Conference Proceeding
Refine
Year of publication
Institute
- Fachbereich Elektrotechnik und Informationstechnik (241)
- Fachbereich Medizintechnik und Technomathematik (217)
- Fachbereich Luft- und Raumfahrttechnik (188)
- Fachbereich Energietechnik (181)
- IfB - Institut für Bioengineering (151)
- Solar-Institut Jülich (110)
- Fachbereich Maschinenbau und Mechatronik (107)
- Fachbereich Bauingenieurwesen (75)
- Fachbereich Wirtschaftswissenschaften (55)
- ECSM European Center for Sustainable Mobility (53)
Language
- English (1191) (remove)
Document Type
- Conference Proceeding (1191) (remove)
Keywords
- Biosensor (25)
- CAD (7)
- Finite-Elemente-Methode (7)
- civil engineering (7)
- Bauingenieurwesen (6)
- Blitzschutz (6)
- Enterprise Architecture (5)
- Clusterion (4)
- Energy storage (4)
- Gamification (4)
Reinforced concrete frames with masonry infill walls are popular form of construction all over the world as well in seismic regions. While severe earthquakes can cause high level of damage of both reinforced concrete and masonry infills, earthquakes of lower to medium intensity some-times can cause significant level of damage of masonry infill walls. Especially important is the level of damage of face loaded infill masonry walls (out-of-plane direction) as out-of-plane load cannot only bring high level of damage to the wall, it can also be life-threating for the people near the wall. The response in out-of-plane direction directly depends on the prior in-plane damage, as previous investigation shown that it decreases resistance capacity of the in-fills. Behaviour of infill masonry walls with and without prior in-plane load is investigated in the experimental campaign and the results are presented in this paper. These results are later compared with analytical approaches for the out-of-plane resistance from the literature. Conclusions based on the experimental campaign on the influence of prior in-plane damage on the out-of-plane response of infill walls are compared with the conclusions from other authors who investigated the same problematic.
Due to the increasing complexity of software projects, software development is becoming more and more dependent on teams. The quality of this teamwork can vary depending on the team composition, as teams are always a combination of different skills and personality types. This paper aims to answer the question of how to describe a software development team and what influence the personality of the team members has on the team dynamics. For this purpose, a systematic literature review (n=48) and a literature search with the AI research assistant Elicit (n=20) were conducted. Result: A person’s personality significantly shapes his or her thinking and actions, which in turn influences his or her behavior in software development teams. It has been shown that team performance and satisfaction can be strongly influenced by personality. The quality of communication and the likelihood of conflict can also be attributed to personality.
Many of today’s factors make software development more and more complex, such as time pressure, new technologies, IT security risks, et cetera. Thus, a good preparation of current as well as future software developers in terms of a good software engineering education becomes progressively important. As current research shows, Competence Developing Games (CDGs) and Serious Games can offer a potential solution.
This paper identifies the necessary requirements for CDGs to be conducive in principle, but especially in software engineering (SE) education. For this purpose, the current state of research was summarized in the context of a literature review. Afterwards, some of the identified requirements as well as some additional requirements were evaluated by a survey in terms of subjective relevance.
Large industrial facilities and power plants often require a huge number fo information and control cables between the differnet structures. These I&C-cables can be routed in reinforced concrete cable ducts or in isolated buried cable runs. KTA 2206 is the German lightning protection standard for nuclear power plants. During the last several years considerable effort has been made to revise this standard. Despite the well established principles and design guidelines for the construction of the lightning protection system, this standard puts special emphasis on the coupling of transient overvoltages to I&C-cables.
For the application of the concept of Lightning Protection Zones (LPZ), the knowledge of the magnetic fields and induced voltages inside a structure is necessary. Laboratory experiments have been conducted at a downscaled model of a building (scale factor 1:6) to determine these electromagnetic quantities in case of a direct strike to the structure. The model (3 m x 2 m x 2 m) represented a small industrial building using the reinforcement of the concrete as electromagnetic shield. The magnetic fields and magnetic field derivatives were measured at several location inside the scaled model. Further, the voltages induced on three typical cable routes inside the model was determined. The influence of the lightning current waveshape, point-of-strike, bonding of the cable routes, and bridging of an expansion joint in the middle of the building on these quantities was studied.
