lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

the inverse galois problem for mathrm psl _ 2 mathbb f _ p we show that the simple group psl2 fp occurs as the galois group of an extension of the rationals for all primes p 5 we obtain our galois extensions by studying the galois action on the second etale cohomology groups of a specific elliptic surface

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

integral crystalline cohomology over very ramified valuation rings in this paper we intend to show how fontaine s comparison theory fol fo2 between crystalline and p adic etale cohomology can be extented to very ramified base rings so far it had been developed either for qp coefficients or zp coefficients if the base is unramified over the witt vectors see fa2 for example it states that for any p adic discrete valuation ring v there exists a ring b v with the following property if x denotes a smooth and proper v scheme the p adic etale cohomology of the generic fiber x xv k is related to the crystalline cohomology of x v0 vo defined below by an isomorphism

small cancellation theory over burnside groups abstract we develop a version of small cancellation theory in the variety of burnside groups more precisely we show that there exists a critical exponent n 0 such that for every odd integer n n 0 the well known classical c 1 6 small cancellation theory as well as its graphical generalization and its version for free products produce examples of infinite n periodic groups our result gives a powerful tool for producing uncountable collections of examples of n periodic groups with prescribed properties it can be applied without any prior knowledge in the subject of n periodic groups as applications we show the undecidability of markov properties in classes of n periodic groups we produce n periodic groups whose cayley graph contains an embedded expander graphs and we give an n periodic version of the rips construction we also obtain simpler proofs of some known results like the existence of uncountably many finitely generated n periodic groups and the sq universality in the class of n periodic groups of free burnside groups

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

conjecture de l inertie moderee de serre on considere k un corps complet pour une valuation discrete de caracteristique nulle et dont le corps residuel est suppose parfait de caracteristique p on appelle e l indice de ramification absolue de k mathcal o k son anneau des entiers et overline k une cloture algebrique soit xk un schema propre et lisse sur k admettant un modele propre et semi stable x sur mathcal o k generalisant les resultats de breuil valables pour e 1 on demontre dans cet article un isomorphisme de periodes reliant le r ieme groupe de cohomologie etale de x overline k a coefficients dans pn et un r ieme groupe de cohomologie log cristalline de la fibre speciale de x nous avons toutefois les restrictions er 1

heat transfer in lattice bgk modeled fluid the thermal lattice bgk model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics the quality of the lattice bgk simulation is checked in this paper by calculating temperature profiles in the couette flow under different eckert and mach numbers a revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect especially in the flow regime with a higher mach number

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

some bounds for ramification of p n torsion semi stable representations let p be an odd prime k a finite extension of q p g k gal kbar k its absolute galois group and e e k q p its absolute ramification index suppose that t is a p n torsion representation of g k that is isomorphic to a quotient of g k stable z p lattices in a semi stable representation with hodge tate weights in 0 r we prove that there exists a constant mu depending only on n e and r such that the upper numbering ramification group g k mu acts on t trivially

tight geodesics in the curve complex the curve graph mathcal g associated to a compact surface is the 1 skeleton of the curve complex defined by harvey masur and minsky showed that this graph is hyperbolic and defined the notion of a tight geodesic therein we prove some finiteness results for such geodesics for example we show that a slice of the union of tight geodesics between any pair of points has cardinality bounded purely in terms of the topological type of we deduce some consequences for the action of the mapping class group on mathcal g in particular we show that it satisfies an acylindricity condition and that the stable lengths of pseudoanosov elements are rational with bounded denominator

rips segev torsion free groups without the unique product property abstract we generalize the graphical small cancellation theory of gromov to a graphical small cancellation theory over the free product we extend gromov s small cancellation theorem to the free product we explain and generalize rips segev s construction of torsion free groups without the unique product property by viewing these groups as given by graphical small cancellation presentations over the free product our graphical small cancellation theorem then provides first examples of gromov hyperbolic groups without the unique product property we construct uncountably many non isomorphic torsion free groups without the unique product property we show that the presentations of generalized rips segev groups are not generic among finite presentations of groups

the lattice boltzmann equation a new tool for computational fluid dynamics abstract we present a series of applications which demonstrate that the lattice boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes ranging from laminar to fully turbulent flows in two and three dimensions

a new lattice boltzmann model for solving the coupled viscous burgers equation abstract in this paper a new lattice boltzmann model for the coupled nonlinear system of viscous burgers equation is proposed by using the double evolutionary equations through selecting equilibrium distribution functions and amending functions properly the governing evolution system can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed the effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail the numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies it is found that the numerical results agree well with the analytic solutions which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous burgers equation

numerical study of the ordering properties of lamellar phase the quench of a binary mixture into a stable lamellar phase is numerically investigated we present a novel approach to study the phenomenological equations governing the system dynamics basedon the combination of lattice boltzmann and1nite d equations we can access large systems on time scales long enough to 1nd evidence of dynamical scaling regime in the ordering process when hydrodynamics is operating c

phase separation of incompressible binary fluids with lattice boltzmann methods we introduce new versions of lattice boltzmann methods lbm for incompressible binary mixtures where fluctuations of total density are inhibited as a test for the improved algorithms we consider the problem of phase separation of two dimensional binary mixtures quenched from a disordered state into the coexistence region we find that the stability properties of lbm are greatly improved the control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent

an improved immersed boundary lattice boltzmann method for simulating three dimensional incompressible flows the recently proposed boundary condition enforced immersed boundary lattice boltzmann method ib lbm 14 is improved in this work to simulate three dimensional incompressible viscous flows in the conventional ib lbm the restoring force is pre calculated and the non slip boundary condition is not enforced as compared to body fitted solvers as a result there is a flow penetration to the solid boundary this drawback was removed by the new version of ib lbm 14 in which the restoring force is considered as unknown and is determined in such a way that the non slip boundary condition is enforced since eulerian points are also defined inside the solid boundary the computational domain is usually regular and the cartesian mesh is used on the other hand to well capture the boundary layer and in the meantime to save the computational effort we often use non uniform mesh in ib lbm applications in our previous two dimensional simulations 14 the taylor series expansion and least squares based lattice boltzmann method tllbm was used on the non uniform cartesian mesh to get the flow field the final expression of tllbm is an algebraic formulation with some weighting coefficients these coefficients could be computed in advance and stored for the following computations however this way may become impractical for 3d cases as the memory requirement often exceeds the machine capacity the other way is to calculate the coefficients at every time step as a result extra time is consumed significantly to overcome this drawback in this study we propose a more efficient approach to solve lattice boltzmann equation on the non uniform cartesian mesh as compared to tllbm the proposed approach needs much less computational time and virtual storage its good accuracy and efficiency are well demonstrated by its application to simulate the 3d lid driven cubic cavity flow to valid the combination of proposed approach with the new version of ibm 14 for 3d flows with curved boundaries the flows over a sphere and torus are simulated the obtained numerical results compare very well with available data in the literature

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

weight cycling and serre type conjectures for unitary groups we prove that for forms of u 3 which are compact at infinity and split at places dividing a prime p in generic situations the serre weights of a mod p modular galois representation which is irreducible when restricted to each decomposition group above p are exactly those previously predicted by herzig we do this by combining explicit computations in p adic hodge theory based on a formalism of strongly divisible modules and breuil modules with descent data which we develop here with a technique that we call weight cycling

two dimensional turbulence with the lattice boltzmann equation the authors investigate the ability of the lattice boltzmann equation to reproduce the basic physics of fully turbulent two dimensional flows and present a qualitative estimate of its computational efficiency with respect to other conventional techniques