construction of binary four and five point non stationary subdivision schemes from hyperbolic b splines binary non stationary four and five point subdivision schemes have been developed using hyperbolic b spline basis functions the proposed subdivision schemes generate pleasing curves near the control polygon as compared to the existing non stationary subdivision schemes developed using trigonometric b splines basis functions the main speciality of the hyperbolic subdivision schemes is that they can regenerate hyperbolas and parabolas quite efficiently

generation of fractal curves and surfaces using ternary 4 point interpolatory subdivision scheme in this paper the generation of fractal curves and surfaces along with their properties using ternary 4 point interpolatory subdivision scheme with one parameter are analyzed the relationship between the tension parameter and the fractal behavior of the limiting curve is demonstrated through different examples the specific range of the tension parameter has also been depicted which provides a clear way to generate fractal curves since the fractal scheme introduces in the paper have more number of control points therefore it gives more degree of freedom to control the shape of the fractal curve

fractal behavior of ternary 4 point interpolatory subdivision scheme with tension parameter in this paper the fractal curves and surfaces of ternary 4 point interpolatory subdivision scheme are developed and analyzed the fractal range of the tension parameter has also been determined the behavior of fractal curves and surfaces corresponding to different values of parameter has been depicted through six examples which offers direct means for an effective generation of subdivision fractals the real life applications of the proposed fractal subdivision scheme has also been demonstrated

shape controlled interpolatory ternary subdivision ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same or higher smoothness but smaller support in this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements we show that both these features can be included in a unique interpolating 4 point subdivision method by means of non stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes this is realized by exploiting local shape parameters associated with the initial polyline edges

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

hyperbolic forms of ternary non stationary subdivision schemes originated from hyperbolic b splines in this work ternary non stationary subdivision schemes based on hyperbolic b spline basis functions have been presented the proposed hyperbolic ternary three point and four point subdivision schemes give pleasing as well as consistent curves with the control polygons as compared to the existing non stationary subdivision schemes obtained from trigonometric b splines the main speciality of the hyperbolic schemes is that they can reproduce hyperbolas and parabolas quite efficiently which has been demonstrated with the help of curvature plots

from approximating subdivision schemes for exponential splines to high performance interpolating algorithms in this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension in particular throughout this paper we will focus on the derivation of 6 point interpolating schemes that turn out to be unique in combining vital ingredients like c 2 continuity simplicity of definition ease of implementation user independency tension control and ability to reproduce salient trigonometric and transcendental curves

lower upper symmetric gauss seidel method for the euler and navier stokes equations on developpe un schema de relaxation multigrille application a des ecoulements transsoniques

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

convergence to travelling waves for quasilinear fisher kpp type equations we consider the cauchy problem ut u xx u t x r r u 0 x u0 x x r when the increasing function satisfies that 0 0 and the equation may degenerate at u 0 in the case of 0 0 we consider the case of u0 l r 0 u0 x 1 a e x r and the special case of u u u we prove that the solution approaches the travelling wave solution with speed c 1 spreading either to the right or to the left or to the two travelling waves moving in opposite directions

binary 3 point and 4 point non stationary subdivision schemes using hyperbolic function in this paper binary 3 point and 4 point non stationary subdivision schemes are presented using hyperbolic function as basis function asymptotic equivalence method is used to investigate the continuity of the proposed schemes comparison between the proposed schemes their stationary counterparts and some existing non stationary schemes has been depicted through examples it can be observed that the proposed schemes have the capability to reproduce conics particularly parabola

optimal shape design of a two dimensional asymmetric diffuser in turbulent flow an optimal shape of two dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm the initial diffuser is taken to be a two dimensional asymmetric diffuser for which much experimental and numerical data are available the reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1 8 10 4 f rom this initial shape optimal diffuser shapes are designed for six different geometric constraints such as the streamwise length and height of the diffuser the optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall the turbulent flow inside the diffuser is predicted using the k v2 f model and optimal shapes are obtained through iterative procedures to satisfy the optimality condition with the shape design flow separation that appeared in the initial diffuser is completely removed or significantly reduced for one of the optimal diffuser shapes obtained large eddy simulation is carried out to validate the result of the shape design the wall shear stress wall pressure mean velocity and turbulence quantities obtained from large eddy simulation are in good agreement with those from the simulation using the turbulence model

