aeroelastic dynamic analysis of a full f 16 configuration for various flight conditions an overview is given of recent advances in a three field methodology for modeling and solving nonlinear fluid structure interaction problems and its application to the prediction of the aeroelastic frequencies and damping coefficients of a full f 16 configuration in various subsonic transonic and supersonic airstreams is reported in this three field methodology the flow is described by the arbitrary lagrangian eulerian form of the euler equations the structure is represented by a detailed finite element model and the fluid mesh is unstructured dynamic and updated by a robust torsional spring analogy method simulation results are presented for stabilized accelerated low g and high g flight conditions and correlated with flight test data consequently the practical feasibility and potential of the described computational fluid dynamics based computational method for the flutter analysis of high performance aircraft particularly in the transonic regime are discussed

joint noncoherent demodulation and decoding for the block fading channel a practical framework for approaching shannon capacity the paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels guided by explicit comparisons with information theoretic benchmarks noncoherent reception is interpreted as joint data and channel estimation assuming that the channel is time varying and a priori unknown we consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection for an information rate of about 1 2 bit per channel use the proposed scheme using a quaternary phase shift keying qpsk alphabet provides performance within 1 6 1 7 db of shannon capacity for the block fading channel and is about 2 5 3 db superior to standard differential demodulation in conjunction with an outer channel code we also provide capacity computations for noncoherent communication using standard phase shift keying psk and quadrature amplitude modulation qam alphabets comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal to noise ratio these results imply that qpsk suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations but that qam is superior to psk for higher information or fading rates motivating further research into efficient noncoherent coded modulation with qam alphabets

new set of symmetries of the integrable equations lie algebra and non isospectral evolution equations ii akns system the authors define directly a new set of symmetries for the akns system and prove that they constitute an infinite dimensional lie algebra with the old symmetries they also point out the relation between the new symmetry and the non isospectral problem they use the reduction technique and point out that the nls mkdv sg and sinh g hierarchies have two sets of symmetries which constitute an infinite dimensional lie algebra these results are extensions of those of chen et al 1982

characterization and computation of optimal distributions for channel coding this paper concerns the structure of capacity achieving input distributions for stochastic channel models and a renewed look at their computational aspects the following conclusions are obtained under general assumptions on the channel statistics i the capacity achieving input distribution is binary for low signal to noise ratio snr the proof is obtained on comparing the optimization equations that determine channel capacity with a linear program over the space of probability measures ii simple discrete approximations can nearly reach capacity even in cases where the optimal distribution is known to be absolutely continuous with respect to lebesgue measure iii a new class of algorithms is introduced based on the cutting plane method to iteratively construct discrete distributions along with upper and lower bounds on channel capacity it is shown that the bounds converge to the true channel capacity and that the distributions converge weakly to a capacity achieving distribution

on the information rate of multiantenna systems with isotropic unitary input signals in the presence of channel estimation errors this correspondence focuses on the evaluation of the information rate conveyed by block faded pilot based multiple input multiple output mimo systems when the input signals are isotropic unitary iu distributed and imperfect e g error affected channel estimates are available at receiver and transmitter main contributions may be so summarized first we develop closed form analytical formulas for the computation of the ergodic information rate conveyed by the considered mimo systems equipped with a large number of transmit antennas second we point out that no rate gain may be accomplished by shaping the transmitted streams on the basis of possibly partial channel state information csi so that the feedback link becomes indeed useless when the system is block faded and fed by iu distributed input signals third we compare the obtained information rate with those supported by the corresponding mimo systems fed by gaussian distributed input signals for various values of the mean squared error mse impairing the available mimo channel estimates so doing we gain some insight about the operating conditions where actual implementation of a feedback link may be justified by the resulting improvement in the rate conveyed by the overall system

on fixed input distributions for noncoherent communication over high snr rayleigh fading channels it is well known that independent and identically distributed gaussian inputs scaled appropriately based on the signal to noise ratio snr achieve capacity on the additive white gaussian noise awgn channel at all values of snr in this correspondence we consider the question of whether such good input distributions exist for frequency nonselective rayleigh fading channels assuming that neither the transmitter nor the receiver has a priori knowledge of the fading coefficients in this noncoherent regime for a gauss markov model of the fading channel we obtain explicit mutual information bounds for the gaussian input distribution the fact that gaussian input generates bounded mutual information motivates the search for better choices of fixed input distributions for high rate transmission over rapidly varying channels necessary and sufficient conditions are derived for characterizing such distributions for the worst case scenario of memoryless fading using the criterion that the mutual information is unbounded as the snr gets large examples of both discrete and continuous distributions that satisfy these conditions are given a family of fixed input distributions with mutual information growth rate of o loglogsnr sup 1 u u 0 are constructed it is also proved that there does not exist a single fixed input distribution that achieves the optimal mutual information growth rate of loglogsnr

