generation of converging regge pole bounds a new formulation of complex rotation quantization we propose an unprecedented bounding theory which generates converging bounds to the regge poles of rational fraction scattering potentials this is made possible by the recent work of handy 2001 j phys a math gen 34 l271 and handy and wang 2001 j phys a math gen 34 8297 which transforms the schrodinger equation into an equivalent fourth order linear differential equation for the probability density this new representation is better suited for numerical considerations since the rapid oscillations of the regge pole wavefunction are factored out more importantly the moments of the probability density can be constrained and thereby the underlying complex angular momentum parameter of the effective potential function through appropriate moment problem theorems as incorporated within the eigenvalue moment method of handy and bessis 1985 phys rev lett 55 931 and handy et al 1988 phys rev lett 60 253

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

the barrier transmission problem treated by the amplitude phase method and expressed in terms of an invariant of the ermakov lewis type transmission and reflection of a quantal particle by a single hump potential barrier are analysed by means of an amplitude phase decomposition of the wavefunction on both sides of the barrier the amplitude phase analysis of the wavefunction provides a particular invariant of the ermakov lewis type which originates in the matching process the transmission and reflection coefficients turn out to be simple functions of this invariant numerical calculations of the invariant for an eckart epstein potential barrier provide very accurate results

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

phase transitions for countable markov shifts we study the analyticity of the topological pressure for some one parameter families of potentials on countable markov shifts we relate the non analyticity of the pressure to changes in the recurrence properties of the system we give sufficient conditions for such changes to exist and not to exist we apply these results to the manneville pomeau map and use them to construct examples with different critical behavior

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

simulation of airflow past a 2d naca0015 airfoil using an isogeometric incompressible navier stokes solver with the spalart allmaras turbulence model abstract the work presented in this paper concerns the efforts of conducting a computational fluid dynamics cfd simulation of air flow past a fixed 2d naca0015 airfoil at high reynolds number r e 2 5 10 6 using an isogeometric finite element methodology with linear quadratic and cubic spline elements flow simulations at such high reynolds numbers require turbulence models or very high resolution the present work employs the spalart allmaras turbulence model combined with a navier stokes solver based on a chorin projection method the first development of its kind in an isogeometric finite element framework the obtained results from the simulations are compared with two sets of experimental results available in the literature

can milne s method work well for the coulomb like potentials we extend the improved milne s milne spline method for obtaining eigenvalues and eigenfunctions to the cases of long range and singular potentials for which we have conjectured that it is difficult to apply the method contrary to our conjecture it turned out that the method is valid also for coulomb potential and repulsive 1 xn n 2 3 type potential further we applied the method for two cases for which the solutions are not known in order to investigate the stability of the multi dimensional universe it has been shown that the extra dimensional internal space of our universe is not stable in classical einstein gravity as well as canonically quantized one two possibilities for stabilization were investigated i noncanonically quantized einstein gravity and ii canonically quantized higher curvature gravity it has been suggested that the space is stable by qualitative and approximate methods exact analytical treatment is very difficult so that numerical investigation is highly desirable numerical investigation shows that the space is stable with sufficient reliability

statistical properties of maps with indifferent periodic points in this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points as applications we apply our results to the well known manneville pomeau equation and the inhomogeneous diophantine approximation algorithm

weak gibbs measures for intermittent systems and weakly gibbsian states in statistical mechanics in this paper we associate weak gibbs measures for intermittent maps with non gibbsian weakly gibbsian states in statistical mechanics in the sense of dobrushin 4 5 we show a higher dimensional intermittent map of which the sinai bowen ruelle measure is a weak gibbs equilibrium state and a weakly gibbsian state in the sense of dobrushin admitting essential discontinuities in its conditional probabilities

implementation and comparison of three isogeometric navier stokes solvers applied to simulation of flow past a fixed 2d naca0012 airfoil at high reynolds number abstract implementation of three different navier stokes solvers in an isogeometric finite element framework is presented in this paper the three solvers chorin projection method and coupled formulation both with the spalart allmaras turbulence model and variational multiscale vms method have been applied to simulate flow past a two dimensional naca0012 airfoil at a high reynolds number r e 3 10 6 for four different angles of attack the predicted flow characteristics have been compared and the effects of increasing the order of the spline element on the accuracy of prediction and computational efficiency are evaluated in this study it turns out that flow separation does not take place up to an angle of attack of 16 up to this angle of attack all three solvers predict similar results in good agreement with each other and with available experimental results however a big spread in lift and drag coefficients is observed in the stall regime our study also shows that for linear spline elements all three solvers are computationally similar for quadratic spline elements the chorin solver compares favorably to the others based on the results presented here

