## Previous seminars - 2018/19 academic year

**Tuesday 18 September (Teaching Statistics Trust Lecture 2018): Statistical Problem Solving: the Art and Science of Learning and Teaching from Data**

- Speaker: Christine Franklin, School Statistics Ambassador, American Statistical Association

Abstract: After nearly 40 years as a statistics educator, Christine often reflects about her professional experience with learning and teaching statistics – remembering the past and feeling guilt about how poorly she must have taught her students those first years, trying to stay current with constantly changing pedagogy and assessment in the present, and making predictions about the future. How often do you reflect about your experience as a statistics teacher? Christine often reflects on what a great feeling it is to start each day knowing we work with students and colleagues aiming to see those light bulb moments of understanding the usefulness of data and statistical reasoning skills, but also the importance of being a healthy sceptic of the interpretation of small and big data we are often presented with.

What are the lessons we have learned that will positively impact the data and statistical literacy of our students in the future? Christine has been fortunate to collaborate with amazing colleagues through the years who have enlightened and inspired her to learn these lessons to continue the journey for advocating data and statistical literacy in our society.

In this presentation she discussed the art and science of learning and teaching from data (as she has experienced from writing four editions of Statistics: The Art and Science of Learning from Data and other resources specifically written for teachers) to help improve teaching statistical problem solving and data literacy at the school level.

**Wednesday 19 September: Dispersion relation for equatorially-trapped internal water waves**

- Speaker: Mateusz Kluczek (University College Cork)

Abstract: Mateusz presented a recently derived exact and explicit solution for the governing equations of geophysical water waves. Assuming no background in fluid mechanics, Mateusz introduced basic ideas behind internal water waves and explain some of the physical complexities of the model. Using numerical simulations, videos were presented of internal waves generated by the oscillation of interfaces inside the fluid body. Finally the dispersion relation was discussed, which is a mathematically elegant formula encoding rich physical information about the flow, particularly the wave speed, in terms of fixed physical parameters.

**Wednesday 19 September: Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups**

Abstract: The moduli space of Higgs bundles has an extremely rich geometry, it is a hyperKaehler variety and fibrates over a vector space becoming an integrable system named the Hitchin system. Its importance in theoretical physics comes from the fact that the dimensional reduction of an N=4 Super Yang-Mills gauge theory can be rewritten as a 2-dimensional sigma-model with the Hitchin system as a target. In this context, Kapustin and Witten reinterpreted the classical limit of S-duality of the original SYM gauge theory as mirror symmetry in the target (the Hitchin system). They also introduced the appropriate notion of branes in the Hitchin system respecting the hyperKaehler structure. In this talk the behaviour under mirror symmetry of a family of branes living on the singular locus of the Hitchin system was studied. their geometry and the role of the Borel subgroup were also described. The picture can be generalised to other parabolic subgroups.

**Wednesday 26 September: Flowing to minimal surfaces**

- Speaker: Melanie Rupflin (Oxford)

Abstract: Melanie discussed the construction and properties of a geometric flow, the Teichmueller harmonic map flow, that is designed to change surfaces into minimal surfaces. She explained this flow, which we defined as a natural gradient flow of the Dirichlet energy, succeeds in decomposing any closed surface in any compact target manifold into minimal surfaces. This is joint work with Peter Topping.

**Wednesday 3 October: Evolution of magnetic field structures in non-linear MHD dynamos**

- Speaker: Daniel Miller (Exeter)

Abstract: ABC flows are an exact solution to the MHD equation of motion. As such they provide an ideal testing ground for examining changes to the magnetic field during the saturation process. Daniel compared how the saturation process affects magnetic field structures in dynamos with and without stagnation points in their forcing.

**Wednesday 3 October: Gravity with more or less gauging**

- Speaker: Steffen Gielen (Nottingham)

Abstract: General Relativity is conventionally formulated as a theory with gauge invariance under the diffeomorphism group of general coordinate transformations, but there are locally equivalent formulations in terms of either a larger (additional local conformal invariance) or smaller (only “special” diffeomorphisms) group of symmetries. Other formulations with the same number of gauge generators, but a different gauge algebra, also exist. We discussed how one can relate these different formulations to each other, and illustrated various applications in which one may prefer one or another formalism. (The talk was mostly based on arXiv:1805.11626.)

