Research Keywords

Molecular dynamics simulations, Radiation damage, liquids, glasses, disordered materials

Research Interests

I am particularly interested in the physics of liquids, amorphous solids, disordered magnetic systems, liquid-glass transition, as well as effects of radiation damage in materials and its effect on materials use in nuclear and fusion applications. This is discussed on my personal website in more detail.

Key Publications

Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN, Tsiok EN and Trachenko K (2013). Liquid-gas transition in the supercritical region: fundamental changes in the particle dynamics. American Physical Society  Phys Rev Lett  vol. 111, (14) 10.1103/PhysRevLett.111.145901

Zarkadoula E, Daraszewicz SL, Duffy DM, Seaton MA, Todorov IT, Nordlund K, Dove MT and Trachenko K (2013). The nature of high-energy radiation damage in iron. J Phys Condens Matter  vol. 25, (12) 10.1088/0953-8984/25/12/125402

Bolmatov D, Brazhkin VV and Trachenko K (2013). Thermodynamic behaviour of supercritical matter. Nat Commun  vol. 4, 10.1038/ncomms3331

Brazhkin VV and Trachenko K (2012). What separates a liquid from a gas? Physics Today  vol. 65, (11) 68-69. 10.1063/PT.3.1796

Bolmatov D, Brazhkin VV and Trachenko K (2012). The phonon theory of liquid thermodynamics. Sci Rep  vol. 2, 10.1038/srep00421

2018

Brazhkin VV, Fomin YD, Ryzhov VN, Tsiok EN and Trachenko K (2018). Liquid-like and gas-like features of a simple fluid: An insight from theory and simulation. Physica a: Statistical Mechanics and Its Applications  vol. 509, 690-702. 10.1016/j.physa.2018.06.084

Yang C, Trachenko K, Hull S, Todorov IT and Dove MT (2018). Emergence of microstructure and oxygen diffusion in yttrium-stabilized cubic zirconia. Physical Review B  vol. 97, (18) 10.1103/PhysRevB.97.184107

Fomin YD, Ryzhov VN, Tsiok EN, Proctor JE, Prescher C, Prakapenka VB, Trachenko K and Brazhkin VV (2018). Dynamics, thermodynamics and structure of liquids and supercritical fluids: crossover at the Frenkel line. J Phys Condens Matter  vol. 30, (13) 10.1088/1361-648X/aaaf39

2017

TRACHENKO K (2017). Lagrangian formulation and symmetrical description of liquid dynamics. American Physical Society  Physical Review E  vol. 96, 062134(1)-062134(5). 10.1103/PhysRevE.96.062134

Wang L, Dove MT, Trachenko K, Fomin YD and Brazhkin VV (2017). Supercritical Gr?neisen parameter and its universality at the Frenkel line. Phys Rev E  vol. 96, (1-1) 10.1103/PhysRevE.96.012107

Prescher C, Fomin YD, Prakapenka VB, Stefanski J, Trachenko K and Brazhkin VV (2017). Experimental evidence of the Frenkel line in supercritical neon. Physical Review B  vol. 95, (13) 10.1103/PhysRevB.95.134114

Fomin YD, Ryzhov VN, Tsiok EN, Brazhkin VV and Trachenko K (2017). Crossover of collective modes and positive sound dispersion in supercritical state (vol 28, 43LT01, 2016). Iop Publishing  Journal of Physics: Condensed Matter  vol. 29, (5) 10.1088/1361-648X/29/5/059501

2016

Fomin YD, Ryzhov VN, Tsiok EN, Brazhkin VV and Trachenko K (2016). The Frenkel line and isotope effect. Physica a: Statistical Mechanics and Its Applications  vol. 444, 890-896. 10.1016/j.physa.2015.10.099

2015

Trachenko K (2015). Varying vacuum energy of a self-interacting scalar field. Annals of Physics  vol. 362, 74-82. 10.1016/j.aop.2015.07.020

Trachenko K and Brazhkin VV (2015). Reply to Comment on 'Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants'. Physical Review E  vol. 91, (3) 10.1103/PhysRevE.91.036102

