Title: Non-newtonian fluid flow simulation using lattice Boltzmann method Author: Bc. Pavel Kuriščák Department: Mathematical Institute, Charles University Supervisor: RNDr. Ing. Jaroslav Hron Ph.D. Supervisor's e-mail address: Jaroslav.Hron@mff.cuni.cz Abstract: The aim of this thesis is to find and estabilish a modification to the Lattice Boltzmann Method, allowing it to simulate non-newtonian behaviour of fluids. In the theoretical part of thesis, there is introduced a derivation, based on the work of [22], that is capable of arriving to macroscopical Navier-Stokes equa- tions completely a priori from the Boltzmann equation, utilizing the Hermite basis expansion. This derivation is afterwards applied to the method suggested by [11], that uses the changed equilibrium distribution to fine-tune the local fluid viscosity according to the non-newtonian model. In the last part of thesis, this method is implemented in the form of lattice kinetic scheme and tested on three sample problems. Keywords: Lattice Boltzmann Method, non-newtonian fluids, Hermite expansion, lattice kinetic scheme

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Call number: LD2668 .T4 1984 T33 / Master of Science

The CKM matrix element |Vus| can be extracted from the experimental measurement of semileptonic K → π decays and theoretical input for the corresponding vector form factor in QCD. The thesis performs a major improvement of the RBC/UKQCD programme to calculate Kl3 form factor in Nf = 2+1 Lattice QCD using domain wall fermions. We use data from several lattice spacings and dfferent quark masses with lightest pion mass of about 170MeV. Systematic error corresponding to interpolation in the momentum transfer is avoided using partially twisted boundary conditions. Using simulated quark masses near the physical point, reduce the systematic error due to the mass extrapolation. This work explores different kinematic arrangements of pion and Kaon momenta for twisted boundary conditions. This thesis proposes a new ansatz for mass extrapolation. Analysing three sets of simulation data allows for a detailed study of systematic effects leading to the prediction f+kπ (0) = 0:9671(17)(+18-46), where the first error is statistical and the second error systematic. The result allows us to extract the CKM matrix element |Vus| = 0:2237(+13-8) and confirm unitarity of the first row CKM matrix in the Standard Model. Also in this thesis, we discuss porting of Clover Lattice fermion action to Blue Gene-Q architecture. Clover action achieves maximum efficiency of 29.1% for single precision with good weak scaling. Strong scaling shows local volume dependency. In a study of different iterative solvers for Domain Wall Fermion action (DWF), we find that Modified Conjugate Residual(MCR) and Multishift MCR as the most efficient solver compared to CG and GCR. A new probing technique for estimating the diagonal of the inverse Dirac operator in Lattice QCD is introduced and this method is found to be closer to the exact solution than stochastic methods.

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published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy

In an interference network, multiple transmitters communicate with multiple receivers using the same communication channel. The capacity region of an interference network is defined as the set of data rates that can be simultaneously achieved by the users of the network. One of the most important example of an interference network is the wireless network, where the communication channel is the wireless channel. Wireless interference networks are known to be interference limited rather than noise limited since the interference power level at the receivers (caused by other user's transmissions) is much higher than the noise power level. Most wireless communication systems deployed today employ transmission strategies where the interfering signals are treated in the same manner as thermal noise. Such strategies are known to be suboptimal (in terms of achieving higher data rates), because the interfering signals generated by other transmitters have a structure to them that is very different from that of random thermal noise. Hence, there is a need to design transmission strategies that exploit this structure of the interfering signals to achieve higher data rates. However, determining optimal strategies for mitigating interference has been a long standing open problem. In fact, even for the simplest interference network with just two users, the capacity region is unknown. In this dissertation, we will investigate the capacity region of several models of interference channels. We will derive limits on achievable data rates and design effective transmission strategies that come close to achieving the limits. We will investigate two kinds of networks - "small" (usually characterized by two transmitters and two receivers) and "large" where the number of users is large. / text

published_or_final_version / Physics / Master / Master of Philosophy

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