the generalized nonlinear initial boundary riemann problem for quasilinear hyperbolic systems of conservation laws abstract in this paper we study the nonlinear initial boundary riemann problem and the generalized nonlinear initial boundary riemann problem for quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions on the domain t x t 0 x 0 under the assumption that each positive eigenvalue is either linearly degenerate or genuinely nonlinear we get the existence and uniqueness of the self similar solution to the nonlinear initial boundary riemann problem and of the global piecewise c 1 solution containing only shocks and or contact discontinuities to the corresponding generalized nonlinear initial boundary riemann problem it shows that the self similar solution to the nonlinear initial boundary riemann problem possesses the global structural stability

predictive un distortion model and 3 d reconstruction by biplane snakes this paper is concerned with the three dimensional 3 d reconstruction of coronary vessel centerlines and with how distortion of x ray angiographic images affects it angiographies suffer from pincushion and other geometrical distortions caused by the peripheral concavity of the image intensifier ii and the nonlinearity of electronic acquisition devices in routine clinical practice where a field of view fov of 17 23 cm is commonly used for the acquisition of coronary vessels this distortion introduces a positional error of up to 7 pixels for an image matrix size of 512 spl times 512 and an fov of 17 cm this error increases with the size of the fov geometrical distortions have a significant effect on the validity of the 3 d reconstruction of vessels from these images we show how this effect can be reduced by integrating a predictive model of un distortion into the biplane snakes formulation for 3 d reconstruction first we prove that the distortion can be accurately modeled using a polynomial for each view also we show that the estimated polynomial is independent of focal length but not of changes in anatomical angles as the ii is influenced by the earth s magnetic field thus we decompose the polynomial into two components the steady and the orientation dependent component we determine the optimal polynomial degree for each component which is empirically determined to be five for the steady component and three for the orientation dependent component this fact simplifies the prediction of the orientation dependent polynomial since the number of polynomial coefficients to be predicted is lower the integration of this model into the biplane snakes formulation enables us to avoid image unwarping which deteriorates image quality and therefore complicates vessel centerline feature extraction moreover we improve the biplane snake behavior when dealing with wavy vessels by means of using generalized gradient vector flow our experiments show that the proposed methods in this paper decrease up to 88 the reconstruction error obtained when geometrical distortion effects are ignored tests on imaged phantoms and real cardiac images are presented as well

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

blow up of solutions to the initial boundary value problem for quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal 66 1 2007 93 124 in the present paper we study the global structure instability of the self similar solution u u x t containing shocks contact discontinuities and at least one rarefaction wave of the initial boundary riemann problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 our result indicates that the kind of riemann solution u u x t mentioned above is globally structurally unstable as an application of our result we consider the model proposed by aw and rascle a aw m rascle resurrection of second order models of traffic flow siam j appl math 60 2000 916 938 describing traffic flow on a road network following the work of garavello and piccoli m garavello b piccoli traffic flow on a road network using the aw rascle model comm partial differential equations 31 2 2006 243 275 we prove the nonexistence of global piecewise c 1 solution containing one rarefaction wave of the initial boundary value problem for this model

global structure instability of riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal tma 66 1 2007 93 124 in this paper we study the global structure instability of the riemann solution u u x t containing shocks at least one rarefaction wave for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane our result indicates that this kind of riemann solution u u x t mentioned above for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given

shock reflection for a system of hyperbolic balance laws abstract this paper concerns shock reflection for a system of hyperbolic balance laws in one space dimension it is shown that the generalized nonlinear initial boundary riemann problem for a system of hyperbolic balance laws with nonlinear boundary conditions in the half space t x t 0 x 0 admits a unique global piecewise c 1 solution u u t x containing only shocks with small amplitude and this solution possesses a global structure similar to that of self similar solution u u x t of the corresponding homogeneous riemann problem if each characteristic field with positive velocity is genuinely nonlinear and the corresponding homogeneous riemann problem has only shocks but no centered rarefaction waves and contact discontinuities this result is also applied to shock reflection for the flow equations of a model class of fluids with viscosity induced by fading memory

