Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “optimal control theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Leveraging prior mean models for faster Bayesian optimization of particle accelerators

Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.

43 PARTICLE ACCELERATORS↗

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Vision–based Robust $\mathcal{H}$ ∞ Gain Scheduling Longitudinal and Lateral Following Controller for Autonomous Vehicles on Urban Curved Roads

Implementing advanced driver assistance systems (ADAS) in congested and intricate urban traffic scenarios poses significant challenges. To address the frequent stop–and–go motions exhibited by autonomous vehicles (AVs) navigating urban roads with changes in curvature, we propose a vision–based robust $\mathcal{H}$ ∞ adaptive cruise control system (ACC) for longitudinal control, plus a lane keeping assist system (LKAS) for lateral control. For the vision-based ACC, a weighted probability objective function for the vehicle following behavior is formulated. We incorporate $\mathcal{H}$ ∞ performance and gain scheduling techniques to mitigate the impact of uncertainty in visual sensor measurements. Furthermore, the optimal time headway is scheduled based on the velocity to ensure traffic flow efficiency and safety during the vehicle following process. For the LKAS, we introduce a road curvature estimation method that integrates lane and vehicle dynamics information to obtain the lateral and heading offsets. Next, the design criterion of the observer–based robust gain scheduling lateral motion controller is established by linear matrix inequality (LMI). Here, a series of experiments conducted within a camera–in–loop platform validate the proposed method.

33 ADVANCED PROPULSION SYSTEMS↗

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

Allowing third-party applications on Radio Access Network (RAN) Intelligent Controllers (RICs) within the OpenRAN (O-RAN) framework introduces conflicting interactions that are often difficult to detect in advance. These conflicts, occurring between third-party applications in the Near RealTime RIC (Near-RT RIC), known as xApps, can lead to performance degradation and instability in O-RAN if not identified early. Existing conflict detection and mitigation solutions in the literature assume that the conflicts are known beforehand, which is not always accurate due to the complex and often hidden relationships between control parameters and Key Performance Indicators (KPIs). In this paper, we propose a novel Recurrent Neural Network (RNN) to detect both known and unknown conflicts in O-RAN xApps as specified in the O-RAN standards. We model the xApps, control parameters, and KPIs with nodes and edges to create graph structures and use the hidden nonEuclidean geometric properties of the Riemannian manifold to train the RNN model. The performance of this proposed model is validated using evaluation metrics and compared with benchmarks. Results demonstrate that the proposed RNN model, leveraging Riemannian geometric properties, can achieve 100% of the F1-score provided by an optimal solution in just 20 iterations.

5G↗

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

Allowing third-party applications on Radio Access Network (RAN) Intelligent Controllers (RICs) within the OpenRAN (O-RAN) framework introduces conflicting interactions that are often difficult to detect in advance. These conflicts, occurring between third-party applications in the Near RealTime RIC (Near-RT RIC), known as xApps, can lead to performance degradation and instability in O-RAN if not identified early. Existing conflict detection and mitigation solutions in the literature assume that the conflicts are known beforehand, which is not always accurate due to the complex and often hidden relationships between control parameters and Key Performance Indicators (KPIs). In this paper, we propose a novel Recurrent Neural Network (RNN) to detect both known and unknown conflicts in O-RAN xApps as specified in the O-RAN standards. We model the xApps, control parameters, and KPIs with nodes and edges to create graph structures and use the hidden nonEuclidean geometric properties of the Riemannian manifold to train the RNN model. The performance of this proposed model is validated using evaluation metrics and compared with benchmarks. Results demonstrate that the proposed RNN model, leveraging Riemannian geometric properties, can achieve 100% of the F1-score provided by an optimal solution in just 20 iterations.

