Dissemination
Conferences
- Linkov, A. M. On Numerical Simulation of Hydraulic Fracturing. Proceedings of The International Summer School-Conference “Advanced Problems in Mechanics”, St. Petersburg, Russia; 1-5 July 2011.
- Dobroskok A., Linkov A. M. Numerical Approach to Interpretation of Acoustic Emission Occurring at Different Scales. Proceedings of The International Summer School-Conference. “Advanced Problems in Mechanics”, St. Petersburg, Russia; 1-5 July 2011. A copy of the presentation can be found here.
- Linkov, A. M. Hydraulic shock on crack surface: Dual reciprocity CV-BEM and asymptotic early time solution. Symposium of the International Association for Boundary Element Method, Brescia, Italy; 5-8 September 2011.
- Mishuris G., Pesetskaya E., Rogosin S. On nonlinear heat conduction in doubly periodic 2D composite materials. XXIII International Conference “Differential Equations and Related Topics”, Moscow, Russia; May 30 – June 4 2011.
- Mishuris G., Rogosin S. Hele-Shaw flow with a small obstacle. International Workshop and Summer School STOP 2011 “Selected Topics of Operator Theory”, Lisbon, Portugal; June 24-28 2011.
- Mishuris G., Pesetskaya E., Rogosin S. Analytical treatment of heat conduction in 2D nonlinear doubly periodic composites. 8th International ISAAC Congress, Moscow, Russia; 22-27 August 2011.
- Piccolroaz A, Mishuris G. Steady-state crack propagation in couple stress elastic materials. Elasticity Day, Workshop on Mathematical Modelling in Solid Mechanics, Liverpool University, UK; 5 May 2012.
- Michalcewicz J., Wrobel M. Oilfield equipment and technologies for enhancing the extraction of hydrocarbons from the unconventional deposits. XIII International Scientific Conference: Servicing of unconventional hydrocarbons deposits, Bobrka, Poland; 25-27 April 2012.
- Piccolroaz, A., Mishuris, G., Movchan, A.B., Movchan, N. Mode III crack advancing in a bimaterial plane with finite array of defects. International Workshop on Computational Mechanics of Materials 2011, University of Limerick, Ireland; 21-24 August 2011.
- Piccolroaz, A., Mishuris, G., Movchan, A.B., Movchan, N. Asymptotic solutions for cracks in heterogeneous media. WIMCS Gregynog Mathematics Colloquium 2011, Gregynog, Wales, UK; 23-25 May 2011.
- Mishuris, G., Wrobel, M., Linkov, A. M. Remarks on Numerical Simulation of the PKN Problem of Hydrofracturing. IUTAM 2012 Symposium - Fracture Phenomena in Nature and Technology. University of Brescia, Italy; 1-5 July 2012.
- Piccolroaz, A., Mishuris, G. Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity. IUTAM 2012 Symposium - Fracture Phenomena in Nature and Technology. University of Brescia, Italy; 1-5 July 2012.
- Linkov, A. M. Numerical Modelling of Hydralic Fractures: State of art and New Results. Proceedings of The International Summer School-Conference "Advanced Problems in Mechanics", St. Petersburg, Russia; 2-8 July 2012.
- Jaworski, D., Linkov, A. M., Rybarska-Rusinek, L. Evaluation of Temporal Derivative for Propagating Front of Hydraulic Fracture. Proceedings of The International Summer School-Conference "Advanced Problems in Mechanics", St. Petersburg, Russia; 2-8 July 2012.
- Rejwer, E., Rybarska-Rusinek, L., Linkov, A. M. Complex Variable Fast Multipole Method for Modelling Hydraulic Fractures in Inhomogeneous Media. Proceedings of The International Summer School-Conference "Advanced Problems in Mechanics", St. Petersburg, Russia; 2-8 July 2012.
- Ferguson, D., Cox, S. Foams in porous media (poster). EuFoam 2012, Lisbon, Portugal; July 8-11, 2012.
- Cox, S. The structure, dynamics (and applications) of foams. Workshop on Mass transport mechanisms in hydrofracturing, Rzeszow University of Technology, Rzeszow, Poland, 27-28 November 2012.
- Kusmierczyk P. Numerical modeling of hydraulic crack propagation - Various leak off regimes (poster). SIAM Chapter Day, Cardiff University, UK; January 21, 2013.
