runge kutta discontinuous galerkin methods with weno limiter for the special relativistic hydrodynamics this paper develops the p k based runge kutta discontinuous galerkin rkdg methods with weno limiter for the one and two dimensional special relativistic hydrodynamics k 1 2 3 which is an extension of the work j x qiu c w shu runge kutta discontinuous galerkin method using weno limiters siam j sci comput 26 2005 907 929 the weno limiter for the rkdg method is adaptively implemented via two following steps the troubled cells are first identified by using a tvb modified minmod function and then a new polynomial solution inside the troubled cells is locally reconstructed to replace the rkdg solution by using the weno technique based on the cell average values of the rkdg solution in the neighboring cells as well as the original cell averages of the troubled cells several test problems in one and two dimensions are computed using the developed rkdg methods with weno limiter the computations demonstrate that our methods are stable accurate and robust in maintaining accuracy for simulating flows in the special relativistic hydrodynamics

minimal structure in the block decoupling problem with stability abstract in this paper we consider the block decoupling problem with stability we characterize the minimal mcmillan degree achievable for the block decoupled system for this we introduce a new list of integers which are feedback invariant these integers are related in a simple way to the minimal number of unstable and infinite zeros of the block decoupled system

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

a well balanced approach for flows over mobile bed with high sediment transport in this paper we deal with the numerical computation of one dimensional unsteady free surface flows over mobile bed we focus on flows characterized by high concentration of sediments and strong interaction between flow and bottom dynamics as in hyper concentrated and debris flows these features are fully considered in the adopted system of equations challenging in its numerical approximation is the preservation of the coupling and the treatment of a non conservative flux in the momentum equation in order to devise a new godunov type approach we analyzed in detail the riemann problem associated with the mobile bed phenomena and the peculiar features of its wave relations the scheme we developed is based on two supports well balanced treatment of the variable updating at the new time level and flux evaluation by three wave approximations of the intercell riemann problem that without any split embody the effect of the non conservative term the properties of the new numerical strategy named awb are assessed by comparison with exact solutions of riemann problems built by handling an inverse technique finally awb has been applied to cases of practical interest where wave interaction and friction effects makes the flow more complex the obtained results point out that the new method is able to predict faithfully the overall behaviour of the solution and of any type of waves the use of awb in this one dimensional frame is therefore fostered in representing rapid transients in river torrent flows with movable bed

physical constraints preserving lagrangian finite volume schemes for one and two dimensional special relativistic hydrodynamics abstract this paper studies the physical constraints preserving pcp lagrangian finite volume schemes for one and two dimensional special relativistic hydrodynamic rhd equations first the pcp property i e preserving the positivity of the rest mass density and the pressure and the bound of the velocity is proved for the first order accurate lagrangian scheme with the hllc riemann solver and forward euler time discretization the key is that the intermediate states in the hllc riemann solver are shown to be admissible or pcp when the hllc wave speeds are estimated suitably then the higher order accurate schemes are proposed by using the high order accurate strong stability preserving ssp time discretizations and the scaling pcp limiter as well as the weno reconstruction finally several one and two dimensional numerical experiments are conducted to demonstrate the accuracy and the effectiveness of the pcp lagrangian schemes in solving the special rhd problems involving strong discontinuities or large lorentz factor or low rest mass density or low pressure etc

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

asymptotics of convex sets in euclidean and hyperbolic spaces we study convex sets c of finite but non zero volume in and we show that the intersection c8 of any such set with the ideal boundary of has minkowski and thus hausdorff dimension of at most n 1 2 and this bound is sharp at least in some dimensions n we also show a sharp bound when c8 is a smooth submanifold of in the hyperbolic case we show that for any k n 1 2 there is a bounded section s of c through any prescribed point p and we show an upper bound on the radius of the ball centered at p containing such a section we show similar bounds for sections through the origin of a convex body in and give asymptotic estimates as 1kn

the busemann petty problem via spherical harmonics abstract the busemann petty problem asks whether symmetric convex bodies in r n with smaller central hyperplane sections necessarily have smaller n dimensional volume the solution has recently been completed and the answer is affirmative if n 4 and negative if n 5 in this article we present a short proof of the affirmative result and its generalization using the funk hecke formula for spherical harmonics

a direct eulerian grp scheme for relativistic hydrodynamics two dimensional case this paper develops a direct eulerian generalized riemann problem grp scheme for two dimensional 2d relativistic hydrodynamics rhd it is an extension of the grp scheme for one dimensional 1d rhds z c yang p he h z tang j comput phys 230 2011 7964 7987 and the grp scheme for the non relativistic hydrodynamics m ben artzi j q li g warnecke j comput phys 218 2006 19 43 in order to derive the direct eulerian grp scheme the local grp of the split 2d rhd equations in the eulerian formulation has to be directly resolved by using corresponding riemann invariants and rankine hugoniot jump conditions so that the crucial and delicate lagrangian treatment in the original grp scheme m ben artzi j falcovitz j comput phys 55 1984 1 32 may be avoided an important difference of resolving the grp of the split 2d rhd equations from the grp of the 1d rhd equations or the non relativistic hydrodynamical equations is coming from the fact that the flow regions across the shock or rarefaction wave in the grp of the split 2d rhd equations are nonlinearly coupled through the lorentz factor which is also built in terms of the tangential velocities it is a purely multi dimensional relativistic feature several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed 2d grp scheme

