simulating the dynamics of inextensible vesicles by the penalty immersed boundary method in this paper we develop an immersed boundary ib method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid in order to take into account the inextensibility constraint of the vesicle the penalty immersed boundary pib method is used to virtually decouple the fluid and vesicle dynamics as numerical tests of our current pib method the dynamics of single and multiple inextensible vesicles under shear flows have been extensively explored and compared with the previous literature the method is also validated by a series of convergence study which confirms its consistent first order accuracy on the velocity field the vesicle configuration the vesicle area and the perimeter errors in addition the method is also applied to study a binary component vesicle problem

a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d we present a new method for the evolution of inextensible vesicles immersed in a stokesian fluid we use a boundary integral formulation for the fluid that results in a set of nonlinear integro differential equations for the vesicle dynamics the motion of the vesicles is determined by balancing the non local hydrodynamic forces with the elastic forces due to bending and tension numerical simulations of such vesicle motions are quite challenging on one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives and a milder constraint due to a transport like stability condition on the other hand an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step we present two semi implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme we discretize the equations by using a spectral method in space and a multistep third order accurate scheme in time we use the fast multipole method fmm to efficiently compute vesicle vesicle interaction forces in a suspension with a large number of vesicles we report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme

an efficient numerical method for studying interfacial motion in two dimensional creeping flows we present new methods for computing the motion of two dimensional closed interfaces in a slow viscous flow the interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex variable theory for the biharmonic equation the numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole based iterative solution procedure which requires only o n operations where n is the number of nodes in the discretization of the interface the interface is described spectrally and we use evolution equations that preserve equal spacing in arclength of the marker points a small scale decomposition is performed to extract the dominant term in the evolution of the interface and we show that this dominant term leads to a cfl type stability constraint when in an equal arclength frame this term is linear and we show that implicit time integration schemes that are explicit in fourier space can be formulated we verify this analysis through several numerical examples

the extended tanh method for new solitons solutions for many forms of the fifth order kdv equations abstract the extended tanh method is used to derive new solitons solutions for several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk sawada kotera parker dye skpd kaup kupershmidt kk kaup kupershmidt parker dye kkpd and the ito equations the criteria established in a m wazwaz abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method appl math comput in press doi 10 1016 j amc 2006 02 047 to build up reliable relations between the parameters of the equation are confirmed by using this new approach entirely new bell shaped solitons are determined

soliton solutions of two bidirectional sixth order partial differential equations belonging to the kp hierarchy in this letter we analyse two bidirectional sixth order partial differential equations which are reductions in 1 1 dimensions of equations belonging to the kp hierarchy they have fourth order and fifth order lax pairs respectively we derive their backlund transformations and from the nonlinear superposition formula we can build their soliton solutions like a grammian the interesting dynamics of these solitons is that they may describe not only the overtaking collision but also the head on collision of solitary waves of different type and shape

a grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion we develop numerical methods for solving partial differential equations pde defined on an evolving interface represented by the grid based particle method gbpm recently proposed in s leung h k zhao a grid based particle method for moving interface problems j comput phys 228 2009 7706 7728 in particular we develop implicit time discretization methods for the advection diffusion equation where the time step is restricted solely by the advection part of the equation we also generalize the gbpm to solve high order geometrical flows including surface diffusion and willmore type flows the resulting algorithm can be easily implemented since the method is based on meshless particles quasi uniformly sampled on the interface furthermore without any computational mesh or triangulation defined on the interface we do not require remeshing or reparametrization in the case of highly distorted motion or when there are topological changes as an interesting application we study locally inextensible flows governed by energy minimization we introduce tension force via a lagrange multiplier determined by the solution to a helmholtz equation defined on the evolving interface extensive numerical examples are also given to demonstrate the efficiency of the proposed approach

