Selected Scientific Papers

1999



1. Homutescu V. M., Comparative Analysis of the Actual Computing Methods of the Film-Cooling Flame Tube Temperature at Gas Turbine Motors. Bul. I.P.I., Tom XLV(XLIX), Fasc. 3-4, 1999.
   
   Abstract. We analyze comparatively the NSM and the LM methods used to calculate the temperature field along a film-cooling flame tube section. For identical conditions are presented the temperature fields calculated with the two methods.
   Keywords: gas turbine motor, cooling flame tube temperature
   
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2000



2. Homutescu V. M., Main Factors that Influence the Film-Cooling Flame Tube Temperature in Gas Turbine Engine Combustion Chamber. Bul. I.P.I., Tom XLVI, Fasc. 3-4, 2000.
   
   Abstract. The paper analyzes a computing method for the gas turboengines flame tube temperature. It also studies the influence of pressure, temperature and film cooling air flow on the flame tube temperature.
   Keywords: gas turbine engine, flame tube temperature, computing method
   
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2001



3. Homutescu V.M., Homutescu C.A., Homutescu A., Appreciations about a variable displacement Stirling engine. Termotehnica, V, no. 2/2001, p. 58-62, ISSN 1222-4057.
   
   Abstract. The paper presents the constructive conception of a variable displacement Stirling engine equipped with two coaxial pistons. The displacement variation is achived in a motive drive derived from the rhombic drive and allows modification - while running on load - of the equivalent length of two rods. Henceforth follows the kinematic analysis of the drive and the thermal calculation and it is analyzed to which extent can the engine power be adjusted by variating the displacement.
   
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2002



4. Homutescu C. A., Dragomir - Stanciu D., Homutescu V. M., Homutescu A., Perspectives on Microcogeneration of Heat and Power using Free Piston Stirling Engines. The 2nd International Conference of Electric and Power Engineering, "EPE 2002", in Bul. I.P.I., Tom XLVIII (LII), Fasc. 5A, p. 111 ... 116, ISSN 0258-9109.
   
   Abstract. The work presents the employment of a free piston Stirling engine in the cogeneration of heat and power needed by a household. The cyclic evolution of the free piston Stirling engine is described and his advantages both as combustion engine engaging in motion an electric generator and as warm gas generator for hot water production as well.
   Keywords: free piston Stirling engine, microcogeneration, heat, power
   
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2003



5. Homutescu C.A., Homutescu V.M., Homutescu A., A new approach on the notion of generalized thermodynamic cycle in gas thermal engines. Termotehnica, V, no. 1-2/2003, p. 46-48, ISSN 1222-4057.
   
   Rezumat. Se introduce un ciclu termodinamic în care agentul primeşte şi cedează căldură prin toate cele trei transformări termodinamice simple (v = ct., p = ct., T = ct.). Cele două lanţuri de cîte trei transformări sînt legate prin transformări adiabatice. Căldura cedată în transformările de răcire izocoră şi izobară este recuperată parţial, fiind reintrodusă în ciclu în timpul transformărilor de încălzire izocoră şi izobară. Transformările simple din ciclu sînt definite prin rapoarte parţiale de comprimare şi de destindere sau prin rapoarte parţiale de temperatură. Se introduce randamentul recuperării căldurii. Se dau relaţiile pentru randamentul termic şi pentru lucrul mecanic produs în ciclul generalizat.
   
   Click to download the paper (in pdf format) from "Termotehnica" journal website.
Homutescu V.M., Homutescu C.A, Dragomir-Stanciu D., Eni M., Determinarea distribuţiei temperaturii în tubul de foc al turbomotoarelor cu gaze folosind analiza cu element finit. A XIII- a Conferinţă Naţională de Termotehnică cu participare internaţională. Reşiţa, mai 2003. În Analele Universităţii “Eftimie Murgu” din Reşiţa, anul X, fasc. I, 2003, vol. I, ISSN 1453-7394, p.161-166.
6. Homutescu C. A., Homutescu V.M., Homutescu A., Influenţa unor factori funcţionali asupra lucrului mecanic produs de motorul Stirling cu cilindree variabilă (in Romanian). A VII-a sesiune de comunicări ştiinţifice „Provocările ştiinţei în secolul XXI“, Academia Forţelor Terestre „Nicolae Bălcescu“ Sibiu, 5 decembrie 2003, ISBN 973-80088-85-2, lucrarea VII-4.9, p. 59-66.
   
