on a micro macro model for polymeric fluids near equilibrium in this paper we study a micro macro model for polymeric fluid the system involves coupling between the macroscopic momentum equation and a microscopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation we employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure for the initial data not far from the equilibrium we prove the global existence and uniqueness of classical solutions to the system 2006 wiley periodicals inc

positive definite solutions of the matrix equations x a x qa q abstract in this paper we investigate nonlinear matrix equations x a x q a q and x a x q a q where q 0 1 we derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations we provide a sufficient condition for the equation x a x q a q to have two different positive definite solutions and a sufficient condition for the equation x a x q a q to have a unique positive definite solution we also propose iterative methods for obtaining positive definite solutions for these equations

kinetic analysis of the lower limbs during walking what information can be gained from a three dimensional model kinetic analyses joint moments powers and work of the lower limbs were performed during normal walking to determine what further information can be gained from a three dimensional model over planar models it was to be determined whether characteristic moment and power profiles exist in the frontal and transverse planes across subjects and how much work was performed in these planes kinetic profiles from nine subjects were derived using a three dimensional inverse dynamics model of the lower limbs and power profiles were then calculated by a dot product of the angular velocities and joint moments resolved in a global reference system characteristic joint moment profiles across subjects were found for the hip knee and ankle joints in all planes except for the ankle frontal moment as expected the major portion of work was performed in the plane of progression since the goal of locomotion is to support the body against gravity while generating movements which propel the body forward however the results also showed that substantial work was done in the frontal plane by the hip during walking 23 of the total work at that joint the characteristic joint profiles suggest defined motor patterns and functional roles in the frontal and transverse planes kinetic analysis in three dimensions is necessary particularly if the hip joint is being examined as a substantial amount of work was done in the frontal plane of the hip to control the pelvis and trunk against gravitational forces

diffusing particles with electrostatic repulsion we study a diffusion model of an interacting particles system with general drift and diffusion coefficients and electrostatic inter particles repulsion more precisely the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations see 2 and then we consider the behaviour of this system when the number of particles n goes to infinity through the empirical measure process in the particular case of affine drift and constant diffusion coefficient we prove that a limiting measure valued process exists and is the unique solution of a deterministic pde our treatment of the convergence problem as n uparrow infty is partly similar to that of t chan 3 and l c g rogers z shi 5 except we consider here a more general case allowing collisions between particles which leads to a second order limiting pde

the iterative method for solving nonlinear matrix equation xs a x ta q abstract nonlinear matrix equation x s a x t a q where q is an hermitian positive definite matrix a is the conjugate transpose of the matrix a and both of s and t are positive integers has widely applied background in this paper necessary conditions and sufficient conditions for the existence of hermitian positive definite solutions of this equation are derived an iterative method for obtaining hermitian positive definite solutions is proposed moreover a perturbation bound for the hermitian positive definite solutions is given

the l2 decay for the 2d co rotation fene dumbbell model of polymeric flows abstract in this paper we mainly study the long time behavior of solutions to the finite extensible nonlinear elastic fene dumbbell model with dimension two in the co rotation case firstly we obtain the l 2 decay rate of the velocity of the 2d co rotation fene model is 1 t 1 2 with small data then by virtue of the littlewood paley theory we can remove the small condition our obtained sharp result improves considerably the recent results in 8 14

