convection diffusion lattice boltzmann scheme for irregular lattices in this paper a lattice boltzmann lb scheme for convection diffusion on irregular lattices is presented which is free of any interpolation or coarse graining step the scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the maxwell boltzmann distribution the axioma holds for both bravais and irregular lattices implying a single framework for lb schemes for all lattice types by solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion furthermore we have compared the performance of the lb schemes with that of finite difference and finite element schemes the comparison shows that the lb scheme has a similar performance as the one step second order lax wendroff scheme it has little numerical diffusion but has a slight dispersion error by changing the relaxation parameter the dispersion error can be balanced by a small increase of the numerical diffusion

stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

the loewner equation maps and shapes an approach called schramm loewner evolution sle provides a new method for dealing with a wide variety of scale invariant problems in two dimensions this approach is based upon an older method called loewner evolution le which connects analytic and geometrical constructions in the complex plane in this paper the bases of le and sle are described and some simple applications are discussed in relatively non technical form a bibliography of the subject is presented

a modified multiple relaxation time lattice boltzmann model for convection diffusion equation a modified lattice boltzmann model with multiple relaxation times mrt for the convection diffusion equation cde is proposed by modifying the relaxation matrix as well as choosing the corresponding equilibrium distribution function properly the present model can recover the cde with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the chapman enskog analysis this model is firstly validated by simulating the diffusion of a gaussian hill which demonstrates it can handle the anisotropic diffusion problem correctly then it is adopted to calculate the longitudinal dispersion coefficient of the taylor aris dispersion numerical results show that the present model can further reduce the numerical error under the condition of non zero velocity vector especially when the dimensionless relaxation time is relatively large

a simple direct heating thermal immersed boundary lattice boltzmann method for its application in incompressible flow abstract a simple direct heating thermal immersed boundary lattice boltzmann method for buoyancy driven incompressible flow with complex geometry boundaries is developed to simulate natural convection with curved boundary in the newly developed method both dirichlet and neumann boundary conditions in macroscopic equation are deduced into a novel mesoscopic discrete heat source the mesoscopic discrete heat source consists of simplified explicit discrete heat source scheme which reduces the computational complexities and is introduced into lattice boltzmann equation for temperature field which extends the idea of the previous direct forcing ib lbm both isothermal boundary condition i e dirichlet boundary condition and constant heat flux boundary condition i e neumann boundary condition are considered in our simulations the efficiency and accuracy of the present method are demonstrated by simulating both two dimensional and three dimensional thermal flow with curved boundaries numerical results indicate that the efficiency and accuracy of the present method are well consistent with experimental and the other numerical results the present method has also been successfully applied to three dimensional simulations of natural convection in a thin annulus with adiabatic wall at both vertical sides

mixed type reverse order laws for 1 3 4 generalized inverses over hilbert spaces abstract the reverse order laws for 1 3 4 generalized inverses of a product of two operators have been studied by wang et al j wang h zhang g ji a generalized reverse order law for the products of two operators journal of shaanxi normal university 38 4 2010 13 17 in this paper using a block operator matrix technique we study mixed type reverse order laws for 1 3 4 generalized inverses over hilbert spaces

a generalized lattice boltzmann model for fluid flow system and its application in two phase flows abstract in this paper a generalized lattice boltzmann lb model with a source term in the continuity equation is proposed to solve both incompressible and nearly incompressible navier stokes n s equations this model can be used to deal with single phase and two phase flows problems with a source term in the continuity equation from this generalized model we can not only get some existing models but also derive new models moreover for the incompressible model derived a modified pressure scheme is introduced to calculate the pressure and then to ensure the accuracy of the model in this work we will focus on a two phase flow system and in the frame work of our generalized lb model a new phase field based lb model is developed for incompressible and quasi incompressible two phase flows a series of numerical simulations of some classic physical problems including a spinodal decomposition a static droplet a layered poiseuille flow and a bubble rising flow under buoyancy are performed to validate the developed model besides some comparisons with previous quasi incompressible and incompressible lb models are also carried out and the results show that the present model is accurate in the study of two phase flows finally we also conduct a comparison between quasi incompressible and incompressible lb models for two phase flow problems and find that in some cases the proposed quasi incompressible lb model performs better than incompressible lb models