5G↗

Estimating Uncertainty in Simulated ENSO Statistics

Abstract Large ensembles of model simulations are frequently used to reduce the impact of internal variability when evaluating climate models and assessing climate change induced trends. However, the optimal number of ensemble members required to distinguish model biases and climate change signals from internal variability varies across models and metrics. Here we analyze the mean, variance and skewness of precipitation and sea surface temperature in the eastern equatorial Pacific region often used to describe the El Niño–Southern Oscillation (ENSO), obtained from large ensembles of Coupled model intercomparison project phase 6 climate simulations. Leveraging established statistical theory, we develop and assess equations to estimate, a priori, the ensemble size or simulation length required to limit sampling‐based uncertainties in ENSO statistics to within a desired tolerance. Our results confirm that the uncertainty of these statistics decreases with the square root of the time series length and/or ensemble size. Moreover, we demonstrate that uncertainties of these statistics are generally comparable when computed using either pre‐industrial control or historical runs. This suggests that pre‐industrial runs can sometimes be used to estimate the expected uncertainty of statistics computed from an existing historical member or ensemble, and the number of simulation years (run duration and/or ensemble size) required to adequately characterize the statistic. This advance allows us to use existing simulations (e.g., control runs that are performed during model development) to design ensembles that can sufficiently limit diagnostic uncertainties arising from simulated internal variability. These results may well be applicable to variables and regions beyond ENSO.

54 ENVIRONMENTAL SCIENCES↗

Interfacial spin–orbit torques

Spin–orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin–orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin–orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin–orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimentally. To facilitate progress, we review interfacial spin–orbit torques from a semiclassical viewpoint and relate these contributions to recent experimental results. In this study, we show the relationship between different interface transport parameters within the same model. For charges and spins flowing perpendicular to the interface, interfacial spin–orbit coupling both modifies the mixing conductance of the magnetoelectronic circuit theory and gives rise to spin memory loss. For in-plane electric fields, interfacial spin–orbit coupling gives rise to torques described by spin–orbit filtering, spin swapping, and precession. In addition, these same interfacial processes generate spin currents that flow into the non-magnetic layer. For in-plane electric fields in trilayer structures, the spin currents generated at the interface between one ferromagnetic layer and the non-magnetic spacer layer can propagate through the non-magnetic layer to produce novel torques on the other ferromagnetic layer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Facet-Dependent Photodegradation of Methylene Blue by Hematite Nanoplates in Visible Light

The expression of specific crystal facets in different nanostructures is known to play a vital role in determining the sensitivity toward photodegradation of organics, which can generally be ascribed to differences in surface structure and energy. Herein, we report the synthesis of hematite nanoplates with controlled relative exposure of basal (001) and edge (012) facets, enabling us to establish direct correlation between surface structure and the photocatalytic degradation efficiency of methylene blue (MB) in the presence of hydrogen peroxide. MB adsorption experiments showed that the capacity on (001) is about three times larger than on (012), and this is supported by density functional theory calculations suggesting adsorption energies about 1.5 times higher. However, this alone cannot explain the observed MB photodegradation rate, which is around 14.5 times faster on (001) than (012). The enhancement we attribute to a higher availability of photoelectron accepting surface Fe3+ sites on the (001) facet. This facilitates more efficient iron valence cycling and the heterogeneous photo-Fenton reaction yielding MB-oxidizing hydroxyl radicals at the surface. Our findings help establish a rational basis for design and optimization of hematite nanostructures as photocatalysts for environmental remediation.

Zong, Meirong↗

Modeling Ring Current Proton Fluxes Using Artificial Neural Network and Van Allen Probe Measurements

Abstract Terrestrial ring current dynamics are a critical part of the near‐space environment, in that they directly drive geomagnetic field variations that control particle drifts, and define geomagnetic storms. The present study aims to specify a global and time‐varying distribution of ring current proton using geomagnetic indices and solar wind parameters with their history as input. We train an artificial neural network (ANN) model to reproduce proton fluxes measured by the Radiation Belt Storm Probes Ion Composition Experiment instrument onboard Van Allen Probes. By choosing optimal feature parameters and their history length, the model results show a high correlation and a small error between model specifications and satellite measurements. The modeled results well capture energy‐dependent proton dynamics in association with geomagnetic storms, including inward radial diffusion, acceleration and decay. Our ANN model produces proton fluxes with their corresponding 3D spatiotemporal variations, capturing the latitudinal distribution and local time asymmetry that are consistent with observations and that can further inform theory.

