a fictitious domain formulation for flows with rigid particles in this paper we present a development of the fictitious domain method proposed in ref c diaz goano p minev k nandakumar a fictitious domain finite element method for particulate flows j comput phys 192 2003 105 the main new feature of the modified method is that after a proper splitting it avoids the need to use lagrange multipliers for imposition of the rigid body motion and instead it resolves the interaction force between the two phases explicitly then the end of step fluid velocity is a solution of an integral equation the most straightforward way to resolve it is via an iteration but a direct extrapolation is also possible if the latter approach is applied then the fictitious domain formulation becomes fully explicit with respect to the rigid body constraint and therefore the corresponding numerical procedure is much cheaper most of the numerical results presented in this article are obtained with such an explicit formulation

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

even sectors of lie superalgebras as locally convex lie algebras let g be a finite dimensional lie superalgebra over a graded commutative local augmented arens michael ground algebra a lie group is associated with a number of pleasant properties to the even sector g0 viewed as an ordinary complete locally convex lie algebra which is in general infinite dimensional

a contribution to nonstandard superanalysis the nonstandard infinitesimal analysis developed by robinson is applied to certain foundational aspects of superanalysis the construction of nonstandard hull due to luxemburg is used to study limit phenomena arising in a grassmann algebra q as the number of generators q tends to infinity an outcome of such an approach is that under transition t a superspace of purely odd dimension 0 q transforms into a superspace of dimension and not 0 as one would expect it is suggested that this construction may have something to do with the problem of adequate mathematical description of collective bosonic effects arising within infinite fermionic dimensions

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

a distributed lagrange multiplier based computational method for the simulation of particulate stokes flow abstract in this paper we present a distributed lagrange multiplier dlm based stokes flow algorithm for particulate flows the entire fluid particle domain is treated as a fluid the fluid in the particle domain is ensured to move rigidly by adding a rigidity constraint we modify the simpler semi implicit method for pressure linked equations revised algorithm for fluids by patankar numerical heat transfer and fluid flow taylor and francis london 1980 to account for the presence of the particle the modification pertains to the presence of the rigidity constraint in the particle domain we validate the algorithm with suitable test cases

superspaces and supersymmetries a theory of graded banach modules over a banach grassmann algebra is developed and applied to differential geometry of super manifolds the explicit structure of superspaces carrying poincare supersymmetry and extended supersymmetry including central charges is described

a fictitious domain method for particulate flows with heat transfer the distributed lagrange multiplier fictitious domain dlm fd method of glowinski et al r glowinski t w pan t i hesla d d joseph a distributed lagrange multiplier fictitious domain method for particulate flows int j multiphase flow 25 1999 755 794 is extended to deal with heat transfer in particulate flows in two dimensions the boussinesq approximation is employed for the coupling between the flow and temperature fields the fluid flow equations are solved with the finite difference projection method on a half staggered grid in our operator splitting scheme the lagrange multipliers at the previous time level are kept in the fluid equations and the new lagrange multipliers for the rigid body motion constraint and the dirichlet temperature boundary condition are determined from the reduced saddle point problem whereas a very simple scheme based on the fully explicit computation of the lagrange multiplier is proposed for the problem in which the solid heat conduction inside the particle boundary is also considered our code for the case of fixed temperature on the immersed boundary is verified by comparing favorably our results on the natural convection driven by a hot cylinder eccentrically placed in a square box and on the sedimentation of a cold circular particle in a vertical channel to the data in the literature the code for the case of freely varying temperature on the boundaries of freely moving particles is applied to analyze the motion of a catalyst particle in a box and in particular the heat conductivities of nanofluids and sheared non colloidal suspensions respectively our preliminary computational results support the argument that the micro heat convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids it is shown that the peclet number plays a negative role in the diffusion related heat conductivity of a sheared non colloidal suspension whereas the reynolds number does the opposite

spectral distributed lagrange multiplier method algorithm and benchmark tests we extend the formulation of the distributed lagrange multiplier dlm approach for particulate flows to high order methods within the spectral hp element framework we implement the rigid body motion constraint inside the particle via a penalty method the high order dlm method demonstrates spectral convergence rate i e discretization errors decrease exponentially as the order of spectral polynomials increases we provide detailed comparisons between the spectral dlm method direct numerical simulations and the force coupling method for a number of 2d and 3d benchmark flow problems we also validate the spectral dlm method with available experimental data for a transient problem the new dlm method can potentially be very effective in many moving body problems where a smaller number of grid points is required in comparison with low order methods