reverse order law for reflexive generalized inverses of products of matrices abstract the relationships between generalized inverses of the product of two matrices a b and the product of generalized inverses of a b have been studied in the literature by applying the product singular value decomposition p svd in this paper we derive equivalent conditions for b 1 2 a 1 2 ab 1 2 ab 1 2 b 1 2 a 1 2 b 1 2 a 1 2 ab 1 2 and equivalent conditions for ab 1 b 1 a 1

some results on partial ordering and reverse order law of elements of c algebras abstract in this paper we establish some results relating star left star right star minus ordering and the reverse order law under certain conditions on moore penrose invertible elements of c algebras

further results on the reverse order law for the group inverse in rings in this paper we use the drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings moreover if the ring has an involution we present more equivalences when both involved elements are ep

asymptotic behaviour of disconnection and non intersection exponents we study the asymptotic behaviour of disconnection and non intersection exponents for planar brownian motionwhen the number of considered paths tends to infinity in particular if n respectively n p denotes the disconnection exponent for n paths respectively the non intersection exponent for n paths versus p paths then we show that limn n n 1 2 and that for a 0 and b 0 limn na nb n a b 2 2

conformal invariance of voronoi percolation it is proved that in the voronoi model for percolation in dimension 2 and 3 the crossing probabilities are asymptotically invariant under conformal change of metric

the generalized moore penrose inverse abstract we define the generalized moore penrose inverse and give necessary and sufficient conditions for its existence over an integral domain we also prove its uniqueness and give a formula for it which leads us towards a generalized cramer s rule to find the generalized moore penrose solution

finite difference lattice boltzmann model for nonlinear convection diffusion equations in this paper a finite difference lattice boltzmann lb model for nonlinear isotropic and anisotropic convection diffusion equations is proposed in this model the equilibrium distribution function is delicately designed in order to recover the convection diffusion equation exactly different from the standard lb model the temporal and spatial steps in this model are decoupled such that it is convenient to study convection diffusion problem with the non uniform grid in addition it also preserves the advantage of standard lb model that the complex valued convection diffusion equation can be solved directly the von neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model to test the performance of the model a series of numerical simulations of some classical problems including the diffusion equation the nonlinear heat conduction equation the sine gordon equation the gaussian hill problem the burgersfisher equation and the nonlinear schrdinger equation have also been carried out the results show that the present model has a second order convergence rate in space and generally it is also more accurate than the standard lb model

an efficient phase field based multiple relaxation time lattice boltzmann model for three dimensional multiphase flows in this paper an efficient phase field based lattice boltzmann lb model with multiple relaxation time mrt collision operator is developed for the simulation of three dimensional multiphase flows this model is an extension of our previous two dimensional model liang etal 2014 to the three dimensions using the d3q7 seven discrete velocities in three dimensions lattice for the cahnhilliard equation and the d3q15 lattice for the navierstokes equations due to the less lattice velocity directions used the computational efficiency can be significantly improved in the study of three dimensional multiphase flows and simultaneously the present model can recover the cahnhilliard equation and the navierstokes equations correctly through the chapmanenskog procedure we compare the present mrt model with its single relaxation time version and the previous lb model by using two benchmark interface tracking problems and numerical results show that the present mrt model can achieve a significant improvement in the accuracy and stability of the interface capturing the developed model can also be able to deal with multiphase fluids with high viscosity ratio which is demonstrated by the simulation of the layered poiseuille flow and rayleightaylor instability at various viscosity ratios the numerical results are found to be in good agreement with the analytical solutions or some available results in addition it is also found that the instability induces a more complex structure of the interface at a low viscosity

intersections of random walks a direct renormalization approach various intersection probabilities of independent random walks ind dimensions are calculated analytically by a direct renormalization method adapted from polymer physics this heuristic approach based on edwards continuum model leads to a straightforward derivation and also to refinements of lawler s results for the simultaneous intersections of two walks in 4 or three walks in 3 these results are generalized top walks in d d frac 2p p 1 p 2 ford 4 an infinite set of universal critical exponents l l 1 are derived they govern the asymptotic probability z l sim s sigma l thatl star walks in d with a common origin do not intersect before times the l s are calculated up to ordero e2 whered 4 e this information is used to calculate the probability z g that a set of independent random walks in d or d d 4 respectivelyd 3 form a given topological networks g of multiple intersection points in the absence of any other double point respectively triple point this is generalized to a network in d leqq frac 2p p 1 dimension with exclusion ofp tuple points the method is quite general and can be used to calculate any critical intersection probability and provides the probabilist with a large variety of exact results yet to be proven rigorously

