conditional stability of solitary waves propagating in elastic rods abstract the problem of dynamic stability of solitary wave solutions of the equations describing bending oscillations of inextensible elastic rods is treated the governing equations describe sufficiently large displacements though we are restricted to small strains we show that under the condition of well posedness of the initial value problem in some specific sense the family of solitary wave solutions of the mentioned equations is stable for the planar elastic rod the framework of the analysis is largely based on the spectral properties of the linearized hamiltonian h we show that for planar oscillations h is positively semidefinite subject to a certain constraint which implies the stability

on the continuity of mean total normal stress in geometrical multiscale cardiovascular problems in this work an iterative strategy to implicitly couple dimensionally heterogeneous blood flow models accounting for the continuity of mean total normal stress at interface boundaries is developed conservation of mean total normal stress in the coupling of heterogeneous models is mandatory to satisfy energetic consistency between them nevertheless existing methodologies are based on modifications of the navier stokes variational formulation which are undesired when dealing with fluid structure interaction or black box codes the proposed methodology makes possible to couple one dimensional and three dimensional fluid structure interaction models enforcing the continuity of mean total normal stress while just imposing flow rate data or even the classical neumann boundary data to the models this is accomplished by modifying an existing iterative algorithm which is also able to account for the continuity of the vessel area when required comparisons are performed to assess differences in the convergence properties of the algorithms when considering the continuity of mean normal stress and the continuity of mean total normal stress for a wide range of flow regimes finally examples in the physiological regime are shown to evaluate the importance or not of considering the continuity of mean total normal stress in hemodynamics simulations

improved prediction of disturbed flow via hemodynamically inspired geometric variables abstract arterial geometry has long been considered as a pragmatic alternative for inferring arterial flow disturbances and their impact on the natural history and treatment of vascular diseases traditionally definition of geometric variables is based on convenient shape descriptors with only superficial consideration of their influence on flow and wall shear stress patterns in the present study we demonstrate that a more studied consideration of the actual cf nominal local hemodynamics can lead to substantial improvements in the prediction of disturbed flow by geometry starting from a well characterized computational fluid dynamics cfd dataset of 50 normal carotid bifurcations we observed that disturbed flow tended to be confined proximal to the flow divider whereas geometric variables previously shown to be significant predictors of disturbed flow included features distal to the flow divider in their definitions flaring of the bifurcation leading to flow separation was redefined as the maximum relative expansion of the common carotid artery cca proximal to the flow divider the beneficial effect of primary curvature on flow inertia via suppression of flow separation was characterized by the in plane tortuosity of cca as it enters the flare region multiple linear regressions of these redefined geometric variables against various metrics of disturbed flow revealed r2 values approaching 0 6 better than the roughly 0 3 achieved using the conventional shape based variables while maintaining their demonstrated real world reproducibility such a hemodynamically inspired approach to the definition of geometric variables may reap benefits for other applications where geometry is used as a surrogate marker of local hemodynamics

the hyperelliptic limit cycles of the lienard systems abstract for lienard systems x y y f m x y g n x with f m and g n real polynomials of degree m and n respectively in h zoladek algebraic invariant curves for the lienard equation trans amer math soc 350 1998 1681 1701 the author showed that if m 3 and m 1 n 2 m there always exist lienard systems which have a hyperelliptic limit cycle llibre and zhang j llibre xiang zhang on the algebraic limit cycles of lienard systems nonlinearity 21 2008 2011 2022 proved that the lienard systems with m 3 and n 5 have no hyperelliptic limit cycles and that there exist lienard systems with m 4 and 5 n 8 which do have hyperelliptic limit cycles so it is still an open problem to characterize the lienard systems which have an algebraic limit cycle in cases m 4 and m 1 n 2 m in this paper we will prove that there exist lienard systems with m 5 and m 1 n 2 m which have hyperelliptic limit cycles

asymptotic stability at infinity for differentiable vector fields of the plane let x r2 d r2 be a differentiable but not necessarily c1 vector field where 0 and d z r2 z denote by r z the real part of z c if for some 0 and for all p r2 d no eigenvalue of dpx belongs to 0 z c r z 0 then a for all p r2 d there is a unique positive semi trajectory of x starting at p b it is associated to x a well defined number i x of the extended real line called the index of x at infinity such that for some constant vector v r2 the following is satisfied if i x is less than zero respectively greater or equal to zero then the point at infinity of the riemann sphere r2 is a repellor respectively an attractor of the vector field x v