Li, Jinxing↗

Understanding the effect of refractory metal chemistry on the stacking fault energy and mechanical property of Cantor-based multi-principal element alloys

Multi-principal-element alloys (MPEAs) based on 3d-transition metals show remarkable mechanical properties. In this study, the stacking fault energy (SFE) in face-centered cubic (fcc) alloys is a critical property that controls underlying deformation mechanisms and mechanical response. Here, we present an exhaustive density-functional theory study on refractory- and copper-reinforced Cantor-based systems to ascertain the effects of refractory metal chemistry on SFE. We find that even a small percent change in refractory metal composition significantly changes SFEs, which correlates favorably with features like electronegativity variance, size effect, and heat of fusion. For fcc MPEAs, we also detail the changes in mechanical properties, such as bulk, Young's, and shear moduli, as well as yield strength. A Labusch-type solute-solution-strengthening model was used to evaluate the temperature-dependent yield strength, which, combined with SFE, provides a design guide for high-performance alloys. We also analyzed the electronic structures of two down-selected alloys to reveal the underlying origin of optimal SFE and strength range in refractory-reinforced fcc MPEAs. These new insights on tuning SFEs and modifying composition-structure-property correlation in refractory- and copper-reinforced MPEAs by chemical disorder, provide a chemical route to tune twinning- and transformation-induced plasticity behavior in fcc MPEAs.

36 MATERIALS SCIENCE↗

An improved representation of the relationship between photosynthesis and stomatal conductance leads to more stable estimation of conductance parameters and improves the goodness-of-fit across diverse data sets

Stomata play a central role in surface-atmosphere exchange by controlling the flux of water and CO 2 between the leaf and the atmosphere. Representation of stomatal conductance (g sw ) is therefore an essential component of models that seek to simulate water and CO 2 exchange in plants and ecosystems. For given environmental conditions at the leaf surface (CO 2 concentration and vapor pressure deficit or relative humidity), models typically assume a linear relationship between g sw and photosynthetic CO 2 assimilation (A). However, measurement of leaf-level g sw response curves to changes in A are rare, particularly in the tropics, resulting in only limited data to evaluate this key assumption. Here, we measured the response of g sw and A to irradiance in six tropical species at different leaf phenological stages. We showed that the relationship between g sw and A was not linear, challenging the key assumption upon which optimality theory is based-that the marginal cost of water gain is constant. Our data showed that increasing A resulted in a small increase in g sw at low irradiance, but a much larger increase at high irradiance. We reformulated the popular Unified Stomatal Optimization (USO) model to account for this phenomenon and to enable consistent estimation of the key conductance parameters g 0 and g 1 . Our modification of the USO model improved the goodness-of-fit and reduced bias, enabling robust estimation of conductance parameters at any irradiance. In addition, our modification revealed previously undetectable relationships between the stomatal slope parameter g 1 and other leaf traits. We also observed nonlinear behavior between A and g sw in independent datasets that included data collected from attached and detached leaves, and from plants grown at elevated CO 2 concentration. We propose that this empirical modification of the USO model can improve the measurement of g sw parameters and the estimation of plant and ecosystem-scale water and CO 2 fluxes.

54 ENVIRONMENTAL SCIENCES↗

Pt Nanoparticle Disintegration at Oxide Interfaces Enhances CO Oxidation Catalysis

Understanding how supported metal nanoparticles dynamically evolve under reaction conditions is critical for controlling their catalytic function. Here, the mechanism behind the dynamic disintegration of Pt nanoparticles (NPs) supported on CeOx-TiO2 (CT) during CO oxidation is elucidated, leading to the formation of single atoms (SAs) and/or sub-nanometer clusters. Density functional theory (DFT) calculations reveal that strong Pt-CO interactions weaken Pt─Pt cohesion, while electronic coupling between Pt and Ce ions stabilizes Pt-CO* intermediates at the oxide interface. Surface oxygen vacancies kinetically trap Pt-CO*, but the vacancies are replenished under oxygen-rich conditions, enabling Pt-CO* surface diffusion and subsequent structural reorganization. In situ spectroscopic analyses confirm the oxygen-driven transformation of Pt NPs, correlating with a threefold increase in mass-specific activity at 150 °C. These findings demonstrate that interfacial oxygen dynamics and metal-support interactions can be leveraged to induce nanoparticle disintegration and optimize catalytic performance, highlighting the catalytic potential of interface-engineered Pt nanostructures.