riemannian symmetric superspaces and their origin in random matrix theory gaussian random matrix ensembles defined over the tangent spaces of the large families of cartan s symmetric spaces are considered such ensembles play a central role in mesoscopic physics as they describe the universal ergodic limit of disordered and chaotic single particle systems the generating function for the spectral correlations of each ensemble is reduced to an integral over a riemannian symmetric superspace in the limit of large matrix dimension such a space is defined as a pair g h m r where g h is a complex analytic graded manifold homogeneous with respect to the action of a complex lie supergroup g and m r is a maximal riemannian submanifold of the support of g h

finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes in this paper we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles the thermal fluctuations are incorporated into the continuum equations using the landau and lifshitz approach 1 the proposed implementation fulfills the fluctuation dissipation theorem exactly at the discrete level since we restrict the equations to the creeping flow case this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation a multi step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation sde describing the evolution of the positions of the particles the proposed approach is validated by simulating the brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity the time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential

global properties of supermanifolds we construct new examples of supermanifolds and determine the vector bundle structure of the supermanifolds commonly used in physics we show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts and which is one of a nested sequence of foliations we point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds for example a compact supermanifold with a single even dimension must have vanishing euler characteristic we also show that a globally defined superfield on a nice compact supermanifold must be constant along the leaves of the foliations by this mechanism the global topology of a supermanifold can be used to impose physically interesting constraints on superfields as an example we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral

infinite clusters in percolation models the qualitative nature of infinite clusters in percolation models is investigated the results which apply to both independent and correlated percolation in any dimension concern the number and density of infinite clusters the size of their external surface the value of their total surface to volume ratio and the fluctuations in their density in particular it is shown thatn0 the number of distinct infinite clusters is either 0 1 or and the casen0 which might occur in sufficiently high dimension is analyzed

convergence analysis of a penalization method for the three dimensional motion of a rigid body in an incompressible viscous fluid we present and analyze a penalization method which extends the the method of ph angot c h bruneau and p fabrie numer math 81 1999 pp 487 520 to the case of a rigid body moving freely in an incompressible fluid the fluid solid system is viewed as a single variable density flow the interface is captured by a color function satisfying a transport equation the solid velocity is computed by averaging at every time the flow velocity in the solid phase this velocity is used to penalize the flow velocity at the fluid solid interface and to move the interface numerical illustrations are provided to illustrate our convergence result a discussion of our result in the light of existing existence results is also given

a fast computation technique for the direct numerical simulation of rigid particulate flows in this paper we present a computation technique for the direct numerical simulation of freely moving rigid bodies in fluids we solve three dimensional laminar flow problems using a control volume approach the key feature of this approach is that the computational overhead relative to a pure fluid solver to solve for the motion of rigid particle is very small the formulation is convenient for handling irregular geometries we present results for the sedimentation of particles of different shapes convergence tests are presented to assess the order of accuracy of the numerical scheme various test cases are considered and the numerical results are compared with experimental values to validate the code due to the ability to perform fast computations this method has been used for animations and its application to the direct numerical simulation of turbulent particulate flows merits investigation the technique is not restricted to any constitutive model of the suspending fluid hence it may potentially be used in large eddy simulations les or reynolds averaged navier stokes rans type simulations

distribution of the smallest eigenvalue in complex and real correlated wishart ensembles for the correlated gaussian wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability we obtain exact results for the complex 2 and for the real case 1 for a particular set of empirical correlation matrices we find universality in the spectral density for both real and complex ensembles and all kinds of rectangularity we calculate the asymptotic and universal results for the gap probability and the distribution of the smallest eigenvalue we use the supersymmetry method in particular the generalized hubbard stratonovich transformation and superbosonization