In IEC 61312-2 equations for the assessment of the magnetic fields inside structures due to a direct lightning strike are given. These equations are based on computer simulations for shields consisting of a single-layer steel grid of a given mesh width. Real constructions, however, contain at least two layers of reinforcement steel grids. The objective of this study was to experimentally determine the additional shielding effectiveness of a second reinforcement layer compared to a single-layer grid. To this end, simulated structures were set up in the high current laboratory. The structures consisted of cubic cages of 2 m side length with one or with two reinforcement grids, respectively. The structures were exposed to direct lightning currents representing the variety of anticipated lightning current waveforms. The magnetic fields and their derivatives at several positions inside the structure as well as the voltage between “floor” and “roof” in the center were determined for different current injection points. From these data the improvement of the shielding caused by a second reinforcement layer is derived.
Recognition of subjects with mild cognitive impairment (MCI) by the use of retinal arterial vessels.
(2019)
Concentrated Solar Power (CSP) systems are able to store energy cost-effectively in their integrated thermal energy storage (TES). By intelligently combining Photovoltaics (PV) systems with CSP, a further cost reduction of solar power plants is expected, as well as an increase in dispatchability and flexibility of power generation. PV-powered Resistance Heaters (RH) can be deployed to raise the temperature of the molten salt hot storage from 385 °C up to 565 °C in a Parabolic Trough Collector (PTC) plant. To avoid freezing and decomposition of molten salt, the temperature distribution in the electrical resistance heater is investigated in the present study. For this purpose, a RH has been modeled and CFD simulations have been performed. The simulation results show that the hottest regions occur on the electric rod surface behind the last baffle. A technical optimization was performed by adjusting three parameters: Shell-baffle clearance, electric rod-baffle clearance and number of baffles. After the technical optimization was carried out, the temperature difference between the maximum temperature and the average outlet temperature of the salt is within the acceptable limits, thus critical salt decomposition has been avoided. Additionally, the CFD simulations results were analyzed and compared with results obtained with a one-dimensional model in Modelica.
Explorer CEOs: The effect of CEO career variety on large firms’ relative exploration orientation
(2018)
Prior studies demonstrate that firms need to make smart trade-off decisions between exploration and exploitation activities in order to increase performance. Chief executive officers (CEOs) are principal decision makers of a firm’s strategic posture. In this study, we theorize and empirically examine how relative exploration orientation of large publicly listed firms varies based on the career variety of their CEOs – that is, how diverse the professional experiences of executives were prior to them becoming CEOs. We further argue that the heterogeneity and structure of the top management team moderates the impact of CEO career variety on firms’ relative exploration orientation. Based on multisource secondary data for 318 S&P 500 firms from 2005 to 2015, we find that CEO career variety is positively associated with relative exploration orientation.
Interestingly, CEOs with high career varieties appear to be less effective in pursuing exploration, when they work with highly heterogeneous and structurally interdependent top management teams.
Smart pixel : photonic mixer device (PMD) ; new system concept of a 3D-imaging camera-on-a-chip
(1998)
An application of a scanning light-addressable potentiometric sensor for label-free DNA detection
(2013)
DNA-hybridization detection using light-addressable potentiometric sensor modified with gold layer
(2014)
Wireless systems for machinery safety : Requirements and solutions for wireless real time systems
(2015)
In this paper, the use of reinforcement learning (RL) in control systems is investigated using a rotatory inverted pendulum as an example. The control behavior of an RL controller is compared to that of traditional LQR and MPC controllers. This is done by evaluating their behavior under optimal conditions, their disturbance behavior, their robustness and their development process. All the investigated controllers are developed using MATLAB and the Simulink simulation environment and later deployed to a real pendulum model powered by a Raspberry Pi. The RL algorithm used is Proximal Policy Optimization (PPO). The LQR controller exhibits an easy development process, an average to good control behavior and average to good robustness. A linear MPC controller could show excellent results under optimal operating conditions. However, when subjected to disturbances or deviations from the equilibrium point, it showed poor performance and sometimes instable behavior. Employing a nonlinear MPC Controller in real time was not possible due to the high computational effort involved. The RL controller exhibits by far the most versatile and robust control behavior. When operated in the simulation environment, it achieved a high control accuracy. When employed in the real system, however, it only shows average accuracy and a significantly greater performance loss compared to the simulation than the traditional controllers. With MATLAB, it is not yet possible to directly post-train the RL controller on the Raspberry Pi, which is an obstacle to the practical application of RL in a prototyping or teaching setting. Nevertheless, RL in general proves to be a flexible and powerful control method, which is well suited for complex or nonlinear systems where traditional controllers struggle.