extremely large scale simulation of a kardar parisi zhang model using graphics cards the octahedron model introduced recently has been implemented onto graphics cards which permits extremely large scale simulations via binary lattice gases and bit coded algorithms we confirm scaling behavior belonging to the two dimensional kardar parisi zhang universality class and find a surface growth exponent 0 2415 15 on 2 17 2 17 systems ruling out 1 4 suggested by field theory the maximum speedup with respect to a single cpu is 240 the steady state has been analyzed by finite size scaling and a growth exponent 0 393 4 is found correction to scaling exponent are computed and the power spectrum density of the steady state is determined we calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered we provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

novel approach for 3 d reconstruction of coronary arteries from two uncalibrated angiographic images three dimensional reconstruction of vessels from digital x ray angiographic images is a powerful technique that compensates for limitations in angiography it can provide physicians with the ability to accurately inspect the complex arterial network and to quantitatively assess disease induced vascular alterations in three dimensions in this paper both the projection principle of single view angiography and mathematical modeling of two view angiographies are studied in detail the movement of the table which commonly occurs during clinical practice complicates the reconstruction process on the basis of the pinhole camera model and existing optimization methods an algorithm is developed for 3 d reconstruction of coronary arteries from two uncalibrated monoplane angiographic images a simple and effective perspective projection model is proposed for the 3 d reconstruction of coronary arteries a nonlinear optimization method is employed for refinement of the 3 d structure of the vessel skeletons which takes the influence of table movement into consideration an accurate model is suggested for the calculation of contour points of the vascular surface which fully utilizes the information in the two projections in our experiments with phantom and patient angiograms the vessel centerlines are reconstructed in 3 d space with a mean positional accuracy of 0 665 mm and with a mean back projection error of 0 259 mm this shows that the algorithm put forward in this paper is very effective and robust

anisotropic ballistic deposition model with links to the ulam problem and the tracy widom distribution we compute exactly the asymptotic distribution of scaled height in a 1 1 dimensional anisotropic ballistic deposition model by mapping it to the ulam problem of finding the longest nondecreasing subsequence in a random sequence of integers using the known results for the ulam problem we show that the scaled height in our model has the tracy widom distribution appearing in the theory of random matrices near the edges of the spectrum our result supports the hypothesis that various growth models in 1 1 dimensions that belong to the kardar parisi zhang universality class perhaps all share the same universal tracy widom distribution for the suitably scaled height variables

initial boundary value problems for conservation laws abstract we establish some general concepts concerning boundary conditions for systems of conservation laws defined on one dimensional space intervals and prove some general results among these is an extension of glimm s existence theorem to initial boundary value problems we also prove the convergence of the time averages of the solutions to certain initial boundary value problems for systems arising in fluid flows in porous media isentropic gas dynamics and elasticity theory

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

reconstructing the 3 d medial axes of coronary arteries in single view cineangiograms describes a technique for reconstructing the skeletal structure of coronary arteries from a succession of frames of a single view cineangiogram the authors use local features in each frame to determine correspondences of arterial segments in successive frames they define a similarity measure in 2d image space as the change in angular coordinates of corresponding pairs they use a form of gradient descent to find those depth coordinates that minimize the average deviation of the 3d angular coordinates of all points on the skeleton from the coordinates produced by a 3d scaling transformation in experiments with software models the reconstruction error was approximately two pixels when the initial guessed reconstruction was as large as 30 pixels

statistics of layered zigzags a two dimensional generalization of tasep a novel discrete growth model in 2 1 dimensions is presented in three equivalent formulations i directed motion of zigzags on a cylinder ii interacting interlaced tasep layers and iii growing heap over 2d substrate with a restricted minimal local height gradient we demonstrate that the coarsegrained behavior of this model is described by the two dimensional kardar parisi zhang equation the coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow density curve the so called fundamental diagram a conjecture concerning the analytical form of this flow density curve is presented and is verified numerically

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

global weakly discontinuous solutions for hyperbolic conservation laws in the presence of a boundary abstract this work is a continuation of our previous work in the present paper we study the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws with non linear boundary conditions in the half space t x t 0 x 0 under the assumption that each characteristic with positive velocity is linearly degenerate we prove the existence and uniqueness of global weakly discontinuous solution u u t x with small amplitude and this solution possesses a global structure similar to that of the self similar solution u u x t of the corresponding riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in physics and other disciplines particularly to the system describing the motion of the relativistic string in minkowski space r 1 n are also given

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process