- Cox, S., Kraynik, A. The rheology of disordered foams (invited lecture), Advances in non-Newtonian Fluid Mechanics. Royal Society Kavli Centre, UK; March 2013.
- Ferguson, D., Cox. S. Simulation of foams in porous media (poster). Advances in non-Newtonian Fluid Mechanics. Royal Society Kavli Centre, UK; March 2013.
- Cox, S., Jones, S. Instability of stretched and twisted soap films in a cylinder. British Applied Mathematics Colloquium. University of Leeds, UK; April 2013.
- Kusmierczyk P. Numerical simulation of PKN model fractures. Various leak off regimes. Wales Mathematics Colloquium, Gregynog, Wales; 20-22 May 2013
- Linkov, A.M., Mishuris, G. Modified Formulation, ε-Regularization and the Efficient Solution of Hydraulic Fracture Problems. International Conference for Effective and Sustainable Hydraulic Fracturing (HF2013), Brisbane, Australia; 20-22 May 2013.
- Rogosin S.V., Mishuris G. Hele-Shaw Flow with a small obstacle. Conformal geometry in mapping, imaging and sensing, Imperial College London, UK; 20-21 June 2013. Full text at www2.imperial.ac.uk/~dgcrowdy/workshop.html.
- Kuzkin, V.A., Krivtsov, A.M., Linkov, A.M. (Key-note lecture) Proppant transport in hydraulic fractures:computer simulation of effective properties and movement of the suspension, Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Linkov, A.M. Using Modified Formulation for Hydraulic Fractures Driven by Thinning Fluids, Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Jaworski, D., Rybarska-Rusinek, L., Rejwer, E., Linkov, A.M. On modelling hydraulic fractures in inhomogeneous media. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Mishuris, G., Wrobel, M. On various strategies of numerical simulation of hydraulic fracturing. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Mishuris, G., Wrobel, M., Kuśmierczyk, P. PKN model of hydrofracturing under various fluid flow regimes. Numerical implementations in different dependent variables, Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Sevostianov, I., Giraud, A. Elastic properties of oolitic limestone: micromechanical modeling and verification. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Kushch, V.I., Sevostianov, I. Effect of crack density, orientation and clustering on SIF statistics and anisotropy of randomly cracked solid. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Ferguson, D. Foams in porous media. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Cox, S.J. The mechanics of liquid foams. Workshop: Advances in numerical simulation of hydraulic fracture during APM-2013, St Petersburg, Russia; 2-8 July 2013.
- Dubatovskaya M.V., Rogosin S. On effective conductivity formula for bounded symmetric composite material. 9th ISAAC Congress, Krakow, Poland; 5-9 August 2013.
- Gryshchuk S., Rogosin S. Effective Conductivity of 2D Disk – Ring Composite Material. 9th ISAAC Congress, Krakow, Poland; 5-9 August 2013.
- Ilchukov A., Rogosin S. Singular integrals in spaces with moduli of continuity. 9th ISAAC Congress, Krakow, Poland; 5-9 August 2013.
- Koroleva A., Mishuris G., Rogosin S. Refinement of the solution to the contact problem for the thin biphasic cartilage layers. . 9th ISAAC Congress, Krakow, Poland; 5-9 August 2013.
- Rogosin S. Complex-analytic model for Hele-Shaw moving boundary value problem. 9th ISAAC Congress, Krakow, Poland; 5-9 August 2013.
- Linkov, A.M. Numerical modeling of seismicity: theory and applications. (Key-note lecture) 8-th International Symposium on Rockbursts and Seismicity in Mines. Saint Petersburg-Moscow, Russia; 1-8 September 2013.
- Rybarska-Rusinek, L., Rejwer, E., Jaworski, D. Evaluation of stresses in strongly inhomogeneous rock with multiple cracks, openings and pillars. 8-th International Symposium on Rockbursts and Seismicity in Mines. Saint Petersburg-Moscow, Russia; 1-8 September 2013.
- Vellender, A. Application of imperfect interface weight function techniques for modelling of glued structures containing cracks and small defects. International Symposium on Dynamic Deformation and Fracture of Advanced Materials 2013, Loughborough, UK; 9-11 September 2013.
- Rogosin S., Mishuris G. Asymptotic behaviour of the solution to Hele-Shaw flow with a small obstacle. In: “Shell and membrane theories in mechanics and biology: from macro- to nanoscale structures”. International Conference, Minsk, Belarus; 16-20 September 2013.
