Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-10-23DOI: 10.1016/j.elstat.2025.104198
J. Ricardo de Sousa , Marcio Gomes , Orion Ciftja
{"title":"Electrostatic self-energy of a disk with arbitrary axisymmetric surface charge distribution","authors":"J. Ricardo de Sousa , Marcio Gomes , Orion Ciftja","doi":"10.1016/j.elstat.2025.104198","DOIUrl":"10.1016/j.elstat.2025.104198","url":null,"abstract":"<div><div>We present a detailed analysis of the electrostatic self-energy of a charged circular disk with axisymmetric surface charge distribution of the form <span><math><mrow><mi>σ</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mfenced><mrow><mn>1</mn><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mi>ν</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span>, where <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is a constant, <span><math><mrow><mi>u</mi><mo>=</mo><mi>ρ</mi><mo>/</mo><mi>a</mi></mrow></math></span> is a dimensionless radial coordinate, <span><math><mi>a</mi></math></span> is the disk radius while <span><math><mi>ν</mi></math></span> and <span><math><mi>p</mi></math></span> are adjustable parameters. We use a closed-form integral expression for the electrostatic potential previously derived for this class of surface charge distributions to calculate the self-energy. The resulting expression for the electrostatic self-energy is presented in two mathematically equivalent formulations. One involving Bessel functions of the first kind and the other one involving complete elliptic integrals. We explore in detail two physically significant limits, the case of a uniformly charged disk and the one where the charged disk behaves as a conducting equipotential. Each of such cases corresponds to specific values of the parameters, <span><math><mi>ν</mi></math></span> and <span><math><mi>p</mi></math></span>. In both cases, we recover known exact results, providing a good consistency check of the general formalism that we employed. The approach considered also allows a deeper understanding of how the surface charge density profile influences the total electrostatic self-energy of the disk. This means that the procedure offers a flexible framework that can be extended to other surface charge density configurations with radial symmetry.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104198"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145361726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling the electrostatic potential and capacitances of a human walking","authors":"Pedro Llovera-Segovia , César Cañas-Peñuelas , Vicente Fuster-Roig , Alfredo Quijano-López","doi":"10.1016/j.elstat.2025.104195","DOIUrl":"10.1016/j.elstat.2025.104195","url":null,"abstract":"<div><div>Measurement of the electrostatic potential in humans when walking is a useful tool for characterizing floors and antistatic measures in industrial facilities. It is an important question from the point of view of ESD or Hazards and Electrostatic Comfort. However, charging of humans when walking is a complex process where many factors are involved: charge generation and separation during the contact of the shoes and the floor, conductivity of the shoes and the floor, ambient conditions, walking style, etc.</div><div>To better understand the physical phenomena involved during charging when walking, a finite element model is presented where capacitances and induced voltages can be calculated in different positions and conditions. There are some models in the litterature representing the human body capacitance and interactions, but the walking process has not been yet represented. In our work, we modify the model presented by R. Kacprzyk and A. Pelesz[1] allowing movement of arms and legs. The presented model is electrostatic since time constants are very short compared to the speed of walking. Electrostatic discharges are not represented, but the conditions before an electrostatic discharge happens can be simulated. Conductivity of materials can be added to the model to simulate the self discharge process.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104195"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145361727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-11-05DOI: 10.1016/j.elstat.2025.104201
Pramodt Srinivasula
{"title":"Dipolar solvent corrections in nanopore electroosmotic flow with different surface electrostatic conditions","authors":"Pramodt Srinivasula","doi":"10.1016/j.elstat.2025.104201","DOIUrl":"10.1016/j.elstat.2025.104201","url":null,"abstract":"<div><div>This work investigates the influence of electrostatic boundary conditions on electroosmotic flow (EOF) in nanochannels when dipolar solvent effects are incorporated through the Langevin–Bikerman (LB) framework, which extends the classical Poisson–Boltzmann (PB) theory by accounting for finite ion size and field-dependent dielectric saturation. In nanofluidic systems, boundary conditions are application-specific: fixed surface charge (FSC) conditions are relevant for functionalized membranes and porous media, whereas fixed surface potential (FSP) conditions describe modern voltage-gated nanopores in nanofluidic logic devices and biosensors. Comparisons show that the LB corrections to PB predictions differ fundamentally between the two cases: under FSP they enhance EOF, whereas under FSC they suppress it. The extent of corrections depend on the solvent dipole moment, channel dimensions, and salt concentration across parameter ranges relevant to nanofluidic applications. These findings demonstrate the critical importance of thermodynamically consistent boundary modeling for accurate nanoscale electrokinetic simulations and provide guidance for the design and interpretation of nanofluidic devices.