Infused Thermal Solutions (ITS) introduces a method for passive thermal control to stabilize structural components thermally without active heating and cooling systems, but with phase change material (PCM) for thermal energy storage (TES), in combination with lattice - both embedded in additive manufactured functional structures. In this ITS follow-on paper a thermal model approach and associated predictions are presented, related on the ITS functional breadboards developed at FH Aachen. Predictive TES by PCM is provided by a specially developed ITS PCM subroutine, which is applicable in ESATAN. The subroutine is based on the latent heat storage (LHS) method to numerically embed thermo-physical PCM behavior. Furthermore, a modeling approach is introduced to numerically consider the virtual PCM/lattice nodes within the macro-encapsulated PCM voids of the double wall ITS design. Related on these virtual nodes, in-plane and out-of-plane conductive links are defined. The recent additive manufactured ITS breadboard series are thermally cycled in the thermal vacuum chamber, both with and without embedded PCM. Related on breadboard hardware tests, measurement results are compared with predictions and are subsequently correlated. The results of specific simulations and measurements are presented. Recent predictive results of star tracker analyses are also presented in ICES-2021-106, based on this ITS PCM subroutine.
In this article we describe an Internet-of-Things sensing device with a wireless interface which is powered by the oftenoverlooked harvesting method of the Wiegand effect. The sensor can determine position, temperature or other resistively measurable quantities and can transmit the data via an ultra-low power ultra-wideband (UWB) data transmitter. With this approach we can energy-self-sufficiently acquire, process, and wirelessly transmit data in a pulsed operation. A proof-of-concept system was built up to prove the feasibility of the approach. The energy consumption of the system is analyzed and traced back in detail to the individual components, compared to the generated energy and processed to identify further optimization options. Based on the proof-of-concept, an application demonstrator was developed. Finally, we point out possible use cases.
Concept, scientific research and managerial applications of Provocative Coaching, according to the „Provocative Therapy“ of Prof. Dr. Frank Farrelly (University of Wisconsin, U.S.A) in terms of an application of the Provocative Communication Style in specific situations of practical leadership, especially in the role of a coach for their subordinates.
A capacitive electrolyte-insulator-semiconductor (EISCAP) biosensor modified with Tobacco mosaic virus (TMV) particles for the detection of acetoin is presented. The enzyme acetoin reductase (AR) was immobilized on the surface of the EISCAP using TMV particles as nanoscaffolds. The study focused on the optimization of the TMV-assisted AR immobilization on the Ta 2 O 5 -gate EISCAP surface. The TMV-assisted acetoin EISCAPs were electrochemically characterized by means of leakage-current, capacitance-voltage, and constant-capacitance measurements. The TMV-modified transducer surface was studied via scanning electron microscopy.
In the Laser Powder Bed Fusion (LPBF) process, parts are built out of metal powder material by exposure of a laser beam. During handling operations of the powder material, several influencing factors can affect the properties of the powder material and therefore directly influence the processability during manufacturing. Contamination by moisture due to handling operations is one of the most critical aspects of powder quality. In order to investigate the influences of powder humidity on LPBF processing, four materials (AlSi10Mg, Ti6Al4V, 316L and IN718) are chosen for this study. The powder material is artificially humidified, subsequently characterized, manufactured into cubic samples in a miniaturized process chamber and analyzed for their relative density. The results indicate that the processability and reproducibility of parts made of AlSi10Mg and Ti6Al4V are susceptible to humidity, while IN718 and 316L are barely influenced.