on the stability of limit cycles for planar differential systems abstract we consider a planar differential system x p x y y q x y where p and q are c 1 functions in some open set u r 2 and d dt let be a periodic orbit of the system in u let f x y u r 2 r be a c 1 function such that p x y f x x y q x y f y x y k x y f x y where k x y is a c 1 function in u and x y f x y 0 we assume that if p u is such that f p 0 and f p 0 then p is a singular point we prove that 0 t p x q y t dt 0 t k t dt where t 0 is the period of as an application we take profit from this equality to show the hyperbolicity of the known algebraic limit cycles of quadratic systems

a note on relaxation oscillators with exact limit cycles abstract in this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle this family constitutes a corrected and wider version of an example given in the work m a abdelkader relaxation oscillators with exact limit cycles j math anal appl 218 1998 308 312 the result given in this note may be used to construct models of lienard differential equations exhibiting a desired limit cycle

non planar curvature and branching of arteries and non planar type flow in this study magnetic resonance imaging techniques have been used to examine the geometry of arterial curvature and branching in casts and in vivo and to measure the distribution of axial velocity in the associated flow it is found contrary to a widely held view that the geometry is commonly non planar moreover relatively small values of the parameters which render the geometry non planar appear significantly to affect the velocity distribution the findings suggest that non planarity is an important factor influencing arterial flows including wall shear the implications are not restricted to vascular biology pathology and surgery but may extend to the design of general piping systems

strong convergence of the semi implicit euler method for nonlinear stochastic volterra integral equations with constant delay abstract this paper is mainly concerned with the strong convergence analysis of the semi implicit euler method for nonlinear stochastic volterra integral equations svies with constant delay the solvability and the boundedness of the numerical solution are established it is proved that the strong convergence order of the semi implicit euler method is 0 5 under lipschitz conditions moreover the strong superconvergence order is 1 0 if further the kernel of the stochastic term satisfies 0 0 the theoretical results are illustrated by extensive numerical examples

optimal superconvergence results for volterra functional integral equations with proportional vanishing delays abstract in this paper we develop a new technique to study the optimal convergence orders of collocation methods for volterra functional integral equations with vanishing delays on quasi geometric meshes basing on a perturbation analysis we show that for m collocation points the global convergence order of the collocation solution is only m however the collocation solution may exhibit superconvergence with order m 1 at the collocation points in particular the local convergence order may attain 2 m 1 at the nodes provided that the collocation is based on the m radau ii points finally some numerical examples are performed to verify our theoretical results

collocation methods for volterra functional integral equations with non vanishing delays abstract in this paper the existence uniqueness regularity properties and in particular the local representation of solutions for general volterra functional integral equations with non vanishing delays are investigated based on the solution representation we detailedly analyze the attainable global and local convergence order of iterated collocation solutions on invariant meshes it turns out that collocation at the m gauss legendre points neither leads to the optimal global convergence order m 1 nor yields the local convergence order 2m on the whole interval which is in sharp contrast to the case of the classical volterra delay integral equations however if the collocation is based on the m radau ii points the local superconvergence order 2 m 1 will exhibit at all mesh points finally some numerical experiments are performed to confirm our theoretical findings

invariant algebraic curves and rational first integrals for planar polynomial vector fields we present three main results the first two provide sufficient conditions in order that a planar polynomial vector field in c2 has a rational first integral and the third one studies the number of multiple points that an invariant algebraic curve of degree n of a planar polynomial vector field of degree m can have in function of m and n

a new approach for the study of limit cycles abstract we prove that star like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non autonomous polynomial system or as heteroclinic solutions of a 3 dimensional polynomial system we illustrate these points of view with several examples one of the key ideas in our approach is to decompose the periodic solutions as the sum of two suitable functions as a first application we use these new approaches to prove that all star like reversible limit cycles are algebraic as a second application we introduce a function whose zeroes control the periodic orbits that persist as limit cycles when we perturb a star like reversible center as far as we know this is the first time that this question is solved in full generality somehow this function plays a similar role that an abelian integral for studying perturbations of hamiltonian systems

nonlinear dynamics of filaments ii nonlinear analysis abstract the linear stability analysis of the full time dependent kirchhoff equations for elastic filaments gives precise information about possible dynamical instabilities the associated dispersion relations derived in the preceding paper provides the selection mechanism for the shapes selected by highly unstable filaments here we perform a nonlinear analysis and derive new amplitude equations which describe the dynamics above the instability threshold the straight filament is studied in detail and the motion is shown to be described by a pair of nonlinear klein gordon equations which couple the local deformation amplitude to the twist density of particular interest is the effect of boundary conditions on the instability threshold it is shown that with suitable choice of boundary conditions the threshold of instability is delayed we also show the existence of pulse like and front like traveling wave solutions