validation of net joint loads calculated by inverse dynamics in case of complex movements application to balance recovery movements the joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation however even if this process is theoretically simple many sources of errors may lead to huge inaccuracies in the results moreover a direct comparison with in vivo measured loads or with gold standard values from literature is only possible for very specific studies therefore assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required this paper presents a simple method to evaluate both 1 the consistency of the results obtained by inverse dynamics 2 the influence of possible modifications in the inverse dynamic hypotheses this technique concerns recursive calculation performed on full kinematic chains and consists in evaluating the loads obtained by two different recursive strategies it has been applied to complex 3d whole body movements of balance recovery a recursive newton euler procedure was used to compute the net joint loads two models were used to represent the subject bodies considering or not the upper body as a unique rigid segment the inertial parameters of the body segments were estimated from two different sets of scaling equations de leva p 1996 adjustments to zatsiorsky suleyanov s segment inertia parameters journal of biomechanics 29 1223 1230 dumas r cheze l verriest j p 2006b adjustments to mcconville et al and young et al body segment inertial parameters journal of biomechanics in press using this comparison technique it has been shown that for the balance recovery motions investigated 1 the use of the scaling equations proposed by dumas et al instead of those proposed by de leva improves the consistency of the results average relative influence up to 30 for the transversal moment 2 the arm motions dynamically influence the recovery motion in a non negligible way average relative influence up to 15 and 30 for the longitudinal force and the transversal moment respectively

whole body inverse dynamics over a complete gait cycle based only on measured kinematics this paper presents a three dimensional 3d whole body multi segment model for inverse dynamics analysis over a complete gait cycle based only on measured kinematic data the sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data a new validated smooth transition assumption was used to solve the indeterminacy problem in the double support phase kinematic data is required for all major body segments and hence a whole body gait measurement protocol is presented finally sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results the model gave reasonably good estimates of sagittal plane ground forces and moment however the estimates in the other planes were less good which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment the errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters a digital filtering cut off frequency of 4 5 hz was found to produce the best results it was also shown that errors in the mass properties of body segments can play a crucial role with changes in properties sometimes having a disproportionate effect on the calculated ground reactions the implication of these results is that even when force plate data is available the estimated joint forces are likely to suffer from similar errors

perturbation analysis of the matrix equation x a x pa q abstract consider the nonlinear matrix equation x a x p a q with 0 p 1 this paper shows that there exists a unique positive definite solution to the equation a perturbation bound and the backward error of an approximate solution to this solution is evaluated we also obtain explicit expressions of the condition number for the unique positive definite solution the theoretical results are illustrated by numerical examples

on the existence of a positive definite solution of the matrix equation x atx 1a i the question is raised under which conditions on the real square matrix a the matrix equation x atx 1a i has a real symmetric positive definite solution x both necessary and sufficient solvability conditions on a are derived moreover we give an algorithm to calculate the solution for a number of special cases we also present an analytic solution

thompson metric method for solving a class of nonlinear matrix equation based on the elegant properties of the thompson metric we prove that the general nonlinear matrix equation x q a f x a q q 1 always has a unique positive definite solution an iterative method is proposed to compute the unique positive definite solution we show that the iterative method is more effective as q increases a perturbation bound for the unique positive definite solution is derived in the end

on the positive definite solutions of nonlinear matrix equation x a x δa q abstract in this paper we consider the positive definite solutions of nonlinear matrix equation x a x a q where 0 1 which appears for the first time in s m el sayed a c m ran on an iteration methods for solving a class of nonlinear matrix equations siam j matrix anal appl 23 2001 632 645 the necessary and sufficient conditions for the existence of a solution are derived an iterative algorithm for obtaining the positive definite solutions of the equation is discussed the error estimations are found

on hermitian positive definite solution of the matrix equation x σ m i 1 a i x r a i q a conjecture that the nonlinear matrix equation email protected i 1 ma i x ra i q email protected r 0 or 0

on the positive definite solutions of the matrix equations xs atx ta in abstract the two matrix equations x s a t x t a i n and x s a t x t a i n are studied based on the fixed point theory the existence of the symmetric positive definite solutions are proved sensitivity analysis of the maximal solution is presented some elegant estimates of the positive definite solutions are obtained three iterative methods for computing the positive solutions are proposed

efficient computation of the extreme solutions of x a x 1 a q and x a x 1 a q we propose a new quadratically convergent algorithm having a low computational cost per step and good numerical stability properties which allows the simultaneous approximation of the extreme solutions of the matrix equations x a x 1 a q and x a x 1 a q the algorithm is based on the cyclic reduction method