a dffd simulation method combined with the spectral element method for solid fluid interaction problems a 2d simulation method for a rigid body moving in an incompressible viscous fluid is proposed it combines one of the immersed boundary methods the dffd direct forcing fictitious domain method with the spectral element method the former is employed for efficiently capturing the two way fsi fluid structure interaction and the geometric flexibility of the latter is utilized for any possibly co existing stationary and complicated solid or flow boundary a pseudo body force is imposed within the solid domain to enforce the rigid body motion and a lagrangian mesh composed of triangular elements is employed for tracing the rigid body in particular a so called sub cell scheme is proposed to smooth the discontinuity at the fluid solid interface and to execute integrations involving eulerian variables over the moving solid domain the accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures the direct forcing fictitious domain method and the spectral element method are combined direct interpolation of eulerian variables onto lagrangian mesh is not necessary non fluctuating pressure fields are obtained with a smoothed pseudo body force the proposed method possesses a spectral accuracy both small and large solid to fluid density ratios are applicable

chern simons forms on principal superfiber bundles a graded weil homomorphism is defined for principal superfiber bundles and the related transgression or chern simons forms are introduced as an example of the application of these concepts a superextension of the dirac monopole is discussed

busemann functions and infinite geodesics in two dimensional first passage percolation we study first passage percolation on mathbb z 2 where the edge weights are given by a translation ergodic distribution addressing questions related to existence and coalescence of infinite geodesics some of these were studied in the late 1990s by c newman and collaborators under strong assumptions on the limiting shape and weight distribution in this paper we develop a framework for working with distributional limits of busemann functions and use it to prove forms of newman s results under minimal assumptions for instance we show a form of coalescence of long finite geodesics in any deterministic direction we also introduce a purely directional condition which replaces newman s global curvature condition and whose assumption we show implies the existence of directional geodesics without this condition we prove existence of infinite geodesics which are directed in sectors last we analyze distributional limits of geodesic graphs proving almost sure coalescence and nonexistence of infinite backward paths this result relates to the conjecture of nonexistence of bigeodesics

numerical methods for the stochastic landau lifshitz navier stokes equations the landau lifshitz navier stokes llns equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes this paper examines explicit eulerian discretizations of the full llns equations several computational fluid dynamics approaches are considered including maccormack s two step lax wendroff scheme and the piecewise parabolic method and are found to give good results for the variance of momentum fluctuations however neither of these schemes accurately reproduces the fluctuations in energy or density we introduce a conservative centered scheme with a third order runge kutta temporal integrator that does accurately produce fluctuations in density energy and momentum a variety of numerical tests including the random walk of a standing shock wave are considered and results from the stochastic llns solver are compared with theory when available and with molecular simulations using a direct simulation monte carlo algorithm

a stochastic immersed boundary method for fluid structure dynamics at microscopic length scales in modeling many biological systems it is important to take into account flexible structures which interact with a fluid at the length scale of cells and cell organelles thermal fluctuations of the aqueous environment become significant in this work it is shown how the immersed boundary method of c s peskin the immersed boundary method acta num 11 2002 1 39 for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations a stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps an important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved partially resolved or fully resolved while retaining a good level of accuracy error estimates in each of these regimes are given for the method a number of theoretical and numerical checks are furthermore performed to assess its physical fidelity for a conservative force the method is found to simulate particles with the correct boltzmann equilibrium statistics it is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters the method is also shown to reproduce a well known hydrodynamic effect of a brownian particle in which the velocity autocorrelation function exhibits an algebraic 3 2 decay for long times b j alder t e wainwright decay of the velocity autocorrelation function phys rev a 1 1 1970 18 21 a few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method specifically we present simulations of osmotic effects of molecular dimers worm like chain polymer knots and a basic model of a molecular motor immersed in fluid subject to a hydrodynamic load force the theoretical analysis and numerical results show that the immersed boundary method with thermal fluctuations captures many important features of small length scale hydrodynamic systems and holds promise as an effective method for simulating biological phenomena on the cellular and subcellular length scales

supersymmetric killing structures in this text we combine the notions of supergeometry and supersymmetry we construct a special class of supermanifolds whose reduced manifolds are pseudo riemannian manifolds these supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects this is the starting point of our definition of supersymmetric killing structures the latter combines subspaces of vector fields and spinor fields provided they fulfill certain field equations this naturally leads to a superalgebra which extends the supersymmetry algebra to the case of non flat reduced space we examine in detail the additional terms which enter into this structure and we give a lot of examples