the γ limit of traveling waves in the fitzhugh nagumo system abstract patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems a common theme in investigating such systems is to identify the intrinsic factors responsible for such self organization the convergence is a well known technique applicable to variational formulations of concentration phenomena of stable patterns recently a geometric variational functional associated with the limit of standing waves of the fitzhugh nagumo system has been built this article studies the limit of traveling waves to the best of our knowledge this is the first attempt to expand the scope of applicability of convergence to cover non stationary problems

linear vs nonlinear selection for the propagation speed of the solutions of scalar reaction diffusion equations invading an unstable equilibrium we revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction diffusion equations with one linearly stable and one linearly unstable equilibrium for a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension we introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism we obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable our method also allows us to obtain efficient lower and upper bounds for the propagation speed c

optimizing a boundary layer ingestion offset inlet by discrete adjoint approach a large amount of low momentum boundary layer flow ingesting into a flush mounted inlet can cause significant total pressure loss and distortion to the extent beyond operability of a fan compressor to improve the quality of incoming flow into the engine shape optimization of the surface geometry at the inlet entrance has been carried out using the discrete adjoint method the inlet floor shape is parameterized by the use of control points on b spline surface patches to resolve the complicated geometry flexibly and wall bounded turbulent flow accurately an overset mesh system is well suited for integrating the flow analysis code sensitivity analysis code and grid modification tools to enhance the convergence characteristics of the sensitivity analysis code additional numerical dissipation for the discrete adjoint formulation is introduced after using this optimization procedure the new inlet yields a significant improvement in performance a more than 50 reduction in flow distortion and a 3 increase in total pressure recovery high performance at off design conditions is also realized with only slight degradation confirming the capability of the adjoint method for a practical design problem finally the physical meaning and implication of the performance improvement are elaborated upon in relation to the flow characteristics resulting from the new design

a new non stationary binary 6 point subdivision scheme in this paper the hyperbolic form of binary 6 point interpolating non stationary subdivision scheme has been constructed using the hyperbolic function some of the important properties of the proposed scheme has been discussed the comparison of the proposed scheme with the trigonometric form of binary 6 point interpolatory non stationary scheme is depicted through examples which indicate that the proposed scheme not only accommodates and is more consistent with the control polygon but also generates pleasing curves corresponding to the larger parametric values in and outside the parametric interval as compared to the trigonometric form of binary 6 point scheme developed by daniel et al comparison with some other interpolating non stationary subdivision schemes has also been demonstrated

analysis of asymptotically equivalent binary subdivision schemes non stationary uniform subdivision schemes are presented including some important examples as the up function and exponential splines the multivariate analysis of subdivision schemes is extended to a class of non stationary schemes which are asymptotically equivalent to converging stationary or non stationary schemes

an interpolating 6 point c2 non stationary subdivision scheme in this paper we consider a 6 point interpolating c 2 binary non stationary subdivision scheme and present some of its important properties we highlight some advantages of the scheme and demonstrate its performance by some examples

minimal speed selection of traveling waves to the lotka volterra competition model abstract in this paper the minimal speed determinacy of traveling wave fronts of a two species competition model of diffusive lotka volterra type is investigated first a cooperative system is obtained from the classical lotka volterra competition model then we apply the upper lower solution technique on the cooperative system to study the traveling waves as well as its minimal speed selection mechanisms linear or nonlinear new types of upper and lower solutions are established previous results for the linear speed selection are extended and novel results on both linear and nonlinear selections are derived

traveling waves for the fitzhugh nagumo system on an infinite channel abstract we are concerned with the traveling wave solutions for the fitzhugh nagumo system on an infinite channel based on a variational formulation in which a non local term depends on a parameter the speed of a traveling wave can be selected out furthermore to show the existence of a traveling wave solution with such a speed we seek a minimizer subject to a constraint in the way of solving the variational problem we apply a truncation technique to the nonlocal term to obtain a minimizer located in a bounded invariant region