the three dimensional determination of internal loads in the lower extremity a three dimensional model of the lower limb containing 47 muscles was developed to study the differences between a two and three dimensional approach for determining internal loads the role of the dynamic joint representation and the behavior of different load bearing criteria in walking and running the problem of redundancy of the musculo skeletal system was resolved by applying inverse dynamics and static optimization methods different hypothetical load bearing capabilities of hinge spherical and intermediate joint types for the knee and the ankle joints were tested it was found that even almost planar movements such as walking and running are associated with significant three dimensional intersegment moments especially in the frontal plane thus a two dimensional approach may underestimate internal loads up to 60 it is shown that pure hinge joints are inappropriate for modeling the dynamical joint function of the knee and ankle joints a more flexible joint representation in combination with a squared muscle stress minimization criterion predicted a lot of synergistic as well as antagonistic muscle activation which was also found in the emg patterns the results indicate the importance of muscular joint stabilization in natural human movements compared to in vivo measurements it is speculated that the predicted force magnitudes are considerably overestimated due to error propagation and still insufficient anatomical models thus increased efforts to improve further the reliability of internal load calculations should be made in the future

on the nonlinear matrix equation x i 1mai xδiai q abstract based on fixed point theorems for monotone and mixed monotone operators in a normal cone we prove that the nonlinear matrix equation x i 1 m a i x i a i q 0 i 1 always has a unique positive definite solution a conjecture which is proposed in x g liu h gao on the positive definite solutions of the matrix equation x s a t x t a i n linear algebra appl 368 2003 83 97 is solved multi step stationary iterative method is proposed to compute the unique positive definite solution numerical examples show that this iterative method is feasible and effective

boundary conditions for the microscopic fene models we consider the microscopic equation of finite extensible nonlinear elasticity fene models for polymeric fluids under a steady flow field it is shown that for the underlying fokker planck type of equations any preassigned distribution on the boundary will become redundant once the nondimensional number text it li frac hb k bt geq 2 where h is the elasticity constant sqrt b is the maximum dumbbell extension t is the temperature and k b is the usual boltzmann constant moreover if the probability density function is regular enough for its trace to be defined on the sphere m sqrt b then the trace is necessarily zero when text it li 2 these results are consistent with our numerical simulations as well as some recent well posedness results by preassuming a zero boundary distribution

well posedness for the fene dumbbell model of polymeric flows we prove local and global well posedness for the fene dumbbell model for a very general class of potentials indeed in prior local or global well posedness results conditions on the strength of the singularity or on the parameter b were made here we give a proof in the general case we also prove global existence results if the data is small or if we restrict to the co rotational model in dimension 2 2008 wiley periodicals inc

existence of global weak solutions to compressible isentropic finitely extensible nonlinear bead spring chain models for dilute polymers the two dimensional case abstract we prove the existence of global in time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids where the polymer molecules are idealized as bead spring chains with finitely extensible nonlinear elastic fene type spring potentials the class of models under consideration involves the unsteady compressible isentropic isothermal navier stokes system in a bounded domain in r d d 2 for the density the velocity u and the pressure p of the fluid with an equation of state of the form p c p where c p is a positive constant and 1 the right hand side of the navier stokes momentum equation includes an elastic extra stress tensor which is the classical kramers expression the elastic extra stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a fokker planck type parabolic equation a crucial feature of which is the presence of a centre of mass diffusion term this extends the result in our paper j w barrett and e suli 2016 9 which established the existence of global in time weak solutions to the system for d 2 3 and 3 2 but the elastic extra stress tensor required there the addition of a quadratic interaction term to the classical kramers expression to complete the compactness argument on which the proof was based we show here that in the case of d 2 and 1 the existence of global in time weak solutions can be proved in the absence of the quadratic interaction term our results require no structural assumptions on the drag term in the fokker planck equation in particular the drag term need not be corotational with a nonnegative initial density 0 l for the continuity equation a square integrable initial velocity datum u 0 for the navier stokes momentum equation and a nonnegative initial probability density function 0 for the fokker planck equation which has finite relative entropy with respect to the maxwellian m associated with the spring potential in the model we prove via a limiting procedure on a pressure regularization parameter the existence of a global in time bounded energy weak solution t t u t t to the coupled navier stokes fokker planck system satisfying the initial condition 0 u 0 0 0 u 0 0