dtn based mixed dimensional coupling using a boundary stress recovery technique abstract a new computational approach for the mixed dimensional modeling of time harmonic waves in elastic structures is proposed a two dimensional 2d structure is considered which includes a part that is assumed to behave in a one dimensional 1d way the 2d and 1d structural regions are discretized by using 2d and 1d finite element fe formulations the hybrid model if designed properly is much more efficient than the standard 2d model taken for the entire problem one important issue related to such hybrid 2d 1d models is the way the 2d 1d coupling is done and the coupling error generated here three closely related coupling methods are considered they are all based on the dirichlet to neumann dtn map associated with the 1d problem on the interface the first coupling method is the dtn method in its usual form where the dtn map is calculated numerically and where the 1d and 2d problems are solved separately the second coupling method is the one devised by carka mear and landis cml which is equivalent to the former one but in which the 2d and 1d interface solutions are solved for simultaneously in the third coupling method the dtn map is enforced on the interface iteratively direct application of these three methods results in low accuracy as a recent study shows therefore these methods are used here in conjunction with a boundary stress recovery bsr technique originally proposed by hughes which provides the same order of accuracy for the stress as for the primary variable the performance of the three methods is demonstrated and they are compared via numerical examples conclusions are drawn on their relative merit

elastic stability of dna configurations i general theory results are presented in the theory of the elastic rod model for dna among which are criteria enabling one to determine whether a calculated equilibrium configuration of a dna segment is stable in the sense that it gives a local minimum to the sum of the segment s elastic energy and the potential of forces acting on it the derived stability criteria are applicable to plasmids and to linear segments subject to strong anchoring end conditions their utility is illustrated with an example from the theory of configurations of the extranucleosomal loop of a dna miniplasmid in a mononucleosome with emphasis placed on the influence that nicking and ligation on one hand and changes in the ratio of elastic coefficients on the other have on the stability of equilibrium configurations in that example the configurations studied are calculated using an extension of the method of explicit solutions to cases in which the elastic rod modeling a dna segment is considered impenetrable and hence excluded volume effects and forces arising from self contact are taken into account

finite element simulation of pulsatile flow through arterial stenosis the problem of blood flow through a stenosis is solved using the incompressible navier stokes equations in a rigid circular tube presenting a partial occlusion calculations are based on a galerkin finite element method the time marching scheme employs a predictor corrector technique using a variable time step results are obtained for steady and physiological pulsatile flows computational experiments analyse the effect of varying the degree of stenosis the stricture length the reynolds number and womersley number the method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows

on the shear thinning and viscoelastic effects of blood flow under various flow rates the aim of this paper is to describe and discuss the results of numerical comparative study performed in order to demonstrate and quantify some of the most relevant non newtonian characteristics of blood flow in medium sized blood vessels namely its shear thinning and viscoelastic behavior the models studied in this work are the classical newtonian and oldroyd b models as well as their generalized shear thinning modifications numerical tests are performed on three dimensional geometries namely an idealized axisymmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images the numerical solution of the system of governing equations is obtained by a finite volume method on a structured grid model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non newtonian effects

some criteria for the existence of limit cycles for quadratic vector fields abstract in this paper we consider real quadratic systems we present new criteria for the existence and uniqueness of limit cycles for such systems by using darbouxian particular solutions some results are based on the study of such systems in cp 2 we also generalize the well know result of bautin on the nonexistence of limit cycles for quadratic lotka volterra systems

numerical investigation of the non newtonian blood flow in a bifurcation model with a non planar branch the pulsatile flow of non newtonian fluid in a bifurcation model with a non planar daughter branch is investigated numerically by using the carreau yasuda model to take into account the shear thinning behavior of the analog blood fluid the objective of this study is to deal with the influence of the non newtonian property of fluid and of out of plane curvature in the non planar daughter vessel on wall shear stress wss oscillatory shear index osi and flow phenomena during the pulse cycle the non newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior the non planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of wss along the vessel in particular in systole phase downstream of the bifurcation the velocity profiles are shifted toward the flow divider and low wss and high shear stress temporal oscillations characterized by osi occur on the outer wall region of the daughter vessels close to the bifurcation secondary motions become stronger with the addition of the out of plane curvature induced by the bending of the vessel and the secondary flow patterns swirl along the non planar daughter vessel a significant difference between the non newtonian and the newtonian pulsatile flow is revealed during the pulse cycle however reasonable agreement between the non newtonian and the rescaled newtonian flow is found calculated results for the pulsatile flow support the view that the non planarity of blood vessels and the non newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology

dynamics of coronary artery curvature obtained from biplane cineangiograms abstract a system was developed to track the centerlines axes of human coronary arteries during the cardiac cycle from biplane cineangiograms the system employs a time interpolation technique on one image plane and a smoothing technique on the other to create simultaneous image pairs the image pairs are then used to reconstruct the three dimensional axes of the vessels during the cardiac cycle once the vessel axes are reconstructed acceleration velocity and geometric parameters such as curvature can be obtained in the present work a sequence of human angiograms is used to obtain the axial and temporal variation of the curvature of a portion of the left anterior descending coronary artery distal to the third diagonal branch during two cardiac cycles for the case studied the change in curvature during the cycle ranged from 0 25 to 1 8 cm 1 depending upon the position of the site

divergence and poincare liapunov constants for analytic differential systems abstract we consider a planar autonomous real analytic differential system with a monodromic singular point p we deal with the center problem for the singular point p our aim is to highlight some relations between the divergence of the system and the poincare liapunov constants of p when these are defined

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

a study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions recent computational fluid dynamics cfd studies relate abnormal blood flow to rupture of cerebral aneurysms however it is still debated how to model blood flow with sufficient accuracy common assumptions made include newtonian behaviour of blood traction free outlet boundary conditions and inlet boundary conditions based on available literature these assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature however the consequences of these assumptions have so far been inadequately addressed this study investigates the effects of 4 different viscosity models 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms the differences are quantified in terms of 3 different wall shear stress wss metrics involving maximal wss average wss and proportion of aneurysm sac area with low wss the results were compared with common geometrical metrics such as volume aspect ratio size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type the results demonstrate strong correlations between the different viscosity models and boundary conditions the correlation between the different wss metrics range from weak to medium no strong correlations were found between the different wss metrics and the geometrical metrics or classifications

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

algebraic limit cycles in polynomial systems of differential equations using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4 5 and 6 we also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3 moreover we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3 as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

on the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation abstract here we present a study on the impact of assumptions on image based hemodynamic simulations of healthy carotid bifurcations in particular we evaluate to which extent assumptions on blood rheology influence bulk flow features driven by the fact that few studies have provided adequate insights into the influence of assumptions to confidently model the 4d hemodynamics within the bifurcation the final goal is to complement integrate and extend with a quantitative characterization of the bulk flow the description currently adopted to classify altered hemodynamics which is based on wall shear stress wss hemodynamic simulations of two image based carotid bifurcation geometries were carried out assuming a reference newtonian viscosity two non newtonian rheology models and newtonian viscosities based on characteristic shear rates wss based and lagrangian based metrics for helical flow quantification and for vorticity dynamics quantification were calculated our findings suggest that the assumption of newtonian rheology 1 could be reasonable for bulk flow metrics differences from non newtonian behavior are lower than 10 2 influences at different levels the wss based indicators depending on the bifurcation model even if in our study it is lower than the major source of uncertainty as recognized by the literature i e uncertainty on geometry reconstruction

dynamic curvature strongly affects wall shear rates in a coronary artery bifurcation model this study was motivated by the need for a better understanding of coronary artery blood flow patterns and their possible role in atherosclerosis formation of particular interest in this study was the effects of the dynamic deformation due to myocardial contraction on wall shear rate patterns in the coronary arteries a better understanding of these effects on wall shear rate in a bifurcation geometry and an evaluation of the importance of these effects was desired a three dimensional computer model of a bifurcation lying on the surface of a sphere with time varying radius of curvature was employed to simulate the motion and deformation of the arteries the results indicated low mean shear rates along the myocardial wall and very high shear rate variations over 100 of the static mean shear rate along the outer wall the results obtained using a quasi static analysis were found to underestimate the dynamic wall shear rate variation along the myocardial and outer walls it was concluded that dynamic geometry effects are important in determining sites of low mean and oscillating wall shear that have been associated with atherogenesis in curved bifurcating arteries