   Abstract. The paper presents the constructive conception of a variable-displacement Stirling engine and the functional parameter influences on the mechanical work yielded.
   
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2004



7. Homutescu V.M., Jugureanu E., Bălănescu D.T., Homutescu A., Power And Heat Cogeneration Using Variable Displacement Stirling Engine. The 3rd International Conference of Electric and Power Engineering, "EPE 2004", 7th-8th of October 2004, in Bul. I.P.I., Tom L (LIV), Fasc. 5A, p. 1113 ... 1118, ISSN 1223-8139.
   
   Abstract. The construction of the Stirling engine with on load variable displacement and its employment in heat and power microcogeneration units is analyzed. Engine performance and power adjustment capability are analyzed.
   Keywords: variable displacement Stirling engine, cogeneration, heat, power
   
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8. Homutescu V.M., Jugureanu E., Homutescu C.A., Homutescu A., Isothermal Model for Vuilleumier Machines. First International Conference “Advanced Concepts in Mechanical Engineering”, Iaşi / Jassy, June 2004, in Bul. I.P.I., Tom L (LIV), Fasc. 6C, p. 111 ... 116, ISSN 1011-2855, paper ACME 04619.
   
   Abstract. This paper presents the isothermal model of the Vuilleumier machine. A numerical example with p-V diagrams for the machine chambers is also provided.
   Keywords: Vuilleumier machine, isothermal model, heat pump, refrigerator
   
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2005



9. Homutescu V.M., Homutescu A., Bălănescu D.-T., Semi-Adiabatic Physico-Mathematical Model of the Vuilleumier Heat Pump. Proceedings of the 5th International Conference on Electromechanical and Power Systems SIELMEN 2005, October 2005, Chişinău, Rep. of Moldova, Vol. I, p. 510-513, ISBN GEN 973-716-208-0.
   
   Abstract. The paper presents a semi-adiabatic model of the Vuilleumier machine. The model assumes the hypothesis that inside the low temperature and inside the high temperature chambers adiabatic processes take place only. Inside the intermediate temperature chambers and inside the heat exchangers only isothermal processes take place. The differential equations of the processes inside the heat pump are deduced.
   Keywords: Vuilleumier machine, semi-adiabatic model, thermal-acted heat pump
   
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10. Homutescu V.M., Kinematic Stirling Motor-Driven Compressors. Conferinţa Naţională de Energetică Industrială cu Participare Internaţională CNEI 2005, „Modelling and Optimization in the Machine Building Field“, MOCM-11, Vol. 3, edited by "Academia Română de Ştiinţe Tehnice" and University of Bacău, ALMA MATER Publishing House, Bacău, 2005, p. 49-52, ISSN 1224-7480.
    
    Abstract. The paper analyzes the possibility of building monoblock kinematic Stirling motor-driven compressors. Such an engine is a combination between a compressor and a kinematic Stirling engine. In the equivalent schematic diagram the power piston of the Stirling engine also performs the function of the compressor piston. The advantages and the disadvantages of these machines are analyzed.
    Keywords: kinematic Stirling engine, motor-driven compressor
    
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11. Homutescu V.M., Bălănescu D.-T., Adiabatic Behavior of a Variable Displacement Stirling Engine. trans & MOTAUTO'05+ International Conference, November 2005, Veliko Tîrnovo, Proceedings, Vol. I, ISBN 954-9322-09-2, Publisher: Scientific-technical union of mechanical engineering, Sofia, Bulgaria, 2005, p. 97...100.
    
    Abstract. The construction of the Stirling engine with on load variable displacement is presented. The variable displacement Stirling engine behavior is analyzed using an adiabatic physico-mathematical model. Engine performance and power adjustment capability are analyzed.
    Keywords: Stirling engine, variable displacement, adiabatic model, rhombic drive
    
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2006



12. Homutescu V.M., Bălănescu D.-T., Theoretical Realization of the Stirling Cycle on Two Pistons Machines. The 2nd International Conference "Advanced Concepts in Mechanical Engineering", 16th-17th of June, 2006, in Bul. I.P.I., Tom LII (LVI), Fasc. 6C, p. 143 ... 150, ISSN 1011-2855.
    