factorization of weighted ep elements in c algebras abstract we present characterizations of weighted ep elements in c algebras using different kinds of factorizations

a new scheme for source term in lbgk model for convection diffusion equation a new scheme for source term in the lattice bgk lbgk model for convection diffusion equation is proposed unlike the models proposed previously the present scheme only requires the source term in order of the knudsen number by adding a differential operator of the source term to the evolution equation the scheme can be applied to reaction diffusion systems directly numerical results are found to be in excellent agreement with the analytical solutions it is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models

further results on the reverse order law for the moore penrose inverse in rings with involution abstract we present some equivalent conditions of the reverse order law for the moore penrose inverse in rings with involution extending some well known results to more general settings then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted moore penrose inverse in c algebras

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

reverse order laws in c algebras abstract in this paper we offer purely algebraic necessary and sufficient conditions for reverse order laws for generalized inverses in c algebras extending rank conditions for matrices and range conditions for hilbert space operators

the tanh method for generalized forms of nonlinear heat conduction and burgers fisher equations generalized forms of the kdv the nonlinear heat conduction and burgers fisher equations are investigated the analysis rests mainly on the standard tanh method the focus is on the case where the parameter m is noninteger a variety of exact travelling wave solutions of distinct physical structures are formally derived

new characterizations of ep generalized normal and generalized hermitian elements in rings abstract we present a number of new characterizations of ep elements in rings with involution in purely algebraic terms then we study equivalent conditions for an element a in a ring with involution to satisfy a n a a a n or a n a n for arbitrary n n for n 1 we present some new characterizations of normal and hermitian elements in rings with involution

higher conformal multifractality we derive from conformal invariance and quantum gravity the multifractal spectrum f of the harmonic measure i e electrostatic potential or diffusion field near any conformally invariant fractal in two dimensions it gives the hausdorff dimension of the set of points where the potential varies with distance r to the fractal frontier as r first examples are a random walk i e a brownian motion a self avoiding walk or a critical percolation cluster the generalized dimensions d n as well as the multifractal functions f are derived and are all identical for these three cases the external frontiers of a brownian motion and of a percolation cluster are thus identical to a self avoiding walk in the scaling limit the multifractal mf function f c of the electrostatic potential near any conformally invariant fractal boundary like a critical o n loop or a q state potts cluster is given as a function of the central charge c of the associated conformal field theory the dimensions dep of the external perimeter and dh of the hull of a critical scaling curve or cluster obey the superuniversal duality equation d text ep 1 d text d 1 tfrac 1 4 finally for a conformally invariant scaling curve which is simple i e without double points we derive higher multifractal functions like the universal function f2 which gives the hausdorff dimension of the points where the potential varies jointly with distance r as r on one side of the curve and as r on the other the general case of the potential distribution between the branches of a star made of an arbitrary number of scaling paths is also treated the results apply to critical o n loops potts clusters and to the sle process we present a duality between external perimeters of potts clusters and o n loops at their critical point as well as the corresponding duality in the sle process for 16

group moore penrose core and dual core inverse in rings with involution abstract let r be a ring with involution the recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary ring case it is shown that the group moore penrose core and dual core inverse are closely related and they can be treated in the same manner using appropriate idempotents the several characterizations of these inverses are given some new properties are obtained and some known results are generalized a number of characterizations of ep elements in r are obtained it is shown that core and dual core inverse belong to the class of inverses along an element and to the class of b c inverses