**Wednesday 17 October: Mini-symposium in medical statistics**

**Practical issues in medical statistics**

Abstract: Statistical methods provide a variety of options for designing a clinical trial: for example, superiority, equivalence and non-inferiority. Selecting a design depends not just on statistical considerations, but contradictory clinical, regulatory and ethical considerations. After completing a study, secondary multivariate analyses are often performed and further choices need to be made: Which exposure group should be chosen as comparator? Or should you fit a no-intercept model? How should the independent variables be parameterised? Tafenoquine is a new chemical entity being developed as a novel treatment for malaria. Gavin illustrated these questions using data from a recently completed phase III trial of tafenoquine in malaria. This was an interactive seminar with the audience asked to suggest and justify design solutions.

**Dietary intake in the early years and its relationship to BMI in a bi-ethnic group: the Born in Bradford 1000 study**

- Speaker: Samuel Mahoney (Covance)

Abstract: The number of infants, toddlers and children who were overweight increased from 32 million globally in 1990 to 42 million in 2013. This figure is predicted to rise to 70 million by 2025. In the UK it is estimated by 2020 that 20% of all boys and 33% of all girls will be obese. Using data from the Born in Bradford 1000 cohort this study aimed to assess relationships between dietary intake at age 12, 18 and 36 months and BMI Z-scores at age 36 months in a bi-ethnic group. Results indicate that dietary intake at 18 and 36 months was somewhat related to BMI Z-score at age 36 months and suggest the importance of early interventions aimed at establishing healthy eating behaviours.

**Wednesday 24 October: Non-linear generation of infragravity waves in deep waters**

- Speaker: Teodor Vrecica (Tel Aviv University)

Abstract: Infragravity (IG) waves are commonly defined as sea surface gravity waves whose frequency is lower than that of the wind sea (0.05 Hz) and higher than that of the tides and internal waves (0.005 Hz). They are important for various aspects in oceanography and marine engineering such as: estimations of sediment transport and harbor resonances, altimetry measurements, the breaking of the ice sheet in the Pacific and Earth’s hum. Their primary known generation mechanism is the nonlinear shoaling of the wave field. Therefore, the focus of most previous related works was limited to coastal areas. Yet, details of the generation, and specially their directional properties, are still not fully understood. Results of recent field measurements confirmed the existence of IG wave climate in deeper waters. A common assumption is that the origin of deep water IG waves is the reflection from coastlines (leaky waves), however not every occurrence can be explained in this manner. Here, we presented a new triad interaction mechanisms for IG wave generation in deep water.

For steady homogeneous deep water wave fields, three wave interactions only produce steady non-resonant interactions. However, for evolving seas waves are able to resonate with changes of the wave field in time and space to yield mean energy transfer to the IG frequency range. The considered effects include simple growth of the wave field, effects of gustiness, and whitecapping. A new model for IG wave generation is constructed, which takes these effects into account. It is used to evaluate several storm events, where data obtained from archived reanalysis is used. Model results are compared to measurements of deep water pressure gauges with a good capability of describing the directional properties of the IG frequency range. The presented work sets the basis for future formulation of an IG wave source term for extending IG wave forecasting models to the deep waters.

This was a joint seminar with CPRG.

**Wednesday 7 November: Perspectives on data, information and mathematics**

- Speaker: Arieh Iserles (Cambridge)

Abstract: The data and information revolution is changing our lives: the way we socialise, shop, elect our leaders and conduct our research. Its impact ranges across all different academic disciplines. Yet, its engine room is mathematics — a set of emerging methodologies in statistics, computation and pure mathematics. In this talk Arieh attempted to explain in a non-technical manner this New Brave World, demystify phrases like “deep learning”, “imaging”, “sparse recovery” and “inverse problems”, describing how mathematics is transforming “Big Data” and how “Big Data” is transforming mathematics.

**Wednesday 21 November: Types of embedded graphs and their Tutte polynomials**

Speaker: Stephen Huggett (Plymouth)

Abstract: We took an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces. We gave a description of each class in terms of coloured ribbon graphs. We then identified a universal deletion-contraction invariant (that is, a Tutte polynomial) for each class. This is joint work with Iain Moffatt.