on positive definite solutions of the nonlinear matrix equations x a x q a q in this paper we investigate the nonlinear matrix equations x a x q a q 0 q 1 and x a x q a q q 1 necessary and sufficient conditions for the unique existence of hermitian positive definite solutions of these equations are derived effective iterative algorithms are also provided to obtain the unique solution of x a x q a q 0 q 1 and the minimal and maximal hermitian positive definite solutions of x a x q a q q 1 numerical examples are included to illustrate the efficiency of the presented iteration algorithms

global existence and uniqueness result for the diffusive peterlin viscoelastic model abstract the aim of this paper is to present the existence and uniqueness result for the diffusive peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids the polymers are treated as two beads connected by a nonlinear spring the peterlin approximation of the spring force is used to derive the equation for the conformation tensor the latter is the time evolution equation with spatial diffusion of the conformation tensor using the energy estimates we prove global in time existence of a weak solution in two space dimensions we are also able to show the regularity and consequently the uniqueness of the weak solution

on the hermitian positive definite solutions of nonlinear matrix equation x s σ m i 1 a i x t i a i q in this paper the hermitian positive definite solutions of nonlinear matrix equation x email protected i 1 ma i x t ia i q are considered where q is a hermitian positive definite matrix a i are nonsingular complex matrices s m are positive numbers and 0

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

on the nonlinear matrix equation x a f x a q solutions and perturbation theory abstract in this paper the nonlinear matrix equation x a f x a q is discussed sufficient conditions for the existence and uniqueness of a positive semidefinite solution are derived also conditions are given under which the solution depends continuously on the matrices a and q

hermitian solutions of the equation x q nx 1n we consider the matrix equation x q nx 1n its hermitian solutions are parametrized in terms of the generalized lagrangian eigenspaces of a certain matrix pencil we show that the equation admits both a largest and a smallest solution the largest solution corresponds to the unique positive definite solution the smallest solution is the unique negative definite solution if and only if n is nonsingular if n is singular no negative definite solution exists an interesting relation between the given equation and a standard algebraic riccati equation of kalman filtering theory is also obtained finally we present an algorithm which converges to the positive definite solution for a wide range of initial conditions

sensitivity of the knee joint response muscle forces and stability to variations in gait kinematics kinetics abstract sensitivity analysis of the knee joint response to variations in gait kinematics kinetics as reported in the literature is crucial for improved understanding and more effective prevention treatment strategies using our validated finite element musculoskeletal fe ms model of lower extremity we investigate the sensitivity of knee anterior cruciate ligament acl muscle and contact forces plus stability to the reported scatter in asymptomatic gait data three highly loaded stance instants 25 50 and 75 with five levels mean 0 5sd and sd for each of six knee joint angles moments are used employing taguchi approach 25 experiments and regression equations acl force drops significantly at larger flexion angles all periods and smaller internal moment at 75 only but increases with the flexion moment tibiofemoral tf medial lateral contact force partitioning is found contrary to the common claim most sensitive to changes in the adduction angle and not in the adduction moment total tf contact force increases significantly at greater moments but not angles especially in the sagittal plane forces in lateral hamstrings are significantly influenced by changes in adduction angles moments larger flexion moments at 25 and 50 significantly increase forces in quadriceps and on patellofemoral pf contact sagittal moment adduction moment at 75 and flexion angle at 25 contribute most to the joint stability a strong inverse correlation exists between the joint stability and the total tf compression force these findings can be exploited to adapt and modify intact injured and reconstructed knee joint responses during gait

on positive definite solutions of the family of matrix equations x a x n a q the nonlinear matrix equation x a x na q and properties of its positive definite solutions are studied sufficient conditions for existence the minimal xs and special x1 positive definite solutions are derived and iterative procedures for computing these solution are discussed

