Stochastic Engine Research Articles

Vesicle and reaction-diffusion hybrid modeling with STEPS

Vesicles carry out many essential functions within cells through the processes of endocytosis, exocytosis, and passive and active transport. This includes transporting and delivering molecules between different parts of the cell, and storing and releasing neurotransmitters in neurons. To date, computational simulation of these key biological players has been rather limited and has not advanced at the same pace as other aspects of cell modeling, restricting the realism of computational models. We describe a general vesicle modeling tool that has been designed for wide application to a variety of cell models, implemented within our software STochastic Engine for Pathway Simulation (STEPS), a stochastic reaction-diffusion simulator that supports realistic reconstructions of cell tissue in tetrahedral meshes. The implementation is validated in an extensive test suite, parallel performance is demonstrated in a realistic synaptic bouton model, and example models are visualized in a Blender extension module.

On the stochastic engine of contagious diseases in exponentially growing populations

The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth and death rates in comparison to disease parameters like the contact rate and the removal rate ensures that the globally stable endemic equilibrium corresponds to a tiny average proportion of infected individuals. Asymptotic equilibrium levels corresponding to low numbers of individuals invalidate the deterministic results.Diffusion effects force probability mass functions of the stochastic model to possess similar stability properties as the deterministic model. Particular simulations of the stochastic model predict, however, oscillatory patterns. Small and isolated populations show longer periods, more violent oscillations, and larger probabilities of extinction.We prove that evolution maximizes the infectiousness of the disease as measured by the ability to increase the proportion of infected individuals. This holds provided the stochastic oscillations are moderate enough to keep the proportion of susceptible individuals near a deterministic equilibrium.We close our paper with a discussion of the herd-immunity concept and stress its close relation to vaccination-programs.

Stochastic thermodynamic engines under time-varying temperature profile

A recently developed stochastic control formalism (Stochastic Thermodynamics) has opened for the first time the possibility to quantify energy exchange and entropy production in finite-time thermodynamic transitions, based on Langevin models for mesoscopic thermodynamic systems. Within this framework we quantify power output and efficiency of overdamped stochastic thermodynamic engines that are powered by a heat bath with temperature that varies periodically with time. Our setting is in contrast to most of the existing literature that considers the Carnot paradigm, alternating contact with heat baths having different fixed temperatures, hot and cold. Specifically, we consider a periodic and bounded but otherwise arbitrary temperature profile and derive explicit bounds on the power and efficiency achievable by a suitably controlling potential that couples the thermodynamic engine to the external world – the time-varying potential represents the control input to the system. A standing assumption in our analysis is that the norm of the gradient of the potentials is bounded – in the absence of any such constraint on the control input, the physically questionable conclusion of arbitrarily large power can be drawn.

Fuel Effects on the Onset of Knock and the Intensity of Superknock at Stochastic Preignition-Relevant Engine Conditions

<div>To have a more complete understanding of the fuel effects on each subsequent stage of a stochastic preignition event in a spark-ignition engine and to build on the previous work of understanding the propensity of fuel to initiate and sustain a preignition flame, this work is focused on examining the role of fuel on the onset of knock and the intensity of superknock once the unburned mixture reaches certain conditions ahead of the preignition flame. Using a “skip advance” spark test method to simulate preignition flames initiated at different cylinder conditions, more than 20 single- and multicomponent fuels were ranked based on the condition required to reach the onset of knock (the start of end-gas autoignition) and the condition that leads to severe superknock intensities. It was found that average knock intensity can be mainly explained by the unburn mixture fraction and the thermodynamic condition of the unburned mixture and, not surprisingly, that the fuel ranking for the onset of knock and superknock based on average knock intensity is correlated to octane index. However, outlier cycles with extremely high knock intensities cannot be fully explained by the average cycle behavior. More interestingly, different fuels exhibit different superknock characteristics. Some fuels, such as toluene, have fewer extreme cycles once the same average knock intensity condition is reached, whereas other fuels, such as ethanol, have more extreme cycles that tend to break engine hardware in a single cycle event. A preliminary study based on the modes of reaction front propagation show that fuels with low-temperature heat release and negative temperature coefficient (NTC) behavior can lead to a higher propensity to produce extreme knock intensities when coupled with the right in-cylinder pressure wave.</div>