**Wednesday 28 November: The Centre Problem in 3-Dimensional Systems and Applications**

- Speaker: Lingling Liu (Chengdu, Sichuan)

Abstract: For high dimensional systems, it is a well-known method to restrict the system to its a centre manifold, but the approximation of the centre manifold brings a greater complexity in the computation of Lyapunov quantities and their dependence even if the original system is not of high degree. Furthermore, in order to determine if a centre-focus equilibrium is a centre, criteria for planar systems, such as time reversibility and integrability, are not available on the approximated centre manifold. In spite of this, we have recently been able to obtain some good results for integrability in a 3-dimensional system. We do this by finding a global centre manifold of the system and reducing the higher dimensional system to the global centre manifold. This result gives a useful method for identifying a focus or centre in high dimensional systems.

**Friday 7 December: Certified numerical implementation of Zariski-Van Kampen method**

- Speaker: Miguel Marco (Universidad de Zaragoza)

Abstract: Van Kampen’s motivation for his celebrated theorem was to give a proof of a fact known by Zariski: that the fundamental group of the complement of a complex plane curve is given by its braid monodromy. Moreover, Lefschetz hyperplane theorem allows to reduce to this case the computation of the complement of every hypersurface in the projective (or affine) space. However, there are no purely algebraic methods to compute this braid monodromy. We present a numerical, but certified, method using interval arithmetic and Newton’s interval criterion. The use of interval arithmatic allows us to work with arbitrary coefficients (either rational, algebraic or even transcendental).

**Wednesday 30 January: Flavour physics in the $D_{(s)}$ and $B_{(s)}$ meson system**

- Speaker: Tobias Tsang (Edinburgh)

Abstract: After a brief motivation, Tobias presented present Edinburgh's (domain wall fermion) charm and bottom physics programme. He first focused on their very recent computation (arXiv:1812.08791) of SU(3) breaking ratios in the $D_{(s)}$ and $B_{(s)}$ meson systems and the ratios of CKM matrix elements $V_{cd}/V_{cs}$ and $V_{td}/V_{ts}$. Tobias then outlined the current status of their wider heavy flavour phenomenology program in the charm and bottom sector.

**Wednesday 6 February: Lattice study of phase properties of cold dense quark matter**

- Speaker: Aleksandr Nikolaev (Swansea)

Abstract: The phase diagram of QCD is of fundamental interest for high energy physics, cosmology and astrophysics, but at the present moment ab-initio calculations in the lattice QCD formalism at finite density are impossible. However, in the regions of high temperature and small density or of high density and small temperature theories with SU(2) and SU(3) gauge groups with the presence of fundamental fermions are expected to have similar properties. SU(2) theory in lattice formulation does not possess a sign problem, which makes computations at finite density possible. Aleksandr presented results for the phase structure of lattice SU(2) QCD with two flavours of quarks at finite quark density and zero temperature. Interaction properties of quarks, real-time inter-quark potential and the confinement/deconfinement transition were examined. Our results indicated that in very dense matter the quark-gluon plasma is in essence a weakly interacting gas of quarks and gluons without a magnetic screening mass in the system, sharply different from a QGP at large temperature. The talk was based on papers arXiv:1808.06466, 1711.01869, 1605.04090, and recent results.

**Wednesday 13 February: Pupil Advantage Index as an Alternative to Subgroup Analysis in RCTs for Education**

- Speaker: ZhiMin Xiao (University of Exeter)

Abstract: Analyses of social interventions need to produce evidence that is relevant to different groups of people in a society. When such a group is not the target group of an intervention, this is called subgroup analysis, even when the group of interest is pre-specified prior to data collection. Amongst statisticians, subgroup analysis is often regarded as a statistical malpractice, as its findings are often underpowered, unreliable, and can be prone to overinterpretation at best, or misleading at worst. Meanwhile, researchers would be criticised for generating irrelevant evidence and accused of wasting research money if they do not conduct relevant subgroup analysis. As a result, “they are damned if they do, and damned if they don’t” (Petticrew et al., 2012).