    Abstract. The paper defines the theoretical Stirling machine, that has heat exchangers with null volume, represented by portions of the cylinder. The paper presents the realization of the Stirling cycle on alpha, beta and gamma Stirling motors. The pressure-volume diagrams inside the machine chambers are obtained. For Stirling motors with identical maximum compression chamber volumes, the thermodynamic inferiority of the gamma scheme is proved.
    Keywords: theoretical Stirling machine, Stirling cycle, p-V diagram, compression and expansion chambers
    
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13. Homutescu V.M., Jugureanu E., Homutescu A., Adiabatic Physico-Mathematical Model of the Vuilleumier Thermal-Acted Heat Pump. The 2nd International Conference "Advanced Concepts in Mechanical Engineering", 16th-17th of June 2006, in Bul. I.P.I., Tom LII (LVI), Fasc. 6C, p. 151 ... 156, ISSN 1011-2855.
    
    Abstract. The paper presents an adiabatic model of the Vuilleumier machine. The model assumes the hypothesis that inside the low and high temperature chambers and inside the intermediate temperature chambers adiabatic processes take place only. Inside the heat exchangers only isothermal processes take place. The differential equations of the processes inside the heat pump are deduced.
    Keywords: Vuilleumier machine, adiabatic model, thermal-acted heat pump
    
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14. Homutescu V.M., Homutescu A., Bălănescu D.-T., Theoretical Thermal acted Heat Pump. The 4th International Conference of Electrical and Power Engineering, "EPE 2006", 12th-14th of October 2006, in Bul. I.P.I., Tom LII (LVI), Fasc. 5C, p. 1261 ... 1268, ISSN 1223-8139.
    
    Abstract. The theoretical Vuilleumier machine is defined, inside which the gas evolves in simple thermodynamic processes. Thus, the theoretical Vuilleumier machine achieves the greatest possible performances. Equal lengths of the functional phases are imposed by the condition that between the movement laws of the displacers a phase angle γ exist. Using the properties of the theoretical Vuilleumier machine, the optimum cylinder diameter ratio (for which the heats exchanged are maximum) is deduced.
    Keywords: theoretical thermal-acted heat pump, Vuilleumier, diameter ratio
    
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2007



15. Homutescu V.M., Bălănescu D.-T., Homutescu A., Physico-mathematical Model with Friction Losses for Vuilleumier Machines. 6th International Conference on Electromechanical and Power Systems, October 2007, Chişinău, Republic of Moldova, published in Annals of the University of Craiova, nr. 31, Vol. II, ISSN 1842-4805, Publisher: Editura Universitaria, Craiova, 2007, p. 237...242.
    
    Abstract. The paper presents a new physico-mathematical model for Vuilleumier machines (thermal-acted heat pumps). The model takes into account the friction losses that appear in the heat exchangers of the machine. The pressure drop caused by friction inside a generic heat exchanger is determined. The coefficients of performance (COP's) calculated with the new model are smaller than the isothermal ones. The adjustment of the theoretical models in order to take into account the pressure losses inside the heat exchangers allow the emphasizing of some phenomena that appear when changing the rotation speed.
    Keywords: Vuilleumier machine, thermal-acted heat pump, physico-mathematical model, isothermal model, friction losses
    
    Click to download the paper (in pdf format) from University of Craiova website.
16. Homutescu V.M., Bălănescu D.-T., Semi-Adiabatic Physico-Mathematical Model for Gamma-Type Stirling Engines. 2nd International Conference on Thermal Engines and Environmental Engineering MET IME 2007, June 2007, Galaţi, Proceedings, vol. 2, ISBN 978-973-1724-17-1, Zigotto Publishers, Galaţi, p. 213...220.
    
    Abstract. A physico-mathematical semi-adiabatic model for γ-type Stirling motors is presented. The model assumes that inside the expansion chamber and inside the compression space delimited by the displacer piston inside its cylinder the gas evolves in adiabatic processes. The differential equation system describing the functioning of the γ-type Stirling motor is obtained. A numerical example is used for comparison between the functioning of the motor accordingly to the proposed model and the isothermal functioning of the γ-type motor.
    Keywords: γ-type motor, Stirling, semi-adiabatic model, compression space, displacer
    
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17. Homutescu V.M., The Impossibility of Modeling the Thermodynamic Stirling Cycle on Gamma-Type Machines. Conferinţa naţională de termotehnică cu participare internaţională, ediţia a XVI-a, 31 mai – 1 iunie 2007, Ploieşti, Vol. 1 – Termodinamică, schimb de căldură şi aplicaţii, ISSN 1843-1992, Editura Universităţii Petrol-Gaze din Ploieşti, p. 88...93.
    