Exploring outputs from concatenated stochastic heat engines

Abstract Recent work on the concatenation of two simple heat engines has shown that it may lead to non-monotonic variations in the efficiency and power with parameters like driving amplitudes and asymmetries in cycle periods. Motivated by this study, we investigate the effect of the concatenation between two stochastic heat engines where colloidal particles have been trapped in harmonic potentials. The stiffness parameters of each engine are varied cyclically, but with different cycle periods, with a common thermal bath that acts as a sink for the first engine but as a source for the second. We consider two types of protocol, the first where the trap strength undergoes sudden jumps, and the second where it varies linearly with time. In both we find several non-trivial effects, like the non-monotonic functional dependence of the engine outputs on several parameters used in the setup. For the protocol that varies linearly with time, the concatenation leads to enhanced output power as compared to a single effective engine, in a suitable range of parameters. It has been shown that the output from the combined system shows a peak with respect to the asymmetry in the cycle times of the engines that have been concatenated. A general relation for the efficiency of an arbitrary number of concatenated engines driven quasistatically has been provided.

Optimal performance of the stochastic thermodynamic engine with a periodic heat bath

Stochastic thermodynamics provides a conceptual framework for describing the fluctuating behavior of small systems like colloids or biomolecules far from thermodynamic equilibriums but still contacted with a heat bath. In contrast to most literature focusing on the classical paradigm of Carnot engines, we herein study the optimal performance of the thermodynamic heat engine with a heat bath that periodically changes temperature, which is outside controllable by a time-dependent harmonic potential. Under reasonable assumptions on the control actuation, we derive the achievable upper bound for the maximal power and also the optimal control protocol. In addition, we also obtain the corresponding efficiency at maximal power, which only depends on the ratio of the minimal and maximal value of the temperature profile.

Carnot, Stirling, and Ericsson stochastic heat engines: Efficiency at maximum power.

This work uses the low-dissipation strategy to obtain efficiency at maximum power from a stochastic heat engine performing Carnot-, Stirling- and Ericsson-like cycles at finite time. The heat engine consists of a colloidal particle trapped by optical tweezers, in contact with two thermal baths at different temperatures, namely hot (T_{h}) and cold (T_{c}). The particle dynamics is characterized by a Langevin equationwith time-dependent control parameters bounded to a harmonic potential trap. In a low-dissipation approach, the equilibrium properties of the system are required, which in our case, can be calculated through a statelike equationfor the mean value 〈x^{2}〉_{eq} coming from a macroscopic expression associated with the Langevin equation.

Stochastic wind farm flow generation using a reduced order model of LES

Large eddy simulations are computationally expensive, which typically limits the simulation time and hence the statistics useful for validation. Here, a reduced order model with a stochastic engine is used to generate stochastic inflow to 48 wind turbines in the Lillgrund wind farm. The stochastic flow realization captures the power production and more importantly the correct cross-correlations in power and blade root flapwise bending moments over the large spatiotemporal region, which the wind farm covers. The analysis show how the cross-correlation increase further into the wind farm, where the highly turbulent flow becomes increasingly self-organized and how the dynamic interaction across the entire wind farm is captured by the first eight modes. Overall, the reduced order model captures the correct dynamics at a fraction of the computational cost, effectively generalizing the LES results beyond a relatively short simulation period.

STEPS 4.0: Fast and memory-efficient molecular simulations of neurons at the nanoscale

Recent advances in computational neuroscience have demonstrated the usefulness and importance of stochastic, spatial reaction-diffusion simulations. However, ever increasing model complexity renders traditional serial solvers, as well as naive parallel implementations, inadequate. This paper introduces a new generation of the STochastic Engine for Pathway Simulation (STEPS) project (http://steps.sourceforge.net/), denominated STEPS 4.0, and its core components which have been designed for improved scalability, performance, and memory efficiency. STEPS 4.0 aims to enable novel scientific studies of macroscopic systems such as whole cells while capturing their nanoscale details. This class of models is out of reach for serial solvers due to the vast quantity of computation in such detailed models, and also out of reach for naive parallel solvers due to the large memory footprint. Based on a distributed mesh solution, we introduce a new parallel stochastic reaction-diffusion solver and a deterministic membrane potential solver in STEPS 4.0. The distributed mesh, together with improved data layout and algorithm designs, significantly reduces the memory footprint of parallel simulations in STEPS 4.0. This enables massively parallel simulations on modern HPC clusters and overcomes the limitations of the previous parallel STEPS implementation. Current and future improvements to the solver are not sustainable without following proper software engineering principles. For this reason, we also give an overview of how the STEPS codebase and the development environment have been updated to follow modern software development practices. We benchmark performance improvement and memory footprint on three published models with different complexities, from a simple spatial stochastic reaction-diffusion model, to a more complex one that is coupled to a deterministic membrane potential solver to simulate the calcium burst activity of a Purkinje neuron. Simulation results of these models suggest that the new solution dramatically reduces the per-core memory consumption by more than a factor of 30, while maintaining similar or better performance and scalability.

