Siddhartha Kumar khaitan | Iowa State University (original) (raw)

Papers by Siddhartha Kumar khaitan

Research paper thumbnail of Design Techniques and Applications of Cyber Physical Systems: A Survey

Cyber physical systems (CPSs) are new class of engineered systems which offer close interaction b... more Cyber physical systems (CPSs) are new class of engineered systems which offer close interaction between cyber and physical components. The field of CPS has been identified as a key area of research and CPSs are expected to play a major role in the design and development of future systems. In this paper, we survey recent advancements made in the development and applications of cyber physical systems. We classify the existing research work based on their characteristics and identify the future challenges. We also discuss the examples of prototypes of CPSs. The aim of this survey is to enable researchers and system designers to get insights into the working and applications of CPSs and motivate them to propose novel solutions for making wide-scale adoption of CPS a tangible reality.

Research paper thumbnail of A Survey Of High-performance Computing Approaches in Power Systems

As the size of power systems increases, conventional serial-execution based computing platforms a... more As the size of power systems increases, conventional serial-execution based computing platforms are proving to be insufficient to fulfil the computational demands of modern power systems. To address this, researchers have proposed several high-performance computing (HPC) approaches for benefiting power systems. In this paper, we survey several HPC approaches proposed for power systems. We classify these approaches based on their key characteristics and briefly summarize the challenges in using HPC for benefiting power systems. We believe that this survey will help the readers gain insights into state-of-the-art of HPC in power systems.

Research paper thumbnail of A Survey of Techniques for Designing and Managing Microgrids

Recent trends of rising demands of electricity for supporting critical infrastructure have led to... more Recent trends of rising demands of electricity for supporting critical infrastructure have led to increasing interest in microgrids. Microgrids hold the promise of being the reliable and economically viable electric system which can greatly improve the efficiency, resiliency and eco-friendliness of future smart grid. Recently, several techniques have been proposed to managing microgrids. In this paper, we present a survey of techniques proposed for designing and controlling microgrids. The aim of this paper is to provide insights to the power-system engineers and researchers into techniques for managing the challenges of microgrids like voltage/frequency control, islanding, stability, power quality and economic optimization.

Research paper thumbnail of Dynamic Load Balancing and Scheduling for Parallel Power System Dynamic Contingency Analysis

Research paper thumbnail of Multifrontal Solver for Online Power System Time Domain Simulation

This paper proposes the application of unsymmetric multifrontal method to solve the differential... more This paper proposes the application of unsymmetric
multifrontal method to solve the differential algebraic equations (DAE) encountered in the power system dynamic simulation. The proposed method achieves great computational efficiency as compared to the conventional Gaussian elimination methods and other linear sparse solvers due to the inherent parallel hierarchy present in the multifrontal methods. Multifrontal methods transform or
reorganize the task of factorizing a large sparse matrix into a sequence of partial factorization of smaller dense frontal matrices which utilize the efficient Basic Linear Algebra Subprograms 3 (BLAS 3) for dense matrix kernels. The proposed method is compared with the full Gaussian elimination methods and other direct sparse solvers on test systems and the results are reported.

Research paper thumbnail of Design of a novel and efficient hydrogen compressor for wind energy based storage systems

International Journal of Hydrogen Energy, 2015

ABSTRACT In a hybrid wind power system, the excess wind energy is stored in the form of compresse... more ABSTRACT In a hybrid wind power system, the excess wind energy is stored in the form of compressed hydrogen. Wind turbine generates electricity from the wind. The excess power (after meeting the load requirements) is used to generate hydrogen using an electrolyzer. The generated hydrogen is compressed using a compressor and sent to storage in a high pressure storage tank. The compressor should be operated at near isothermal conditions to reduce the power consumed by the compressor, thereby increasing the efficiency of the system. This paper deals with CFD modeling of a novel water spray cooled reciprocating hydrogen compressor which provides efficient cooling of the system during compression. Water is sprayed directly into the compressor cylinder during the compression stage. The water spray breaks into droplets, which provides large surface area to absorb the heat of compression thereby reducing the temperature. The heat capacity of water being order of magnitudes higher than that of hydrogen provides efficient cooling of the compressed gas with small water to hydrogen volumetric ratio. The concept of water spray cooling during compression is demonstrated through a three dimensional computational fluid dynamics (CFD) simulation.