riemann hilbert problems for the shapes formed by bodies dissolving melting and eroding in fluid flows the classical stefan problem involves the motion of boundaries during phase transition but this process can be greatly complicated by the presence of a fluid flow here we consider a body undergoing material loss due to either dissolution from molecular diffusion melting from thermodynamic phase change or erosion from fluid mechanical stresses in a fast flowing fluid in each case the task of finding the shape formed by the shrinking body can be posed as a singular riemann hilbert problem a class of exact solutions captures the rounded surfaces formed during dissolution melting as well as the angular features formed during erosion thus unifying these different physical processes under a common framework this study which merges boundary layer theory separated flow theory and riemann hilbert analysis represents a rare instance of an exactly solvable model for high speed fluid flows with free boundaries 2017 wiley periodicals inc

viscous regularization and r adaptive remeshing for finite element analysis of lipid membrane mechanics as two dimensional fluid shells lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses this property gives membranes the ability to adopt dramatic shape changes in this paper a finite element model is developed to study static equilibrium mechanics of membranes in particular a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers the augmented lagrangian method is used to enforce global constraints on area and volume during membrane deformations as a validation of the method equilibrium shapes for a shape phase diagram of lipid bilayer vesicle are calculated these numerical techniques are also shown to be useful for simulations of three dimensional large deformation problems the formation of tethers long tube like extensions and ginzburg landau phase separation of a two lipid component vesicle to deal with the large mesh distortions of the two phase model modification of viscous regularization is explored to achieve r adaptive mesh optimization

modeling simple locomotors in stokes flow motivated by the locomotion of flagellated micro organisms and by recent experiments of chemically driven nanomachines we study the dynamics of bodies of simple geometric shape that are propelled by specified tangential surface stresses we develop a mathematical description of the body dynamics based on a mixed type boundary integral formulation we also derive analytic axisymmetric solutions for the case of a single locomoting sphere and ellipsoid based on spherical and ellipsoidal harmonics and compare our numerical results to these the hydrodynamic interactions between two spherical and ellipsoidal swimmers in an infinite fluid are then simulated using second order accurate spatial and temporal discretizations we find that the near field interactions result in complex and interesting changes in the locomotors orientations and trajectories stable as well as unstable pairwise swimming motions are observed similar to the recent findings of pooley et al c m pooley g p alexander j m yeomans hydrodynamic interaction between two swimmers at low reynolds number phys rev lett 99 2007 228103

variational discretization of axisymmetric curvature flows we present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail although numerical methods for geometric flows have been used frequently in axisymmetric settings numerical analysis results so far are rare in this paper we present stability equidistribution existence and uniqueness results for the introduced approximations numerical computations show that these schemes are very efficient in computing numerical solutions of geometric flows as only a spatially one dimensional problem has to be solved the good mesh properties of the schemes also allow them to compute in very complex axisymmetric geometries

generalized kaup kupershmidt solitons and other solitary wave solutions of the higher order kdv equations new types of exact explicit solitary wave solutions of the higher order kdv equations are identified by applying a direct method designed specifically for constructing solitary wave solutions of evolution equations the first type is the generalized kaup kupershmidt gkk solitary waves which unify the structures of the sech2 kdv like soliton and the kaup kupershmidt soliton and also provide solutions of some other equations one of those equations is found to possess the multi soliton solutions which makes it a good candidate for being integrable in terms of the gkk solitons another type of solutions of the higher order kdv equations identified by applying the method represents the steady state localized structures the variety of equations possessing such solutions includes the integrable in terms of the sech2 solitons sawada kotera equation which thus appears to provide the localized solutions of two types

a fast integral equation method for solid particles in viscous flow using quadrature by expansion boundary integral methods are advantageous when simulating viscous flow around rigid particles due to the reduction in number of unknowns and straightforward handling of the geometry in this work