Probabilistic programming with stochastic variational message passing

Stochastic approximation methods for variational inference have recently gained popularity in the probabilistic programming community since these methods are amenable to automation and allow online, scalable, and universal approximate Bayesian inference. Unfortunately, common Probabilistic Programming Languages (PPLs) with stochastic approximation engines lack the efficiency of message passing-based inference algorithms with deterministic update rules such as Belief Propagation (BP) and Variational Message Passing (VMP). Still, Stochastic Variational Inference (SVI) and Conjugate-Computation Variational Inference (CVI) provide principled methods to integrate fast deterministic inference techniques with broadly applicable stochastic approximate inference. Unfortunately, implementation of SVI and CVI necessitates manually driven variational update rules, which does not yet exist in most PPLs. In this paper, we cast SVI and CVI explicitly in a message passing-based inference context. We provide an implementation for SVI and CVI in ForneyLab, which is an automated message passing-based probabilistic programming package in the open source Julia language. Through a number of experiments, we demonstrate how SVI and CVI extends the automated inference capabilities of message passing-based probabilistic programming.

Second moments of work and heat for a single-particle stochastic heat engine in a breathing harmonic potential

Abstract We consider a simple model of a stochastic heat engine, which consists of a single Brownian particle moving in a one-dimensional periodically breathing harmonic potential. The overdamped limit is assumed. Expressions for the second moments (variances and covariances) of heat and work are obtained in the form of integrals, whose integrands contain functions satisfying certain differential equations. The results in the quasi-static limit are simple functions of the temperatures of hot and cold thermal baths. The coefficient of variation of the work is suggested to give an approximate probability for the work to exceed a given threshold. During the derivation, we get the expression of the cumulant-generating function.

Modelling Asymmetric Unemployment Dynamics: The Logarithmic-Harmonic Potential Approach.

Asymmetric behaviour has been documented in unemployment rates which increase quickly in recessions but decline relatively slowly during expansions. To model such asymmetric dynamics, this paper provides a rigorous derivation of the asymmetric mean-reverting fundamental dynamics governing the unemployment rate based on a model of a simple labour supply and demand (fundamental) relationship, and shows that the fundamental dynamics is a unique choice following the Rayleigh process. By analogy, such a fundamental can be considered as a one-dimensional overdamped Brownian particle moving in a logarithmic–harmonic potential well, and a simple prototype of stochastic heat engines. The solution of the model equation illustrates that the unemployment rate rises faster with more flattened potential well of the fundamental, more ample labour supply, and less anchored expectation of the unemployment rate, suggesting asymmetric unemployment rate dynamics in recessions and expansions. We perform explicit calibration of both the unemployment rate and fundamental dynamics, confirming the validity of our model for the fundamental dynamics.

Borehole Geophysical Joint Inversion to Fully Evaluate Shaly Sandstone Formations

Simultaneous inversion of sonic, density, and electrical resistivity borehole-derived well logs, has been addressed in literature in recent years. However, this problem is not broadly studied for dual-porosity sandstone formations. In addition, most authors presumed salinity and matrix properties as known parameters in their studies. We integrate the conservation of mass to model density, a differential effective medium theory for elastic modeling, and a laboratory-supported model for electrical resistivity of dual-porosity sandstones. Utilizing this methodology, we simulate electrical resistivity, sonic, and density well-log data. We develop a stochastic global search engine to jointly invert petrophysical properties. We build a dual-porosity formation with associated petrophysical properties and show the proposed workflow accurately replicates true well-log responses in the oil column, water leg, and transition zone. Local petrophysical properties (microporosity, intergranular porosity, total porosity, and water saturation) and global model parameters (salinity, matrix properties, critical porosity, resistivity lithology exponents, and sonic length scales for different pore networks) are all well recovered. The developed multiphysics calibrated rock models will assist petrophysicists and seismic analysts to identify and distinguish sandstone facies characteristics from well-log and prestack seismic data.

Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance

We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the $L^2$-Wasserstein distance. Because the $L^2$-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency.