iterative solution of two matrix equations we study iterative methods for finding the maximal hermitian positive definite solutions of the matrix equations x a x 1 a q and x a x 1 a q where q is hermitian positive definite general convergence results are given for the basic fixed point iteration for both equations newton s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation numerical results are reported to illustrate the convergence behaviour of various algorithms

improved methods and starting values to solve the matrix equations x a x 1a i iteratively the two matrix iterations x k 1 i a x 1 k a are known to converge linearly to a positive definite solution of the matrix equations x a x 1 a i respectively for known choices of x 0 and under certain restrictions on a the convergence for previously suggested starting matrices x 0 is generally very slow this paper explores different initial choices of x 0 in both iterations that depend on the extreme singular values of a and lead to much more rapid convergence further the paper offers a new algorithm for solving the minus sign equation and explores mixed algorithms that use newton s method in part

existence of solution for a micro macro model of polymeric fluid the fene model abstract we analyse a non linear micro macro model of polymeric fluids in the case of a shear flow more precisely we consider the fene dumbbell model which models polymers by nonlinear springs accounting for the finite extensibility of the polymer chain we prove the existence of a unique solution to the stochastic differential equation which rules the evolution of a representative polymer in the flow and next deduce a local in time existence and uniqueness result on the system coupling the stochastic differential equation and the momentum equation on the fluid

on equations that are equivalent to the nonlinear matrix equation x a x α a q the nonlinear matrix equation x 1 a x aa q 0 email protected 1 is equivalent to the nonlinear matrix equation x a x aa q 0 email protected 1 the nonlinear matrix equation x 1 axa 1 a q 1 a is equivalent to the nonlinear matrix equation x 1 a x aa q 1 a the necessary and sufficient conditions for the existence of a positive definite solution of x 1 a x aa q 0 email protected 1 and x 1 axa 1 a q 1 a are given in the process two iterative algorithms are obtained estimations of the errors of the iterative algorithms are derived two numerical examples are given that demonstrate that the iterative algorithms are applicable

contractive maps on normed linear spaces and their applications to nonlinear matrix equations in this paper we will give necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space these conditions are already well known for maps on intervals in r using the conditions and banach s fixed point theorem we can prove a fixed point theorem for operators on a normed linear space the fixed point theorem will be applied to the matrix equation x in a f x a where f is a map on the set of positive definite matrices induced by a real valued map on 0 this will give conditions on a and f under which the equation has a unique solution in a certain set we will consider two examples of f in detail in one example the application of the fixed point theorem is the first step in proving that the equation has a unique positive definite solution under the conditions on a

global existence of weak solutions to the fene dumbbell model of polymeric flows systems coupling fluids and polymers are of great interest in many branches of sciences one of the most classical models to describe them is the fene finite extensible nonlinear elastic dumbbell model we prove global existence of weak solutions to the fene dumbbell model of polymeric flows the main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties the proof uses many weak convergence techniques in particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure in addition this quantity controls a rescaled defect measure of the gradient of the velocity

a three dimensional kinematic and dynamic model of the lower limb a model describing the kinematics and dynamics of the lower limb is presented the lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip knee and ankle joints each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom a method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study the gait variables are then used in an iterative newton euler formulation to compute the moments exerted about the axes of each joint during gait

positive solutions to x a bx 1 b abstract we study the positive semidefinite solutions to the matrix equation x a bx 1 b under the assumption that a 0 we show that a positive solution exists if and only if a certain block tridiagonal operator is positive in which case the solution is given by the shorted operator or generalized schur complement of that operator