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

the probability of intersection of independent random walks in four dimensions lets1 ands2 be independent simple random walks of lengthn inz4 starting at 0 andx0 respectively if x0 2 n it is shown that the probability that the paths intersect is of order logn 1 ifx0 0 it is shown that the probability of no intersection of the paths decays no faster than logn 1 and no slower than logn 1 2 it is conjectured that logn 1 2 is the actual decay rate

a unified lattice boltzmann model for immiscible and miscible ternary fluids abstract based on the phase field theory we develop a unified lattice boltzmann model for ternary flow in which the miscibility between the three fluid components can be adjusted independently based on a modified free energy function we derive the conservative phase field equations using the gradient flow method a generalized continuous surface tension force formulation is deduced by using the virtual work method the wetting boundary condition is derived based on mass conservation law the proposed model for ternary fluids is consistent with the binary fluid models in the absence of one fluid a lattice boltzmann lb model is developed to solve the phase field equations and hydrodynamic equations and this model can deal with problems involving high density and viscosity contrasts the proposed method is examined through several test cases a layered poiseuille flow and droplet coalescence problems are carried out to validate the present lb model several dynamic problems in ternary fluid problems involving a solid are simulated including the wetting of two droplets on a circular cylinder and impacting of a multiphase droplet on a fixed particle finally we apply the model to a three dimensional multi bubbles rising problem to access its numerical accuracy and stability

non intersection exponents for brownian paths letx andy be independent 3 dimensional brownian motions x 0 0 0 0 y 0 1 0 0 and letp r p x 0 r y 0 r then the non intersection exponent mathop lim limits r to infty log p r mathord left vphantom log p r log r right kern nulldelimiterspace log r exists and is equal to a similar non intersection exponent for random walks analogous results hold inr2 and for more than 2 paths

nonintersection exponents for brownian paths ii estimates and applications to a random fractal let x and y be independent two dimensional brownian motions x 0 0 0 y 0 e 0 and let p e p x 0 1 y 0 1 o q e y 0 1 does not contain a closed loop around 0 asymptotic estimates when e 0 of p e q e and some related probabilities are given let f be the boundary of the unbounded connected component of r 2 z 0 1 where z t x t tx 1 for t 0 1 then f is a closed jordan arc and the hausdorff dimension of f is less or equal to 3 2 1 4 2

the absorption laws for the generalized inverses abstract in this paper we give necessary and sufficient conditions for the absorption laws in terms of 1 1 2 1 3 and 1 4 inverses also we consider the various types of mixed absorption law for the generalized inverses

weighted partial isometries and weighted ep elements in c algebras we investigate weighted partial isometries weighted ep elements weighted star dagger weighted normal and weighted hermitian elements of c algebras

lattice boltzmann model for nonlinear convection diffusion equations a lattice boltzmann model for convection diffusion equation with nonlinear convection and isotropic diffusion terms is proposed through selecting equilibrium distribution function properly the model can be applied to the common real and complex valued nonlinear evolutionary equations such as the nonlinear schrodinger equation complex ginzburg landau equation burgers fisher equation nonlinear heat conduction equation and sine gordon equation by using a real and complex valued distribution function and relaxation time detailed simulations of these equations are performed and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies

limit lognormal multifractal as an exponential functional the limiting distribution of the limit lognormal multifractal first introduced by mandelbrot statistical models and turbulence m rosenblatt and c van atta eds lecture notes in physics 12 springer new york 1972 p 333 and constructed explicitly by bacry et al phys rev e 64 026103 2001 is investigated using its laplace transform a partial differential equation for the laplace transform is derived and it is shown that multifractality alone does not determine the limiting distribution the increments of the limit multifractal process are strongly stochastically dependent the precise nature of this stochastic dependence structure of increments sdsi is the determining characteristic of the limiting distribution the sdsi of the limit process is quantified by means of two integro differential relations obtained by renormalization in the sense of leipnik j aust math soc b 32 327 347 1991 one is interpreted as a counterpart of the star equation of mandelbrot and the other is shown to be an analogue of the classical girsanov theorem in the weak intermittency limit an approximate single variable equation for the laplace transform is obtained and successfully tested numerically by simulation