Research paper thumbnail of SCALE: A hybrid MPI and multithreading based work stealing approach for massive contingency analysis in power systems

Electric Power Systems Research, 2014

Research paper thumbnail of A High-Performance Parallelization and Load-Balancing Approach for Modern Power-Systems

International Journal of Business Analytics, 2015

Research paper thumbnail of Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant

An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has ... more An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has been developed. Huntorf gas turbine plant is taken as the case study to validate the model. Accurate dynamic modeling of CAES involves formulating both the mass and ...

Research paper thumbnail of High Performance Computing for Power System Dynamic Simulation

Research paper thumbnail of System simulation of compressed hydrogen storage based residential wind hybrid power systems

Journal of Power Sources, 2012

ABSTRACT This paper deals with the storage of excess wind energy, in a hybrid wind power system, ... more ABSTRACT This paper deals with the storage of excess wind energy, in a hybrid wind power system, in the form of compressed hydrogen. A system simulation model is developed in Matlab/Simulink platform for the charging and discharging dynamics of compressed hydrogen storage system integrated with the wind turbine and the fuel cell. Wind model is used to estimate the power generation in the wind turbine. When the wind power generation exceeds the load, the excess power is diverted to the electrolyzer to produce hydrogen. As and when the pressure inside the electrolyzer builds, a compressor is operated intermittently (for higher efficiency) to divert the hydrogen into high pressure cylinders. When demand exceeds the power generation, fuel cell supplies the power to the load. A number of fuel cell stacks are provided to meet the required load. The overall efficiency of the storage system, defined as the ratio of the useful energy derived from the storage system to the energy diverted to the storage system is found to be 24.5% for the compressed hydrogen storage based system.

Research paper thumbnail of Dynamics of hydrogen powered CAES based gas turbine plant using sodium alanate storage system

International Journal of Hydrogen Energy, 2012

ABSTRACT Typical compressed air energy storage (CAES) based gas turbine plant operates on natural... more ABSTRACT Typical compressed air energy storage (CAES) based gas turbine plant operates on natural gas or fuel oils as fuel for its operation. However, the use of hydro-carbon fuels will contribute to carbon emissions leading to pollution of the environment. On the other hand, the use of hydrogen as fuel for the gas turbine will eliminate the carbon emissions leading to a cleaner environment. Hydrogen can be produced using renewable energy sources like wind, solar etc. Storage of hydrogen is a bottleneck for such a system. A high capacity sodium alanate metal hydride bed is used in this study to store the hydrogen. The dynamics of the CAES based gas turbine plant operating with hydrogen fuel is presented along with discharge dynamics of the metal hydride bed. The heat required for desorbing the hydrogen from the metal hydride bed is provided partly by the hot flue gas exiting from the low pressure turbine and partly by external heating. Thus some of the heat from the flue gas is extracted. A novel multiple bed strategy is employed for efficient desorption. Each bed consists of a shell and tube, with alanate in the shell and heating fluid flowing through the helical coiled tube. Hydrogen combustor is modeled using a simplified Continuous Stirred Tank Reactor (CSTR) assumption in CANTERA. The NOx emissions in the low pressure turbine exhaust stream are presented.

Research paper thumbnail of Dynamic simulation of air storage-based gas turbine plants

International Journal of Energy Research, 2013

Cavern storage is a proven energy storage technology, capable of storing energy in the form of co... more Cavern storage is a proven energy storage technology, capable of storing energy in the form of compressed air inside a cavern. The Huntorf plant and the Alabama plants use this technology to store electrical energy during the off-peak load hours by compressing the air ...

