the absolute galois group acts faithfully on regular dessins and on beauville surfaces in this article we study the action of the absolute galois group gal q q on dessins d enfants and beauville surfaces a foundational result in grothendieck s theory of dessins d enfants is the fact that the absolute galois group gal q q acts faithfully on the set of all dessins however the question of whether this holds true when the action is restricted to the set of the more accessible regular dessins seems to be still an open question in the first part of this paper we give an affirmative answer to it in fact we prove the strongest result that the action is faithful on the set of quasiplatonic or triangle curves of any given hyperbolic type beauville surfaces are an important kind of algebraic surfaces introduced by catanese they are rigid surfaces of general type closely related to dessins d enfants here we prove that for any gal q q different from the identity and the complex conjugation there is a beauville surface s such that s and its galois conjugate s have non isomorphic fundamental groups this in turn easily implies that the action of gal q q on the set of beauville surfaces is faithful these results were conjectured by bauer catanese and grunewald and immediately imply that gal q q acts faithfully on the connected components of the moduli space of surfaces of general type a result due to the above mentioned authors

isosceles trapezoid central configurations of the newtonian four body problem we use a simple direct and basic method to prove that there is a unique isosceles trapezoid central configuration of the planar newtonian four body problem when two pairs of equal masses are located at adjacent vertices of a trapezoid such isosceles trapezoid central configurations are an exactly one dimensional family explicit expressions for masses are given in terms of the size of the quadrilateral

convex central configurations of the 4 body problem with two pairs of equal adjacent masses we study the convex central configurations of the 4 body problem assuming that they have two pairs of equal masses located at two adjacent vertices of a convex quadrilateral under these assumptions we prove that the isosceles trapezoid is the unique central configuration

finiteness and bifurcations of some symmetrical classes of central configurations we consider here the classical question of finiteness see smale 13 and wintner 15 given n point masses is the corresponding number of central configurations finite we prove finiteness for a particular family of d dimensional symmetrical configurations of d 2 point masses also we study the bifurcations of these configurations and provide the exact number of central configurations when d 2 3 all our results stem from the application of a new method for studying symmetrical classes of central configurations which is presented in this work

constructing an entropy stable upwind scheme for compressible fluid flow computations a relationship between entropy processes and numerical upwinding is examined in the context of computational gasdynamics a discretized form of the entropy inequality is constructed at the integration point where convection diffusion modeling occurs in finite volume methods conventional upwinding schemes may violate the local form of the second law of thermodynamics but a modified upwinding scheme uses additional momentum constraints and pressure terms to provide a positive entropy production rate the second law is seen as an important quantitative measure of nonphysical numerical results as well as a sound basis for error analysis applications to converging diverging nozzle and blunt body flow problems demonstrate the promising performance of the overall numerical algorithm

a comparison of hybrid and quadratic upstream differencing in high reynolds number elliptic flows abstract numerical computations have been performed of various two dimensional elliptic flows at high reynolds number with a view to assessing the relative merits of the widely used hybrid i e upwind central interpolation and the recently proposed quadratic upstream interpolation of leonard known as quick the latter scheme possesses less intrinsic stability than hybrid differencing by selectively evaluating some of the convective elements at a previous iteration level however satisfactorily rapid convergence has been obtained it is concluded from the flows tested that the extra computational effort per node required for quick over the hybrid difference scheme is more than repaid by the greater numerical accuracy that results

a computational strategy for the regularized 13 moment equations with enhanced wall boundary conditions the challenge of modeling low speed rarefied gas flow in the transition regime is well known in this paper we propose a numerical solution procedure for the regularized 13 moment equations within a finite volume framework the stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first order approximation to model confined flows a complete set of wall boundary conditions for the 13 moment equations are derived based on the maxwell wall boundary model this has been achieved by expanding the molecular distribution function to fourth order accuracy in hermite polynomials empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation monte carlo data the numerical predictions obtained from the regularized 13 moment equations and the navier stokes fourier equations are compared with data generated using the direct simulation monte carlo method for planar couette flow for a range of wall velocities and knudsen numbers 0 012 1 0 the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation monte carlo data the results also highlight limitations that are caused by the use of a first order expansion of the third moment