    Abstract. The paper analyzes the gamma-type theoretical Stirling machine. It was showed that on such a machine the thermodynamic Stirling cycle could not be obtained. The gamma-type Stirling motor functioning and the energy amounts exchanged with the exterior were analyzed. It was showed that the efficiency of the gamma-type isothermal motor with heat regeneration is equal to the efficiency of a Carnot cycle working between the same extreme temperatures, due to the isothermal hypotheses. The work produced is less than the one of the other Stirling engines (for the same conditions - volumes, temperatures, gas mass).
    Keywords: theoretical Stirling machine, gamma type motor, p-V diagram, performance
    
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2008



18. Homutescu V.M., Dumitraşcu Gh., Horbaniuc B., Evaluation of the Work Lost Due to Leaks Through Cylinder - Displacer Gap. COFRET'08, 11 – 13 June 2008, Nantes - France, ISSN 2.6905267.61.5 (CD), paper also published by Termotehnica, no. 2/2008, p. 70-74, Bucharest, ISSN 1222-4057.
    
    Abstract. The paper presents an uncoupled model (based on the principle of effects superposition) that assesses the lost work due to working agent leaks through the gap between the cylinder and the displacer of beta- or gamma-type Stirling machines. The work yielded when working agent leaks are taken into account is calculated by integrating the differential expression of the volume variation work, considering the pressure changes inside the chambers of the machine. The modeling hypotheses consider the ideal gas model and the influence of leaks. The model was applied to a beta-type Stirling engine. The model allows the calculation of the work lost.
    Keywords: beta- and gamma-type Stirling motor / lost work / cylinder-displacer gap
    
    Click to download the paper (in pdf format) from "Termotehnica" journal website.
19. Horbaniuc B., Dumitraşcu Gh., Homutescu V.M., Gas Turbine System with Interstage Cooling and Steam Injection Using Oxy-combustion. 6th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment (HTE'08) Rhodes, Greece, August 20-22, 2008, ISSN: 1790-5095, ISBN: 978-960-6766-97-8, p. 120-125.
    
    Abstract. The intake air temperature influences the power output of a gas turbine. In order to control it, the paper considers the interstage air cooling by adiabatic humidification. Steam injection after the combustor is considered to control the flue gases temperature in the inlet section of the turbine. Both techniques are intended to increase the shaft work rate of the gas turbine. The first section of the paper studies the influences exerted by the intake air temperature and by the injected steam/air ratio on the flue gas temperature and composition. The second section tackles the analysis of the compression and expansion processes respectively, allowing the estimation of the shaft work of the turbine. The third section of the paper considers the opportunity of using oxy-combustion to increase the power of the turbine or to counterbalance the effect of the compressor power consumption increase due to high intake air temperatures.
    Keywords: gas turbine, interstage cooling, adiabatic humidification, steam injection, oxy-combustion
    
    Click to download the paper (in pdf format) from "www.wseas.us" website.
20. Homutescu V.M., Optimization of Diameter Ratio for the Vuilleumier Machine Based on the Isothermal Functioning. The 3rd International Conference "Advanced Concepts in Mechanical Engineering", 5th-6th of June 2008, Bul. I.P.I., Tom LIV (LVIII), Fasc. 2, p. 475 ... 482, ISSN 1011-2855.
    
    Abstract. A method for optimizing the diameter ratio for the Vuilleumier machine is presented. The optimum ratio giving maximum performances was determined with an isothermal functioning model. The optimum ratio depends on the heat exchanger volumes and on the stem diameter. If the stem diameter is null, the COP’s are independent of diameter ratio.
    Keywords: Vuilleumier machine, thermal-acted, diameter optimization, isothermal model
    
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2009



21. Homutescu A., Homutescu V.M., Homutescu C.-A., Physico-mathematical models of the Vuilleumier machine. Termotehnica, nr. 2/2009, p. 32-37 (on-line: p. 33-38), AGIR Printing House, Bucharest, ISSN 1222-4057.
    