- Rogosin S., Mainardi F. George William Scott Blair, the pioneer of fractional calculus in rheology. “Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments”, Bilbao, Basque Country, Spain; 6-8 November 2013.
- Kusmierczyk P. Numerical modelling of hydrofracturing various leak off regimes and multifracture (poster). PMPM Research Network, Edinburgh, UK; 8-10 January 2014.
- Rogosin S., Mishuris G. Factorization of matrix functions. LMS-WIMCS Analysis Day, Cardiff; 15 January 2014.
- Cox, S.J. Instability of stretched and twisted soap films in a cylinder. Foams and Minimal Surfaces - 12 Years On, Isaac Newton Institute, Cambridge, UK; February 2014.
- Dobroskok, A., Jaworski, D, Rybarska-Rusinek, L. Simulation of seismicity accompanying hydraulic fracture propagation in 3D. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Mishuris, G., Wrobel, M. Various approaches for numerical simulation of hydraulic fracturing. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Kuśmierczyk, P. PKN based multifracturing model. New approach and implementation. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Perkowska, M., Mishuris, G. Remarks on implementation of universal algorithm for hydraulic fracturing. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Rogosin, S. Hele-Shaw flow with a small obstacle. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Peck, D. An improved estimate for threshold fracture energy in solid particle erosion. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Rogosin, S. An asymptotic method of factorisation of a class of matrix-functions. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Vellender, A. Weight functions problems for the fracture along soft imperfect interfaces. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Ferguson, D. Surface Evolver simulations of foam lamellae traversing an idealised bi-conical rock pore. British Applied Mathematics Colloquium, Cardiff University, UK; 28-30 April 2014.
- Perkowska, M., Mishuris, G., Wrobel, M. Is it possible to improve performance of the hydrofracturing algorithm through straightforward ODE analysis?. Wales Mathematics Colloquium, Gregynog, Wales; 19-21 May 2014.
- Peck, D. An Improved Estimate for Threshold Fracture Energy in Solid Particle Erosion. Wales Mathematics Colloquium, Gregynog, Wales; 19-21 May 2014.
- Kuśmierczyk, P. PKN based multifracturing model. New approach and implementation. Wales Mathematics Colloquium, Gregynog, Wales; 19-21 May 2014.
- Dubatovskaya M., Rogosin S. On the role of the Mittag-Leffler function in fractional modelling. XIX Int. Conference “Mathematical Modelling and Analysis” (MMA2014), Druskininkai, Lithuania; 26-29 May 2014..
- Cox, S.J. Bubble-scale simulations of foam rheology. Séminaire MSC Université Paris Diderot, France; May 2014.
- Mishuris, G., Rogosin S. An asymptotic method of factorisation of a class matrix functions. WIMCS-CIDMA Wiener-Hopf Workshop, Aveiro, Portugal; 23-24 June 2014.
- Vellender, A. Wiener-Hopf derived weight functions for fracture problems along imperfect interfaces. WIMCS-CIDMA Third Wiener-Hopf Workshop, Aveiro, Portugal; 23-24 June 2014.
- Cox, S.J. The Effects Of Channel Geometry On Foam Structure And Flow. EuFoam 2014, Thessaloniki, Greece; July 2014.
- Jaworski, D., Linkov, A., Rejwer, E., Rybarska-Rusinek, L. Numerical simulation of local field concentration near the contour of a fracture. Advanced Problems in Mechanics, APM 2014, St. Petersburg (Repino), Russia; 30 June-6 July 2014. (Abstract)
- Linkov, A. Speed equation, asymptotic umbrella and explicit level set method in hydraulic fracture modeling. Advanced Problems in Mechanics, APM 2014, St. Petersburg (Repino), Russia; 30 June-6 July 2014. (Abstract)
- Perkowska, M., Mishuris, G., Wrobel, M. Numerical simulation of PKN model of hydrofracturing for shear-thinning fluids. Advanced Problems in Mechanics, APM 2014, St. Petersburg (Repino), Russia; 30 June-6 July 2014.
- Wrobel, M., Mishuris, G. Universal algorithm for hydraulic fractures simulation based on the particle velocity. Advanced Problems in Mechanics, APM 2014, St. Petersburg (Repino), Russia; 30 June-6 July 2014.
- Kusmierczyk, P., Mishuris, G. PKN based multifracturing model featuring fracture interactions. New approach and implementation. Advanced Problems in Mechanics, APM 2014, St. Petersburg (Repino), Russia; 30 June-6 July 2014.
