped heat engine.

Efficient simulation and auto-calibration of soot particle processes in Diesel engines

Parameters describing soot particle processes are generally derived from a limited number of experimental studies. These parameters then have to be carefully calibrated for different operating conditions in internal combustion engine applications. This paper presents an innovative calibration procedure for soot simulation in Diesel engines. A Diesel engine is simulated using the Stochastic Reactor Model engine code, which is implemented with the Moment Projection Method for handling the soot particle dynamics. The main advantage of the engine-soot model is its low computational cost. The model is then coupled with an advanced statistical toolkit, Model Development Suite, where the Hooke-Jeeves algorithm is adopted to calibrate seven soot model parameters automatically based on the measurement data. The ability of the integrated code for soot model calibration is evaluated by simulating the soot formation and oxidation processes in a heavy-duty Diesel engine which is operated under 18 different conditions. Results suggest that the integrated code is able to calibrate the soot model parameters effectively. A significant improvement in the match between the simulation results and experimental soot emission is obtained after calibration.

The computational complexity of Angry Birds

The physics-based simulation game Angry Birds has been heavily researched by the AI community over the past five years, and has been the subject of a popular AI competition that is currently held annually as part of a leading AI conference. Developing intelligent agents that can play this game effectively has been an incredibly complex and challenging problem for traditional AI techniques to solve, even though the game is simple enough that any human player could learn and master it within a short time. In this paper we analyse how hard the problem really is, presenting several proofs for the computational complexity of Angry Birds. By using a combination of several gadgets within this game's environment, we are able to demonstrate that the decision problem of solving general levels for different versions of Angry Birds is either NP-hard, PSPACE-hard, PSPACE-complete or EXPTIME-hard. Proof of NP-hardness is by reduction from 3-SAT, whilst proof of PSPACE-hardness is by reduction from True Quantified Boolean Formula (TQBF). Proof of EXPTIME-hardness is by reduction from G2, a known EXPTIME-complete problem similar to that used for many previous games such as Chess, Go and Checkers. To the best of our knowledge, this is the first time that a single-player game has been proven EXPTIME-hard. This is achieved by using stochastic game engine dynamics to effectively model the real world, or in our case the physics simulator, as the opponent against which we are playing. These proofs can also be extended to other physics-based games with similar mechanics.

Elements of a stochastic 3D prediction engine in larval zebrafish prey capture.

The computational principles underlying predictive capabilities in animals are poorly understood. Here, we wondered whether predictive models mediating prey capture could be reduced to a simple set of sensorimotor rules performed by a primitive organism. For this task, we chose the larval zebrafish, a tractable vertebrate that pursues and captures swimming microbes. Using a novel naturalistic 3D setup, we show that the zebrafish combines position and velocity perception to construct a future positional estimate of its prey, indicating an ability to project trajectories forward in time. Importantly, the stochasticity in the fish's sensorimotor transformations provides a considerable advantage over equivalent noise-free strategies. This surprising result coalesces with recent findings that illustrate the benefits of biological stochasticity to adaptive behavior. In sum, our study reveals that zebrafish are equipped with a recursive prey capture algorithm, built up from simple stochastic rules, that embodies an implicit predictive model of the world.

A joint moment projection method and maximum entropy approach for simulation of soot formation and oxidation in diesel engines

A joint moment projection method and maximum entropy approach for treating the soot population balance equations is developed and presented in this work. The moment projection method is used to solve the population balance equations and generate moments that are supplied to the maximum entropy approach as a post-processing technique to reconstruct the soot particle size distribution. The particle size range required by the maximum entropy for particle size distribution reconstruction is determined based on the weighted particles generated in the moment projection method. The performance of the joint approach is first evaluated by solving a set of simplified population balance equations in MatLab, then it is implemented into a Stochastic Reactor Model engine code to simulate the formation and oxidation of soot particles in a single-cylinder direct injection diesel engine. Results suggest that the joint approach has the advantages of ease of implementation, high accuracy and low computational cost. It enables a detailed analysis on the soot formation and oxidation processes in diesel engines. Complete information on the soot particle size distribution can be provided with little CPU cost induced.