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

super beltrami differentials superconformal structures on a given 2 2 dim supermanifold give rise to the notion of super riemann surfaces srs s we investigate super beltrami coefficients which parametrize almost superconformal structures on the supermanifold the integrability condition of the structure reduces to a simple relation among the coefficients taking this into account we can write the super beltrami equations in a transparent form then an analysis of these equations enables us to prove the possibility of the special gauge choice of the wess zumino type for the super beltrami differentials this gauge choice simplifies the description of the deformations of srs s considerably and its existence will afford a better understanding of the structure of the super teichmuller space

on the number of infinite geodesics and ground states in disordered systems we study first passage percolation models and their higher dimensional analogs models of surfaces with random weights we prove that under very general conditions the number of lines or in the second case hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to as corollaries we show that in any dimensiond 2 the number of ground states of an ising ferromagnet with random coupling constants equals with probability one 2 or proofs employ simple large deviation estimates and ergodic arguments

a new mathematical formulation and fast algorithm for fully resolved simulation of self propulsion we present a computational algorithm for fully resolved numerical simulation frs of rigid and deforming bodies moving in fluids given the deformation of the body in its own reference frame the method solves for the swimming velocity of the body together with the surrounding flow field and the hydrodynamic forces on the body we provide the mathematical foundation of the algorithm based on distributed lagrange multipliers and show that it naturally connects with vortex methods through a vorticity source at the interface we demonstrate applications to rigid and flexible bodies membranes and bodies with a propelling membrane attached to them in contrast to some existing methods the swimming velocity of the body is not prescribed but is computed along with the forces without requiring a body fitted grid the algorithm is designed to be fast efficient and easy to implement in existing fluid dynamics codes for practical solid fluid problems in engineering and biology

geodesics and spanning trees for euclidean first passage percolation the metric d q q on the set q of particle locations of a homogeneous poisson process on r d defined as the infimum of i q i q i 1 1 over sequences in q starting with q and ending with q where denotes euclidean distance has nontrivial geodesics when a 1 the cases 1 are the euclidean first passage percolation fpp models introduced earlier by the authors while the geodesics in the case are exactly the paths from the euclidean minimal spanning trees forests of aldous and steele we compare and contrast results and conjectures for these two situations new results for 1 and any d include inequalities on the fluctuation exponents for the metric x 1 2 and for the geodesies 3 4 in strong enough versions to yield conclusions not yet obtained for lattice fpp almost surely every semiinfinite geodesic has an asymptotic direction and every direction has a semiinfinite geodesic from every q for d 2 and 2 further results follow concerning spanning trees of semiinfinite geodesics and related random surfaces

direct numerical simulation of the brownian motion of particles by using fluctuating hydrodynamic equations in this paper we present a direct numerical simulation scheme for the brownian motion of particles in this approach the thermal fluctuations are included in the fluid equations via random stress terms solving the fluctuating hydrodynamic equations coupled with the particle equations of motion result in the brownian motion of the particles there is no need to add a random force term in the particle equations the particles acquire random motion through the hydrodynamic force acting on its surface from the surrounding fluctuating fluid the random stress in the fluid equations are easy to calculate unlike the random terms in the conventional brownian dynamics type approaches we present a three dimensional implementation along with validation

density and uniqueness in percolation two results on site percolation on thed dimensional lattice d 1 arbitrary are presented in the first theorem we show that for stationary underlying probability measures each infinite cluster has a well defined density with probability one the second theorem states that if in addition the probability measure satisfies the finite energy condition of newman and schulman then there can be at most one infinite cluster with probability one the simple arguments extend to a broad class of finite dimensional models including bond percolation and regular lattices

the axioms of supermanifolds and a new structure arising from them on presente une analyse des supervarietes sur un algebre arbitraire commutative graduee en partant d un ensemble d axiomes dont le premier est que les derivations de la structure faisceau d une supervariete sont localement libres

lie supergroup actions on supermanifolds lie supergroups are here understood as group objects in the category of supermanifolds as in 2 5 and 15 actions of lie supergroups in supermanifolds are defined by means of diagrams of supermanifold morphisms examples of such actions are given among them emerge the linear actions discussed in 2 5 and 12 and the natural actions on the grassmannian supermanifolds studied in 6 9 and 13 the nature of the isotropy subsupergroup associated to an action is fully elucidated it is exhibited as an embedded subsupergroup in the spirit of the theory of smooth manifolds and lie groups and with no need for the lie hopf algebraic approach of kostant in 3 the notion of orbit is also discussed explicit calculations of isotropy subsupergroups are included also an alternative proof of the fact that the structural sheaf of a lie supergroup is isomorphic to the sheaf of sections of a trivial exterior algebra bundle is given based on the triviality of its supertangent bundle