Flow separation is a phenomenon that occurs in all kinds of supersonic nozzles sometimes during run-up and shut-down operations. Especially in expansion nozzles of rocket engines with large area ratio, flow separation can trigger strong side loads that can damage the structure of the nozzle. The investigation presented in this paper seeks to establish measures that may be applied to alter the point of flow separation. In order to achieve this, a supersonic nozzle was placed at the exit plane of the conical nozzle. This resulted in the generation of cross flow surrounding the core jet flow from the conical nozzle. Due to the entrainment of the gas stream from the conical nozzle the pressure in its exit plane was found to be lower than that of the ambient. A Cold gas instead of hot combustion gases was used as the working fluid. A mathematical simulation of the concept was validated by experiment. Measurements confirmed the simulation results that due to the introduction of a second nozzle the pressure in the separated region of the conical nozzle was significantly reduced. It was also established that the boundary layer separation inside the conical nozzle was delayed thus allowing an increased degree of overexpansion. The condition established by the pressure measurements was also demonstrated qualitatively using transparent nozzle configurations.
Manufacturing Process Simulation for the Prediction of Tool-Part-Interaction and Ply Wrinkling
(2019)
Manufacturing Process Simulation for the Prediction of Tool-Part-Interaction and Ply Wrinkling
(2015)
Aim of the AXON2 project (Adaptive Expert System for Object Recogniton using Neuml Networks) is the development of an object recognition system (ORS) capable of recognizing isolated 3d objects from arbitrary views. Commonly, classification is based on a single feature extracted from the original image. Here we present an architecture adapted from the Mixtures of Eaqerts algorithm which uses multiple neuml networks to integmte different features. During tmining each neural network specializes in a subset of objects or object views appropriate to the properties of the corresponding feature space. In recognition mode the system dynamically chooses the most relevant features and combines them with maximum eficiency. The remaining less relevant features arz not computed and do therefore not decelerate the-recognition process. Thus, the algorithm is well suited for ml-time applications.
The quest for life on other planets is closely connected with the search for water in liquid state. Recent discoveries of deep oceans on icy moons like Europa and Enceladus have spurred an intensive discussion about how these waters can be accessed. The challenge of this endeavor lies in the unforeseeable requirements on instrumental characteristics both with respect to the scientific and technical methods. The TRIPLE/nanoAUV initiative is aiming at developing a mission concept for exploring exo-oceans and demonstrating the achievements in an earth-analogue context, exploring the ocean under the ice shield of Antarctica and lakes like Dome-C on the Antarctic continent.
We report on the synthesis and CO gas-sensing properties of mesoporous tin(IV) oxides (SnO2). For the synthesis cetyltrimethylammonium bromide (CTABr) was used as a structure-directing agent; the resulting SnO2 powders were applied as films to commercially available sensor substrates by drop coating. Nitrogen physisorption shows specific surface areas up to 160 m2·g-1 and mean pore diameters of about 4 nm, as verified by TEM. The film conductance was measured in dependence on the CO concentration in humid synthetic air at a constant temperature of 300 °C. The sensors show a high sensitivity at low CO concentrations and turn out to be largely insensitive towards changes in the relative humidity. We compare the materials with commercially available SnO2-based sensors.
The management of knowledge in organizations considers both established long-term processes and cooperation in agile project teams. Since knowledge can be both tacit and explicit, its transfer from the individual to the organizational knowledge base poses a challenge in organizations. This challenge increases when the fluctuation of knowledge carriers is exceptionally high. Especially in large projects in which external consultants are involved, there is a risk that critical, company-relevant knowledge generated in the project will leave the company with the external knowledge carrier and thus be lost. In this paper, we show the advantages of an early warning system for knowledge management to avoid this loss. In particular, the potential of visual analytics in the context of knowledge management systems is presented and discussed. We present a project for the development of a business-critical software system and discuss the first implementations and results.
The RoboCup Logistics League (RCLL) is a robotics competition in a production logistics scenario in the context of a Smart Factory. In the competition, a team of three robots needs to assemble products to fulfill various orders that are requested online during the game. This year, the Carologistics team was able to win the competition with a new approach to multi-agent coordination as well as significant changes to the robot’s perception unit and a pragmatic network setup using the cellular network instead of WiFi. In this paper, we describe the major components of our approach with a focus on the changes compared to the last physical competition in 2019.
Having well-defined control strategies for fuel cells, that can efficiently detect errors and take corrective action is critically important for safety in all applications, and especially so in aviation. The algorithms not only ensure operator safety by monitoring the fuel cell and connected components, but also contribute to extending the health of the fuel cell, its durability and safe operation over its lifetime. While sensors are used to provide peripheral data surrounding the fuel cell, the internal states of the fuel cell cannot be directly measured. To overcome this restriction, Kalman Filter has been implemented as an internal state observer.