method for efficient shape parametrization of fluid membranes and vesicles in this paper we describe a method for the parametrization of the shapes adopted by fluid membranes and vesicles the method is based upon a boundary value approach to geometry description in which smooth surfaces are produced as the solution to an elliptic partial differential equations shape parameters are introduced through the boundary conditions which control the shape of the vesicle models in combination with a model for the surface energy and a method for numerical minimization it is shown how the method can accurately approximate the shapes of both axisymmetric and nonaxisymmetric vesicles over a wide range of control parameters the particular value of the method lies in its ability to parametrize complicated shapes efficiently a feature that becomes especially valuable when seeking shapes of minimal energy using direct optimization techniques

accuracy enhancement for higher derivatives using chebyshev collocation and a mapping technique a new method is investigated to reduce the roundoff error in computing derivatives using chebyshev collocation methods by using a grid mapping derived by kosloff and tal ezer and the proper choice of the parameter alpha the roundoff error of the k th derivative can be reduced from o n 2k to o n lge k where epsilon is the machine precision and n is the number of collocation points this drastic reduction of roundoff error makes mapped chebyshev methods competitive with any other algorithm in computing second or higher derivatives with large n several other aspects of the mapped chebyshev differentiation matrix are also studied revealing that the mapped chebyshev methods require much less than pi points to resolve a wave the eigenvalues are less sensitive to perturbation by roundoff error and larger time steps can be used for solving pdes all these advantages of the mapped chebyshev methods can be achieved while maintaining spectral accuracy

an immersed boundary method for simulating vesicle dynamics in three dimensions we extend our previous immersed boundary ib method for 3d axisymmetric inextensible vesicle in navier stokes flows hu et al 2014 17 to general three dimensions despite a similar spirit in numerical algorithms to the axisymmetric case the fully 3d numerical implementation is much more complicated and is far from straightforward a vesicle membrane surface is known to be incompressible and exhibits bending resistance as in 3d axisymmetric case instead of keeping the vesicle locally incompressible we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension lagrange multiplier for the incompressible constraint can be avoided nevertheless the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension the vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex lagrangian marker in the ib method of the triangulation a series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method we perform the convergence study for the immersed boundary forces and the fluid velocity field we then study the vesicle dynamics in various flows such as quiescent simple shear and gravitational flows our numerical results show good agreements with those obtained in previous theoretical experimental and numerical studies

adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations in this paper a three dimensional adaptive finite element method is developed for a variational phase field bending elasticity model of vesicle membrane deformations using a mixed finite element formulation residual type a posteriori error estimates are derived for the associated nonlinear system of equations and they are used to introduce the mesh refinement and coarsening the resulting mesh adaptivity significantly improves the efficiency of the phase field simulation of vesicle membranes and enhances its capability in handling complex shape and topological changes the effectiveness of the adaptive method is further demonstrated through numerical examples

a generalized traction integral equation for stokes flow with applications to near wall particle mobility and viscous erosion abstract a double layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and or the presence of a plane wall the lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere or hemisphere for wall bounded flows the derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free space and wall bounded domains two sample applications of the method are discussed we study the tractions on an ellipsoid moving near a plane wall which provides a more detailed understanding of the well studied glancing and reversing trajectories in the context of particle sedimentation and the erosion of bodies by a viscous flow in which the surface is ablated at a rate proportional to the local viscous shear stress simulations and analytical estimates suggest that a spherical body in a uniform flow first reduces nearly but not exactly to the drag minimizing profile and then vanishes in finite time the shape dynamics of an eroding body in a shear flow and near a wall are also investigated stagnation points on the body surface lead generically to the formation of cusps whose number depends on the flow configuration and or the presence of nearby boundaries

an integral equation formulation for rigid bodies in stokes flow in three dimensions abstract we present a new derivation of a boundary integral equation bie for simulating the three dimensional dynamics of arbitrarily shaped rigid particles of genus zero immersed in a stokes fluid on which are prescribed forces and torques our method is based on a single layer representation and leads to a simple second kind integral equation it avoids the use of auxiliary sources within each particle that play a role in some classical formulations we use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials so that only a small number of spatial discretization points per particle are required the resulting discrete sums are computed in o n time where n denotes the number of particles using the fast multipole method fmm the particle positions and orientations are updated by a high order time stepping scheme we illustrate the accuracy conditioning and scaling of our solvers with several numerical examples