spring like gait mechanics observed during walking in both young and older adults a spring loaded inverted pendulum model successfully demonstrated the oscillatory behavior of the center of mass com and corresponding ground reaction forces grfs of young healthy subjects this study questioned whether spring like leg walking dynamics are consistently observed in the walking of older adults that exhibit different gait characteristics such as slower gait speed from the young eight young and eight older adult subjects participated in overground walking experiments performed at four different gait speeds ranging from their self selected speed to a maximum walking speed to calculate the effective leg stiffness the damped compliant leg model with a curved foot was used the model parameters of leg stiffness and damping constant were optimized to achieve the best fit between model and human grfs data we observed that the grfs data from both age groups were reasonably well fitted by spring like leg dynamics throughout the broad range of gait speeds the leg stiffness and damping constant consistently increased as a function of the walking speed in both age groups but slightly greater variations of the model parameters were observed for the older adults trials the results imply that human walking dynamics and the variation with respect to age can be well captured by spring like leg dynamics

necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation x a x 1a q abstract we consider the problem of when the matrix equation x a x 1 a q has a positive definite solution here q is positive definite we study both the real and the complex case this equation plays a crucial role in solving a special case of the discrete time riccati equation we present both necessary and sufficient conditions for its solvability this result is obtained by using an analytic factorization approach moreover we present algebraic recursive algorithms to compute the largest and smallest the solution of the equation respectively finally we discuss the number of solutions

on the matrix equation x atx 1a i simple necessary and sufficient conditions for the matrix equation x atx 1a i to have a positive definite solution are given these conditions are used to explain some properties of the equation and to obtain new information finally we prove a conjecture on the extremal solutions

solving the nonlinear matrix equation x q i 1mmixδimi via a contraction principle abstract in this paper we consider the nonlinear matrix equation x q i 1 m m i x i m i where q is positive resp semidefinite definite and m i s are arbitrary resp nonsingular matrices we prove that if max i 1 i m 1 then the equation has a unique positive definite solution which is realized as the unique fixed point of a strict contraction with the lipschitz constant less than or equal to furthermore we show that the solution map varying over the determining coefficient matrices is continuous

on the hermitian positive definite solutions of nonlinear matrix equation xs a x ta q abstract nonlinear matrix equation xs a x ta q where a q are n n complex matrices with q hermitian positive definite has widely applied background in this paper we consider the hermitian positive definite solutions of this matrix equation with two cases s 1 0

effect of low pass filtering on joint moments from inverse dynamics implications for injury prevention analyses of joint moments are important in the study of human motion and are crucial for our understanding of e g how and why acl injuries occur such analyses may be affected by artifacts due to inconsistencies in the equations of motion when force and movement data are filtered with different cut off frequencies the purpose of this study was to quantify the effect of these artifacts and compare joint moments calculated with the same or different cut off frequency for the filtering of force and movement data 123 elite handball players performed sidestep cutting while the movement was recorded by eight 240 hz cameras and the ground reaction forces were recorded by a 960 hz force plate knee and hip joint moments were calculated through inverse dynamics with four different combinations of cut off frequencies for signal filtering movement 10 hz force 10 hz 10 10 movement 15 hz force 15 hz movement 10 hz force 50 hz 10 50 movement 15 hz force 50 hz the results revealed significant differences especially between conditions with different filtering of force and movement mean sd peak knee abduction moment for the 10 10 and 10 50 condition were 1 27 0 53 and 1 64 0 68 nm kg respectively ranking of players based on knee abduction moments were affected by filtering condition out of 20 players with peak knee abduction moment higher than mean 1 sd with the 10 50 condition only 11 were still above mean 1 sd when the 10 10 condition was applied hip moments were very sensitive to filtering cut off mean sd peak hip flexion moment was 3 64 0 75 and 5 92 1 80 under the 10 10 and 10 50 conditions respectively based on these findings force and movement data should be processed with the same filter conclusions from previous inverse dynamics studies where this was not the case should be treated with caution