lattice boltzmann modeling of three phase incompressible flows in this paper based on multicomponent phase field theory we intend to develop an efficient lattice boltzmann lb model for simulating three phase incompressible flows in this model two lb equations are used to capture the interfaces among three different fluids and another lb equation is adopted to solve the flow field where a new distribution function for the forcing term is delicately designed different from previous multiphase lb models the interfacial force is not used in the computation of fluid velocity which is more reasonable from the perspective of the multiscale analysis as a result the computation of fluid velocity can be much simpler through the chapman enskog analysis it is shown that the present model can recover exactly the physical formulations for the three phase system numerical simulations of extensive examples including two circular interfaces ternary spinodal decomposition spreading of a liquid lens and kelvin helmholtz instability are conducted to test the model it is found that the present model can capture accurate interfaces among three different fluids which is attributed to its algebraical and dynamical consistency properties with the two component model furthermore the numerical results of three phase flows agree well with the theoretical results or some available data which demonstrates that the present lb model is a reliable and efficient method for simulating three phase flow problems

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

moore penrose inverse in rings with involution abstract we study the moore penrose inverse mp inverse in the setting of rings with involution the results include the relation between regular mp invertible and well supported elements we present an algebraic proof of the reverse order rule for the mp inverse valid under certain conditions on mp invertible elements applications to c algebras are given

when is b a a generalized inverse of ab in practice factorizations of a generalized inverse often arise from factorizations of the matrix which is to be inverted in addition to full rank factorizations normal factorizations and singular value decompositions svd there are other factorizations of particular matrices that are natural to certain problems for instance in statistics answers to questions like when is b a a generalized inverse of ab may thus be a computational tool besides they are of significant interest because they provide us with insights into the g inversion of matrix products

moore penrose invertible normal and hermitian elements in rings in this paper we present several new characterizations of normal and hermitian elements in rings with involution in purely algebraic terms and considerably simplify proofs of already existing characterizations

reverse order law for the moore penrose inverse abstract in this paper we present new results related to the reverse order law for the moore penrose inverse of operators on hilbert spaces some finite dimensional results are extended to infinite dimensional settings

reverse order laws for generalized inverses of multiple matrix products abstract in this article we study reverse order laws for generalized inverses and reflexive generalized inverses of the products of multiple matrices a 1 a n and the products of generalized inverses and reflexive generalized inverses of a n a 1 by applying the multiple product singular value decomposition we obtain necessary and sufficient conditions for one side inclusion relation of reverse order law for generalized inverses and necessary and sufficient conditions of reverse order law for reflexive generalized inverses

fractal structure of spin clusters and domain walls in the two dimensional ising model the fractal structure of spin clusters and their boundaries in the critical two dimensional ising model is investigated numerically the fractal dimensions of these geometrical objects are estimated by means of monte carlo simulations on relatively small lattices through standard finite size scaling the obtained results are in excellent agreement with theoretical predictions and partly provide significant improvements in precision over existing numerical estimates

the intersection of brownian paths as a case study of a renormalization group method for quantum field theory a new approach is presented for the study of the probability that the random paths generated by two independent brownian motions in d intersect or more generally are within a short distance a of each other the well known behavior of that function of a above below and at the critical dimension d 4 as well as further corrections are derived here by means of a single renormalization group equation the equation s derivation is expected to shed some light on the function of the o d 4 quantum field theory

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

the reverse order law revisited abstract necessary and sufficient conditions are given for the triple reverse order law abc c b a to hold some special cases are considered

a lattice boltzmann model for reaction dynamical systems with time delay nonlinear reaction dynamical systems with time delay are investigated to evaluate the capability of the lattice boltzmann model for delay differential dynamical systems the stiff delay systems multi delay systems and two dimensional partial delay differential equation are studied computation precise efficiency delay appearances are observed the simulation results indicate that the lattice boltzmann method is an innovative and effective numerical method to simulate the nonlinear delay differential dynamical systems

explicit finite difference lattice boltzmann method for curvilinear coordinates in this paper a finite difference based lattice boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method r mei and w shyy j comput phys 143 426 1998 in which the collision term of the boltzmann bhatnagar gross krook equation for discrete velocities is treated implicitly in the present method the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently as a result an explicit finite difference lattice boltzmann method for curvilinear coordinates is obtained the scheme is applied to a two dimensional poiseuille flow an unsteady couette flow a lid driven cavity flow and a steady flow around a circular cylinder the numerical results are in good agreement with the results of previous studies extensions to other lattice boltzmann models based on nonuniform meshes are also discussed