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

structure smith macmillan form and coprime mfds of a rational matrix inside a region p ω abstract the structure of the smith macmillan form of a rational matrix t s inside a region p where is asymmetric with respect to the real axis subset of the finite complex plane c is determined algorithmic procedures based on elementary row and column operations over the euclidean ring r p s consisting of all rational functions with no poles in p are given coprimeness in p of a pair of rational matrices is studied in detail these results lead to constructive procedures for determining the coprime in p matrix fraction descriptions of t a

the minimal delay decoupling problem feedback implementation with stability in this paper we solve the minimal delay decoupling problem of linear multivariable systems we look for feedback implementable solutions which moreover guarantee closed loop stability we prove that dynamic state feedback decoupling with stability is achievable if the number of independent inputs is large enough to compensate the intrinsic nondecouplability of the system we introduce new feedback invariants characterizing the minimal number of infinite and unstable zeros of the decoupled system

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

an iterative riemann solver for relativistic hydrodynamics an approximate method for solving the riemann problem is needed to construct godunov schemes for relativistic hydrodynamical equations such an approximate riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous therefore jump conditions for shocks are approximately used for rarefaction waves the solver is easy to implement in a godunov scheme and converges rapidly for relativistic hydrodynamics the fast convergence of the solver indicates the potential of a higher performance of a godunov scheme in which the solver is used

linear feedback decoupling transfer function analysis the problem of linear system decoupling is examined based on recent results on linear feedback new insight is obtained through which resolution of the decoupliug problem is accomplished by calculations performed directly on the given transfer matrix computation of the decoupling compensators follows by easy constructions the problem of feedback block decoupling with internal stability is also formulated and resolved

feedback block decoupling and infinite structure of linear systems abstract using factorizations at infinity of the transfer matrix two interesting necessary and sufficient conditions arc obtained for the block decoupling problem of linear systems by state feedback and a constant non singular input transformation these conditions are expressed in a very simple way in terms of integers which are feedback invariants for the system under consideration these feedback invariants are related either to the system infinite structure or to the reachability indices of the feedback reduced system

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

invariant spaces at infinity of linear systems application to block decoupling the dynamic state feedback block decoupling problem in the general case i e with singular or nonsingular input transformations is solved it is proven that the problem is solvable if the number of inputs is large enough the main tools for this study are some invariant spaces associated with the columns infinite behavior of a rational matrix it turns out that when the problem is solvable it is also solvable with stability

block decoupling by precompensation revisited the block decoupling problem by admissible dynamic precompensation for lti systems is considered admissibility refers to the preservation of the class of controlled output trajectories i e functional output controllability is concerned which is more demanding than just pointwise output controllability this problem has been solved by hautus and heyman within a transfer function matrix approach different new equivalent solvability conditions in terms of controllability subspaces transfer function matrices or matrix pencils are given one of these conditions expressed in the input space is at the origin of new necessary and sufficient conditions for block decoupling by general precompensation possibly non admissible and nonsquare in the wider sense of basile and marro

a positive answer to the busemann petty problem in three dimensions we prove that in e3 the busemann petty problem concerning cen tral sections of centrally symmetric convex bodies has a positive answer together with other results this settles the problem in each dimension

new feedback invariants and the block decoupling problem a new list of feedback invariant integers is introduced we give several equivalent characterizations of these invariants within both geometric and transfer matrix approaches when solving the block decoupling problem it turns out that when decoupling is possible these integers represent the minimal mcmillan degree achievable for the blocks of the decoupled system

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

the block essential orders and the dynamic block decoupling problem abstract in recent papers 8 it has been pointed out that two invariant lists of integers the infinite zero orders and the essential orders play a key role in the solution of the so called morgan s problem i e the row by row decoupling problem the purpose of the present paper is to define the block essential orders of a linear system with respect to the block decoupling problem this is done through a new dynamic solution to the latter based upon a procedure which extends to the block case that previously given in 15 for morgan s problem this procedure is minimal in the sense that it leads to the least infinite zero structure for any decoupled system reachable from the original one

a complement about almost controllability subspaces abstract we show that for any almost controllability subspace there exist a maximal input chain and a family of state feedbacks which lead to the well known feedback chain expression for this subspace

a definition of column reduced proper rational matrices the aim of this work is to develop analogue concepts of column reduced polynomial matrices for proper rational matrices a definition of column reducedness for a class of proper rational matrices is proposed and the properties of such matrices are studied in particular reduction to column reduced form by elementary operations over the ring of proper rational functions and the relationship between the degrees of the invariant factors of a column reduced matrix and the so defined column indices the physical significance of such matrices in terms of their finite structure is explained this interpretation completely complements the physical interpretation of a column reduced polynomial matrix an application of the properties of column reduced proper rational matrices to the decoupling problem is also presented the infinite structure which can be obtained while decoupling a linear multivariable system by non regular static state feedback is completely characterized