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104201"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145473487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-10-15DOI: 10.1016/j.elstat.2025.104197
Khursheed Ahmad Sheikh, Mohammad Mohsin Khan
{"title":"Experimental analysis and voltage optimization of water-solid triboelectric nanogenerators for sustainable energy harvesting using a hybrid PSO–random forest model","authors":"Khursheed Ahmad Sheikh, Mohammad Mohsin Khan","doi":"10.1016/j.elstat.2025.104197","DOIUrl":"10.1016/j.elstat.2025.104197","url":null,"abstract":"<div><div>The study investigates the design, fabrication, and performance optimization of water-solid triboelectric nanogenerators for sustainable energy harvesting. Utilizing mechanical energy from falling water droplets, the research explores how droplet height, surface angle between the water droplets and the triboelectric nanogenerator (TENG) strip, and triboelectric material pairing influence electrical output. Four TENG configurations were tested using aluminum or copper as electron donors and fluorinated ethylene propylene (FEP) or Kapton tape as electron acceptors. The experimental results revealed that the Aluminum–FEP combination yielded the highest voltage (591 mV) at a droplet height of 300 mm and 75° angle. A Random Forest (RF) regression model was developed to predict voltage output based on experimental parameters, achieving a high R<sup>2</sup> value of 0.88. Particle Swarm Optimization (PSO) was employed alongside RF to determine the optimal configuration for maximum voltage generation. The PSO optimization revealed that the highest voltage output of 587.18 mV was obtained at a 68° inclination angle and a droplet height of 277 mm, with aluminium as the donor and FEP as the acceptor material. These findings suggest that water-solid triboelectric nanogenerators hold substantial promise for powering low-energy devices and supporting decentralized energy systems.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104197"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145332380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-07-31DOI: 10.1016/j.elstat.2025.104127
Toni Viheriäkoski , Pasi Tamminen , Jarmo Pöllänen , Paul Holdstock , Jeremy Smallwood
{"title":"Indoor air purification using electrostatic fields without traditional air circulation","authors":"Toni Viheriäkoski , Pasi Tamminen , Jarmo Pöllänen , Paul Holdstock , Jeremy Smallwood","doi":"10.1016/j.elstat.2025.104127","DOIUrl":"10.1016/j.elstat.2025.104127","url":null,"abstract":"<div><div>Electrostatic air purification is typically based on air circulation through an electrostatic filtering system. In contrast, this study explores the direct removal of airborne particles from an emission source using electrically charged attraction panels. The charge relaxation of particles appears to be sufficiently long in low-humidity conditions, where dust and other charged particles are more easily released into the air. The results indicate that the method can be useful in environments where airborne particles are naturally charged and released, for example, by moving objects or people. Unlike conventional systems, electrostatic purification without air circulation requires minimal energy, making it a cost-efficient and suitable for environments with limited air exchange. This research includes airborne concentration tests and contamination experiments examining the effects of electrostatic fields on electrically charged panels, demonstrating the potential of this simple yet effective technology for various indoor applications.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104127"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-11-15DOI: 10.1016/j.elstat.2025.104206
Zhijin Zhang , Hang Zhang , Xingliang Jiang , Chao Zhou , Rong Liu , Yutai Li