Research paper thumbnail of Proactive task scheduling and stealing in master-slave based load balancing for parallel contingency analysis

Electric Power Systems Research, 2013

Research paper thumbnail of VANTAGE: A Lyapunov exponents based technique for identification of coherent groups of generators in power systems

Electric Power Systems Research, 2013

ABSTRACT Recent trends of deregulation and expansion in power systems have greatly increased thei... more ABSTRACT Recent trends of deregulation and expansion in power systems have greatly increased their stress levels and hence, ensuring their safety has become a critical challenge. In the event of disturbances, detecting the groups of coherent generators is important to study the characteristics of the system. We propose VANTAGE, a Lyapunov exponents based technique for identification of coherent groups of generators in power systems. VANTAGE performs time domain simulation of contingencies and uses this data to analyze rotor angle stability. VANTAGE offers an efficient algorithmic procedure for identification of coherent groups of generators using Lyapunov exponents method (LEM). VANTAGE does not require a priori estimation of number of groups of coherent generators. We evaluate VANTAGE using a 39-bus system and a 13029-bus system. The results demonstrate the effectiveness of VANTAGE in correctly identifying the coherent groups of generators.

Research paper thumbnail of Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant

Applied Energy, 2012

An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has ... more An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has been developed. Huntorf gas turbine plant is taken as the case study to validate the model. Accurate dynamic modeling of CAES involves formulating both the mass and ...

Research paper thumbnail of Achieving Load-Balancing in Power System Parallel Contingency Analysis Using X10 Programming Language

Due to recent trends of expansion and deregulation in power systems, the stress level of power sy... more Due to recent trends of expansion and deregulation in power systems, the stress level of power systems has increased which has highlighted the importance of conducting stability analysis. Further, due to increasing emphasis on analyzing N − k contingency, the number of contingencies which are required to be analyzed has greatly increased. To address this challenge, researchers have used parallel computing resources, however, in absence of efficient load-balanced scheduling, parallelization leads to wastage of computation resources. In this paper, we present an approach to paral-lelize power system contingency analysis using X10 language. We discuss the features of X10 which enable us to achieve high performance gains. Our approach is evaluated using a large 13029-bus power systems. We parallelize contingency analysis over 2, 4, 8 and 16 threads and use efficient work-stealing algorithm to achieve load-balancing. The results have shown that our approach scales effectively with the number of cores and provides large computational gains. Also, it outperforms a conventional scheduling technique, namely master-slave scheduling.

Research paper thumbnail of MASTER: A JAVA Based Work-Stealing Technique For Parallel Contingency Analysis

In this paper, we present MASTER, a Java based multithreaded work-stealing technique for parallel... more In this paper, we present MASTER, a Java based multithreaded work-stealing technique for parallel contingency analysis in power systems. MASTER analyzes contingencies using time domain simulation and scales contingency analysis task to multiple cores using multithreading in Java. To achieve load balancing, MASTER uses efficient implementation of work-stealing algorithm. We discuss several implementation issues and design time choices which are crucial for achieving efficient implementation. Experiments performed with contingencies of a 13029 bus power system shows that MASTER provides high computational gains and provides much better load-balancing than the conventional scheduling techniques.

Research paper thumbnail of System Topology based Identification of High Risk N-k Contingencies

Research paper thumbnail of Statistical Modeling of Accelerated Pavement Failure Using Response Surface Methodology

Rutting is one of the major load-related distresses in airport flexible pavements. Rutting in pav... more Rutting is one of the major load-related distresses in airport flexible pavements. Rutting in paving materials develop gradually with an increasing number of load applications, usually appearing as longitudinal depressions in the wheel paths and it may be accompanied by small upheavals to the sides. Significant research has been conducted to determine the factors which affect rutting and how they can be controlled. Using the experimental design concepts, a series of tests can be conducted while varying levels of different parameters, which could be the cause for rutting in airport flexible pavements. If proper experimental design is done, the results obtained from these tests can give a better insight into the causes of rutting and the presence of interactions and synergisms among the system variables which have influence on rutting. Although traditionally, laboratory experiments are conducted in a controlled fashion to understand the statistical interaction of variables in such situations, this study is an attempt to identify the critical system variables influencing airport flexible pavement rut depth from a statistical DoE perspective using real field data from a full-scale test facility. The test results do strongly indicate that the response (rut depth) has too much noise in it and it would not allow determination of a good model. From a statistical DoE perspective, two major changes proposed for this experiment are: (1) actual replication of the tests is definitely required, (2) nuisance variables need to be identified and blocked properly. Further investigation is necessary to determine possible sources of noise in the experiment.

