twisted rings and moduli stacks of fat point modules in non commutative projective geometry abstract the hilbert scheme of point modules was introduced by artin tate van den bergh to study non commutative graded algebras the key tool is the construction of a map from the algebra to a twisted ring on this hilbert scheme in this paper we study moduli stacks of more general fat point modules and show that there is a similar map to a twisted ring associated to the stack this is used to provide a sufficient criterion for a non commutative projective surface to be birationally pi it is hoped that such a criterion will be useful in understanding mike artin s conjecture on the birational classification of non commutative surfaces

the q division ring and its fixed rings abstract we prove that the fixed ring of the q division ring k q x y under any finite group of monomial automorphisms is isomorphic to k q x y for the same q in a similar manner we also show that this phenomenon extends to an automorphism that is defined only on k q x y and does not restrict to k q x 1 y 1 we then use these results to answer several questions posed by artamonov and cohn about the endomorphisms and automorphisms of k q x y

a lattice boltzmann approach for the non newtonian effect in the blood flow abstract a new lattice boltzmann approach within the framework of d2q9 lattice for simulating shear thinning non newtonian blood flows described by the power law carreau yasuda and casson rheology models is proposed in this study the essence of this method lies in splitting the complete non newtonian effect up into two portions one as the newtonian result and the other as an effective external source this arrangement takes the advantage in remaining fixed relaxation time during the whole course of numerical simulation that can avoid the potential numerical instability caused by the relaxation time approaches to 1 2 an inherent difficulty in the conventional lattice boltzmann methods using varying relaxation times for the non newtonian effect macroscopically consistency of the proposed model with the equations of motion for the three target non newtonian models is demonstrated through the technique of chapman enskog multi scale expansion the feasibility and accuracy of the method are examined by comparing with the analytical solutions of the two dimensional poiseuille flows based on the power law and casson models the results show that the velocity profiles agree very well with those of analytical solutions and the error analyses demonstrate that the proposed scheme is with second order accuracy the present approach also demonstrates its superiority over the conventional lattice boltzmann method in the extent of numerical stability for simulating the power law based shear thinning flows the straightforwardness in scheme derivation and implementation renders the present approach as a potential method for the complex non newtonian flows

optimal design for non newtonian flows using a topology optimization approach we study non newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach the flow is modeled with the single relaxation hydrodynamic lattice boltzmann method and the shear dependence of viscosity is included through the carreau yasuda model for non newtonian fluids to represent the viscosity of blood in this model we use non newtonian similarity further we introduce a scaling to decrease the effects of the non newtonian model in porous regions in order to stabilize the coupling of the lbm porosity and non newtonian flow models for the resulting flow model we derive the non newtonian sensitivity analysis for steady state conditions and illustrate the non newtonian effect on channel layouts for a 2d dual pipe design problem at different reynolds numbers

flow of power law fluids in self affine fracture channels the two dimensional pressure driven flow of non newtonian power law fluids in self affine fracture channels at finite reynolds number is calculated the channels have constant mean aperture and two values ensuremath zeta 0 5 and 0 8 of the hurst exponent are considered the calculation is based on the lattice boltzmann method using a different tecnique to obtain a power law variation in viscosity and the behavior of shear thinning newtonian and shear thickening liquids is compared local aspects of the flow fields such as maximum velocity and pressure fluctuations are studied and the non newtonian fluids are compared to the previously studied newtonian case we find a scaling relation between permeability and mean aperture in the low reynolds number regime generalizing an earlier result for newtonian fluids as the reynolds number increases we observe the same sequence of transitions to nonlinearity found in intergranular porous media furthermore the permeability results may be collapsed into a master curve of friction factor vs reynolds number using a scaling similar to that employed for power law fluids in porous media

field of fractions of certain quantum algebras abstract in this paper we show that the field of fractions of certain algebras appearing in the theory of quantum groups are isomorphic to the field of fractions of quantum n space when the parameter q is not a root of 1 more precisely the quantum serre relations of type a n and the relations defining the quantum weyl algebra induce q communtation relations in the field of fractions also we study the problem of separation of these skew fields using the standard embeddings in non commutative series

complete semi thue systems for abelian groups abstract we show that there are infinitely many examples of finite semi thue systems with decidable word problem and which have no finite equivalent noetherian and confluent complete reduction system these examples have a very simple algebraic structure they are abelian groups more precisely we develop necessary and sufficient conditions for the existence of complete semi thue systems for presentations of finitely generated abelian groups