Trachenko K and Brazhkin VV (2015). Reply to Comment on 'Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants' . Phys Rev E Stat Nonlin Soft Matter Phys  vol. 91, (3) 10.1103/PhysRevE.91.036102

Yang C, Brazhkin VV, Dove MT and Trachenko K (2015). Frenkel line and solubility maximum in supercritical fluids. Phys Rev E Stat Nonlin Soft Matter Phys  vol. 91, (1) 012112-012112. 10.1103/PhysRevE.91.012112

2014

Little W, Karatutlu A, Bolmatov D, Trachenko K, Sapelkin AV, Cibin G, Taylor R, Mosselmans F, Dent AJ and Mountjoy G (2014). Structural origin of light emission in germanium quantum dots. Sci Rep  vol. 4, 10.1038/srep07372

Trachenko K, Brazhkin VV and Bolmatov D (2014). Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics  vol. 89, (3) 10.1103/PhysRevE.89.032126

Trachenko K, Brazhkin VV and Bolmatov D (2014). Dynamic transition of supercritical hydrogen: defining the boundary between interior and atmosphere in gas giants. Phys Rev E Stat Nonlin Soft Matter Phys  vol. 89, (3) 10.1103/PhysRevE.89.032126

Trachenko K, Brazhkin VV and Bolmatov D (2014). Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants. Physical Review E  vol. 89, (3) 10.1103/PhysRevE.89.032126

Zarkadoula E, Daraszewicz SL, Duffy DM, Seaton MA, Todorov IT, Nordlund K, Dove MT and Trachenko K (2014). Electronic effects in high-energy radiation damage in iron. J Phys Condens Matter  vol. 26, (8) 10.1088/0953-8984/26/8/085401

Zarkadoula E, Devanathan R, Weber WJ, Seaton MA, Todorov IT, Nordlund K, Dove MT and Trachenko K (2014). High-energy radiation damage in zirconia: Modeling results. Journal of Applied Physics  vol. 115, (8) 10.1063/1.4866989

Brazhkin VV, Lyapin AG, Ryzhov VN, Trachenko K, Fomin YD and Tsiok EN (2014). The Frenkel line and supercritical technologies. Russian Journal of Physical Chemistry B  vol. 8, (8) 1087-1094. 10.1134/S199079311408003X

Widdicombe AT, Ravindrarajah P, Sapelkin A, Phillips AE, Dunstan D, Dove MT, Brazhkin VV and Trachenko K (2014). Measurement of bitumen viscosity in a room-temperature drop experiment: Student education, public outreach and modern science in one. Physics Education  vol. 49, (4) 406-411. 10.1088/0031-9120/49/4/406

Trachenko K and Brazhkin VV (2014). Non-perturbative treatment of strongly-interacting fields: Insights from liquid theory. Annals of Physics  vol. 347, 92-109. 10.1016/j.aop.2014.04.025

2013

Bolmatov D, Brazhkin VV, Fomin YD, Ryzhov VN and Trachenko K (2013). Evidence for structural crossover in the supercritical state. J Chem Phys  vol. 139, (23) 10.1063/1.4844135

Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN, Tsiok EN and Trachenko K (2013). Liquid-gas transition in the supercritical region: fundamental changes in the particle dynamics. American Physical Society  Phys Rev Lett  vol. 111, (14) 10.1103/PhysRevLett.111.145901

Bolmatov D, Musaev ET and Trachenko K (2013). Symmetry breaking gives rise to energy spectra of three states of matter. Sci Rep  vol. 3, 10.1038/srep02794

Andritsos EI, Zarkadoula E, Phillips AE, Dove MT, Walker CJ, Brazhkin VV and Trachenko K (2013). The heat capacity of matter beyond the Dulong-Petit value. J Phys Condens Matter  vol. 25, (23) 10.1088/0953-8984/25/23/235401

Zarkadoula E, Daraszewicz SL, Duffy DM, Seaton MA, Todorov IT, Nordlund K, Dove MT and Trachenko K (2013). The nature of high-energy radiation damage in iron. J Phys Condens Matter  vol. 25, (12) 10.1088/0953-8984/25/12/125402