an immersed boundary method for simulating the dynamics of three dimensional axisymmetric vesicles in navier stokes flows in this paper we develop a simple immersed boundary method to simulate the dynamics of three dimensional axisymmetric inextensible vesicles in navier stokes flows instead of introducing a lagrange s multiplier to enforce the vesicle inextensibility constraint we modify the model by adopting a spring like tension to make the vesicle boundary nearly inextensible so that solving for the unknown tension can be avoided we also derive a new elastic force from the modified vesicle energy and obtain exactly the same form as the originally unmodified one in order to represent the vesicle boundary we use fourier spectral approximation so we can compute the geometrical quantities on the interface more accurately a series of numerical tests on the present scheme have been conducted to illustrate the applicability and reliability of the method we first perform the accuracy check of the geometrical quantities of the interface and the convergence check for different stiffness numbers as well as fluid variables then we study the vesicle dynamics in quiescent flow and in gravity finally the shapes of vesicles in poiseuille flow are investigated in detail to study the effects of the reduced volume the confinement and the mean flow velocity the numerical results are shown to be in good agreement with those obtained in literature

a small scale decomposition for 3d boundary integral computations with surface tension abstract an efficient non stiff boundary integral method for the initial value problem for interfacial darcy flow which is a model of porous media flow in three space dimensions is presented we consider a doubly periodic interface separating two fluids with surface tension present at the boundary surface tension introduces high order i e high derivative terms in the governing equation and this imposes a severe stability constraint on explicit time integration methods furthermore the high order terms appear in a nonlocal operator which makes it difficult to design an efficient implicit method the stiffness is removed by developing a small scale decomposition in the spirit of prior work in the two dimensional problem by hou lowengrub and shelley in order to develop this small scale decomposition we formulate the problem using a generalized isothermal parameterization of the free surface an additional difficulty is the efficient calculation of the birkhoff rott integral for the velocity of the interface we present a new algorithm based on ewald summation to compute this in o n log n operations where n is the number of interface grid points our non stiff method is expected to apply widely to problems for doubly periodic interfacial flow with surface tension which have a boundary integral formulation

a fast chebyshev method for simulating flexible wing propulsion abstract we develop a highly efficient numerical method to simulate small amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid we allow the wing s elastic modulus and mass density to vary arbitrarily with an eye towards optimizing these distributions for propulsive performance the method to determine the wing kinematics is based on chebyshev collocation of the 1d beam equation as coupled to the surrounding 2d fluid flow through small amplitude analysis of the euler equations with trailing edge vortex shedding the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1d wing kinematics a class of semi analytical solutions permits fast evaluation of this operator with o n log n operations where n is the number of collocation points on the wing this is in contrast to the minimum o n 2 cost of a direct 2d fluid solver the coupled wing fluid problem is thus recast as a pde with nonlocal operator which we solve using a preconditioned iterative method these techniques yield a solver of near optimal complexity o n log n allowing one to rapidly search the infinite dimensional parameter space of all possible material distributions and even perform optimization over this space

on bidirectional fifth order nonlinear evolution equations lax pairs and directionally dependent solitary waves in this paper lax pairs are constructed for two fifth order nonlinear evolution equations of boussinesq type which govern wave propagation in two opposite directions one of the equations is related to the well known sawada kotera sk equation and through its bilinear form is identified with the ramani equation the second equation about which very little seems to be known may be considered a bidirectional version of the kaup kupershmidt kk equation and is the main focus of this study the anomalous solitary wave of this latter equation is derived and is found to possess the remarkable property that its profile depends on the direction of propagation this type of directional dependence would appear to be quite unusual and to our knowledge has not been reported in the literature before now by taking an appropriate undirectional long wave limit it is shown that neither the ramani nor the bidirectional kaup kupershmidt bkk equation can be classified as truly boussinesq in character a distinction that is made precise in the study recursion formulas are given for generating an infinity of conserved densities for both equations these are used to obtain the first few conservation laws of the bkk and ramani equations explicitly not surprisingly they exhibit the same lacunary behavior as their unidirectional counterparts in conclusion a canonical interpretation of the n soliton solution of the bkk equation is proposed which provides a basis for constructing these anomalous solitons in a future work