implicit method for incompressible flow calculations in three dimensional ducts and cascades a method is presented for the numerical solution of the incompressible navier stokes equations in three dimensional ducts and cascades both laminar and turbulentows are resolved the latter through the k turbu lence model the method is based on an elliptic formulation which consists of the sequential solution of the mean ow and the turbulence equations through an approximate factorization technique the cost of factorization is minimized through the formation and inversion of a single matrix for all but the continuity equations the conti nuity constraint is enforced by means of thepressure correction technique forwhich a moreef cient variant of the approximate factorization scheme is employed the method exhibitsgood convergence characteristics asdepicted from the analyzed three dimensional problems the prediction capabilities of this method are demonstrated by analyzing thelaminarowin a three dimensional bend and theturbulentowin a linearcompressorcascade with zero and nonzero tip clearance for cascadeow problems with nonzero tip clearances a variant of the present method accommodating multiple patched subdomains is devised

bicentric quadrilateral central configurations abstract a bicentric quadrilateral is a tangential cyclic quadrilateral in a tangential quadrilateral the four sides are tangents to an inscribed circle and in a cyclic quadrilateral the four vertices lie on a circumscribed circle in this paper we classify all planar central configurations of the 4 body problem where the four bodies are at the vertices of a bicentric quadrilateral

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

local mesh refinement within a multi block structured grid scheme for general flows abstract a multi level flow adaptive mesh refinement strategy has been formulated and implemented within a structured grid multiblock scheme for 2d laminar transitional and turbulent recirculating flow although the locally refined irregular grid portions are organised as block structured patches within coarse grid blocks a special data structure allows high storage economy to be achieved issues of particular interest in the study include the performance of different flow adaptation sensors based on solution properties and error and the response of the solution accuracy to inter grid interpolation practices based on bi linear bi quadratic and compact interpolation the effectiveness of the local refinement strategy especially in terms of cpu and memory resources is examined by reference to four test cases ranging from an analytically prescribed scalar field over a square domain to a transitional flow over a highly loaded compressor blade the study demonstrates that cpu and memory savings with a three level refinement for the compressor blade case are of order 70 and 90 respectively relative to the requirements of globally fine grids returning similar accuracy levels

central configurations of the 4 body problem with masses m 1 m 2 m 3 m 4 m 0 and m small in this paper we give a complete description of the families of central configurations of the planar 4 body problem with two pairs of equals masses and two equal masses sufficiently small in particular we give an analytical proof that this particular 4 body problem has exactly 34 different classes of central configurations moreover for this problem we prove the following two conjectures there is a unique convex planar central configuration of the 4 body problem for each ordering of the masses in the boundary of its convex hull which appears in albouy and fu 2007 3 we also prove the conjecture there is a unique convex planar central configuration having two pairs of equal masses located at the adjacent vertices of the configuration and it is an isosceles trapezoid finally the families of central configurations of this 4 body problem are numerically continued to the 4 body problem with four equal masses

semi implicit second order schemes for numerical solution of level set advection equation on cartesian grids abstract a new parametric class of semi implicit numerical schemes for a level set advection equation on cartesian grids is derived and analyzed an accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial lax wendroff procedure and numerical von neumann stability analysis the obtained semi implicit scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one dimensional scheme that is not the case for analogous fully explicit or fully implicit schemes a further improvement is obtained by using so called corner transport upwind extension in two dimensional case the extended semi implicit scheme with a specific velocity dependent value of is 3rd order accurate in space and time for a constant advection velocity and it is unconditional stable according to the numerical von neumann stability analysis for the linear advection equation in general

a finite volume method with linearisation in time for the solution of advection reaction diffusion systems the numerical solution in one space dimension of advection reaction diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models this work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest the basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method the resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations

convex central configurations for the n body problem abstract we give a simple proof of a classical result of macmillan and bartky trans amer math soc 34 1932 838 which states that for any four positive masses and any assigned order there is a convex planar central configuration moreover we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia this allows us to show that there are at least six local minimum central configurations for the planar four body problem we also show that for any assigned order of five masses there is at least one convex spatial central configuration of local minimum type our method also applies to some other cases