P systems in the time of COVID-19

In this paper, we present LOIMOS, which is an epidemiological scenario simulator developed in the context of the fight against the pandemic caused by coronavirus SARS-CoV-2 on a global scale. LOIMOS has been fully developed under the paradigm of membrane computing using transition P systems with communication rules, active membranes and a stochastic simulator engine. In this paper we detail the main components of the system and we report some examples of epidemiological scenarios evaluated with LOIMOS.

Underdamped stochastic thermodynamic engines in contact with a heat bath with arbitrary temperature profile.

We study thermodynamic processes in contact with a heat bath that may have an arbitrary time-varying periodic temperature profile. Within the framework of stochastic thermodynamics, and for models of thermodynamic engines in the idealized case of underdamped particles in the low-friction regime subject to a harmonic potential, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.

Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines.

In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global and local Onsager coefficients, defined over one cycle and at any instant of a cycle, respectively, is not derived. To address this limitation, we develop a linear response theory for the speed of adiabatically changing parameters and temperature differences in generic Gaussian heat engines obeying Fokker-Planck dynamics. We establish a hierarchical relationship between the global linear response relations, defined over one cycle of the heat engines, and the local ones, defined at any instant of the cycle. This yields a detailed expression for the global Onsager coefficients in terms of the local Onsager coefficients. Moreover, we derive an efficiency bound, which is tighter than the Carnot bound, for adiabatically driven linear irreversible heat engines based on the detailed global Onsager coefficients. Finally, we demonstrate the application of the theory using the simplest stochastic Brownian heat engine model.

Development of a Computationally Efficient Tabulated Chemistry Solver for Internal Combustion Engine Optimization Using Stochastic Reactor Models

The use of chemical kinetic mechanisms in computer aided engineering tools for internal combustion engine simulations is of high importance for studying and predicting pollutant formation of conventional and alternative fuels. However, usage of complex reaction schemes is accompanied by high computational cost in 0-D, 1-D and 3-D computational fluid dynamics frameworks. The present work aims to address this challenge and allow broader deployment of detailed chemistry-based simulations, such as in multi-objective engine optimization campaigns. A fast-running tabulated chemistry solver coupled to a 0-D probability density function-based approach for the modelling of compression and spark ignition engine combustion is proposed. A stochastic reactor engine model has been extended with a progress variable-based framework, allowing the use of pre-calculated auto-ignition tables instead of solving the chemical reactions on-the-fly. As a first validation step, the tabulated chemistry-based solver is assessed against the online chemistry solver under constant pressure reactor conditions. Secondly, performance and accuracy targets of the progress variable-based solver are verified using stochastic reactor models under compression and spark ignition engine conditions. Detailed multicomponent mechanisms comprising up to 475 species are employed in both the tabulated and online chemistry simulation campaigns. The proposed progress variable-based solver proved to be in good agreement with the detailed online chemistry one in terms of combustion performance as well as engine-out emission predictions (CO, CO2, NO and unburned hydrocarbons). Concerning computational performances, the newly proposed solver delivers remarkable speed-ups (up to four orders of magnitude) when compared to the online chemistry simulations. In turn, the new solver allows the stochastic reactor model to be computationally competitive with much lower order modeling approaches (i.e., Vibe-based models). It also makes the stochastic reactor model a feasible computer aided engineering framework of choice for multi-objective engine optimization campaigns.

Maximal power output of a stochastic thermodynamic engine

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and Th hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by M8(ThTc−1). Moreover, we show that this bound can be reached to within a factor of (ThTc−1)∕(ThTc+1) by operating the cyclic thermodynamic process with a quadratic potential.

Unified approach to stochastic thermodynamics: Application to a quantum heat engine.

In the present study we have developed an alternative formulation for the quantum stochastic thermodynamics based on the c-number Langevin equation for the system-reservoir model. This is analogous to the classical one. Here we have considered both Markovian and non-Markovian dynamics (NMD). Consideration of the NMD is an important issue at the current state of the stochastic thermodynamics. Applying the present formalism, we have carried out a comparative study on the heat absorbed and the change of entropy with time for a linear quantum system and its classical analog for both Markovian and NMD. Here the strength of the thermal noise and its correlation time for the respective cases are the leading quantities to explain any distinguishable feature which may appear with the equilibration kinetics. For another application, we have proposed a formulation with classical look for a quantum stochastic heat engine. Using it we have presented a comparative study on the efficiency and its value at maximum power for a quantum stochastic heat engine and its classical analog. The engines are Carnot like which are coupled with their respective Markovian thermal baths. Here also the noise strength as well as the diffusion constant are the leading quantities to explain any noticeable feature.