Zarkadoula E, Daraszewicz SL, Duffy DM, Seaton MA, Todorov IT, Nordlund K, Dove MT and Trachenko K (2013). The nature of high-energy radiation damage in iron. Journal of Physics Condensed Matter  vol. 25, (12) 10.1088/0953-8984/25/12/125402

Bolmatov D, Brazhkin VV and Trachenko K (2013). Helium at elevated pressures: Quantum liquid with non-static shear rigidity. Journal of Applied Physics  vol. 113, (10) 10.1063/1.4795340

Chappell HF, Dove MT, Trachenko K, McKnight REA, Carpenter MA and Redfern SAT (2013). Structural changes in zirconolite under ?-decay. J Phys Condens Matter  vol. 25, (5) 10.1088/0953-8984/25/5/055401

Bolmatov D, Brazhkin VV and Trachenko K (2013). Thermodynamic behaviour of supercritical matter. Nat Commun  vol. 4, 10.1038/ncomms3331

Trachenko K and Brazhkin VV (2013). Duality of liquids. Sci Rep  vol. 3, 10.1038/srep02188

2012

Brazhkin VV and Trachenko K (2012). What separates a liquid from a gas? Physics Today  vol. 65, (11) 68-69. 10.1063/PT.3.1796

Trachenko K, Zarkadoula E, Todorov IT, Dove MT, Dunstan DJ and Nordlund K (2012). Modeling high-energy radiation damage in nuclear and fusion applications. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions With Materials and Atoms  vol. 277, 6-13. 10.1016/j.nimb.2011.12.058

Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN and Trachenko K (2012). Universal crossover of liquid dynamics in supercritical region. Jetp Letters  vol. 95, (3) 164-169. 10.1134/S0021364012030034

Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN and Trachenko K (2012). Two liquid states of matter: A dynamic line on a phase diagram. Phys Rev E Stat Nonlin Soft Matter Phys  vol. 85, (3-1)

Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN and Trachenko K (2012). Two liquid states of matter: a dynamic line on a phase diagram. Phys Rev E Stat Nonlin Soft Matter Phys  vol. 85, (3 Pt 1) 10.1103/PhysRevE.85.031203

Brazhkin VV, Lyapin AG, Ryzhov VN, Trachenko K, Fomin YD and Tsiok EN (2012). Where is the supercritical fluid on the phase diagram? Physics-Uspekhi  vol. 55, (11) 1061-1079. 10.3367/UFNr.0182.201211a.1137

Bolmatov D, Brazhkin VV and Trachenko K (2012). The phonon theory of liquid thermodynamics. Sci Rep  vol. 2, 10.1038/srep00421

2011

Trachenko K (2011). Understanding the spin glass transition as a dynamic phenomenon. J Phys Condens Matter  vol. 23, (36) 10.1088/0953-8984/23/36/366003

Bolmatov D and Trachenko K (2011). Liquid heat capacity in the approach from the solid state: Anharmonic theory (vol 84, 054106, 2011). Phys Rev B  vol. 84, (5) 10.1103/PhysRevB.84.059907

Bolmatov D and Trachenko K (2011). Erratum: Liquid heat capacity in the approach from the solid state: Anharmonic theory (Physical Review B (2011) 84 (054106)). Physical Review B - Condensed Matter and Materials Physics  vol. 84, (5) 10.1103/PhysRevB.84.059907

Bolmatov D and Trachenko K (2011). Liquid heat capacity in the approach from the solid state: Anharmonic theory. Physical Review B - Condensed Matter and Materials Physics  vol. 84, (5) 10.1103/PhysRevB.84.054106

Pronin AA, Trachenko K, Kondrin MV, Lyapin AG and Brazhkin VV (2011). Nonlocal dielectric relaxation in glycerol. Phys Rev B  vol. 84, (1) 10.1103/PhysRevB.84.012201

Pronin AA, Trachenko K, Kondrin MV, Lyapin AG and Brazhkin VV (2011). Nonlocal dielectric relaxation in glycerol. Physical Review B  vol. 84, (1) 10.1103/PhysRevB.84.012201