Other safety conditions are evaluated using real-time data from every connected sensor and corrective actions automatically take place to ensure safety. The algorithms discussed in this paper have been validated thorough Model-in-the-Loop (MiL) tests as well as practical validation at a dedicated test bench.
Turbulent dispersion in bounded horizontal jets : RANS capabilities and physical modeling comparison
(2016)
Air-water flows can be found in different engineering applications: from nuclear engineering to huge hydraulic structures. In this paper, a single tip fibre optical probe has been used to record high frequency (over 1 MHz) phase functions at different locations of a stepped spillway. These phase functions have been related to the interfacial velocities by means of Artificial Neural Networks (ANN) and the measurements of a classical double tip conductivity probe. Special attention has been put to the input selection and the ANN dimensions. Finally, ANN have shown to be able to link the signal rising times and plateau shapes to the air-water interfacial velocity.
Digital twins are seen as one of the key technologies of Industry 4.0. Although many research groups focus on digital twins and create meaningful outputs, the technology has not yet reached a broad application in the industry. The main reasons for this imbalance are the complexity of the topic, the lack of specialists, and the unawareness of the twin opportunities. The project "Digital Twin Academy" aims to overcome these barriers by focusing on three actions: Building a digital twin community for discussion and exchange, offering multi-stage training for various knowledge levels, and implementing realworld use cases for deeper insights and guidance. In this work, we focus on creating a flexible learning platform that allows the user to select a training path adjusted to personal knowledge and needs. Therefore, a mix of basic and advanced modules is created and expanded by individual feedback options. The usage of personas supports the selection of the appropriate modules.
Adapting augmented reality systems to the users’ needs using gamification and error solving methods
(2021)
Animations of virtual items in AR support systems are typically predefined and lack interactions with dynamic physical environments. AR applications rarely consider users’ preferences and do not provide customized spontaneous support under unknown situations. This research focuses on developing adaptive, error-tolerant AR systems based on directed acyclic graphs and error resolving strategies. Using this approach, users will have more freedom of choice during AR supported work, which leads to more efficient workflows. Error correction methods based on CAD models and predefined process data create individual support possibilities. The framework is implemented in the Industry 4.0 model factory at FH Aachen.
Gamification applications are on the rise in the manufacturing sector to customize working scenarios, offer user-specific feedback, and provide personalized learning offerings. Commonly, different sensors are integrated into work environments to track workers’ actions. Game elements are selected according to the work task and users’ preferences. However, implementing gamified workplaces remains challenging as different data sources must be established, evaluated, and connected. Developers often require information from several areas of the companies to offer meaningful gamification strategies for their employees. Moreover, work environments and the associated support systems are usually not flexible enough to adapt to personal needs. Digital twins are one primary possibility to create a uniform data approach that can provide semantic information to gamification applications. Frequently, several digital twins have to interact with each other to provide information about the workplace, the manufacturing process, and the knowledge of the employees. This research aims to create an overview of existing digital twin approaches for digital support systems and presents a concept to use digital twins for gamified support and training systems. The concept is based upon the Reference Architecture Industry 4.0 (RAMI 4.0) and includes information about the whole life cycle of the assets. It is applied to an existing gamified training system and evaluated in the Industry 4.0 model factory by an example of a handle mounting.
The determination of spacing, edge and end distance requirements for self-tapping screws requires numerous and comprehensive insertion tests. Yet the results of such tests cannot be transferred to other types of screws or even to screws of different diameter because of differences in shape or geometry. To reduce the effort of insertion tests a new method was developed which allows the estimation of required spacings, distances and timber thickness.
Various planar technologies are employed for developing solid-state sensors having low cost, small size and high reproducibility; thin- and thick-film technologies are most suitable for such productions. Screen-printing is especially suitable due to its simplicity, low-cost, high reproducibility and efficiency in large-scale production. This technology enables the deposition of a thick layer and allows precise pattern control. Moreover, this is a highly economic technology, saving large amounts of the used inks. In the course of repetitions of the film-deposition procedure there is no waste of material due to additivity of this thick-film technology. Finally, the thick films can be easily and quickly deposited on inexpensive substrates. In this contribution, thick-film ion-selective electrodes based on ionophores as well as crystalline ion-selective materials dedicated for potentiometric measurements are demonstrated. Analytical parameters of these sensors are comparable with those reported for conventional potentiometric electrodes. All mentioned thick-film strip electrodes have been totally fabricated in only one, fully automated thickfilm technology, without any additional manual, chemical or electrochemical steps. In all cases simple, inexpensive, commercially available materials, i.e. flexible, plastic substrates and easily cured polymer-based pastes were used.