    Abstract. Several theoretical physico-mathematical models of the thermally acted Vuilleumier machine are compared. The hypotheses on which each model relies together with the physical laws based on which numerical simulations of the machine can be performed and machine performances can be estimated are briefly presented. For a particular Vuilleumier machine, a good similarity is obtained by comparing the results of the numerical simulation with the results obtained by different theoretical models; the causes of this similarity are studied.
    Keywords: thermally acted, Vuilleumier machine, theoretical physico-mathematical isothermal or semi-adiabatic model
    
    Click to download the paper (in pdf format) from "Termotehnica" journal website.
22. Jugureanu E., Horbaniuc B., Dragomir-Stanciu D., Homutescu V.M., Atanasiu M., Sârbu I., Replacement of the Cooling with CaCl2 Mixture with the Cooling Using Direct Evaporation. Bulletin of the Transilvania University of Braşov, 2(51), Series I, Special Issue No. 1, Vol 1., ISSN 2065-2119, ISBN 978-973-598-521-9, 207-216, 2009.
    
    Abstract. The purpose of the present paper was to find new cooling systems in the rubber manufacturing process.
    Keywords: synthetic-styrene rubber, autoclaves heat exchange, cooling system, production line, heat exchange coefficients
    
    Click to download the paper (in pdf format) from "Transilvania" University of Braşov website.

2010



23. Homutescu V.M., Bălănescu D.-T., Optimization of Diameter Ratio for Alpha-Type Stirling Engines. Cinquieme edition du colloque francophone, COFRET 2010, Iaşi / Jassy, 5th-7th of May 2010, in Bul. I.P.I., Tom L (LVI), Fasc. 3a, p. 313 ... 322, ISSN 1011-2855, paper also published by Termotehnica, no. 1/2010, p. 53-57, AGIR Printing House, Bucharest, ISSN 1222-4057.
    
    Abstract. The problem of the constructive dimensioning and optimization of the Stirling machines is still insufficiently studied. The paper analyzes the alpha-type Stirling engine from the point of view of the constructive optimization, by choosing the optimum ratio between the diameters of the two cylinders in the machine composition. This theoretical analysis showed that, by analyzing the functioning of the engine with either an isothermal model or the adiabatic model without or with losses taken into consideration, an optimum value of the diameter ratio exists, for which the work produced by the engine takes a maximum value. The optimum diameter ratio is calculated for a numerical example.
    Keywords: alpha-type Stirling engine, diameter ratio optimization, adiabatic model
    
    Click to download the paper (in pdf format, Bul. I.P.Iaşi version).
    Click to download the paper (in pdf format) from "Termotehnica" journal website.

2012 / 2013



24. Homutescu V.M., Maximum Performances of the Stirling Machine Working as Motor-Driven Compressor. 5th International Conference “Advanced Concepts in Mechanical Engineering”, Iaşi / Jassy, 14th-15th of June 2012, Bul. I.P.I., Tom LIX (LXIII), Fasc. 3, 2013, p. 27 ... 38.
    
    Abstract. The functioning of an engine-driven Stirling compressor is analyzed using two isothermal physico-mathematical models. The maximum performances of a beta-type machine and the performances that can be achieved by the theoretical engine-driven Stirling compressor (working after the Stirling thermodynamic cycle) are obtained. These maximum performances can be used as references for comparing different physical embodiments of engine-driven Stirling compressors among them.
    Keywords: Stirling machine, engine-driven compressor, maximum performances, isothermal models
    
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2013



25. Bălănescu D.-T., Homutescu V.M., Recovering Energy from Wood Wastes in a Semi-closed Cycle Power Plant. Termotehnica, supplement 1/2013, p. 5-8, AGIR Printing House, Bucharest, ISSN 1222-4057.
    
    Abstract. The paper presents a solution for the power generation in a Hot Air Turbine Power Plant using the wood wastes as fuel. The parameters for the estimated performances of the Power Plant and the overall specific heat exchange surface of the Hot Air Generator had been calculated for different values of the compressor pressure ratio. The resulted curves are presented and analyzed.
    Keywords: Hot Air Turbine Power Plant, Hot Air Generator, semi-closed cycle, efficiency, power, specific heat exchange surface
    
    Click to download the paper (in pdf format) from "Termotehnica" journal website.