CO oxidation↗

Analysis and prediction of reaction kinetics using the degree of rate control

“Degree of rate control” (DRC) analysis provides a quantitative approach for analysing the kinetics of multi-step reaction mechanisms that has been widely applied to both heterogeneous and homogeneous catalysis research, as well as electrocatalysis. The DRC of any given transition state or intermediate is defined as a partial derivative such that it approximately equals the fractional increase in net rate to the product of interest per differential decrease in its standard-state free energy for that species (÷RT), holding constant the standard-state free energies of all other transition states and intermediates. Even very complex mechanisms usually have only a few species with non-zero DRCs and are thus the species whose interactions with the catalyst most strongly affect the net rate. These key DRC values thus offer a simple and intuitive route to optimize catalyst materials, especially with the assistance of computational methods like density functional theory (DFT). These high-DRC species are also the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. In simple cases with a single “rate-determining step”, the DRC for its transition state (TS) is + 1. Catalyst-bound intermediates, on the other hand, often have negative DRCs equal to a small integer times their fractional occupancy of catalyst sites. The apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its DRC (+RT). It has been shown that the apparent transfer coefficient in electrocatalysis, an inverted form of the Tafel slope, is a weighted average of the number of electrons transferred to generate each intermediate or product species in the mechanism, weighted again by the DRC. Quantitative analysis of kinetic isotope effects (KIEs, or the ratio of net rates for different reactant isotopes) in complex mechanisms has shown that the logarithm of the KIE equals the weighted average over all species in the mechanism of the difference between the two isotopes in their standard-state free energies (÷RT), again weighted by the DRC. The reaction orders with respect to fluid-phase concentrations of reactants, products and intermediates have also been proven to be directly related to DRCs. Thus, there are numerous experimental observables which equate to short linear combinations of DRCs, so that combinations of experimental measurements might provide access to DRC values. Since its invention for transition states in 1994 and its generalization to include intermediates in 2009, the DRC has thus far mainly been calculated for microkinetic models based either entirely on DFT or on DFT with the key energies (i.e., those for high-DRC species) being fine-tuned to match experiments. The relationships summarized in this work provide new opportunities for using experiments earlier in the development and optimization of microkinetic models that require input from computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Density functional theory-based surrogate kinetic models for heterogeneous reactions of hydrocarbon intermediates on silicon carbide

The increasing demand for high-performance materials in advanced technologies highlights the importance of achieving a fundamental understanding and potential control of silicon carbide (SiC) deposition processes. However, existing models often lack sufficient theoretical detail, relying heavily on empirical data and offering limited predictive capability. In particular, the complex surface chemistry governing SiC growth remains poorly understood. This study addresses these challenges by employing density functional theory (DFT) to investigate key heterogeneous reactions involving hydrocarbon intermediates on SiC surfaces, including dehydrogenation, hydrogenation, and carbon deposition. Transition state searches were conducted to identify reaction pathways and energy barriers. While first-principles calculations offer high accuracy, they are computationally intensive. To extend the utility of these first-principles results, vibrational analyses were performed using phonon-based statistical thermochemistry to compute temperature-dependent reaction rates which were used to develop Arrhenius-type surrogate kinetic models. Furthermore, the resulting framework provides a more rigorous, physically grounded basis for integrating atomistic insights into continuum-scale modeling, ultimately enabling improved prediction and optimization of SiC film growth in high-performance material systems.

Density Functional Theory↗

Understanding Solid-Electrolyte Interphase Formation at the Lithium Metal Anode of Lithium-Sulfur Batteries

Lithium-sulfur (Li-S) batteries are one of the most promising chemistries for the next generation of energy storage devices. In a standard Li-S cell, the metallic lithium anode is an essential component of the battery due to its low density, extremely high theoretical specific capacity, and very low negative electrochemical potential. However, several challenges related to the use of Li metal have prevented this battery technology from becoming commercially available. For instance, Li-anodes are highly reactive, which results in the continuous decomposition of the electrolyte and the formation of the solid-electrolyte interphase (SEI) layer. This, combined with the non-uniform deposition of Liions during plating at the anode surface, can seriously affect the performance, cycling, and safety of the battery. In addition, it has been suggested that a controlled SEI formation at the metallic Li anode can yield enhanced battery performance. Hence, a comprehensive understanding of how the SEI layer is formed can help elucidate improvements in this battery technology. In this work, the formation of the SEI layer in Li-S batteries is investigated using density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations. The stability of liquid organic-based electrolyte components, salt concentration, electron-rich environments, and the use of inorganic solid-state electrolyte (SSE) materials are explored in order to provide molecular-level fundamental insights into how the nature and composition of the electrolyte can alter the initial stages of the SEI formation. The products of electrolyte decomposition and electro-/chemical reaction pathways of liquid electrolyte component such as solvent and salts are predicted from AIMD simulations of electrolyte-anode interfaces. Energetics of reactions from DFT ground-state optimizations are also presented to confirm the decomposition mechanisms. Some significant differences are then drawn regarding the use of low and high salt concentrations. Simulations under electron-rich environments show additional multielectron electrochemical reactions of solvent and salt decomposition taking place due to the excess of electrons and the presence of radical anions in the solution. Finally, the initial stages of formation, stability, and main constituents of interfaces between Li-metal and Sbased electrodes with sulfide-based SSEs are characterized in detail.