on the p q outer generalized inverse in banach algebra abstract in this note the p q outer generalized inverse in banach algebra is considered a new representation based on the 1 5 inverse is presented also we construct an iterative method for computing the p q outer generalized inverse in banach algebra

reverse order laws for the generalized inverses of multiple matrix products by using the ranks of matrices this article gives necessary and sufficient conditions for the reverse product a n a 2a 1of the moore penrose inverses of a1 a2 an to a 1 inverse inner inverse 1 2 inverse reflexive inner inverse 1 3 inverse 1 4 inverse 1 2 3 inverse 1 2 4 inverse or moore penrose inverse of matrix product a a1a2 an

ep elements in rings in this paper we present a number of new characterizations of ep elements in rings with involution in purely algebraic terms and considerably simplify proofs of already existing characterizations

mixed type reverse order law for products of three operators abstract we present new results related to the mixed type reverse order law for the moore penrose inverse of various products of three operators on hilbert spaces some finite dimensional results are extended to infinite dimensional settings

computation of moore penrose generalized inverses of matrices with meromorphic function entries abstract in this paper given a field with an involutory automorphism we introduce the notion of moore penrose field by requiring that all matrices over the field have moore penrose inverse we prove that only characteristic zero fields can be moore penrose and that the field of rational functions over a moore penrose field is also moore penrose in addition for a matrix with rational functions entries with coefficients in a field k we find sufficient conditions for the elements in k to ensure that the specialization of the moore penrose inverse is the moore penrose inverse of the specialization of the matrix as a consequence we provide a symbolic algorithm that given a matrix whose entries are rational expression over c of finitely many meromorphic functions being invariant by the involutory automorphism computes its moore penrose inverve by replacing the functions by new variables and hence reducing the problem to the case of matrices with complex rational function entries

reverse order law in c algebras we study equivalent conditions for the reverse order law a1a2 an an a1 a1a2 anan a1 in c algebras as corollaries we obtain some recent and special results

a lattice boltzmann model for multiphase flows with large density ratio a lattice boltzmann model for simulating multiphase flows with large density ratios is described in this paper the method is easily implemented it does not require solving the poisson equation and does not involve the complex treatments of derivative terms the interface capturing equation is recovered without any additional terms as compared to other methods m r swift w r osborn j m yeomans lattice boltzmann simulation of liquid gas and binary fluid systems phys rev e 54 1996 5041 5052 t inamuro t ogata s tajima n konishi a lattice boltzmann method for incompressible two phase flows with large density differences j comput phys 198 2004 628 644 t lee c l lin a stable discretization of the lattice boltzmann equation for simulation of incompressible two phase flows at high density ratio j comput phys 206 2005 16 47 besides it requires less discrete velocities as a result its efficiency could be greatly improved especially in 3d applications it is validated by several cases a bubble in a stationary flow and the capillary wave the numerical surface tension obtained from the laplace law and the interface profile agrees very well with the respective analytical solution the method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods all the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios

identities concerning the reverse order law for the moore penrose inverse we prove some identities related to the reverse order law for the moore penrose inverse of operators on hilbert spaces extending some results from y tian s cheng linear multilinear algebra 52 2004 and r e cline siam rev vol 6 no 1 1964 to infinite dimensional settings

copolymer networks and stars scaling exponents we explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods we establish a field theoretic description in terms of composite operators our third order resummation of the spectrum of scaling dimensions brings about remarkable features the special convexity properties of the spectra allow for a multifractal interpretation while preserving stability of the theory this behavior could not be found for power of field operators of usual ensuremath varphi 4 field theory the two dimensional 2d limit of the mutually avoiding walk star apparently corresponds to results of a conformal kac series such a classification seems not possible for the 2d limit of other copolymer stars we furthermore provide a consistency check of two complementary renormalization schemes ensuremath varepsilon expansion and renormalization at fixed dimension calculating a large collection of independent exponents in both approaches

the moore penrose inverses of products and differences of projections in a c algebra abstract for two given projections p and q in a c algebra we investigate how to express moore penrose inverses of products pq and differences p q and pq qp moreover it is shown that pq qp is moore penrose invertible if and only if pq and p q are moore penrose invertible in addition some related topics are considered