Integral fluctuation relations for entropy production at stopping times

A stopping time T is the first time when a trajectory of a stochastic process satisfies a specific criterion. In this paper, we use martingale theory to derive the integral fluctuation relation for the stochastic entropy production in a stationary physical system at stochastic stopping times T. This fluctuation relation implies the law , which states that it is not possible to reduce entropy on average, even by stopping a stochastic process at a stopping time, and which we call the second law of thermodynamics at stopping times. This law bounds the average amount of heat and work a system can extract from its environment when stopped at a random time. Furthermore, the integral fluctuation relation implies that certain fluctuations of entropy production are universal or are bounded by universal functions. These universal properties descend from the integral fluctuation relation by selecting appropriate stopping times: for example, when T is a first-passage time for entropy production, then we obtain a bound on the statistics of negative records of entropy production. We illustrate these results on simple models of nonequilibrium systems described by Langevin equations and reveal two interesting phenomena. First, we demonstrate that isothermal mesoscopic systems can extract on average heat from their environment when stopped at a cleverly chosen moment and that the second law at stopping times bounds the average extracted heat. Second, we demonstrate that the efficiency at stopping times of an autonomous stochastic heat engine, such as Feymann’s ratchet, can be larger than the Carnot efficiency and that the second law of thermodynamics at stopping times bounds its efficiency at stopping times.

Stochastic Novikov Engine with Fourier Heat Transport

Abstract The Stochastic Novikov engine is an endoreversible model for heat engines where the heat supply takes place at a fluctuating temperature. These fluctuations can be observed for example at solar thermal power plants. While recently the influence of the temperature fluctuations on the engine’s performance has been studied for Newtonian heat transport, the relation between the used heat transport type and the performance measures remained open. Therefore, we here consider a Stochastic Novikov engine with Fourier heat transport. Based on a short summary of the concept of a Stochastic Novikov engine and the corresponding different control types, the maximum work output and the corresponding efficiency are derived. In particular, we discuss the influence of the distribution’s parameters on the engine’s performance assuming a uniform temperature distribution. We find that the heat transport type has a significant effect on some of the engine’s fundamental properties.

Proposal of a Realistic Stochastic Rotor Engine Based on Electron Shuttling

We propose and analyse an autonomous engine, which combines ideas from electronic transport and self-oscillating heat engines. It is based on the electron-shuttling mechanism in conjunction with a rotational degree of freedom. We focus in particular on the isothermal regime, where chemical work is converted into mechanical work or vice versa, and we especially pay attention to use parameters estimated from experimental data of available single components. Our analysis shows that for these parameters the engine already works remarkably stable, albeit with moderate efficiency. Moreover, it has the advantage that it can be up-scaled to increase power and reduce fluctuations further.

Evaluation of zero-dimensional stochastic reactor modelling for a Diesel engine application

Prediction of engine-out emissions with high fidelity from in-cylinder combustion simulations is still a significant challenge early in the engine development process. This article contributes to this fast evolving body of knowledge by focusing on the evaluation of NO x emission prediction capability of a probability density function–based stochastic reactor engine models for a Diesel engine. The research implements a systematic approach to the study of the stochastic reactor engine model performance, underpinned by a detailed space-filling design of experiments (DoE)-based sensitivity analysis of both external and internal parameters, evaluating their effects on the accuracy in matching physical measurements of both in-cylinder conditions and NO x output. The approach proposed in this article introduces an automatic stochastic reactor engine model calibration methodology across the engine operating envelope, based on a multi-objective optimization approach. This aims to exploit opportunities for internal stochastic reactor engine model parameters tuning to achieve good overall modelling performance as a trade-off between physical in-cylinder measurements accuracy and the output NO x emission predictions error. The results from the case study provide a valuable insight into the effectiveness of the stochastic reactor engine model, showing good capability for NO x emissions prediction and trends, while pointing out the critical sensitivity to the external input parameters and modelling conditions.

Optimisation of a class of heat engines with explicit solution

A specific class of stochastic heat engines driven cyclically by time-dependent potential, which is defined in the half-line (0<x<+∞), is analysed. For such engines, most of their physical quantities can be obtained explicitly, including the entropy and internal energy of the heat engine, as well as output work (power) and heat exchange with the environment during a finite time interval. The optimisation method based on the external potential to reduce irreversible work and increase energy efficiency is presented. With this optimised potential, efficiency η∗ and its particular value at maximum power ηEMP∗ are calculated and discussed briefly.

An out-of-equilibrium non-Markovian quantum heat engine

We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.