a consistently formulated quick scheme for fast and stable convergence using finite volume iterative calculation procedures abstract previous applications of quick for the discretization of convective transport terms in finite volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme instead earlier formulations have been established numerically by trial and error the new formulation for quick presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance careful testing performed for the wall driven square enclosure flow configuration shows that the consistently derived version of quick is more stable and converges faster than any of the formulations previously employed this testing includes the relative evaluation of boundary conditions approximated by second and third order finite difference schemes as well as calculations performed at higher reynolds numbers than previously reported

improved low reynolds number k e model based on direct numerical simulation data an improved low reynolds number e turbulence model is proposed the model is designed not only to conform with the near wall characteristics obtained with direct numerical simulation data but also to possess the correct asymptotic behavior in the vicinity of the wall the key features of this model are the adoption of the taylor microscale in the damping function and the inclusion of the pressure diffusion terms in the and e equations further applications of the present model to a two dimensional backward facing step flow indicate that the present model reproduces correctly the skin friction and near wall heat transfer coefficients

finiteness of central configurations of five bodies in the plane we prove there are finitely many isometry classes of planar central configurations also called relative equilibria in the newtonian 5 body problem except perhaps if the 5 tuple of positive masses belongs to a given codimension 2 subvariety of the mass space

stable numerical method applying a total variation diminishing scheme for incompressible flow to solve incompressible navier stokes equations a stable finite difference method applying a total variation diminishing tvd upwind scheme originally designed for compressible flow is proposed the validity and the receptivity of this method employing such a tvd scheme for application to incompressible flow analysis are investigated by the evaluation of the accuracy stability and convergence rate using the generalized implicit simplified marker and cell smac solution method combined with the tvd scheme three dimensional developing entry flows through a square curved duct are calculated and compared with available experimental data and some computational results obtained by quadratic upstream interpolations for the convective kinematics quick schemes as well as by third order upwind schemes

an assessment of flow oriented schemes for reducing false diffusion un facteur limitatif important dans la modelisation precise des problemes d ecoulement est la representation numerique des termes de convection dans les equations de navier stokes revue des differentes methodes d approximation des termes de convection pour reduire les erreurs de fausse diffusion dans le contexte des methodes de differences finies et de volumes finis

a lagrangian stochastic modeling framework for multi phase flow in porous media many of the complex physical processes relevant for compositional multi phase flow in porous media are well understood at the pore scale level in order to study co 2 storage in sub surface formations however it is not feasible to perform simulations at these small scales directly and effective models for multi phase flow description at darcy scale are needed unfortunately in many cases it is not clear how the micro scale knowledge can rigorously be translated into consistent macroscopic equations here we present a new methodology which provides a link between lagrangian statistics of phase particle evolution and darcy scale dynamics unlike in finite volume methods the evolution of lagrangian particles representing small fluid phase volumes is modeled each particle has a state vector consisting of its position velocity fluid phase information and possibly other properties like phase composition while the particles are transported through the computational domain according to their individual velocities the properties are modeled via stochastic processes honoring specified lagrangian statistics note that the conditional expectations of the particle velocities are different for different fluid phases the goal of this paper is to present the general framework for this alternative modeling approach various one and two dimensional numerical experiments demonstrate that with appropriate stochastic rules the particle solutions are consistent with a standard two phase darcy flow formulation in the end we demonstrate how to model non equilibrium phenomena within the stochastic particle framework which will be the main focus of the future work

simple accurate and efficient revisions to maccormack and saulyev schemes high peclet numbers abstract stream water quality modeling often involves numerical methods to solve the dynamic one dimensional advection dispersion reaction equations adre there are numerous explicit and implicit finite difference schemes for solving these problems and two commonly used schemes are the maccormack and saulyev schemes this paper presents simple revisions to these schemes that make them more accurate without significant loss of computation efficiency using advection dominated high peclet number problems as test cases performances of the revised schemes are compared to performances of five classic schemes forward time centered space ftcs backward time centered space btcs crank nicolson and the traditional maccormack and saulyev schemes all seven of the above numerical schemes were tested against analytical solutions for pulse and step inputs of mass to a steady flow in a channel and performances were considered with respect to stability accuracy and computational efficiency results indicated that both the modified saulyev and the maccormack schemes which are named the saulyevc and maccormackc schemes respectively greatly improved the prediction accuracy over the original ones the computation efficiency in terms of cpu time was not impacted for the saulyevc scheme the maccormackc scheme demonstrated increased time consumption but was still much faster than implicit schemes

central configurations with many small masses abstract by using the method of analytical continuation we find the exact numbers of central configurations for some open sets of n positive masses for any choice of n it turns out that the numbers increase dramatically as n increases e g for some open set of 18 positive masses some 2 08766 1020 classes of distinctive central configurations are found in the mean time we obtained some results about the hausdorff measure for the set of n positive masses where degenerate central configuration arises