Research paper thumbnail of Design Techniques and Applications of Cyber Physical Systems: A Survey

Cyber physical systems (CPSs) are new class of engineered systems which offer close interaction b... more Cyber physical systems (CPSs) are new class of engineered systems which offer close interaction between cyber and physical components. The field of CPS has been identified as a key area of research and CPSs are expected to play a major role in the design and development of future systems. In this paper, we survey recent advancements made in the development and applications of cyber physical systems. We classify the existing research work based on their characteristics and identify the future challenges. We also discuss the examples of prototypes of CPSs. The aim of this survey is to enable researchers and system designers to get insights into the working and applications of CPSs and motivate them to propose novel solutions for making wide-scale adoption of CPS a tangible reality.

Research paper thumbnail of A Survey Of High-performance Computing Approaches in Power Systems

As the size of power systems increases, conventional serial-execution based computing platforms a... more As the size of power systems increases, conventional serial-execution based computing platforms are proving to be insufficient to fulfil the computational demands of modern power systems. To address this, researchers have proposed several high-performance computing (HPC) approaches for benefiting power systems. In this paper, we survey several HPC approaches proposed for power systems. We classify these approaches based on their key characteristics and briefly summarize the challenges in using HPC for benefiting power systems. We believe that this survey will help the readers gain insights into state-of-the-art of HPC in power systems.

Research paper thumbnail of A Survey of Techniques for Designing and Managing Microgrids

Recent trends of rising demands of electricity for supporting critical infrastructure have led to... more Recent trends of rising demands of electricity for supporting critical infrastructure have led to increasing interest in microgrids. Microgrids hold the promise of being the reliable and economically viable electric system which can greatly improve the efficiency, resiliency and eco-friendliness of future smart grid. Recently, several techniques have been proposed to managing microgrids. In this paper, we present a survey of techniques proposed for designing and controlling microgrids. The aim of this paper is to provide insights to the power-system engineers and researchers into techniques for managing the challenges of microgrids like voltage/frequency control, islanding, stability, power quality and economic optimization.

Research paper thumbnail of Dynamic Load Balancing and Scheduling for Parallel Power System Dynamic Contingency Analysis

Research paper thumbnail of Multifrontal Solver for Online Power System Time Domain Simulation

This paper proposes the application of unsymmetric multifrontal method to solve the differential... more This paper proposes the application of unsymmetric
multifrontal method to solve the differential algebraic equations (DAE) encountered in the power system dynamic simulation. The proposed method achieves great computational efficiency as compared to the conventional Gaussian elimination methods and other linear sparse solvers due to the inherent parallel hierarchy present in the multifrontal methods. Multifrontal methods transform or
reorganize the task of factorizing a large sparse matrix into a sequence of partial factorization of smaller dense frontal matrices which utilize the efficient Basic Linear Algebra Subprograms 3 (BLAS 3) for dense matrix kernels. The proposed method is compared with the full Gaussian elimination methods and other direct sparse solvers on test systems and the results are reported.

Research paper thumbnail of Design of a novel and efficient hydrogen compressor for wind energy based storage systems

International Journal of Hydrogen Energy, 2015

ABSTRACT In a hybrid wind power system, the excess wind energy is stored in the form of compresse... more ABSTRACT In a hybrid wind power system, the excess wind energy is stored in the form of compressed hydrogen. Wind turbine generates electricity from the wind. The excess power (after meeting the load requirements) is used to generate hydrogen using an electrolyzer. The generated hydrogen is compressed using a compressor and sent to storage in a high pressure storage tank. The compressor should be operated at near isothermal conditions to reduce the power consumed by the compressor, thereby increasing the efficiency of the system. This paper deals with CFD modeling of a novel water spray cooled reciprocating hydrogen compressor which provides efficient cooling of the system during compression. Water is sprayed directly into the compressor cylinder during the compression stage. The water spray breaks into droplets, which provides large surface area to absorb the heat of compression thereby reducing the temperature. The heat capacity of water being order of magnitudes higher than that of hydrogen provides efficient cooling of the compressed gas with small water to hydrogen volumetric ratio. The concept of water spray cooling during compression is demonstrated through a three dimensional computational fluid dynamics (CFD) simulation.