lattice boltzmann modeling of bingham plastics abstract a new lattice boltzmann model within the framework of d2q9 lattices for bingham plastics is proposed the essence of the present model lies in incorporation of the effect of local shear rate into the lattice equilibrium distribution function with this arrangement particle distribution functions are able to relax to the states containing proper local shear rate information during collisions that makes the proposed scheme a more efficient and stable one macroscopically consistency of the proposed lattice boltzmann model with the equations of motion for bingham plastics are demonstrated through the technique of chapman enskog multi scale expansion the benchmark problem of a 2 1 sudden expansion flow in a planar channel for a wide range of bingham numbers 0 b n 2000 and reynolds numbers 0 2 re 200 are executed to verify the applicability of the present model it is shown that both the extent and shape for yielded unyielded regions and for corner vortexes are accurately captured and their numerical values are also in good agreement with existing results

cyclic cohomology and chern connes pairing of some crossed product algebras abstract we compute the cyclic and hochschild cohomology groups for the algebras a a l g z 3 a a l g z 4 and a a l g z 6 we also compute the partial chern connes index table for each of these algebras

numerical simulations of flows in cerebral aneurysms using the lattice boltzmann method with single and multiple relaxation time collision models abstract lattice boltzmann simulations of flows in tof mra based cerebral aneurysm models are carried out using the single two and multiple relaxation time collision models srt trt and mrt to investigate the effects of the collision model on predicted velocity fields in the aneurysms the non newtonian characteristics of blood are accounted for by using the casson model whereas a simulation with the newtonian viscous stress model is also carried out to investigate the effects of the viscous stress model on predicted velocity and wall shear stress distributions four cerebral aneurysm models are used in the simulation the shapes of cerebral arteries are extracted from tof mra data as stl meshes and the level set function representing the artery wall is reconstructed from the stl mesh data by making use of the level set function in the interpolated bounce back scheme the complex structures of arteries having aneurysms can be easily dealt with in the lb framework as a result the following conclusions are obtained 1 the srt can give reasonable predictions comparable to the mrt provided that the spatial resolution is high enough otherwise numerical errors can be large and numerical instabilities take place 2 numerical errors in velocity is apt to take place in the near aneurysm wall region due to a small velocity scale 3 although the trt is less stable than the mrt predictions of the trt under stable numerical conditions are almost the same as those of the mrt and 4 although the bingham number effect on the flow structure is small the mean wall shear stress may change over several percent depending on the configuration of the aneurysm and the main blood flow by neglecting the non newtonian nature of blood

lattice boltzmann simulation of pattern formation under cross diffusion in this paper a lattice boltzmann model for cross reaction diffusion system is proposed in order to recover the cross diffusion equations by lattice boltzmann method we transform the equations into a complex reaction diffusion equation this complex reaction diffusion equation is recovered with higher order accuracy of the truncation error based on this model two typical reaction diffusion systems with cross diffusion predator prey system and inhomogeneous brusselator model are simulated the numerical results show that this model can be used to simulate the cross reaction diffusion systems

transport in rough self affine fractures transport properties of three dimensional self affine rough fractures are studied by means of an effective medium analysis and numerical simulations using the lattice boltzmann method the numerical results show that the effective medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations in terms of the aperture of the fracture the roughness exponent and the characteristic length of the fracture surfaces in the limit of small separation between surfaces the permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces and it is shown that it can be bounded by the permeability of two dimensional fractures the development of channel like structures in the velocity field is also numerically investigated for different relative displacements between surfaces finally the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods the asymptotic dominant role of the geometric dispersion due to velocity fluctuations and their spatial correlations is shown in the limit of very small separation between fracture surfaces

effect of the forcing term in the multiple relaxation time lattice boltzmann equation on the shear stress or the strain rate tensor in this work the effect of the forcing term or external force in the multiple relaxation time lattice boltzmann equation mrtlbe on the shear stress or the strain rate tensor is studied theoretically and numerically through a chapman enskog analysis and numerical simulations we show that the shear stress or the strain rate tensor derived from the mrtlbe is second order accurate in space we then examine the influence of the forcing term on the shear stress or the strain rate tensor and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function

accuracy of non newtonian lattice boltzmann simulations this work deals with the accuracy of non newtonian lattice boltzmann simulations previous work for newtonian fluids indicate that depending on the numerical value of the dimensionless collision frequency additional artificial viscosity is introduced which negatively influences the accuracy since the non newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency a dependent error e is introduced and its influence on the overall error is investigated here simulations with the srt and the mrt model are carried out for power law fluids in order to numerically investigate the accuracy of non newtonian lattice boltzmann simulations a goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation mach number respectively for the non newtonian case an error estimate for e in the form of a functional is derived on the basis of a series expansion of the lattice boltzmann equation this functional can be solved analytically for the case of the hagen poiseuille channel flow of non newtonian fluids with the help of the error functional the prediction of the global error minimum of the velocity field is excellent in regions where the e error is the dominant source of error with an optimal simulation mach number the simulation is about one order of magnitude more accurate additionally for both collision models a detailed study of the convergence behavior of the method in the non newtonian case is conducted the results show that the simulation mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation mach number