Brazhkin VV, Lyapin AG and Trachenko K (2011). Atomistic modeling of multiple amorphous-amorphous transitions in SiO2 and GeO2 glasses at megabar pressures. Phys Rev B  vol. 83, (13) 10.1103/PhysRevB.83.132103

Trachenko K and Brazhkin VV (2011). Heat capacity at the glass transition. Physical Review B - Condensed Matter and Materials Physics  vol. 83, (1) 10.1103/PhysRevB.83.014201

2009

Trachenko K and Brazhkin VV (2009). Understanding the problem of glass transition on the basis of elastic waves in a liquid. J Phys-Condens Mat  vol. 21, (42) 10.1088/0953-8984/21/42/425104

Trachenko K and Brazhkin VV (2009). Understanding the problem of glass transition on the basis of elastic waves in a liquid. Journal of Physics Condensed Matter  vol. 21, (42) 10.1088/0953-8984/21/42/425104

2008

Trachenko K, Brazhkin VV, Ferlat G, Dove MT and Artacho E (2008). First-principles calculations of structural changes in B2O3 glass under pressure. Phys Rev B  vol. 78, (17) 10.1103/PhysRevB.78.172102

Trachenko K (2008). Heat capacity of liquids: An approach from the solid phase. Phys Rev B  vol. 78, (10) 10.1103/PhysRevB.78.104201

Trachenko K (2008). The Vogel-Fulcher-Tammann law in the elastic theory of glass transition. J Non-Cryst Solids  vol. 354, (32) 3903-3906. 10.1016/j.jnoncrysol.2008.05.021

Brazhkin VV, Katayama Y, Trachenko K, Tsiok OB, Lyapin AG, Artacho E, Dove M, Ferlat G, Inamura Y and Saitoh H (2008). Nature of the structural transformations in B2O3 glass under high pressure. Phys Rev Lett  vol. 101, (3) 10.1103/PhysRevLett.101.035702

Trachenko K, Roland CM and Casalini R (2008). Relationship between the nonexponentiality of relaxation and relaxation time in the problem of glass transition. Journal of Physical Chemistry B  vol. 112, (16) 5111-5115. 10.1021/jp800347w

Trachenko K, Roland CM and Casalini R (2008). Relationship between the nonexponentiality of relaxation and relaxation time in the problem of glass transition. J Phys Chem B  vol. 112, (16) 5111-5115. 10.1021/jp800347w

Trachenko K and Brazhkin VV (2008). Liquid elasticity length, universal dynamic crossovers, and glass transition. J Phys-Condens Mat  vol. 20, (7) 10.1088/0953-8984/20/7/075103

2007

Walker AM, Sullivan LA, Trachenko K, Bruin RP, White TOH, Dove MT, Tyer RP, Todorov IT and Wells SA (2007). The origin of the compressibility anomaly in amorphous silica: a molecular dynamics study. J Phys-Condens Mat  vol. 19, (27) 10.1088/0953-8984/19/27/275210

Trachenko K, Brazhkin VV, Tsiok OB, Dove MT and Salje EKH (2007). Logarithmic relaxation in radiation-amorphized zircon. Phys Rev B  vol. 76, (1) 10.1103/PhysRevB.76.012103

Trachenko K (2007). Slow dynamics and stress relaxation in a liquid as an elastic medium. Phys Rev B  vol. 75, (21) 10.1103/PhysRevB.75.212201

Lumpkin GR, Pruneda M, Rios S, Smith KL, Trachenko K, Whittle KR and Zaluzec NJ (2007). Nature of the chemical bond and prediction of radiation tolerance in pyrochlore and defect fluorite compounds. J Solid State Chem  vol. 180, (4) 1512-1518. 10.1016/j.jssc.2007.01.028

Trachenko K, Brazhkin VV, Tsiok OB, Dove MT and Salje EKH (2007). Pressure-induced structural transformation in radiation-amorphized zircon. Phys Rev Lett  vol. 98, (13) 10.1103/PhysRevLett.98.135502

Trachenko K (2007). Structural flexibility of cuprate superconductors. Phil Mag Lett  vol. 87, (9) 637-643. 10.1080/09500830701422194