on the structure at infinity of linear block decouplable systems the general case the aim of this note is to show that a linear system c a b is block decouplable by means of static state feedback laws f g with g invertible if and only if the infinite structure of c a b equals the union of the infinite structures of the subsystems c i a b extracted from the given output partition this result generalizes the ones recently obtained for morgan s problem 6 and for the particular cases of right invertible 7 or left invertibie 8 systems

block decoupling and pole assignment of singular systems a frequency domain approach the problem of block decoupling of singular systems via state feedback and regular input transformation is solved by following an approach based on the matrix fraction description mfd of the system the solvability condition is obtained from the numerator matrix of a coprime and column reduced mfd of the given system the characterization of the fixed poles is given and it is shown that all the non fixed poles can be arbitrarily assigned

decoupling through specified input output channels with internal stability abstract a system with two sets of inputs u 1 u 2 and two sets of outputs y 1 y 2 is considered the objective is to construct a dynamic feedback compensator between u 1 and y 1 so that the closed loop transfer matrix between u 2 and y 2 is diagonal and nonsingular internal stability of the closed loop system is also required this problem can be regarded as the general version of the standard diagonal decoupling problem where the output to be controlled decoupled and the measured output are not distinguished along these lines it is shown that the diagonal causality degree dominance dcdd which is the key concept in standard diagonal decoupling problems also arises in the present context in a modified form the first modification is due to the constraint of internal stability which gives rise to a new notion diagonal stability and causality degree dominance dscdd these two notions are investigated in the first part of the paper the second modification comes from the crosschannel transfer matrices between u 1 and y 2 and u 2 and y 1 this yields another new notion joint essential stability functions the solvability conditions of the problem are expressed in terms of the properties of the subrings of the ring of stable and proper rational functions and their quotient rings these subrings are generated by joint essential stability functions of the cross channel transfer matrices the degrees of the joint essential stability functions are called the joint essential stability orders which are extensions of the well known essential orders and essential stability orders to the problem considered here

two dimensional relativistic euler equations in a convex duct abstract in this paper we investigate the motion of supersonic flow governed by 2 d steady isentropic irrotational relativistic euler system entered into a convex duct we will give the propagation and interactions of rarefaction waves between the upward and downward wall and obtain the global existence of piecewise continuous solutions furthermore in some cases the vacuum state may appear and we also give a sufficient condition to the appearance of the vacuum in finite domain

bound preserving discontinuous galerkin methods for relativistic hydrodynamics in this paper we develop a discontinuous galerkin dg method to solve the ideal special relativistic hydrodynamics rhd and design a bound preserving bp limiter for this scheme by extending the idea in x zhang and c w shu 2010 56 for rhd the density and pressure are positive and the velocity is bounded by the speed of light one difficulty in numerically solving the rhd in its conservative form is that the failure of preserving these physical bounds will result in ill posedness of the problem and blowup of the code especially in extreme relativistic cases the standard way in dealing with this difficulty is to add extra numerical dissipation while in doing so there is no guarantee of maintaining the high order of accuracy our bp limiter has the following features it can theoretically guarantee to preserve the physical bounds for the numerical solution and maintain its designed high order accuracy the limiter is local to the cell and hence is very easy to implement moreover it renders l 1 stability to the numerical scheme numerical experiments are performed to demonstrate the good performance of this bound preserving dg scheme even though we only discuss the bp limiter for dg schemes it can be applied to high order finite volume schemes such as weighted essentially non oscillatory weno finite volume schemes as well

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

set of open loop block diagonalizers of transfer matrices abstract the set of open loop right block diagonalizers of a given p m transfer matrix z with specified block sizes is studied a characterization of this set is obtained in terms of a maximal open loop block diagonalizer and a minimal proper basis of the kernel of z the relevance of the results to some non interacting control problems is pointed out in particular the results obtained yield a minimum delay solution to the block decoupling problem using dynamic state feedback

block decoupling of generalized state space systems abstract the problem of input output block decoupling of generalized state space systems via a regular static state feedback law is studied for the first time the necessary and sufficient conditions for the problem to have a solution are established the necessary and sufficient conditions for block decoupling with simultaneous stabilizability and the necessary and sufficient conditions for block decoupling with simultaneous arbitrary assignment of the system poles are established 1997 elsevier science ltd

finite volume local evolution galerkin method for two dimensional relativistic hydrodynamics the paper proposes a second order accurate finite volume local evolution galerkin fvleg method for two dimensional special relativistic hydrodynamical rhd equations instead of using the dimensional splitting method or solving one dimensional local riemann problem in the direction normal to cell interface the fvleg method couples a finite volume formulation with the genuinely multi dimensional approximate local evolution operator which is derived by evolving the solutions of corresponding locally linearized rhd equations along all bicharacteristic directions several numerical examples are given to demonstrate the accuracy and the performance of the proposed fvleg method