{"title":"Detection of zero-value insulators in ±800 kV DC porcelain strings based on spatial electric field variation","authors":"Zhijin Zhang , Hang Zhang , Xingliang Jiang , Chao Zhou , Rong Liu , Yutai Li","doi":"10.1016/j.elstat.2025.104206","DOIUrl":"10.1016/j.elstat.2025.104206","url":null,"abstract":"<div><div>Accurate detection of zero-value insulators in transmission line porcelain insulator strings remains a challenging problem. The infrared imaging and harmonic electric field methods, which rely heavily on environmental conditions and multidimensional image processing. In this study, a full-scale coupled-field model was developed in COMSOL, to closely approximate the real operating environment of ±800 kV DC systems to detect zero-value. On this basis, a differential spatial electric field criterion was proposed, where the field intensity differences between adjacent insulator segments were extracted as features. These features were then cascaded with a probabilistic neural network (PNN) to enhance detection accuracy. The proposed electric field–based method requires only one-dimensional data for classification, thereby simplifying implementation and improving robustness for practical applications. The results show that the electric field curve at the zero-value insulator exhibits a pronounced “dip”, particularly under wet pollution conditions, while the electric field of adjacent normal insulators increases. Using this approach, the position of zero-value insulators in the string was identified with an accuracy of 96.3 %. This study adopts a simulation-based verification approach and has not yet completed field measurements and cross-calibration. In the future, scaled experiments and UAV-based line application tests will be conducted for validation.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104206"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-08-16DOI: 10.1016/j.elstat.2025.104156
Ali Khoshnejad, Sohrab Gholamhosein Pouryoussefi, Alireza Doostmahmudi, Reza Ebrahimi
{"title":"Experimental investigation of flow separation delay in S-shaped duct using multiple dielectric barrier discharge plasma actuators","authors":"Ali Khoshnejad, Sohrab Gholamhosein Pouryoussefi, Alireza Doostmahmudi, Reza Ebrahimi","doi":"10.1016/j.elstat.2025.104156","DOIUrl":"10.1016/j.elstat.2025.104156","url":null,"abstract":"<div><div>This study experimentally investigates the effects of multiple parallel dielectric barrier discharge (DBD) plasma actuators on controlling the flow separation in an S-shaped duct with an elliptical inlet and circular outlet. An open-loop suction-type test rig composed of composite materials was designed for this purpose. The synergistic effects of multiple DBD plasma actuators (MDBD) were initially examined on a flat plate before being applied to the complex geometry of the S-shaped duct. Additionally, the impact of varying plasma applied voltages (6, 6.5, 7, 7.5, 8 kV) and S-duct inlet velocities (24, 35, and 47 m/s) on the performance of the plasma actuators were investigated. Also, the pressure coefficient distribution on the lower surface of the duct was measured under various conditions. The use of MDBD plasma actuators on a flat plate resulted in a significant increase in the maximum induced velocity, approximately 50 % higher than that achieved with a single actuator. This enhancement is attributed to the synergistic effects of the multiple actuators on the induced flow. The application of the MDBD plasma actuator configuration within the S-shaped duct effectively delayed flow separation across all tested inlet velocities (Reynolds numbers of 2.35 × 10<sup>5</sup>, 3.51 × 10<sup>5</sup>, and 4.75 × 10<sup>5</sup>). However, actuator effectiveness decreased with increasing inlet velocity. Higher actuation voltages resulted in a more pronounced delay in separation. Also, at a Reynolds number of 2.35 × 10<sup>5</sup>, the MDBD configuration with 8 kV and 15 Hz achieved a 35.9 % increase in the pressure coefficient compared to the no-plasma condition.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104156"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-08-28DOI: 10.1016/j.elstat.2025.104154
Giuseppe Andriani , Gianmaria Pio , Chiara Vianello , Paolo Mocellin , Ernesto Salzano
{"title":"Electrical conductivity as an indicator for early warning detection systems in chemical reactors","authors":"Giuseppe Andriani , Gianmaria Pio , Chiara Vianello , Paolo Mocellin , Ernesto Salzano","doi":"10.1016/j.elstat.2025.104154","DOIUrl":"10.1016/j.elstat.2025.104154","url":null,"abstract":"<div><div>Early Warning Detection Systems (EWDS) are essential for preventing runaway reactions in chemical reactors by providing timely alerts before uncontrolled exothermic events. Conventional EWDS rely predominantly on temperature monitoring; however, industrial temperature sensors often suffer from delayed response and are highly dependent on sensor positioning, limiting their effectiveness during rapid or localized thermal excursions.</div><div>This study introduces an alternative detection strategy based on electrical conductivity monitoring, which offers faster response times and higher sensitivity—especially in reactions where ionic or charged species are released at the onset of runaway. A theoretical framework is presented to demonstrate how this method can overcome key limitations of temperature-based systems, enabling more accurate and responsive detection.</div><div>Compared to the benchmark divergence method, the conductivity-based approach detects runaway onset within 2 °C of the true temperature (vs. <span><math><mo>∼</mo></math></span> 3 °C deviation with temperature sensors), and anticipates the event 200–300 s before peak temperature. This allows earlier intervention and significantly reduces the maximum temperature rise at onset (by 30%–40% compared to temperature-based detection). Integrating advanced conductivity sensors into existing EWDS infrastructures could markedly improve reactor safety and control. This work lays the foundation for future experimental validation and broader adoption in chemical reaction engineering safety systems.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104154"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-09-15DOI: 10.1016/j.elstat.2025.104168