Research paper thumbnail of SCALE: A hybrid MPI and multithreading based work stealing approach for massive contingency analysis in power systems

Electric Power Systems Research, 2014

Research paper thumbnail of A High-Performance Parallelization and Load-Balancing Approach for Modern Power-Systems

International Journal of Business Analytics, 2015

Research paper thumbnail of Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant

An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has ... more An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has been developed. Huntorf gas turbine plant is taken as the case study to validate the model. Accurate dynamic modeling of CAES involves formulating both the mass and ...

Research paper thumbnail of High Performance Computing for Power System Dynamic Simulation

Research paper thumbnail of System simulation of compressed hydrogen storage based residential wind hybrid power systems

Journal of Power Sources, 2012

ABSTRACT This paper deals with the storage of excess wind energy, in a hybrid wind power system, ... more ABSTRACT This paper deals with the storage of excess wind energy, in a hybrid wind power system, in the form of compressed hydrogen. A system simulation model is developed in Matlab/Simulink platform for the charging and discharging dynamics of compressed hydrogen storage system integrated with the wind turbine and the fuel cell. Wind model is used to estimate the power generation in the wind turbine. When the wind power generation exceeds the load, the excess power is diverted to the electrolyzer to produce hydrogen. As and when the pressure inside the electrolyzer builds, a compressor is operated intermittently (for higher efficiency) to divert the hydrogen into high pressure cylinders. When demand exceeds the power generation, fuel cell supplies the power to the load. A number of fuel cell stacks are provided to meet the required load. The overall efficiency of the storage system, defined as the ratio of the useful energy derived from the storage system to the energy diverted to the storage system is found to be 24.5% for the compressed hydrogen storage based system.

Research paper thumbnail of Dynamics of hydrogen powered CAES based gas turbine plant using sodium alanate storage system

International Journal of Hydrogen Energy, 2012

ABSTRACT Typical compressed air energy storage (CAES) based gas turbine plant operates on natural... more ABSTRACT Typical compressed air energy storage (CAES) based gas turbine plant operates on natural gas or fuel oils as fuel for its operation. However, the use of hydro-carbon fuels will contribute to carbon emissions leading to pollution of the environment. On the other hand, the use of hydrogen as fuel for the gas turbine will eliminate the carbon emissions leading to a cleaner environment. Hydrogen can be produced using renewable energy sources like wind, solar etc. Storage of hydrogen is a bottleneck for such a system. A high capacity sodium alanate metal hydride bed is used in this study to store the hydrogen. The dynamics of the CAES based gas turbine plant operating with hydrogen fuel is presented along with discharge dynamics of the metal hydride bed. The heat required for desorbing the hydrogen from the metal hydride bed is provided partly by the hot flue gas exiting from the low pressure turbine and partly by external heating. Thus some of the heat from the flue gas is extracted. A novel multiple bed strategy is employed for efficient desorption. Each bed consists of a shell and tube, with alanate in the shell and heating fluid flowing through the helical coiled tube. Hydrogen combustor is modeled using a simplified Continuous Stirred Tank Reactor (CSTR) assumption in CANTERA. The NOx emissions in the low pressure turbine exhaust stream are presented.

Research paper thumbnail of Dynamic simulation of air storage-based gas turbine plants

International Journal of Energy Research, 2013

Cavern storage is a proven energy storage technology, capable of storing energy in the form of co... more Cavern storage is a proven energy storage technology, capable of storing energy in the form of compressed air inside a cavern. The Huntorf plant and the Alabama plants use this technology to store electrical energy during the off-peak load hours by compressing the air ...