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

the influence of out of plane geometry on pulsatile flow within a distal end to side anastomosis we present an experimental and computational investigation of time varying flow in an idealized fully occluded 45 distal end to side anastomosis two geometric configurations are assessed one where the centerlines of host and bypass vessels lie within a plane and one where the bypass vessel is deformed out of the plane of symmetry respectively termed planar and non planar flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral hp algorithm results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time averaged peak wall shear stress magnitude by 10 in the non planar model as compared to the planar configuration in the planar geometry the stagnation point follows a straight line path along the host artery bed with a path length of 0 8 diameters by contrast in the non planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall and follows a parabolic path with a 0 7 diameter longitudinal and 0 5 diameter transverse excursion a definition of the oscillatory shear index osi is introduced that varies between 0 and 0 5 and that accounts for a continuous range of wall shear stress vector angles in both models regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow the mean oscillatory shear magnitude considering sites where osi 0 1 in the non planar geometry was reduced by 22 as compared to the planar configuration these changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out of plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions

multiplicity of limit cycles and analytic m solutions for planar differential systems abstract this work deals with limit cycles of real planar analytic vector fields it is well known that given any limit cycle of an analytic vector field it always exists a real analytic function f 0 x y defined in a neighborhood of and such that is contained in its zero level set in this work we introduce the notion of f 0 x y being an m solution which is a merely analytic concept our main result is that a limit cycle is of multiplicity m if and only if f 0 x y is an m solution of the vector field we apply it to study in some examples the stability and the bifurcation of periodic orbits from some non hyperbolic limit cycles

direct operatorial tau method for pantograph type equations abstract the lanczos tau method is applied to find chebyshev polynomial approximations for the solutions of pantograph differential equations the results are accompanied by an error analysis numerical examples calculated by our matlab package chebpack confirm the theory and prove the importance for practice of this approach

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

the influence of the non newtonian properties of blood on the flow in large arteries unsteady flow in a 90 curved tube a numerical and experimental investigation of unsteady entry ow in a 903 curved tube is presented to study the impact of the non newtonian properties of blood on the velocity distribution the time dependent ow rate for the newtonian and the nonnewtonian blood analog uid were identical for the numerical computation a carreau yasuda model was employed to accommodate the shear thinning behavior of the xanthan gum solution the viscoelastic properties were not taken into account the experimental results indicate that signi cant di erences between the newtonian and non newtonian uid are present the numerical results for both the newtonian and the non newtonian uid agree well with the experimental results since viscoelasticity was not included in the numerical code shear thinning behavior of the blood analog uid seems to be the dominant non newtonian property even under unsteady ow conditions finally a comparison between the non newtonian uid model and a newtonian uid at a rescaled reynolds number is presented the rescaled reynolds number based on a characteristic rather than the high shear rate viscosity of the xanthan gum solution was about three times as low as the original reynolds number comparison reveals that the character of ow of the non newtonian uid is simulated quite well by using the appropriate reynolds number 1999 elsevier science ltd all rights reserved

invariant algebraic curves of large degree for quadratic system in this paper we present for the first time examples of algebraic limit cycles and saddle loops of degree greater than 4 for planar quadratic systems in particular we give examples of algebraic limit cycles of degree 5 and 6 and algebraic saddle loops of degree 3 and 5 surrounding a strong focus we also give an example of an invariant algebraic curve of degree 12 for which the quadratic system has no darboux integrating factors or first integrals

modeling dimensionally heterogeneous problems analysis approximation and applications in the present work a general theoretical framework for coupled dimensionally heterogeneous partial differential equations is developed this is done by recasting the variational formulation in terms of coupling interface variables in such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation this approach also allows the development of different iterative substructuring solution methodologies involving dimensionally homogeneous subproblems numerical experiments are carried out to test our theoretical results

comparison between a generalized newtonian model and a network type multiscale model for hemodynamic behavior in the aortic arch validation with 4d mri data for a case study abstract blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties thus an appropriate non newtonian model is advisable and we choose a modified version of the rheological model of phan thien and tanner mptt the different parameters of this model derived from the rheology of polymers allow characterization of the non newtonian nature of blood taking into account the behavior of red blood cells in plasma using the mptt model that we implemented in the open access software openfoam numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient we started from a patient specific model which was constructed from medical images exiting flow boundary conditions have been developped based on a 3 element windkessel model to approximate physiological conditions the parameters of the windkessel model were calibrated with in vivo measurements of flow rate and pressure the influence of the selected viscosity of red blood cells on the flow and wall shear stress wss was investigated results obtained from this model were compared to those of the newtonian model and to those of a generalized newtonian model as well as to in vivo dynamic data from 4d mri during a cardiac cycle upon evaluating the results the mptt model shows better agreement with the mri data during the systolic and diastolic phases than the newtonian or generalized newtonian model which confirms our interest in using a complex viscoelastic model