Khaled Daioui, Thami Zeghloul, Lucian Dascalescu
{"title":"Electric charge neutralization of granular materials using an air-assisted ionizer under different operational conditions","authors":"Khaled Daioui, Thami Zeghloul, Lucian Dascalescu","doi":"10.1016/j.elstat.2025.104168","DOIUrl":"10.1016/j.elstat.2025.104168","url":null,"abstract":"<div><div>An operation of electric charge neutralization is often integrated in complex electrostatic separation processes targeted at the selective sorting of the constituents of granular mixtures in a wide range of industrial applications. The aim of the present work is to prove the possibility of increasing the charge elimination efficiency of a commercial air-assisted neutralizer, under various dynamic conditions simulating realistic industrial scenarios. Three experimental setups were tested. In the first one, particles were charged by triboelectric effect and then transported by a grounded metallic conveyor belt before being subjected to ionic bombardment from the commercial neutralizer. The second configuration employed a custom-designed rotating-roll corona-electrostatic separator. Particles were charged by corona discharge and then transported on the rotating roll electrode before being neutralized by an air-assisted ionizer installed opposite the roll electrode. In the third experimental configuration, the neutralization system was installed downstream from the particle detachment step of the second configuration. After being dislodged from the grounded rotating drum by a mechanical brush, the charged insulating particles fell freely under gravity through the ionization zone. This zone comprised the commercial ionizing neutralizer positioned opposite a grounded rectangular metal plate. The factors investigated were the applied voltage (<em>U</em><sub><em>n</em></sub>) and the distance (<em>d</em><sub><em>n</em></sub>) between the neutralizing electrode and the grounded (belt, roll, the plate) electrode, as well as the air velocity (<em>v</em>). The findings highlight the substantial role of airflow in enhancing ion dispersion and promoting charge neutralization, particularly through its interaction with the electric field geometry and particle dynamics. For instance, residual charge-to-mass ratio dropped to as low as 1–2 nC/g in the first configuration at air velocity of 2 m/s. This study clearly demonstrates the critical importance of finely tuning geometry, electrical field strength, and air dynamics to optimize electrostatic neutralization. These findings provide valuable guidelines for designing more efficient electrostatic separation systems, particularly for industrial recycling processes involving insulating materials.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104168"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of ElectrostaticsPub Date : 2025-12-01Epub Date: 2025-10-09DOI: 10.1016/j.elstat.2025.104188
Stefan H. Spitzer , Fabian Reitmeier , Enrico Danzi , Bretislav Janovsky , Michael Paul
{"title":"The Exploding Wire: A novel ignition source for the determination of safety characteristics of dusts and hybrid mixtures","authors":"Stefan H. Spitzer , Fabian Reitmeier , Enrico Danzi , Bretislav Janovsky , Michael Paul","doi":"10.1016/j.elstat.2025.104188","DOIUrl":"10.1016/j.elstat.2025.104188","url":null,"abstract":"<div><div>For the determination of safety characteristics of dusts there are mainly chemical igniters in use. Especially for the maximum explosion pressure and the maximum rate of pressure rise there is no standard with another ignition source. The chemical igniters have the disadvantage of being very hard to obtain in most countries and they are even illegal in some. This leads to the fact, that those countries are not able to investigate the safety characteristics or only with a high effort by sending dust samples to facilities outside the country. This article presents a novel ignition source and describes how to build it. It is also the first step to place this ignition source into the dust standards in the future.</div></div>","PeriodicalId":54842,"journal":{"name":"Journal of Electrostatics","volume":"138 ","pages":"Article 104188"},"PeriodicalIF":2.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145265969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}