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

finiteness of relative equilibria of the four body problem we show that the number of relative equilibria of the newtonian four body problem is finite up to symmetry in fact we show that this number is always between 32 and 8472 the proof is based on symbolic and exact integer computations which are carried out by computer

a semi lagrangian finite volume method for newtonian contraction flows a new finite volume method for solving the incompressible navier stokes equations is presented the main features of this method are the location of the velocity components and pressure on different staggered grids and a semi lagrangian method for the treatment of convection an interpolation procedure based on area weighting is used for the convection part of the computation the method is applied to flow through a constricted channel and results are obtained for reynolds numbers based on half the flow rate up to 1000 the behavior of the vortex in the salient corner is investigated qualitatively and quantitatively and excellent agreement is found with the numerical results of dennis and smith proc roy soc london a 372 1980 pp 393 414 and the asymptotic theory of smith j fluid mech 90 1979 pp 725 754

symmetry of planar four body convex central configurations we study the relationship between the masses and the geometric properties of central configurations we prove that in the planar four body problem a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal if these two masses are unequal then the less massive one is closer to the former diagonal finally we extend these results to the case of non planar central configurations of five particles

evaluation of a bounded high resolution scheme for combustor flow computations the present paper is concerned with the application of a high resolution scheme for a finite volume discretization method the capability of the chosen scheme is evaluated for the numerical simulation of three dimensional flowfields special emphasis lies in the calculation of the processes in the mixing zone of gas turbine combustors thus numerical results are compared with detailed measurements of velocity and temperature in a model mixing zone the velocity field as well as the temperature field strongly depend on the scheme used for the discretization of the momentum and energy equations the proposed high resolution scheme and the well known quick scheme yield similar results which are superior to those obtained with the simple upwind scheme for the simulation of turbulent transport the standard fc model is employed the effect of numerical diffusion caused by the usual upwind discretization of the convective transport of a and e is assessed by the application of the high resolution scheme of the discretization of the a and e equations as a result it is found that the velocity and temperature fields are insensitive to the scheme that is applied for the discretization of the a and e equations

assessment of finite difference approximations for the advection terms in the simulation of practical flow problems abstract an assessment of seven discretization schemes for the advection terms of the transport equation to reduce numerical diffusion in practical flow problems has been established the schemes have been evaluated using three test cases for laminar flow problems the test cases consist of the transport of a scalar step in a uniform velocity field two interacting parallel streams and a slot jet the performance of the schemes is evaluated for advection dominated flows in transient and steady state solutions the considered schemes include four that have not been evaluated before for practical flow problems in general schemes which produced less numerical diffusion suffered from more numerical dispersion or oscillations two bounding techniques considered in the study were effective in significantly elliminating numerical dispersion

an efficient immersed boundary treatment for complex moving object an efficient immersed boundary treatment for simulation of flexible moving body immersed in fluid is presented the level set signed distance function is used to indicate body surface a simple mapping strategy is proposed to avoid costly signed distance re initialization computations the strategy is efficient for both rigid and deformable structures and can be extended to 3 d case easily with the use of signed distance function reconstruction of flow variables on a body surface can be easily implemented through linear bilinear or quadratic interpolation in order to suppress the pressure oscillations caused by the role conversion of forcing points and fluid points a modified interpolation scheme is presented by introducing a dynamic weight term to the fluid point together with local grid refinement and using larger time step the pressure oscillations can be effectively diminished by the modified interpolation scheme the proposed method is validated by 2 d numerical simulations on a uniform flow past a fixed cylinder in line and transversely oscillating cylinders a flapping wing a 3 d simulation on a uniform flow past a rectangle plane with an initial attack angle and a moving anguilliform swimmer present numerical results are compared with other cfd solutions as well as experimental results