an efficient approach to study the pulsatile blood flow in femoral and coronary arteries by differential quadrature method abstract in this paper flow analysis for a non newtonian third grade blood in coronary and femoral arteries is simulated numerically blood is considered as the third grade non newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient differential quadrature method dqm and crank nicholson method cnm are used to solve the partial differential equation pde governing equation by which a good agreement between them was observed in the results the influences of some physical parameters such as amplitude lead angle and body acceleration frequency on non dimensional velocity and profiles are considered for instance the results show that increasing the amplitude a g and reducing the lead angle of body acceleration make higher velocity profiles in the center line of both arteries

uniqueness of algebraic limit cycles for quadratic systems abstract we know five different families of algebraic limit cycles in quadratic systems one of degree 2 and four of degree 4 moreover if there are other families of algebraic limit cycles for quadratic systems then their degrees must be larger than 4 it is known that if a quadratic system has an algebraic limit cycle of degree 2 then this is the unique limit cycle of the system the first main goal of this paper is to prove that if a quadratic system has an algebraic limit cycle of degree 4 then this is the unique limit cycle of the system for the yablonskii and filiptsov algebraic limit cycles the problem of proving their uniqueness has been open since 1966 and 1973 respectively the second main goal is to provide sufficient conditions in order that all the limit cycles of a quadratic system to be algebraic

a characteristic finite element algorithm for the 3 d navier stokes equations using unstructured grids abstract this paper discusses a finite element algorithm for solution of the 3 d navier stokes equations that is based on the method of characteristics the algorithm which is based on a time slitting of the convective terms from the generalized stokes problem comprises a point wise characteristic integration of the convective terms and uzawa integration of the generalized stokes problem the most costly part of the characteristic integration scheme is the search for an element containing the foot of a given characteristic the present study uses a very efficient algorithm for element searching which is particularly useful for complex geometries the implementation of the algorithm is discussed in the paper and the resulting code s performance is compared to that of a code based on a more conventional fourth order runge kutta convection integration a variety of flow problems are tested including an analytical solution of the navier stokes equations flow in a lid driven cavity flow over a backward facing step and flow in an end to side anastomoses in all cases the proposed algorithm demonstrated performance superior to that of a conventional explicit treatment of the convective terms

a unified variational approach for coupling 3d 1d models and its blood flow applications in this work we propose an extended variational formulation in order to handle the problem of the flow of an incompressible fluid in compliant vessels with discontinuous fields this approach makes possible to tackle in a consistent variational manner problems like the coupling between models of different dimensionality the main ideas of the work are presented for a simple heat transfer problem and then are used in the context of modelling blood flow in large vessels a computational implementation of the proposed formulation is also shown and discussed by presenting examples of practical applications

inlet boundary conditions for blood flow simulations in truncated arterial networks in the context of patient specific cardiovascular applications hemodynamics models going from 3d to 0d are often limited to a part of the arterial tree this restriction implies the set up of artificial interfaces with the remaining parts of the cardiovascular system in particular the inlet boundary condition is crucial it supplies the impulsion to the system and receives the reflected backward waves created by the distal network some aspects of this boundary condition need to be properly defined such as the treatment of backward waves reflected or absorbed and the value of the imposed hemodynamic wave total or forward component most authors prescribe as inlet boundary condition bc the total measured variable pressure velocity or flow rate in a reflective way we show that with this type of inlet boundary condition the model does not produce physiological waveforms we suggest instead to prescribe only the forward component of the prescribed variable in an absorbing way in this way the computed reflected waves superpose with the prescribed forward waves to produce the total wave at the inlet in this work different inlet boundary conditions are implemented and compared for a 1d blood flow model we test our boundary conditions on a truncated arterial model presented in the literature as well as on a patient specific lower limb model of a femoral bypass we show that with this new boundary condition a much better fitting is observed on the shape and intensity of the simulated pressure and velocity waves

helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear abstract the main purpose of the study is to verify if helical flow might be a surrogate marker of the exposure to disturbed shear in normal carotid bifurcations based on hemodynamic simulations data of 50 carotid bifurcations we defined appropriate helicity based bulk flow descriptors and multivariate linear regression analysis was performed to assess the potential for a combination of helicity based indicators in describing the exposure to disturbed shear to select the optimal combination of helicity based descriptors in the regression model the akaike information criterion was applied the identified statistical model is composed of two bulk flow descriptors proposed here to quantify helicity intensity and the balance between counter rotating helical flow patterns in the flow field the model revealed the existence of a significant relationship with adjusted squared pearson s correlation coefficient in the range 0 4 0 7 p