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

well posedness for the dumbbell model of polymeric fluids the dumbbell model is a coupled hydrodynamic kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations we prove well posedness of this model by deriving directly a priori estimates on the stochastic model our results can be used to analyze stochastic simulation methods such as the ones that are based on brownian configuration fields

solution of a class of nonlinear matrix equations abstract in this paper we solve nonlinear matrix equations of the form x q i 1 p a i f i x a i r i and x q i 1 p a i f i x a i r i j 1 q b j g j x b j q j where 1 1 r i q j 1 1 q p n the collection of all n n hermitian positive definite matrices and a i b j s are n n matrices also f i g j s are monotone mappings from p n into p n examples are given to illustrate that the equations can not be solved by previously known theorems

existence of global weak solutions to finitely extensible nonlinear bead spring chain models for dilute polymers with variable density and viscosity abstract we prove the existence of global in time weak solutions to a general class of coupled bead spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains with finitely extensible nonlinear elastic fene spring potentials the class of models under consideration involves the unsteady incompressible navier stokes equations with variable density and density dependent dynamic viscosity in a bounded domain in r d d 2 or 3 for the density the velocity and the pressure of the fluid with an elastic extra stress tensor appearing on the right hand side in the momentum equation the extra stress tensor stems from the random movement of the polymer chains and is defined by the kramers expression through the associated probability density function that satisfies a fokker planck type parabolic equation a crucial feature of which is the presence of a centre of mass diffusion term and a nonlinear density dependent drag coefficient we require no structural assumptions on the drag term in the fokker planck equation in particular the drag term need not be corotational with initial density 0 min max for the continuity equation where min 0 a square integrable and divergence free initial velocity datum u 0 for the navier stokes equation and a nonnegative initial probability density function 0 for the fokker planck equation which has finite relative entropy with respect to the maxwellian m associated with the spring potential in the model we prove via a limiting procedure on certain regularization parameters the existence of a global in time weak solution t t u t t to the coupled navier stokes fokker planck system satisfying the initial condition 0 u 0 0 0 u 0 0 such that t t min max t u t belongs to the classical leray space and t t has bounded relative entropy with respect to m and t t m has integrable fisher information w r t the gibbs measure d m q d q d x over any time interval 0 t t 0

solvability and sensitivity analysis of polynomial matrix equation xs atxta q abstract in this paper we present a sufficient condition for the existence of the symmetric positive definite solution of polynomial matrix equation x s a t x t a q where s t are both nonnegative integers a q r n n and q 0 we firstly define the condition number of the unique spd solution and reduce its representation form we also give the algebraic perturbation analysis of the unique spd solutions with respect to perturbations of matrices a and q

positive definite solutions of the matrix equations x a x q a q q 1 in this paper we investigate nonlinear matrix equations x a x qa q where q 1 we derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations we provide a sufficient condition for the equation x a x qa q to have two different positive definite solutions and several sufficient conditions for the equation x a x qa q to have a unique positive definite solution we also propose iterative methods for obtaining positive definite solutions of these equations numerical examples are given to illustrate the effectiveness of the methods

on positive definite solutions of nonlinear matrix equation xs a x ta qxs a x ta q in this paper the nonlinear matrix equation xs a x ta qxs a x ta q is investigated based on the fixed point theory the existence and the uniqueness of the positive definite solution are studied an effective iterative method to obtain the unique positive definite solution is established given a q 1 s ts st in addition some computable estimates of the unique positive definite solution are derived finally numerical examples are given to illustrate the effectiveness of the algorithm and the perturbation estimates

positive definite solutions of the nonlinear matrix equation x a xqa q q 0 abstract in this paper the nonlinear matrix equation x a x q a q q 0 is investigated some necessary and sufficient conditions for existence of hermitian positive definite solutions of the nonlinear matrix equations are derived an effective iterative method to obtain the positive definite solution is presented some numerical results are given to illustrate the effectiveness of the iterative methods

iterative methods for the extremal positive definite solution of the matrix equation x a x αa q in this paper the inversion free variant of the basic fixed point iteration methods for obtaining the maximal positive definite solution of the nonlinear matrix equation x a x aa q with the case 0 1 are proposed some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived numerical examples to illustrate the behavior of the considered algorithms are also given

global well posedness for the 2d micro macro models in the bounded domain in this paper we establish new a priori estimates for the coupled 2d navier stokes equations and fokker planck equation as its applications we prove the global existence of smooth solutions for the coupled 2d micro macro models for polymeric fluids in the bounded domain