25 ENERGY STORAGE↗

Non-reactive facet specific adsorption as a route to remediation of chlorinated organic contaminants

The present work quantifies metal-contaminant interactions between palladium substrates and three salient chlorinated organic contaminants, namely trichloroethylene 1,3,5-trichlorobenzene (TCB), and 3,3′,4,4′-tetrachlorobiphenyl (PCB77). Given that Pd is one of the conventional catalytically active materials known for contaminant removal, maximizing catalytic efficiency through optimal adsorption dynamics reduces the cost of remediation of contaminants that are persistent water pollutants chronically affecting public health. Adsorption efficiency analyses from all-atom molecular dynamics (MD) simulations advance the understanding of reaction mechanisms available from density functional theory (DFT) calculations to an extractable feature scale that can fit the parametric design of supported metal catalytic systems and feed into high throughput catalyst selection. Data on residence time, site-specific adsorption, binding energies, packing geometries, orientation profiles, and the effect of adsorbate size show the anomalous behaviour of organic contaminant adsorption on the undercoordinated {110} surface as compared to the {111} and {100} surfaces. The intermolecular interaction within contaminants from molecular dynamics simulation exhibits refreshing results than ordinary single molecule density functional theory calculation. Since complete adsorption and dechlorination is an essential step for chlorinated organic contaminant remediation pathways, the presented profiles provide essential information for designing efficient remediation systems through facet-controlled palladium nanoparticles.

Guo, Hao↗

Batch Extraction Studies to Evaluate Trace Element Behavior in PUREX Conditions

The multilab Intentional Forensics Venture is working to identify which stable elements (i.e., taggants) at trace concentrations relative to U would persist throughout the nuclear fuel cycle in a voluntary fuel tagging scheme. A taggant would provide the nuclear forensics community with a “barcode” to help identify nuclear materials found outside of regulatory control. A portion of this project was focused on reprocessing effects and determining which, if any, elements would coextract with U(VI) in standard Pu–U reduction extraction (PUREX) conditions. Elements with a propensity to coextract could, in theory, be used as taggants from a PUREX perspective. Although retention is not a performance requirement, the taggant signature would need to partition predictably from the U stream after the PUREX process to maintain forensic utility. This report documents results from several batch extraction studies with numerous trace elements from HNO 3 (1.5–5 M), with and without U(VI), into 30% tri-n-butyl phosphate (TBP) in kerosene. Extraction and back-extraction tests were used to evaluate nearly 60 elements in surrogate conditions for PUREX, and distribution coefficients (i.e., D-values) for most species were <0.1, indicating few species are likely to co-extract with U through PUREX. Additional studies are needed to optimize sample volumes and dilutions to dial in these low D-values. The D-values (D) were determined for several of the more promising elements, including Re and Se. Ultimately, we conclude that only a limited number of the ~ 60 elements investigated are extractable in the U stream of PUREX, based on measured D values, meaning most candidate elemental taggants would likely be lost at this stage of the nuclear fuel cycle, even when considering a range of acid concentrations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Game Theoretic Orchestration for Cooperation among Power Distribution System Applications

The evolving transformation with the proliferation of distributed energy resources and advanced metering, necessitates advanced distribution systems to integrate and orchestrate a large number of grid-edge devices while also serving multiple system-level objectives such as resilience, decarbonization, equity and other system mandates. The parallel deployment and control of resources towards achieving diverse objectives may lead to conflicts between applications that want to control overlapping sets of device setpoints, potentially leading to oscillatory behavior and suboptimal performance. This work aims at leveraging game theoretic framework to drive cooperative behavior among competitive applications. The work proposes a weighted-consensus based game design to facilitate conflict resolution through consensus-building iterations for modular platform. Simulation-based evaluation on a sample test system demonstrates the performance the proposed deconfliction strategy in resolving operational conflicts and achieving close-to-optimal trade off among the applications. Results also compare the proposed strategy with a distribution optimization approach and illustrate it effectiveness in diverse apps regardless of their design while also incentivizing apps with flexible design.

Advanced distribution operations, cooperation, app↗