Though weir flow has been studied for centuries, there still remains some nuances of weir flow that are not well understood. Therefore, an international study was conducted in which 20 different hydraulics laboratories from around the world built and tested two linear weirs (quarter-round and half-round crested weirs) of common geometry. The only unconstrained dimension was the weir length, which could be adjusted to match the width of the test flume. Participating laboratories used the instrumentation and data collection methodologies of their choosing for head and discharge measurements.
The experimental results found significant variability in the discharge coefficients as a function of dimensionless upstream head, as well as in the head-discharge relationships (as much as 50% in some cases). Potential sources contributing to the scatter may have included head meter instrumentation, flow meter instrumentation, approach flow length (flume length upstream of weir), head measurement location, nappe behavior, laboratory measurement methods and experimental setup, and the care and skill of the investigator (human error). Analyzing the data as a function of instrumentation types, approach length, and head measurement location did not provide any insight regarding the variations. Nappe behavior (e.g., aeration), which could be influenced by laboratory-specific conditions, varied among the datasets primarily for the half-round crested weir (about 20%).
A procedure for the evaluation of the failure probability of elastic-plastic thin shell structures is presented. The procedure involves a deterministic limit and shakedown analysis for each probabilistic iteration which is based on the kinematical approach and the use the exact Ilyushin yield surface. Based on a direct definition of the limit state function, the non-linear problems may be efficiently solved by using the First and Second Order Reliabiblity Methods (Form/SORM). This direct approach reduces considerably the necessary knowledge of uncertain technological input data, computing costs and the numerical error. In: Computational plasticity / ed. by Eugenio Onate. Dordrecht: Springer 2007. VII, 265 S. (Computational Methods in Applied Sciences ; 7) (COMPLAS IX. Part 1 . International Center for Numerical Methods in Engineering (CIMNE)). ISBN 978-1-402-06576-7 S. 186-189
Proceedings of the International Conference on Material Theory and Nonlinear Dynamics. MatDyn. Hanoi, Vietnam, Sept. 24-26, 2007, 8 p. In this paper, a method is introduced to determine the limit load of general shells using the finite element method. The method is based on an upper bound limit and shakedown analysis with elastic-perfectly plastic material model. A non-linear constrained optimisation problem is solved by using Newton’s method in conjunction with a penalty method and the Lagrangean dual method. Numerical investigation of a pipe bend subjected to bending moments proves the effectiveness of the algorithm.
Shakedown analysis of two dimensional structures by an edge-based smoothed finite element method
(2010)
Summary: This paper presents a methodology to study and understand the mechanics of stapled anastomotic behaviors by combining empirical experimentation and finite element analysis. Performance of stapled anastomosis is studied in terms of leakage and numerical results which are compared to in vitro experiments performed on fresh porcine tissue. Results suggest that leaks occur between the tissue and staple legs penetrating through the tissue.
Direct methods comprising limit and shakedown analysis is a branch of computational mechanics. It plays a significant role in mechanical and civil engineering design. The concept of direct method aims to determinate the ultimate load bearing capacity of structures beyond the elastic range. For practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and onstraints. If strength and loading are random quantities, the problem of shakedown analysis is considered as stochastic programming. This paper presents a method so called chance constrained programming, an effective method of stochastic programming, to solve shakedown analysis problem under random condition of strength. In this our investigation, the loading is deterministic, the strength is distributed as normal or lognormal variables.
A new formulation to calculate the shakedown limit load of Kirchhoff plates under stochastic conditions of strength is developed. Direct structural reliability design by chance con-strained programming is based on the prescribed failure probabilities, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem. We restrict uncertainty to strength, the loading is still deterministic. A new formulation is derived in case of random strength with lognormal distribution. Upper bound and lower bound shakedown load factors are calculated simultaneously by a dual algorithm.