a comparison of non newtonian models for lattice boltzmann blood flow simulations in the present paper three non newtonian models for blood are used in a lattice boltzmann flow solver to simulate non newtonian blood flows exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow original results for the use of the k l model in addition to the casson and carreau yasuda models are reported for non newtonian flow simulations using a lattice boltzmann lb flow solver numerical simulations of non newtonian flow in a 2d channel show that these models predict different mass flux and velocity profiles even for the same channel geometry and flow boundary conditions which in turn suggests a more careful model selection for more realistic blood flow simulations the agreement between predicted velocity profiles and those of exact solutions is excellent indicating the capability of the lb flow solver for such complex fluid flows

power law fluid flow in driven enclosures with undulation using mrt lattice boltzmann method abstract in this article the flow of non newtonian fluid which is represented by the power law model in two dimensional 2d driven enclosures is studied the enclosure consists of regular rectangular shaped undulations on the bottom wall multiple relaxation time mrt collision model for the lattice boltzmann equation method lbm is employed first numerical validation is performed by comparing the mrt lbm results of power law fluid flow inside the wall driven square enclosure no undulation and flow inside diagonally flipped l shaped enclosure with the literature the strain rate profiles for square enclosure without undulations are compared using various equations available for strain rate calculation in the lbm literature further the effect of different values of the non hydrodynamic relaxation parameters on the flow is examined then for the undulated enclosures flow features and eddy dynamics are analyzed and discussed for the variations in the power law index n to represent shear thinning and shear thickening fluids the effects of various parameters such as reynolds numbers wall undulation heights and wavelength of undulations on the power law fluid flow are analyzed also the variation of viscosity with spatial location for steady state flow and total kinetic energy within the computational domain are presented for various values of power law index

permeability of self affine rough fractures the permeability of two dimensional fractures with self affine fractal roughness is studied via analytic arguments and numerical simulations the limit where the roughness amplitude is small compared with average fracture aperture is analyzed by a perturbation method while in the opposite case of narrow aperture we use heuristic arguments based on lubrication theory numerical simulations using the lattice boltzmann method are used to examine the complete range of aperture sizes and confirm the analytic arguments

the computation of strain rate tensor in multiple relaxation time lattice boltzmann model abstract the multiple relaxation time mrt lattice boltzmann lb model is an important class of lb model with lots of advantages over the traditional single relaxation time srt lb model generally the computation of strain rate tensor is crucial for the mrt lb simulations of some complex flows at present only two formulae are available to compute the strain rate tensor in the mrt lb model one is to compute the strain rate tensor using the non equilibrium parts of macroscopic moments yu formula the other is to compute the strain rate tensor using the non equilibrium parts of density distribution functions chai formula the mathematical expressions of these two formulae are so different that we do not know which formula to choose for computing the strain rate tensor in the mrt lb model to overcome this problem this paper presents a theoretical study of the relationship between chai and yu formulae the results show that the yu formula can be deduced from the chai formula although they have their own advantages and disadvantages in particular the yu formula is computationally more efficient while the chai formula is applicable to more lattice patterns of the mrt lb models furthermore the derivation of the yu formula in a particular lattice pattern from the chai formula is more convenient than that proposed by yu et al

complexity combinatorial group theory and the language of palutators abstract after a brief survey of the known results about group languages we prove that many of the familiar classes of groups have word problems whose complexity is linear time we also consider the complexity of extensions and hnn extensions finally in an attempt to find languages that have complexity which is greater than linear time we discuss the language of palutators where a palutator is defined as a generalization of a palindrome and a commutator

groups presented by finite two monadic church rosser thue systems it is shown that a group g can be defined by a monoid presentation of the form 2 7 where t is a finite two monadic church rosser thue system over 2 if and only if g is isomorphic to the free product of a finitely generated free group with a finite number of finite groups

lattice boltzmann method for non newtonian power law fluids we study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models we extensively test the accuracy of the method for the case of shear thinning and shear thickening truncated power law fluids in the parallel plate geometry and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution finally we also tested the method in the reentrant flow geometry in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points in this geometry we also found excellent agreement with the solutions obtained by standard finite element methods and the agreement improves with higher lattice resolution

commutative monoids have complete presentations by free non commutative monoids abstract any finitely generated commutative monoid has a presentation by a finite noetherian confluent semi thue system over a free monoid