In this study, we estimated intervention effects for Free School Meal (FSM) pupils in English schools, which is a pre-specified subgroup in most educational interventions funded by the Education Endowment Foundation (EEF) in England. Specifically, we first ran a treatment-FSM interaction test in each and every outcome to see if the difference-in-effects is statistically significant between FSM and Non-FSM pupils. We then calculated separate effect sizes within the two subgroups. Finally, we examined the p-values from the interaction tests and compared the overall effect sizes for both FSM and Non-FSM pupils with the two separate subgroup estimates. We found that conventional interaction tests can produce self-contradictory results. To help solve the problem, we propose a new approach, Pupil Advantage Index (PAI), as an alternative to subgroup analysis and apply it to real RCT data extracted from the EEF data archive. We demonstrate that PAI does not just indicate where an intervention worked and by how much in existing trials, but it can also be utilised to optimise treatment recommendation for future interventions.

**Wednesday 20 February: Modelling numbers of births by day of the week in relation to onset of labour and mode of giving birth in England 2005–2014 ****(Mario Cortina Borja, in collaboration with Professor Alison Macfarlane, Ms Nirupa Dattani, Dr Miranda Dodwell, Mr Rod Gibson, Dr Gill Harper, Dr Peter Martin and Dr Mary Newburn)**

- Speaker: Mario Cortina Borja (UCL)

Abstract: Maternity care has to be available 24 hours a day, seven days a week. It is known that obstetric intervention can influence the time of birth, but no previous analysis at a national level in England has yet investigated in detail the ways in which the day and time of birth varies by onset of labour and mode of giving birth. We linked data from birth registration, birth notification, and Maternity Hospital Episode Statistics and analysed 5,093,615 singleton births in NHS maternity units in England from 2005 to 2014. We built statistical models to establish how patterns of timing of birth vary by onset of labour, mode of giving birth and gestational age. We found that the timing of birth by time of day and day of the week varies considerably by onset of labour and mode of birth. These patterns have implications for midwifery and medical staffing.

**Wednesday 20 February: The Dai-Freed theorem and anomalies**

- Speaker: Iñaki García-Etxebarría (University of Durham)

Abstract: The Dai-Freed theorem provides a bridge between the theory of bordism and Quantum Field Theory (and more specifically, anomalies). I will review how these two areas are related, and then summarise some computations of bordism groups of classifying spaces of Lie groups and cyclic groups that we have performed recently, which are of particular interest for applications to four dimensional physics.

**Wednesday 20 February: Axions and X-ray polarimetry**

- Speaker: Francesca Day (DAMTP)

Abstract: Axions are one of the best motivated extensions to the Standard Model, both solving the strong CP problem and providing a natural dark matter candidate. X-Ray telescope observations have already placed world leading bounds on the axion-photon coupling by searching for axion-photon interconversion in the magnetic fields of galaxy clusters. However, current X-ray telescopes are unable to exploit one of the most striking features of this effect: only photons polarised parallel to the background magnetic field mix with axions. This leads to distinctive polarisation signatures from astrophysical sources. The next generation of polarising X-ray telescopes could detect these signatures. Francesca will discuss the opportunities and difficulties of detecting axions with X-ray polarimetry.

**Friday 22 February: Higher length-twist coordinates for character varieties**

- Speaker: Omar Kidwai (Toronto)

Abstract: We describe joint work with L Hollands on a construction of special holomorphic Darboux coordinates on certain SL_N (particularly N=2,3) character varieties. We consider degenerate examples of “spectral networks” of Gaiotto-Moore-Neitzke (certain graphical objects on a Riemann surface), generalising the so-called “Fenchel-Nielsen” networks of Hollands-Neitzke. We compute the associated “spectral coordinates” using the “abelianisation map”, taking connections on the Riemann surface to abelian holonomy data on a spectral cover, generalising the “complexified Fenchel-Nielsen” coordinates of Kourouniotis-Tan for SL(2)-connections to higher rank. Time permitting, Omar will discuss some physical applications to computing superpotentials coming from 4d N=2 supersymmetric QFTs.