- Jaworski, D., Linkov, A., Rybarska-Rusinek, L. On efficient evaluation of influence coefficients for triangular, rectangular and trapezoid ordinary and edge elements. Advances in Micromechanics of Materials, Rzeszów, Poland; 8-11 July 2014.
- Vellender, A., Mishuris, G., Piccolroaz, A. The effect of defects’ presence upon crack propagation along a soft imperfect interface. Advances in Micromechanics of Materials, Rzeszów, Poland; 8-11 July 2014.
- Mishuris, G., Rogosin, S. An asymptotic method of factorization of a class of matrix-functions. Advances in Micromechanics of Materials, Rzeszów, Poland; 8-11 July 2014.
- Peck, D., Mishuris, G., Wrobel, M., Petrov, Yu. An improved estimate for threshold fracture energy in solid particle erosion (poster). Advances in Micromechanics of Materials, Rzeszów, Poland; 8-11 July 2014.
- Linkov, A., Rybarska-Rusinek, L. On numerical simulation of seismicity induced by hydraulic fracturing. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Cox, S.J. The effects of pore geometry on foam flow in porous media. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Mishuris, G., Wrobel, M. Numerical simulation of hydraulic fracturing: universal algorithm based on the particle velocity. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Kusmierczyk, P. New multifracuring model build on improved PKN formulation. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Peck, D. Multiple particles in the Hele-Shaw flow. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Perkowska, M. Universal hydrofracturing algorithm for shear-thinning fluids. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Rogosin, S. Moving stone in the Hele-Shaw flow. Recent Advances in Numerical Simulation of Hydraulic Fracture, Rzeszow, Poland; 14-16 July 2014.
- Dubatovskaya M., Rogosin S., Mishuris G. Nonlinear heat conduction problem in doubly periodic 2D composite materials. 2014 International Conference on Mathematical Models and Methods in Applied Sciences (MMMAS '14), St.Petersburg, Russia; 23-25 September 2014.
- Rogosin S., Bosiakov S. Fractional viscoelastic model of the tooth root displacements in "noncompensable" periodontal ligament. 2014 International Conference on Mathematical Models and Methods in Applied Sciences (MMMAS '14), St.Petersburg, Russia; 23-25 September 2014.
- Vellender, A. Weight functions for fracture problems along soft imperfect interfaces. LMS-WIMCS Analysis Day, Swansea, UK; 25 September 2014
- Rogosin S., Argatov I., Mishuris G. Biphasic cartilage layer: modelling, exact and asymptotic solution, perturbation. Workshop “Perturbation, Elliptic and Parabolic” (PEP2014), Aveiro, Portugal; 6-7 November 2014
- Mishuris G., Wrobel M. Particle velocity based simulation of hydraulic fractures. The 4th Joint British Mathematical Colloquium & British Applied Mathematics Colloquium, Cambridge, UK; 30 March - 2 April 2015.
- Perkowska M., Wrobel M., Mishuris G. Mathematical modeling of hydraulic fractures: shear-thinning fluids. The 4th Joint British Mathematical Colloquium & British Applied Mathematics Colloquium, Cambridge, UK; 30 March - 2 April 2015
- Peck D., Rogosin S., Wrobel M., Mishuris G. Hele-Shaw Flow in the Presence of Various Obstacles and Moving Particles. The 4th Joint British Mathematical Colloquium & British Applied Mathematics Colloquium, Cambridge, UK; 30 March - 2 April 2015
- Wróbel M., Mishuris G. Hydraulic fracture: a crack of special care. 8th International Symposium on Mechanics of Materials and Structures and Fracture and Fragmentation in Science and Engineering Conference, Augustow, Poland; 31 May - 3 June 2015.
- Perkowska M., Wróbel M., Mishuris G. Hydraulic fracture: crack propagation induced by shear-thinning fluid. 8th International Symposium on Mechanics of Materials and Structures and Fracture and Fragmentation in Science and Engineering Conference, Augustow, Poland; 31 May - 3 June 2015.