2006

Dove MT, Sullivan LA, Walker AM, Bruin RP, White TOH, Trachenko K, Murray-Rust P, Todorov IT, Tyer RP, Couch PA, van Dam KK and Smith W (2006). Molecular dynamics in a grid computing environment: experiences using DL_POLY_3 within the eMinerals escience project. Mol Simulat  vol. 32, (12-13) 945-952. 10.1080/08927020600883293

Trachenko K (2006). A stress relaxation approach to glass transition. J Phys-Condens Mat  vol. 18, (19) L251-L258. 10.1088/0953-8984/18/19/L04

Trachenko K, Dove MT, Artacho E, Todorov IT and Smith W (2006). Atomistic simulations of resistance to amorphization by radiation damage. Phys Rev B  vol. 73, (17) 10.1103/PhysRevB.73.174207

Todorov IT, Smith W, Trachenko K and Dove MT (2006). DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism. J Mater Chem  vol. 16, (20) 1911-1918. 10.1039/b517931a

Trachenko K and Turlakov M (2006). Tunneling and interaction effects in two-level systems in glasses studied by atomistic simulations. Phys Rev B  vol. 73, (1) 10.1103/Phys.RevB.73.012203

2005

Trachenko K, Pruneda JM, Artacho E and Dove MT (2005). How the nature of the chemical bond governs resistance to amorphization by radiation damage. Phys Rev B  vol. 71, (18) 10.1103/PhysRevB.71.184104

Trachenko K, Dove MT, Salje EKH, Todorov I, Smith W, Pruneda M and Artacho E (2005). Radiation damage in the bulk and at the surface. Mol Simulat  vol. 31, (5) 355-359. 10.1080/08927020500066825

Pruneda JM, le Polles L, Farnan I, Trachenko K, Dove MT and Artacho E (2005). Calculation of the effect of intrinsic point defects and volume swelling in the nuclear magnetic resonance spectra of ZrSiO4. Mol Simulat  vol. 31, (5) 349-354. 10.1080/08927020500066916

2004

Trachenko K (2004). Understanding resistance to amorphization by radiation damage. J Phys-Condens Mat  vol. 16, (49) R1491-R1515. 10.1088/0953-8984/16/49/R03

Trachenko K, Pruneda M, Artacho E and Dove MT (2004). Radiation damage effects in the perovskite CaTiO3 and resistance of materials to amorphization. Phys Rev B  vol. 70, (13) 10.1103/PhysRevB.70.134112

Trachenko K and Dove MT (2004). Local events and stretched-exponential relaxation in glasses. Phys Rev B  vol. 70, (13) 10.1103/PhysRevB.70.132202

Trachenko K, Dove MT, Brazhkin V and El'kin FS (2004). Network rigidity and properties of SiO2 and GeO2 glasses under pressure. Phys Rev Lett  vol. 93, (13) 10.1103/PhysRevLett.93.135502

Trachenko K, Dove MT, Geisler T, Todorov I and Smith B (2004). Radiation damage effects and percolation theory. J Phys-Condens Mat  vol. 16, (27) S2623-S2627. 10.1088/0953-8984/16/27/002

2003

Trachenko K, Dove MT, Brazhkin VV and Phillips JC (2003). Rigidity and logarithmic relaxation in network glasses. J Phys-Condens Mat  vol. 15, (49) L743-L748. 10.1088/0953-8984/15/49/L02

Trachenko K, Dove MT and Salje EKH (2003). Reply to comment on 'large swelling and percolation in irradiated zircon'. J Phys-Condens Mat  vol. 15, (37) 6457-6471. 10.1088/0953-8984/15/37/N02

Geisler T, Trachenko K, Rios S, Dove MT and Salje EKH (2003). Impact of self-irradiation damage on the aqueous durability of zircon (ZrSiO4): implications for its suitability as a nuclear waste form. J Phys-Condens Mat  vol. 15, (37) L597-L605. 10.1088/0953-8984/15/37/L07

Trachenko K and Dove MT (2003). Intermediate state in pressurized silica glass: Reversibility window analogue. Phys Rev B  vol. 67, (21) 10.1103/PhysRevB.67.212203

Trachenko K and Dove MT (2003). Compressibility, kinetics, and phase transition in pressurized amorphous silica. Phys Rev B  vol. 67, (6) 10.1103/PhysRevB.67.064107