cohomology of supermanifolds the aim of this chapter is to unfold a basic cohomological theory for supermanifolds which will be exploited in the next chapter to study the structure of superbundles in particular to build a theory of characteristic classes this cohomology theory does not embody only trivial extensions of results valid for differentiable manifolds for instance the natural analogue of the de rham theorem does not hold in general and similarly in the case of complex supermanifolds there is generally speaking no analogue of the dolbeault theorem these features are consequences of the fact that the structure sheaf of a supermanifold does not need to be cohomologically trivial related to this is also the fact that the cohomology of the complex of global graded differential forms on a g supermanifold m a i e the super de rham cohomology of m a depends on the g supermanifold structure of m a so that homeomorphic and even smoothly diffeomorphic g supermanifolds may have a different super de rham cohomology that is super de rham cohomology is a fine invariant of the supermanifold structure

geodesics and the competition interface for the corner growth model we study the directed last passage percolation model on the planar integer lattice with nearest neighbor steps and general i i d weights on the vertices outside the class of exactly solvable models in georgiou et al probab theory relat fields 2016 doi 10 1007 s00440 016 0729 x we constructed stationary cocycles and busemann functions for this model using these objects we prove new results on the competition interface on existence uniqueness and coalescence of directional semi infinite geodesics and on nonexistence of doubly infinite geodesics

characteristic classes of super vector bundles a theory of characteristic classes for complex super vector bundles over supermanifolds is developed such characteristic classes are proved to fulfill the usual properties and it is shown that under suitable conditions they can be represented in terms of supersmooth curvature forms

divergence of shape fluctuations in two dimensions we consider stochastic growth models such as standard first passage percolation on z d where to leading order there is a linearly growing deterministic shape under natural hypotheses we prove that for d 2 the shape fluctuations grow at least logarithmically in all directions although this bound is far from the expected power law behavior with exponent 1 3 it does prove divergence with additional hypotheses we obtain inequalities involving and the related exponent which is expected to equal 2 3 for d 2 combining these inequalities with previously known results we obtain for standard first passage percolation the bounds 1 8 for d 2 and 3 4 for all d

spatially adaptive stochastic methods for fluid structure interactions subject to thermal fluctuations in domains with complex geometries we develop stochastic mixed finite element methods for spatially adaptive simulations of fluid structure interactions when subject to thermal fluctuations to account for thermal fluctuations we introduce a discrete fluctuation dissipation balance condition to develop compatible stochastic driving fields for our discretization we perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics we show the gibbs boltzmann distribution is invariant under the stochastic dynamics of the semi discretization to generate efficiently the required stochastic driving fields we develop a gibbs sampler based on iterative methods and multigrid to generate fields with o n computational complexity our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on fast fourier transforms to demonstrate in practice our stochastic computational methods we investigate within channel geometries having internal obstacles and no slip walls how the mobility diffusivity of particles depends on location our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications

remarks on the complete integrability of dynamical systems with fermionic variables the authors study the role of 1 1 graded tensor field t in the analysis of complete integrability of dynamical systems with fermionic variables they find that such a tensor t can be a recursion operator if and only if t is even as a graded map namely if and only if p t 0 they clarify this fact by constructing an odd tensor for two examples a supersymmetric toda chain and a supersymmetric harmonic oscillator they explicitly show that it cannot be a recursion operator since it does not allow new constants of motion to be built from the first two in contrast to what usually happens with ordinary i e nongraded systems

on the foundations of the stochastic immersed boundary method we explore the theoretical foundations for the inclusion of thermal fluctuations in the immersed boundary method for simulating microscale fluid systems with immersed flexible structures as in cellular and subcellular biology we investigate in particular the physical validity of the thermal forcing scheme with respect to the coupling of fluid and immersed structural degrees of freedom and non equilibrium conditions we discuss also the shortcomings of a natural alternative scheme in which the thermal fluctuations are applied directly to the structural degrees of freedom through langevin type dynamics