notes on the interpolation of discrete periodic signals using sinc function related approaches considering the sinc interpolation of discrete periodic signals this correspondence establishes the equivalence of two recently published methods furthermore the interpolation methods are equivalent to a fractional delay filter designed using the frequency sampling technique a numerically stable and computationally attractive form of the equivalent methods is presented

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

sinc interpolation of discrete periodic signals the paper introduces a method for the sinc interpolation of discrete periodic signals the convolution of the sinc kernel with the infinite sequence of a periodic function is rewritten as a finite summation the method is equivalent to trigonometrical interpolation by fourier series expansion

second kind integral equation formulation of stokes flows past a particle of arbitary shape the problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear fredholm integral equations of the second kind for a

realizable ideal d c and c d conversions for band limited periodic signals and characterization of single carrier block transmission for a real band limited periodic signal there are reconstruction formulas that realize the ideal discrete to continuous d c conversion within one period of the signal however the previous results may not be suitable for general complex band limited periodic signals for complex band limited periodic signals in this paper we first propose the reconstruction formulas which lead to realizable forms of ideal d c conversion we then derive the correlation function of the interpolation pulse and this helps us construct a matched filter that can implement the exact sampling c d conversion of a complex band limited periodic signal when there exists noise in the sampling process comparing with the ideal impulse sampling the proposed c d conversion can maintain finite output noise variance the correlation function of the output noise is also given and the oversampling effect of noise is analyzed for a complex interpolation pulse in general we cannot decouple the ideal d c or c d conversion into two independent d c or c d conversions for the real and imaginary parts of the signal we also give the extended forms and decomposition forms of the proposed d c and c d conversions our results are applied to derive the ideal d c and c d conversions in the precoded orthogonal frequency division multiplexing pofdm system the resulted interpolation pulses are used to characterize the single carrier sc block transmission under the pofdm architecture we give characteristics that distinguish the sc block transmission from traditional sc transmission

nonlinear superposition formula for the kaup kupershmidt partial differential equation abstract the fifth order kaup kupershmidt kk equation is one of the solitonic equations related to the integrable cases of the henon heiles system as opposed to the sawada kotera equation which is its dual equation the construction of the n soliton solutions of kk is not an easy task in using a perturbation scheme or the hirota bilinear formalism from the backlund transformation obtained by singularity analysis considerations we here establish the permutability theorem for the kk equation this allows us to explain the anomalous structure of the n soliton solution empirically obtained by parker physica d 137 2000 25 33 34 48

precoded and vector ofdm robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems the performance of orthogonal frequency division multiplexing ofdm systems may be degraded when intersymbol interference isi channels have spectral nulls also when isi channels have many taps the data rate overhead due to the insertion of the cyclic prefix is high we first propose a precoded ofdm system that may improve the performance of the ofdm systems for spectral null channels we also propose size k spl times x1 vector ofdm vofdm systems that reduce the cyclic prefix length by k times compared to the conventional ofdm systems the precoding scheme is simply to insert one or more zeros between each two sets of k consecutive information symbols although it can be generalized to a general form this precoding scheme may be able to remove the spectral nulls of an isi channel without knowing the isi channel when no zero is inserted between each two sets of k consecutive information symbols and only each k consecutive symbols are blocked together we obtain vofdm systems both theoretical performance analysis and simulation results are presented finally we compare the combination of the vofdm systems and the unitary matrix modulation with the conventional ofdm systems and the phase shift keying modulation where both differential noncoherent and coherent modulations and demodulations are considered