Probabilistic Fatigue Software Platform (ProbFat) for Optimizing Life-Cycle Decisions

Fatigue is inherently uncertain. Thus, the use of technology for prediction of fatigue damage to ensure the long-term reliability of equipment must embrace such uncertainty. The proposed probabilistic fatigue software platform (ProbFat) accomplishes just that. The stochastic engine behind ProbFat is a collection of Bayesian Decision Networks (BDN) that assess risk to recommend the optimal life-cycle strategy for maximizing overall return (i.e. return = benefit – cost). Benefit is a measure of profitability (e.g. annualized revenue) and cost is a measure of expense (e.g. design, inspection, repair, replacement, failure, et cetera). To optimize the return, the BDN must incorporate all aspects of LCM including: (i) design and construction, (ii) monitoring, inspection, and maintenance scheduling, (iii) identification of damage, (iv) assessment of observed damage, and (v) decision strategies to either run, repair, rerate, replace, or retire the component(s) of interest at the best possible times. BDNs are structured as graphical cause-effect relationships, represented by probabilistic nodes with directional links. Populating conditional probabilities associated with nodes is accomplished through assessment of laboratory and site-specific data, contributions from subject matter experts and simulations from in-house deterministic and stochastic fatigue models. In this paper, two industry examples are used to demonstrate the effectiveness of ProbFat: (i) low cycle thermo-mechanical fatigue of a coke drum, and (ii) very-high cycle vibration fatigue of a piping system. For both applications the fatigue methods available in API 579-1/ASME FFS-1 are utilized for deterministic/probabilistic prediction of fatigue damage accumulation and remaining life. Methods available in API RBI are used for inspection planning and maintenance scheduling.

Ca2+ Requirements for Long-Term Depression Are Frequency Sensitive in Purkinje Cells.

Cerebellar long-term depression (LTD) is a form of synaptic plasticity dependent on postsynaptic Ca2+ changes. One fundamental question is how LTD is selectively induced by specific numbers of Ca2+ pulses and which are the frequency and duration of this train of pulses required for LTD induction. The molecular mechanism which leads the integration of postsynaptic Ca2+ pulses in the LTD signaling network has not been elucidated either. Recent publications have shown that Ca2+/calmodulin-dependent protein kinase II (CaMKII) is required for LTD induction. Additionally, protein kinase C (PKC), CaMKII, and MAPK play an important role to transduce the frequency of Ca2+ pulses into their enzymatic activity levels; however, it is still unknown which enzymes are involved in decoding Ca2+ pulses in LTD. We have extended a stochastic model of LTD by adding the molecular network regulating CaMKII activity and its activation. We solved this model with stochastic engine for pathway simulation to include the effect of biochemical noise in LTD. We systematically investigated the dependence of LTD induction on stimulus frequencies, and we found that LTD is selectively induced by a specific number of Ca2+ spikes at different frequencies. We observed that CaMKII is essential to induce LTD, and LTD is only weakly induced when its Thr286 phosphorylation site has been deleted. We found that CaMKII decodes the frequency of Ca2+ spikes into different amounts of kinase activity during LTD induction. In addition, PKC and ERK enzyme activity is highly sensitive to the frequency and the number of Ca2+ pulses and this sensitivity has an important effect on LTD activation. This research predicts the postsynaptic Ca2+ requirements to induce LTD using a typical synaptic activation sequence and explains how LTD is selectively induced by specific number of Ca2+ pulses at different frequencies.

Stochastic heat engine powered by active dissipation

Thermodynamics of nanoscale devices is an active area of research. Despite their noisy surroundings, they often produce mechanical work (e.g. micro-heat engines) and display rectified Brownian motion (e.g. molecular motors). This invokes research in terms of experimentally quantifiable thermodynamic efficiencies. Here, a Brownian particle is driven by a harmonic confinement with time-periodic contraction and expansion. This system produces work by being alternately (time-periodically) connected to baths with different dissipations. We analyze the system theoretically using stochastic thermodynamics. Averages of thermodynamic quantities like work, heat, efficiency, entropy are found analytically for long cycle-times. Simulations are also performed in various cycle-times. They show excellent agreement with analytical calculations in the long-cycle time limit. Distributions of work, efficiency, and large deviation function for efficiency are studied using simulations. We believe that the experimental realization of our model is possible.

Stochastic Novikov engine with time dependent temperature fluctuations

In this article a Stochastic Novikov engine is used to model a solar power plant. This heat engine is characterized by a fluctuating hot heat bath temperature. The distribution function of these fluctuations is derived based on a stochastic solar irradiation model. Using this distribution the control problem of determining the maximum of the expected work output is solved. This work output as well as the corresponding efficiency is deduced in dependence of the chosen control type. Considering this work output and this efficiency, which can be considered as performance measures of the solar power plant, the influence of the system parameters is discussed. It turns out that these performance measures increase monotonously with the parameter of the hot temperature’s distribution function and that more control leads to higher efficiencies.