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

improved amplitude phase method for complex angular momentum analysis an amplitude phase formula for the s matrix using two milne solutions and the regular schrodinger solution is derived the formula is particularly useful in the analysis of regge poles located far

subexponential decay of correlations we describe a method for proving subexponential lower bounds for correlations functions and apply it to study decay of correlations for maps with countable markov partitions one result is that ls young s upper estimates y2 are optimal in many situations our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on banach spaces which we apply to the iterates of the transfer operator

on regge pole trajectories for a rational function approximation of thomas fermi potentials the positions of two regge poles caused by the rational function approximate thomas fermi potential a screened attractive coulomb potential are studied in detail as a function of the scattering e

optimal quadrature for univariate and tensor product splines abstract numerical integration is a core subroutine in many engineering applications including the finite element method fem isogeometric analysis is a fem technology that uses smooth b spline and nurbs basis functions traditionally gaussian quadrature was used for numerical integration but this yields suboptimal performance this is attributed to the fact that gaussian quadrature rules do not take inter element smoothness of the spline basis into account resulting in over integration the equations for exact quadrature are well known but prove notoriously hard to solve due to their nonlinear nature these generalized gauss rules were first introduced in hughes et al 2010 in the context of isogeometric analysis where newton iteration was utilized to study and tabulate several cases later homotopy continuation barto and calo 2015 was used as an alternative strategy for finding these rules in this paper we describe an algorithm to generalize on both of these techniques it is optimal in the sense that it will integrate a space of dimension n using no more than n 1 2 quadrature points the algorithm works on arbitrary nonuniform knot vectors of any polynomial degree and continuity and is demonstrated on polynomial orders up to 15 it extends to 2d and 3d integrals by tensor product

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

note on invariants for uncoupled ermakov systems several invariants for an ermakov system consisting of a parametric oscillator and a milne oscillator in one dimension are derived this system appears in amplitude phase analysis of parametric oscillator solutions first and second order invariants for such a system are derived using the wronskian relations of a fundamental pair of parametric oscillator solutions in this way wronskian invariants of the parametric oscillator system alone imply ermakov lewis type invariants for the combined ermakov system as well as invariants for the milne oscillator alone

coupled radial schrodinger equations written as dirac type equations application to an amplitude phase approach the classical amplitude phase method due to milne wilson young and wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found the key for the efficient computations is that the original single state radial schr dinger equation is transformed to a nonlinear equation the milne equation such an equation has solutions that may or may not oscillate depending on boundary conditions which then requires a robust recipe for locating the optimal almost constant solutions for its use in the method for scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity and there is no problem locating the optimal amplitude functions from a low order semiclassical approximation in the present work the amplitude phase approach is generalized to two coupled schr dinger equations similar to an earlier generalization to radial dirac equations the original scalar amplitude then becomes a vector quantity and the original milne equation is generalized accordingly numerical applications to resonant electron atom scattering are illustrated

generalization of the amplitude phase s matrix formula for coupled scattering states the amplitude phase method is generalized to coupled schr dinger scattering states with a common angular momentum quantum number a pair of exponential type amplitude phase solutions u j r exp ij r for each channel is obtained containing a common complex scalar phase function j r and two column vector amplitudes u j r the amplitude functions satisfy certain nonlinear generalized milne equations and the scalar product of the two amplitudes determines the derivative of the common phase function fundamental amplitude phase matrix solutions that are proportional to jost like schr dinger matrix solutions are constructed it is shown how a generalized amplitude phase s matrix formula can be derived from wronskian relations involving the two amplitude phase matrix solutions and a regular matrix solution

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

scattering s matrix derived from invariants of the ermakov lewis type an amplitude phase formula for the s matrix due to a central potential is derived the derivation makes use of invariants of the ermakov lewis type

attainable conditions and exact invariant for the time dependent harmonic oscillator the time dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables the solutions exhibit a finite time dependent parameter whenever the squared amplitude times the derivative of the phase is invariant if the invariant relationship does not hold the time dependent parameter has divergent singularities these observations lead to the proposition that the harmonic oscillator equation with finite time dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship since the time dependent parameter or the potential must be finite for any real oscillator implementation the invariant must hold for any such physically realizable system

equilibriums of some non holder potentials we consider one sided subshifts with some potential functions which satisfy the holder condition everywhere except at a fixed point and its preimages we prove that the systems have conformal measures and invariant measures absolutely continuous with respect to where may be finite or infinite we show that the systems are exact and are weak gibbs measures and equilibriums for we also discuss uniqueness of equilibriums and phase transition these results can be applied to some expanding dynamical systems with an indifferent fixed point