absence of geodesics in first passage percolation on a half plane an h geodesic is a doubly infinite path which locally minimizes the passage time in the i i d first passage percolation model on a half plane h under the assumption that the bond passage times are continuously distributed with a finite mean we prove that with probability 1 h geodesics do not exist as a corollary we show that with probability 1 any geodesic in the analogous model on the whole plane z 2 has to intersect all straight lines with rational slopes

a fictitious domain finite element method for particulate flows the paper presents a finite element method for the direct numerical simulation of 3d incompressible fluid flows with suspended rigid particles it uses the fictitious domain approach extending the fluid domain into the domain occupied by the particles although the idea for the present formulation came from the fictitious domain formulation of glowinski et al j comput phys 169 2001 363 it finally yielded a new scheme which allows for a more efficient integration of the system of equations and which is easier to implement algorithmically it also avoids the need to grid the rigid particles and solves the entire problem on a single eulerian grid the spatial discretization is performed with p2 p1 finite elements but any other stable pair of approximations can be used the present scheme is compared to a second order scheme based on the approach in glowinski et al loc cit using the test case of a single sphere in a viscous liquid its accuracy costs performance is excellent

an interface fitted subspace projection method for finite element simulations of particulate flows abstract a novel finite element method for the direct numerical simulation of particles in a newtonian carrier fluid is presented the proposed method is based on a fictitious or one domain formulation and a subspace projection method to account for the rigid body motion of the particles underlying equations are posed in an ale arbitrary lagrangian eulerian formulation allowing for moving computational meshes the mesh is adapted to the particles by a novel mesh smoothing approach guaranteeing both mesh optimality and a sharp representation of the particles boundaries we show that by using quadratic taylor hood finite elements for the discretization of the navier stokes equations and isoparametric elements to represent the geometry second order convergence with respect to the energy norm can be achieved as opposed to a sharp h 1 2 result which holds if no mesh adaptation is performed we present numerical examples in 2d confirming the theoretical convergence results furthermore we validate the approach by simulating the sedimentation process of a single particle and show the potential of the method by simulating a lid driven cavity flow with 100 particles

a unified mathematical framework and an adaptive numerical method for fluid structure interaction with rigid deforming and elastic bodies many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid in this work we develop a mathematical framework and an adaptive numerical method for such fluid structure interaction fsi problems in which the structure may be rigid deforming or elastic we employ an immersed boundary ib formulation of the problem that permits us to avoid body conforming discretizations and to use fast cartesian grid solvers rigidity and deformational kinematic constraints are imposed using a formulation based on distributed lagrange multipliers and a conventional ib method is used to describe the elasticity of the immersed body we use cartesian grid adaptive mesh refinement amr to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid solid interfaces as well as flow structures shed from such interfaces this adaptive methodology is validated for several benchmark problems in two and three spatial dimensions in addition we use this scheme to simulate free swimming including the maneuvering of a two dimensional model eel and a three dimensional model of the weakly electric black ghost knifefish

fluctuating force coupling method for simulations of colloidal suspensions abstract the resolution of brownian motion in simulations of micro particle suspensions can be crucial to reproducing the correct dynamics of individual particles as well as providing an accurate characterisation of suspension properties including these effects in simulations however can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step in this paper we introduce the fluctuating force coupling method fcm to overcome this difficulty providing a fast approach to simulate colloidal suspensions at large scale we show explicitly that by forcing the surrounding fluid with a fluctuating stress and employing the fcm framework to obtain the motion of the particles one obtains the random particle velocities and angular velocities that satisfy the fluctuation dissipation theorem this result holds even when higher order multipoles such as stresslets are included in the fcm approximation through several numerical experiments we confirm our analytical results and demonstrate the effectiveness of fluctuating fcm showing also how brownian drift can be resolved by employing the appropriate time integration scheme and conjugate gradient method

variational calculus and poincare cartan formalism on supermanifolds in this work we show how the poincare cartan form can be used to describe the symmetries of lagrangian supersymmetric possibly p adic field theories we show that the existence of the poincare cartan form in supermanifold theory is ensured only in a relevant class of lagrangian densities moreover we give an abstract characterization of supersymmetric invariance based on the poincare cartan form