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

pulsatile flow of non newtonian fluids through arterial stenoses the problem of blood flow through stenoses is solved using the incompressible generalized newtonian model the herschel bulkley bingham and power law fluids are incorporated the geometry corresponds to a rigid circular tube with a partial occlusion calculations are performed by a galerkin finite element method for the pulsatile case a predictor corrector time marching scheme is used with an adaptive time step results are obtained for steady and pulsatile physiological flows computations show that the memory effects taken into account in the model affect deeply the flow compared with newtonian reference case the disturbances are stronger by their vorticity intensity and persist after the geometrical obstacle this is especially true for severe stenoses

multidimensional modelling for the carotid artery blood flow abstract in this work a multidimensional 3d 1d fem model of the whole arterial tree is implemented it comprises a 3d compliant model of the carotid bifurcation coupled with a 1d model for the remaining part of the arterial tree with this approach difficulties arising from the treatment of boundary conditions for the 3d model are naturally handled the navier stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall also the a l e formulation is considered within the 3d blood regions taking into account the domain deformations produced by the moving artery wall this 3d model is complemented with a 1d model of the entire arterial tree in order to appropriately set inflow and outflow boundary conditions for the former the reduced 1d model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network also a volumetric flow rate is imposed at the inlet to model the systolic work of the heart the peripheral arteriole beds are simulated with the well known lumped windkessel model a standard geometry of the carotid bifurcation is discretized with p1 bubble p1 tetrahedral elements the obtained results properly reproduce the general flow patterns reported in the literature very good agreement between the outcomes of a pure 1d model and those of the combined multidimensional model was obtained it is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases

assessment of blood volume flow in slightly curved arteries from a single velocity profile abstract non invasive estimation of arterial blood volume flow bvf has become a central issue in assessment of cardiovascular risk poiseuille and womersley approaches are commonly used to assess the bvf from centerline velocity but both methods neglect the influence of curvature based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine the bvf can also be estimated by averaging velocities at opposite radial positions referred to as the cosine model ctm this study investigates the accuracy of bvf estimation in slightly curved arteries for bvf waveforms obtained in the brachial artery of 6 volunteers computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles the bvf was then estimated from the simulation results with the ctm and methods based on poiseuille womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed and compared to the prescribed bvf the simulations show that the influence of curvature is strongest when the flow decelerates for poiseuille and womersley the time average bvf was underestimated by maximally 10 4 and 7 8 for a radius of curvature of 50 and 100 mm respectively the estimation error is lower for the ctm and equals 4 2 and 1 2 for a radius of curvature of 50 and 100 mm respectively from this study we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the womersley method should be chosen the ctm improves current estimation techniques if in vivo velocity distributions are available

transversal conics and the existence of limit cycles this paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems we provide a method to construct poincar e bendixson regions by using transversal conics we present several examples of known systems in the literature showing different features about limit cycles hyperbolicity hopf bifurcation sky blue bifurcation rotated vector fields ldots for which the obtained poincar e bendixson region allows to locate the limit cycles our method gives bounds for the bifurcation values of parametrical families of planar vector fields and intervals of existence of limit cycles

healthy and diseased coronary bifurcation geometries influence near wall and intravascular flow a computational exploration of the hemodynamic risk abstract local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near wall and intravascular flow patterns different bifurcation angles and cardiac curvatures were varied in population based idealized models of both stenosed and unstenosed bifurcations representing the left anterior descending lad coronary artery with its diagonal branch local hemodynamics was analyzed in terms of helical flow and exposure to low oscillatory shear stress by performing computational fluid dynamics simulations results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases instead curvature radius influences the generation and transport of helical flow structures with smaller cardiac curvature radius associated to higher helicity intensity stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases cardiac curvature radius moderately affects near wall hemodynamics of the stenosed cases with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress in conclusion the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the lad diagonal bifurcation highlighting that cardiac curvature influences near wall and intravascular hemodynamics while bifurcation angle has a minor effect

algebraic limit cycles of degree 4 for quadratic systems abstract yablonskii differential equations 2 1996 335 and filipstov differential equations 9 1973 983 proved the existence of two different families of algebraic limit cycles of degree 4 in the class of quadratic systems it was an open problem to know if these two algebraic limit cycles where all the algebraic limit cycles of degree 4 for quadratic systems chavarriga a new example of a quartic algebraic limit cycle for quadratic sytems universitat de lleida preprint 1999 found a third family of this kind of algebraic limit cycles here we prove that quadratic systems have exactly four different families of algebraic limit cycles the proof provides new tools based on the index theory for algebraic solutions of polynomial vector fields