Research paper thumbnail of Proactive task scheduling and stealing in master-slave based load balancing for parallel contingency analysis

Electric Power Systems Research, 2013

Research paper thumbnail of VANTAGE: A Lyapunov exponents based technique for identification of coherent groups of generators in power systems

Electric Power Systems Research, 2013

ABSTRACT Recent trends of deregulation and expansion in power systems have greatly increased thei... more ABSTRACT Recent trends of deregulation and expansion in power systems have greatly increased their stress levels and hence, ensuring their safety has become a critical challenge. In the event of disturbances, detecting the groups of coherent generators is important to study the characteristics of the system. We propose VANTAGE, a Lyapunov exponents based technique for identification of coherent groups of generators in power systems. VANTAGE performs time domain simulation of contingencies and uses this data to analyze rotor angle stability. VANTAGE offers an efficient algorithmic procedure for identification of coherent groups of generators using Lyapunov exponents method (LEM). VANTAGE does not require a priori estimation of number of groups of coherent generators. We evaluate VANTAGE using a 39-bus system and a 13029-bus system. The results demonstrate the effectiveness of VANTAGE in correctly identifying the coherent groups of generators.

Research paper thumbnail of Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant

Applied Energy, 2012

An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has ... more An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has been developed. Huntorf gas turbine plant is taken as the case study to validate the model. Accurate dynamic modeling of CAES involves formulating both the mass and ...

Research paper thumbnail of Achieving Load-Balancing in Power System Parallel Contingency Analysis Using X10 Programming Language

Due to recent trends of expansion and deregulation in power systems, the stress level of power sy... more Due to recent trends of expansion and deregulation in power systems, the stress level of power systems has increased which has highlighted the importance of conducting stability analysis. Further, due to increasing emphasis on analyzing N − k contingency, the number of contingencies which are required to be analyzed has greatly increased. To address this challenge, researchers have used parallel computing resources, however, in absence of efficient load-balanced scheduling, parallelization leads to wastage of computation resources. In this paper, we present an approach to paral-lelize power system contingency analysis using X10 language. We discuss the features of X10 which enable us to achieve high performance gains. Our approach is evaluated using a large 13029-bus power systems. We parallelize contingency analysis over 2, 4, 8 and 16 threads and use efficient work-stealing algorithm to achieve load-balancing. The results have shown that our approach scales effectively with the number of cores and provides large computational gains. Also, it outperforms a conventional scheduling technique, namely master-slave scheduling.

Research paper thumbnail of MASTER: A JAVA Based Work-Stealing Technique For Parallel Contingency Analysis

In this paper, we present MASTER, a Java based multithreaded work-stealing technique for parallel... more In this paper, we present MASTER, a Java based multithreaded work-stealing technique for parallel contingency analysis in power systems. MASTER analyzes contingencies using time domain simulation and scales contingency analysis task to multiple cores using multithreading in Java. To achieve load balancing, MASTER uses efficient implementation of work-stealing algorithm. We discuss several implementation issues and design time choices which are crucial for achieving efficient implementation. Experiments performed with contingencies of a 13029 bus power system shows that MASTER provides high computational gains and provides much better load-balancing than the conventional scheduling techniques.

Research paper thumbnail of System Topology based Identification of High Risk N-k Contingencies

Research paper thumbnail of Statistical Modeling of Accelerated Pavement Failure Using Response Surface Methodology

Rutting is one of the major load-related distresses in airport flexible pavements. Rutting in pav... more Rutting is one of the major load-related distresses in airport flexible pavements. Rutting in paving materials develop gradually with an increasing number of load applications, usually appearing as longitudinal depressions in the wheel paths and it may be accompanied by small upheavals to the sides. Significant research has been conducted to determine the factors which affect rutting and how they can be controlled. Using the experimental design concepts, a series of tests can be conducted while varying levels of different parameters, which could be the cause for rutting in airport flexible pavements. If proper experimental design is done, the results obtained from these tests can give a better insight into the causes of rutting and the presence of interactions and synergisms among the system variables which have influence on rutting. Although traditionally, laboratory experiments are conducted in a controlled fashion to understand the statistical interaction of variables in such situations, this study is an attempt to identify the critical system variables influencing airport flexible pavement rut depth from a statistical DoE perspective using real field data from a full-scale test facility. The test results do strongly indicate that the response (rut depth) has too much noise in it and it would not allow determination of a good model. From a statistical DoE perspective, two major changes proposed for this experiment are: (1) actual replication of the tests is definitely required, (2) nuisance variables need to be identified and blocked properly. Further investigation is necessary to determine possible sources of noise in the experiment.