2014



26. Homutescu V.M., Bălănescu D.-T., Gamma-Type Stirling Motor-Driven Compressor. International Scientific Conference ACME 2014, Iaşi / Jassy, Applied Mechanics and Materials Journal, Vol. 659 (2014) - Advanced Concepts Mechanical Engineering II, ISSN 1660-9336, Trans Tech Publications, Switzerland, p. 377-382, DOI 10.4028/www.scientific.net/AMM.659.377.
    
    Abstract. Paper is analyzing an engine-driven gamma-type Stirling compressor by means of an isothermal physico-mathematical model. The maximum performances of an engine-driven gamma-type Stirling compressor (working after a quasi-Stirling thermodynamic cycle) are obtained. By using these maximum performances as reference, a comparison between different physical embodiments of engine-driven gamma-type Stirling compressors can be achieved.
    Keywords: gamma-type Stirling machine, engine-driven compressor, maximum performances, isothermal models
    
    Preview 1st page at "Scientific.net by Trans Tech Publications" website.
27. Homutescu V.M., Bălănescu D.-T., Physico-Mathematical Model of the Theoretical Gamma-Type Stirling Motor-Driven Compressor. International Scientific Conference ACME 2014, Iaşi / Jassy, Applied Mechanics and Materials Journal, Vol. 659 (2014) - Advanced Concepts Mechanical Engineering II, ISSN 1660-9336, Trans Tech Publications, Switzerland, p. 383-388, DOI 10.4028/www.scientific.net/AMM.659.383.
    
    Abstract. Paper is analyzing a physico-mathematical isothermal model of the theoretical engine-driven gamma-type Stirling compressor. The absolute maximum performances of an theoretical engine-driven gamma-type Stirling compressor (that function after a thermodynamic cycle comprising two isochoric processes of heating and cooling the agent, one isothermal compression and one partially-cooled expansion process) are obtained. Using these absolute maximum performances as reference, it is possible to assess the degree in which several real physical constructions of this machine can approach to the ideal functioning.
    Keywords: theoretical gamma-type Stirling machine, engine-driven compressor, maximum performances, isothermal model
    
    Preview 1st page at "Scientific.net by Trans Tech Publications" website.

2015 / 2016



28. Homutescu V. M., Bălanescu D.-T., Panaite Carmen Ema, Atanasiu M.-V., Physico-Mathematical Model of a Hot Air Engine Using Heat From Low-Temperature Renewable Sources of Energy. 7th International Conference on Energy and Environment "Clean and Safe Power" CIEM 2015, Iaşi / Jassy, 22nd-23rd of October 2015, U.P.B. Sci. Bulletin, series D, volume 78, iss. D, 2016, ISSN 1223-7027, p. 183-190.
    
    Abstract. The paper provides a novel physico-mathematical model able to estimate the maximum performances of a hot air Ericsson-type engine - which is capable to run on renewable energy, such as solar energy, geothermal energy or biomass. The computing program based on this new model allows to study the influences of the main parameters over the engine performances and to optimize their values.
    Keywords: Ericsson-type engine, renewable energy, theoretical model, maximum performances
    
    Click to download the paper (in pdf format) from "U.P.B. Sci. Bulletin" journal website.

2016



29. Homutescu V. M., Bălanescu D.-T., Panaite Carmen Ema, Atanasiu M.-V., Variable displacement alpha-type stirling engine. 7th International Conference on Advanced Concepts in Mechanical Engineering, 9th–10th of June 2016, Iaşi / Jassy, Romania, IOP Conference Series: Materials Science and Engineering, volume 147, 2016, paper 012143, 7 pp., DOI: 10.1088/1757-899X/147/1/012143.
    
    Abstract. The basic design and construction of an alpha-type Stirling engine with on load variable displacement is presented. The variable displacement is obtained through a planar quadrilateral linkage with one on load movable ground link. The physico-mathematical model used for analyzing the variable displacement alpha-type Stirling engine behavior is an isothermal model that takes into account the real movement of the pistons. Performances and power adjustment capabilities of such alpha-type Stirling engine are calculated and analyzed. An exemplification through the use of the numerical simulation was performed in this regard.
    
    Click to download the paper (in pdf format) from "IOPscience" website.