the classification of kleinian surface groups ii the ending lamination conjecture thurston s ending lamination conjecture states that a hyperbolic 3manifold n with nitely generated fundamental group is uniquely determined by its topological type and its end invariants in this paper we prove this conjecture for kleinian surface groups the general case when n has incompressible ends relative to its cusps follows readily the main ingredient is a uniformly bilipschitz model for the quotient of h 3 by a kleinian surface group

numerical simulation of filamentary discharges with parallel adaptive mesh refinement direct simulation of filamentary gas discharges like streamers or dielectric barrier micro discharges requires the use of an adaptive mesh the objective of this paper is to develop a strategy which can use a set of grids with suitable local refinements for the continuity equations and poisson s equation in 2d and 3d geometries with a high order discretization the advantages of this approach are presented with a filamentary discharge simulation in plane plane geometry in nitrogen within the diffusion drift approximation

four body central configurations with some equal masses we prove firstly that any convex non collinear central configuration of the planar 4 body problem with equal opposite masses 0 such that the diagonal corresponding to the mass is not shorter than that corresponding to the mass must possess a symmetry and therefore must be a kite then by a recent result of bernat llibre and perez chavela this kite is actually a rhombus secondly we prove that a convex non collinear planar 4 body central configuration with three equal masses must be a kite too we also prove that the concave central configuration with three equal masses forming a triangle and the fourth one with any given mass in the interior must be either an equilateral triangle with the fourth mass at its geometric center or an isosceles triangle with the fourth mass on the symmetry axis

the symmetric central configurations of the 4 body problem with masses m1 m2 m3 m4 we characterize the planar central configurations of the 4 body problem with masses m 1 m 2 m 3 m 4 which have an axis of symmetry it is known that this problem has exactly two classes of convex central configurations one with the shape of a rhombus and the other with the shape of an isosceles trapezoid we show that this 4 body problem also has exactly two classes of concave central configurations with the shape of a kite this proof is assisted by computer

profinite rigidity of graph manifolds and jsj decompositions of 3 manifolds abstract there has been much recent interest into those properties of a 3 manifold determined by the profinite completion of its fundamental group in this paper we give readily computable criteria specifying precisely when two orientable graph manifold groups have isomorphic profinite completions our results also distinguish graph manifolds among the class of all 3 manifolds and give information about the structure of totally hyperbolic manifolds and give control over the pro p completion of certain graph manifold groups

a finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement abstract this paper describes a finite volume method for simulating transport processes governed by convection diffusion type equations the formulation is based on a cell centred unstructured grid with an edge based data structure discretisation is independent of control volume or cell shape by using a surface vector decomposition at the midpoint of the interface between cells along with a deferred correction approach any cross diffusion due to grid skewness can be readily accounted for when discretising the diffusive flux for modelling fluid flow processes a collocated arrangement of variables is employed so that a single coefficient matrix applies for the momentum equations of each velocity component to avoid checkerboard oscillation arising from pressure velocity decoupling occurring under the collocated variable arrangement when a pressure based solution algorithm is employed a novel pseudo flux interpolation method is proposed for unstructured grids ensuring that the solution is both under relaxation factor and time step for transient calculation independent the methodology can be formulated within a framework whereby either a coupled or a decoupled solution algorithm can be employed the features and advantages of the method are demonstrated by solution of the navier stokes equations for two benchmark flow problems

a comparison of higher order bounded convection schemes this paper presents a comparison of recently developed four higher order bounded convection schemes soucup hlpa smarter and lppa which employ different characteristics in a normalized variable diagram all the schemes are formulated on a non uniform non orthogonal grid and their relative performances are compared through applications to the several test problems the results of numerical experiments show that all the tested bounded schemes resolve the boundedness problem retaining the accuracy of the higher order scheme the hlpa smarter and lppa schemes result in nearly the same solution behaviours and the soucup scheme is shown to be relatively more diffusive than the other three bounded schemes

third order upwind finite element computation of the incompressible navier stokes equations part i computation of flow around rectangular cylinders abstract aerodynamic behaviours of two dimensional unsteady flows around rectangular cylinders are numerically investigated by third order upwind finite element computation of the incompressible navier stokes equations a turbulence model such as the two equation model is not incorporated in the computational scheme so that the rectangular cylinders at depth breadth ratios from 0 7 to 4 to be considered are located in a uniform flow it is found that the numerical results of flows around the rectangular cylinders obtained by using the third order upwind finite element scheme are in good agreement with other computational and experimental results