Trachenko K, Dove MT and Salje EKH (2003). Large swelling and percolation in irradiated zircon. J Phys-Condens Mat  vol. 15, (2) L1-L7. 10.1088/0953-8984/15/2/101

2002

Trachenko K and Dove MT (2002). Densification of silica glass under pressure. J Phys-Condens Mat  vol. 14, (32) 7449-7459. 10.1088/0953-8984/14/32/304

Wells SA, Dove MT, Tucker MG and Trachenko K (2002). Real-space rigid-unit-mode analysis of dynamic disorder in quartz, cristobalite and amorphous silica. J Phys-Condens Mat  vol. 14, (18) 4645-4657. 10.1088/0953-8984/14/18/302

Trachenko K, Dove MT and Salje EKH (2002). Structural changes in zircon under alpha-decay irradiation (vol B 65, art no 180102, 2002). Phys Rev B  vol. 65, (18) 10.1103/PhysRevB.65.189902

Trachenko K, Dove MT and Salje EKH (2002). Structural changes in zircon under alpha-decay irradiation. Phys Rev B  vol. 65, (18) 10.1103/PhysRevB.65.180102

Trachenko K, Dove MT and Salje EKH (2002). Erratum: Publisher's note: Structural changes in zircon under ?-decay irradiation (Physical Review B - Condensed Matter and Materials Physics (2002) 65 (180102)). Physical Review B - Condensed Matter and Materials Physics  vol. 65, (18)

Trachenko K, Dove MT and Heine V (2002). Origin of the T1+alpha dependence of the heat capacity of glasses at low temperature. Phys Rev B  vol. 65, (9) 10.1103/PhysRevB.65.092201

Trachenko K and Dove MT (2002). Floppy modes in silica glass under pressure. J Phys-Condens Mat  vol. 14, (6) 1143-1152. 10.1088/0953-8984/14/6/303

2001

Trachenko K, Dove MT and Heine V (2001). Simulation of two-level tunneling states and floppy modes in silica glass. 2001 International Conference On Computational Nanoscience - Iccn 2001  121-124.

Trachenko K, Dove MT and Salje EKH (2001). Atomistic modelling of radiation damage in zircon. 2001 International Conference On Computational Nanoscience - Iccn 2001  145-148.

Trachenko KO, Dove MT and Salje EKH (2001). Atomistic modelling of radiation damage in zircon. J Phys-Condens Mat  vol. 13, (9) 1947-1959. 10.1088/0953-8984/13/9/317

2000

Trachenko KO, Dove MT, Harris MJ and Heine V (2000). Dynamics of silica glass: two-level tunnelling states and low-energy floppy modes. J Phys-Condens Mat  vol. 12, (37) 8041-8064. 10.1088/0953-8984/12/37/304

Trachenko K, Dove MT and Salje E (2000). Modelling the percolation-type transition in radiation damage. J Appl Phys  vol. 87, (11) 7702-7707. 10.1063/1.373444

Dove MT, Hammonds KD, Harris MJ, Heine V, Keen DA, Pryde AKA, Trachenko K and Warren MC (2000). Amorphous silica from the Rigid Unit Mode approach. Mineral Mag  vol. 64, (3) 377-388. 10.1180/002646100549454

Dove MT, Craig MS, Keen DA, Marshall WG, Redfern SAT, Trachenko KO and Tucker MG (2000). Crystal structure of the high-pressure monoclinic phase-II of cristobalite, SiO2. Mineral Mag  vol. 64, (3) 569-576. 10.1180/002646100549436

Dove MT, Trachenko KO, Tucker MG and Keen DA (2000). Rigid unit modes in framework structures: Theory, experiment and applications. Rev Mineral Geochem  vol. 39, 1-33. 10.2138/rmg.2000.39.01

1998

Trachenko K, Dove MT, Hammonds KD, Harris MJ and Heine V (1998). Low energy dynamics and tunneling states in silica glass. Phys Rev Lett  vol. 81, (16) 3431-3434. 10.1103/PhysRevLett.81.3431

TBC

TBC