**Wednesday 20 March: $\zeta$-regularized vacuum expectation values**

- Speaker: Tobias Hartung (Kings College London)

Abstract: Computing vacuum expectation values is paramount in studying Quantum Field Theories (QFTs) since they provide relevant information for comparing the underlying theory with experimental results. However, unless the ground state of the system is explicitly known, such computations are very difficult and Monte Carlo simulations generally run months to years on state-of-the-art high performance computers. Additionally, there are various physically interesting situations, in which most numerical methods currently in use are not applicable at all (e.g., the early universe or settings requiring Lorentzian backgrounds). Thus, new algorithms are required to address such problems in QFT. In recent joint work with K. Jansen (NIC, DESY Zeuthen), Tobias has shown that $\zeta$-functions of Fourier integral operators can be applied to regularise vacuum expectation values with Euclidean and Lorentzian backgrounds and that these $\zeta$-regularised vacuum expectation values are in fact physically meaningful. In order to prove physicality, we introduced a discretisation scheme which is accessible on a quantum computer. Using this discretisation scheme, we can efficiently approximate ground states on a quantum device and henceforth compute vacuum expectation values. Furthermore, the Fourier integral operator $\zeta$-function approach is applicable to Lattice formulations in Lorentzian background.

**Wednesday 27 March: Virtual Source Method Simulation of Progressive Water Waves**

• Speaker: Omar Al-Tameemi (Plymouth)

Abstract: The virtual source method (VSM) has been developed to simulate water waves based upon the solution of Laplace’s equation for the velocity potential integral equations with full nonlinear surface conditions. The basis of the method is the use of specific Green’s functions for a rectangular ‘virtual domain’ which is an extension of the physical domain. The solution variables are frequency components of the velocity potential at the upper virtual boundary and these are found by specifying appropriate conditions on the physical boundaries. This talk presented the results of the VSM simulations to generate nonlinear progressive waves in a numerical wave tank. The VSM results were compared with those from both second order Stokes theory and from a boundary element method (BEM).

**W****ednesday 27 March: Gauge ambiguities in ultrastrong coupling QED **

• Speaker: Ahsan Nazir (Manchester)

Abstract: Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well. More generally, even in the absence of two-level approximations, gauge-freedom implies that there are many different definitions of light and matter as quantum subsystems, which only coincide when interactions vanish. Considering time-dependent light-matter interactions, we show that in the absence of an argument to choose a particular gauge when promoting the coupling parameter to a time-dependent function, the description that results is essentially ambiguous. For sufficiently strong and non-adiabatic (i.e. fast switching) interactions, the qualitative physical predictions of final subsystem properties, such as entanglement and photon number, depend on the gauge chosen. This occurs even when the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.

**Wednesday 3 April: Network Time Series**

• Speaker: Guy Nason (Royal Statistical Society Vice President for Academic Affairs; University of Bristol)

Abstract: A network time series is a multivariate time series where the individual series are known to be linked by some underlying network structure. Sometimes this network is known a priori, and sometimes the network has to be inferred, often from the multivariate series itself. Network time series are becoming increasingly common, long, and collected over a large number of variables. We are particularly interested in network time series whose network structure changes over time.

Guy described some recent developments in the modeling and analysis of network time series via network autoregressive integrated moving average (NARIMA) process models. NARIMA models provide a network extension to a familiar environment that can be used to extract valuable information and aid prediction. As with classical ARIMA models, trend can impair the estimation of NARIMA parameters. The scope for trend removal is somewhat wider with NARIMA models and we exhibit some possibilities. Guy illustrated the operation of NARIMA modeling on some real data sets.

This is joint work with Kathryn Leeming (Bristol), Marina Knight (York) and Matt Nunes (Lancaster).

**Wednesday 3 April: Soliton fission in a fluid of non-uniform depth**

• Speaker: Alan Compelli (Cork)

Abstract: A surface water wave over a bed of non-uniform depth is considered. The fluid is incompressible, inviscid and irrotational. The Hamiltonian is determined in terms of wave-only quantities using a Dirichlet-Neumann operator. By introducing an appropriate scaling regime, and considering the bottom to vary slowly, a KdV equation with variable coefficients is derived. A one-soliton solution approaching a ramp on the seabed was then considered and numerical results demonstrated the effect the ramp shape has on the birth of new solitons as the soliton passes over it.