relationships between limit cycles and algebraic invariant curves for quadratic systems abstract algebraic limit cycles for quadratic systems started to be studied in 1958 up to now we know 7 families of quadratic systems having algebraic limit cycles of degree 2 4 5 and 6 here we present some new results on the limit cycles and algebraic limit cycles of quadratic systems these results provide sometimes necessary conditions and other times sufficient conditions on the cofactor of the invariant algebraic curve for the existence or nonexistence of limit cycles or algebraic limit cycles in particular it follows from them that for all known examples of algebraic limit cycles for quadratic systems those cycles are unique limit cycles of the system

tetrahedralhpfinite elements we present a new discretisation for the incompressible navier stokes equations that extends spectral methods to three dimensional complex domains consisting of tetrahedral subdomains the algorithm is based on standard concepts ofhpfinite elements as well as tensorial spectral elements this new formulation employs a hierarchical modal basis constructed from a new apex co ordinate system which retains a generalised tensor product these properties enable the development of computationally efficienct algorithms for use on standard finite volume unstructured meshes a detailed analysis is presented that documents the stability and exponential convergence of the method and several flow cases are simulated and compared with analytical and experimental results

bending and twisting of an in vivo coronary artery at a bifurcation abstract dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer tomographically reconstructed three dimensional images of an in situ beating heart of an anesthetized dog wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion for quantifying the local bending and twisting of the left coronary artery tree the anatomic landmarks of the bifurcation points are selected as focussed locations at these points the space curves of the tree at different cardiac instants were first derived in parametric forms curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter this analysis revealed that during the initial contraction of the heart wall a 2 reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart when the left ventricular chamber reached a maximum value the radius of curvature was found to decrease at a rate of 2 3 ms 1 at the end of diastole an increase in the radius of curvature at a rate of 5 7 ms 1 was observed the twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from 0 62 to 0 63 ms 1

nonlinear dynamics of filaments i dynamical instabilities abstract the kirchhoff model provides a well established mathematical framework to study both computationaly and theoretically the dynamics of thin filaments within the approximations of linear elasticity theory the study of static solutions to these equations has a long history and the usual approach to describing their instabilities is to study the time dependent version of the kirchhoff model in the euler angle frame here we study the linear stability of the full time independent equations by introducing a new are length preserving perturbation scheme as an application we consider the instabilities of various stationary solutions such as the planar ring and straight rod subjected to twisting perturbations this scheme gives a direct proof of the existence of dynamical instabilities and provides the selection mechanism for the shape of unstable filaments

non nested configuration of algebraic limit cycles in quadratic systems this work deals with algebraic limit cycles of planar polynomial differential systems of degree two more concretely we show among other facts that a quadratic vector field cannot possess two non nested algebraic limit cycles contained in different irreducible invariant algebraic curves

hybrid element based approximation for the navier stokes equations in pipe like domains abstract motivated by its applicability to model blood flow in the cardiovascular system in this work we propose a numerical approximation of the navier stokes equations maintaining comparable accuracy with traditional finite element methods while performing a substantial reduction in the problem size the method is envisaged for domains in which flow phenomena exhibits a dominant axial direction the strategy consists of combining a finite element approximation for the description of fields velocity components and pressure in the primary axial direction while taking a polynomial spectral approximation for the description of fields across the secondary transversal direction in essence this method can be understood as an extension of the so called hierarchical modeling himod approach special attention is given to domains featuring sudden constrictions expansions and bifurcations for which a modified spectral approximation is considered the capabilities and potentialities of the proposed approach to simulate fluid flow phenomena in pipe like domains are presented through several examples

the nonlinear dynamics of elastic tubes conveying a fluid abstract the kirchhoff equations for elastic tubes are modified to include the effect of fluid flow using the techniques of linear and nonlinear analysis specially developed for the kirchhoff equations the effect of the fluid flow on the basic twist to writhe instability is investigated the results suggest an intriguing modification of the bifurcation threshold due to the flow beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics

collocation methods for general volterra functional integral equations with vanishing delays we analyze the existence uniqueness and regularity properties of solutions for general volterra functional integral equations with the delay function theta t vanishing at the initial point of the given interval 0 t with theta t qt 0 q 1 representing an important special case the focus of the paper is then on the the attainable order of convergence and the question of possible superconvergence for collocation solutions in certain piecewise polynomial spaces numerical experiments complement the theoretical convergence results