an adaptive meshfree method for phase field models of biomembranes part ii a lagrangian approach for membranes in viscous fluids we present a lagrangian phase field method to study the low reynolds number dynamics of vesicles embedded in a viscous fluid in contrast to previous approaches where the field variables are the phase field and the fluid velocity here we exploit the fact that the phase field tracks a material interface to reformulate the problem in terms of the lagrangian motion of a background medium containing both the biomembrane and the fluid we discretize the equations in space with maximum entropy approximants carefully shown to perform well in phase field models of biomembranes in a companion paper the proposed formulation is variational lending itself to implicit time stepping algorithms based on minimization of a time incremental energy which are automatically nonlinearly stable the proposed method deals with two of the major challenges in the numerical treatment of coupled fluid phase field models of biomembranes namely the adaptivity of the grid to resolve the sharp features of the phase field and the stiffness of the equations leading to very small time steps in our method local refinement follows the features of the phase field as both are advected by the lagrangian motion and large time steps can be robustly chosen in the variational time stepping algorithm which also lends itself to time adaptivity the method is presented in the axisymmetric setting but it can be directly extended to 3d

a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows we extend shravan k veerapaneni denis gueyffier denis zorin george biros a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d journal of computational physics 228 7 2009 2334 2353 to the case of three dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows although the main components of the algorithm are similar in spirit to the 2d case spectral approximation in space semi implicit time stepping scheme the main differences are that the bending and viscous force require new analysis the linearization for the semi implicit schemes must be rederived a fully implicit scheme must be used for the toroidal topology to eliminate a cfl type restriction and a novel numerical scheme for the evaluation of the 3d stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations by introducing these novel components we obtain a time scheme that experimentally is unconditionally stable has low cost per time step and is third order accurate in time we present numerical results to analyze the cost and convergence rates of the scheme to verify the solver we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid to illustrate the applicability of method we consider a few vesicle flow interaction problems the sedimentation of a vesicle interactions of one and three vesicles with a background poiseuille flow

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

comments on sinc interpolation of discrete periodic signals in a recent paper by t schanze see ibid vol 43 p 1502 3 1995 the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation the expression obtained however is not numerically stable when evaluated at or near integer values of time this correspondence presents a numerically stable formulation that is equivalent to the results reported in the above cited paper and that when sampled is also shown to be equivalent to the inverse discrete fourier transform idft

simulating the dynamics and interactions of flexible fibers in stokes flows the dynamics of slender filaments or fibers suspended in stokesian fluids are fundamental to understanding many flows arising in physics biology and engineering such filaments can have aspect ratios of length to radius ranging from a few tens to several thousands full discretizations of such 3d flows are very costly instead we employ a nonlocal slender body theory that yields an integral equation along the filament centerline relating the force exerted on the body to the filament velocity this hydrodynamical description takes into account the effect of the filament on the fluid and is extended to capture the interaction of multiple filaments as mediated by the intervening fluid we consider filaments that are inextensible and elastic replacing the force in the slender body integral equation by an explicit expression that uses euler bernoulli theory to model bending and tensile forces yields an integral expression for the velocity of the filament centerlines coupled to auxiliary integro differential equations for the filament tensions based on a regularized version of these slender body equations that is asymptotically equivalent to the original formulation we construct a numerical method which uses a combination of finite differences implicit time stepping to avoid severe stability constraints and special quadrature methods for nearly singular integrals we present simulations of single flexible filaments as well as multiple interacting filaments evolving in a background shear flow these simulations show shear induced buckling and relaxation of the filaments leading to the storage and release of elastic energy these dynamics are responsible for the development of positive first normal stress differences commonly associated with visco elastic fluids that are suspensions of microscopic elastic fibers

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

a phase field approach in the numerical study of the elastic bending energy for vesicle membranes in this paper we compute the equilibrium configurations of a vesicle membrane under elastic bending energy with prescribed volume and surface area a variational phase field method is developed for such a problem discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases different energetic bifurcation phenomena are discussed