**Wednesday 17 April: Smoothed Particle Hydrodynamics (SPH) Modelling of Tsunami Waves Generated by a Fault Rupture**

• Speaker: Ruaa Wana (Plymouth)

Abstract: Smoothed Particle Hydrodynamics (SPH) is a meshfree, Lagrangian, particle method. It is particularly well suited to simulating flow problems that have large deformations or contain free surfaces. In this talk we used a single phase weakly compressible SPH model to simulate a dam break flow and the flow that occurs in experimental models of Tsunamis generated by a fault rupture. The experiments have been carried out at the University's COAST laboratory.

**Wednesday 8 May: Challenges in ensuring that the evaluation of medical tests helps to improve patient health**

- Speaker: Jon Deeks (University of Birmingham)

Abstract: Healthcare organisations around the world need to make recommendations of the choice and provision of medical tests. In 2018, the WHO for the first time, published the Essential Diagnostic Tests (the EDL) listing in vitro diagnostics which should be available around the world to ensure Universal Health Coverage. In doing so they have faced challenges in identifying evidence required to make rational decisions about test selection. Ideally medical tests, as with interventions, should be recommended for use when there is evidence that they do more good than harm. However, medical tests rarely directly improve patient outcomes – rather the medical interventions that are taken consequent on use of a test create benefit for patients – and it is rare to be able to obtain evidence that shows how tests save lives. While evaluations of diagnostic or prognostic tests have typically focused on their accuracy to predict the numbers receiving appropriate or inappropriate treatment, extrapolating from these data to predict overall patient benefit is not always appropriate. In this talk Jon reviewed challenges that healthcare organisations face in identifying evidence required to assess benefits and harms of testing, drawing on experience working with the WHO EDL.

**Wednesday 8 May:
An introduction to variational integrators**

- Speaker: Fernando Jimenez Alburquerque (Oxford)

Abstract: Fernando introduced the basic notions of geometric integration of mechanical systems, naturally described by Lagrangian/Hamiltonian dynamics. The numerical approximation of such dynamics, respecting its underlying geometrical aspects, represents a crucial challenge in modern geometric integration. Variational integrators [MaWe2001], a class of geometric integrators that has received a lot of attention from the mathematical community in the last two decades, are a well-established example of numerical schemes that succeed in such a task, and moreover display a superior performance in some aspects than benchmark numerical integrators. We shall go over their definition and fundamental properties. Finally, Fernando also introduced future challenges of variational integrators when approximating the dynamics of dissipative mechanical systems.

*[MaWe2001] J.E.Marsden and M. West: “Discrete mechanics and variational integrators”, Acta Numerica 10, pp. 357-514, (2001).*

**Wednesday 15 May: A skein-theoretic model for the double affine Hecke algebras**

- Speaker: Hugh Morton (University of Liverpool)

Abstract: Hugh illustrated pictorially the use of ${\mathbb Z}[s^{\pm 1}, q^{\pm 1}]$-linear combinations of braids in the thickened torus $T^{2}\times I$ to construct an algebra induced by composing $n$-string braids. Hugh showed, with the help of pictures, that this algebra satisfies the relations of the double affine Hecke algebra $\ddot{H}_{n}$, which was introduced algebraically. The talk finished with a rather speculative plan to include closed curves in our model in an attempt to incorporate earlier work with Peter Samuelson on the Homfly skein of $T^{2}$ into the setting of the algebras $\ddot{H}_{n}$. This was done with an eye on the elliptic Hall algebra and the work of Schiffman and Vasserot, which was discussed very briefly.

**Wednesday 22 May: ****Lattice Boltzmann Modelling of Two-Dimensional Flow in Micro-Channel by Using Moment Boundary Conditions**

- Speaker: Zainab Bu Sinnah (Plymouth)

Abstract: The Lattice Boltzmann Method (LBM) has been developed and used to simulate fluid flow problems for a various geometries and boundary conditions. In this seminar, Zainab presented results obtained using a Lattice Boltzmann (LB) model to simulate rarefaction and compressibility effects for two-dimensional flow in a micro-channel. Moment boundary conditions are used to implement Navier-slip boundary conditions on walls and pressure boundaries are used to drive the flow. For the simulations, we use a second-order single relaxation time model and investigate convergence behaviour of the model.