- Peck D., Rogosin S., Wrobel M., Mishuris G. Asymptotic Analysis of the Hele-Shaw Flow with Obstacles. Minicourses on Mathematical Analysis, Padova, Italy; 22-26 June 2015
- Linkov A. New formulation of hydraulic fracture problem: Revised theory, universal asymptotic umbrella, applications. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Mishuris G., Wrobel M. Particle velocity based universal solver for numerical simulation of hydraulic fractures. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Perkowska M., Mishuris G., Wrobel M. Particle Velocity Based Universal Hydrofracturing Algorithm for Non-Newtonian Fluids. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Rejwer E., Jaworski D. On interaction and propagation of closely located, nearly parallel hydraulic fractures. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Rybarska-Rusinek L., Linkov A. Universal edge boundary element for the asymptotic umbrella of hydraulic fracture problem. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Mishuris G., Peck D., Wrobel M., Rogosin S. Mass Transport in the Hele-Shaw Cell. 9th European Solid Mechanics Conference, Madrid, Spain; 6-10 July 2015
- Wróbel M., Mishuris G. Mathematical modeling of hydraulic fractures: particle velocity based simulation. VI Annual Conference of the Georgian Mathematical Union, Batumi, Georgia; 12-16 July 2015
- Perkowska M., Wrobel M., Mishuris G. Mathematical modeling of hydraulic fractures: shear-thinning fluids. VI Annual Conference of the Georgian Mathematical Union, Batumi, Georgia; 12-16 July 2015
- Perkowska M., Mishuris G., Wróbel M. Numerical modeling of hydraulic fractures for non-Newtonian fluids. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
- Mishuris G., Wróbel M. Numerical simulation of hydraulic fracture: particle velocity based approach. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
- Dobroskok A., Linkov A.M., Rybarska-Rusinek L. On simulation and interpretation of seismicity accompanying hydraulic fractures. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
- Jaworski D., Linkov A.M., Rybarska-Rusinek L. Almost analytical evaluation of influence coefficients for ordinary and edge power-type boundary elements. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
- Linkov A.M. Modified theory, universal asymptotic umbrella and efficient simulation of hydraulic fracturing. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
- Rejwer E., Jaworski D. On propagation of closely located hydraulic fractures. 3d Polish Congress of Mechanics & 21st International Conference on Computer Methods in Mechanics, Gdansk, Poland; 8-11 September 2015
Seminars
- Linkov, A. M. Speed equation and its application to solving ill-posed problems of hydraulic fracture. Saint-Petersburg seminar on mechanics, Institute for Problems of Mechanical Engineering, 17 March, 2011, St. Petersburg, Russia.
- Cox, S. Soap bubble geometry. Aberystwyth University, UK, 3 November 2011.
- Mishuris, G. Crack propagation of fluid-filled cracks (in 3 parts). Aberystwyth University, UK, February-March 2012.
- Krivtsov, A.M., Kuzkin, V.A. Computer simulation of proppant transport in hydraulic fracturing. Rzeszow University of Technology, Rzeszow, Poland, June 2012.
- Kuzkin, V.A. Rheological properties of proppant-fluid mixture at high proppant concentrations. Rzeszow University of Technology, Rzeszow, Poland, June 2013.
- Kuzkin, V.A. Rheological properties of proppant-fluid mixture: comparison of Poiseuille and Couette flows. Rzeszow University of Technology, Rzeszow, Poland, September, 2013.
- Krivtsov, A.M., Kuzkin, V.A. Modeling of proppant transport in hydraulic fracturing: The state of the art. Rzeszow University of Technology, Rzeszow, Poland, November, 2013.
- Rogosin, S. Applications of the Mittag-Leffler function in Statistical Physics. Department of Physics, Bologna University, Italy, 11 November 2013.
- Rogosin, S. Constructive methods for matrix-functions factorization. Department of Mathematics, Padova University, Italy, 22 November 2013.
- Rogosin, S. Factorization of matrix-functions: known results and open problems. Centre for Mathematical Sciences, Cambridge University, UK, 4 December 2013.
- Rogosin, S. Fractional Calculus and Fractional Modelling, Department of Mathematics. Brunel University, London, UK, 13 February 2014.
- Rogosin, S. George William Scott Blair - the pioneer of fractional calculus in rheology. Aberystwyth University, UK, 21 March 2014.
- Rogosin, S. An asymptotic method for factorization of matrix-function. Leeds University, UK, 14 September 2014.
Contact Details
Institute of Mathematics and PhysicsAberystwyth University
Physical Sciences Building
Aberystwyth
Ceredigion
SY23 3BZ
Tel: 01970 622 808 Fax: 01970 622 826 Email: imaps@aber.ac.uk