validity of linearized unsteady euler equations with shock capturing by examining the nature of shock movement we first show that the unsteady lift due to the movement of a shock is linear with the magnitude of the shock movement the argument that is presented holds true regardless of the shock structure which is determined by the level of viscosity this proof is the basis for showing that the linear perturbation equations can be used to determine not only the unsteadiness of the flowfield away from the shock but also the effect of the shock movement as well shock capturing is a computational technique that in effet adds a large amount of viscosity in the shock region smearing shocks over several cells

wing flutter prediction by a small disturbance euler method on body fitted curvilinear grids time accurate coupled fluid and structure solutions for the unsteady euler equations are too expensive for routine aeroelastic computation the small disturbance euler sd euler method is shown to

on the asymptotic capacity of stationary gaussian fading channels we consider a peak power limited single antenna flat complex gaussian fading channel where the receiver and transmitter while fully cognizant of the distribution of the fading process have no knowledge of its realization upper and lower bounds on channel capacity are derived with special emphasis on tightness in the high signal to noise ratio snr regime necessary and sufficient conditions in terms of the autocorrelation of the fading process are derived for capacity to grow double logarithmically in the snr for cases in which capacity increases logarithmically in the snr we provide an expression for the pre log i e for the asymptotic ratio between channel capacity and the logarithm of the snr this ratio is given by the lebesgue measure of the set of harmonics where the spectral density of the fading process is zero we finally demonstrate that the asymptotic dependence of channel capacity on the snr need not be limited to logarithmic or double logarithmic behaviors we exhibit power spectra for which capacity grows as a fractional power of the logarithm of the snr

on the mutual information and low snr capacity of memoryless noncoherent rayleigh fading channels the memoryless noncoherent single input single output siso rayleigh fading channel is considered closed form expressions are derived for the mutual information between the output and the input of this channel when the input magnitude distribution is discrete and is restricted to having two mass points it is subsequently shown how these expressions can be used to obtain closed form expressions for the capacity of this channel for signal to noise ratio snr values of up to approximately 0 db and a tight capacity lower bound for snr values between 0 db and 10 db the expressions for the channel capacity and its lower bound are given as functions of a parameter which can be obtained via numerical root finding algorithms

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

linearized euler predictions of unsteady aerodynamic loads in cascades a linearized euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and vibratory blade motion is presented using the linearized euler technique one decomposes the flow into a mean or steady flow plus an unsteady harmonically varying small disturbance flow linear variable coefficient equations describe the small disturbance behavior of the flow and are solved using a pseudotime time marching lax wendroff scheme for the blade motion problem a harmonically deforming computational grid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition

an induced additive noise model for memoryless rayleigh fading channels this correspondence investigates a noncoherent discrete time memoryless rayleigh fading channel a logarithmic transform converts it into an induced channel with additive noise that is independent of the channel input from this perspective it is natural and convenient for us to revisit several known results and gain new insights in particular we specify a class of simple log scale uniform channel input distributions that performs well for moderate to high signal to noise ratio snr furthermore a continuous amplitude log scale uniform distribution is asymptotically capacity achieving in the sense that the difference between the resulting mutual information and the channel capacity approaches zero as snr becomes large we also extend the induced additive noise channel approach to memoryless multiple antenna channels possibly with transmit but without receive spatial correlation

sensitivity analysis of unsteady inviscid flow through turbomachinery cascades we present a novel sensitivity analysis for predicting the effect of airfoil shape on the unsteady aerodynamic and aeroacoustic response of turbomachinery blading the nominal steady and unsteady e ow in a cascade of turbomachinery blades is modeled using the steady euler equations and the time linearized euler equations respectively boththesteadyandunsteadyeulerequationsaresolvedusing atwo stepe nite volumelax wendroff discretizationwithmultigrid acceleration wecomputetheunsteady aerodynamicloadsduetoboth incominggusts and plunging motion of the cascade airfoils once the nominal steady and unsteady e ows have been computed a sensitivity analysis is performed using the discrete adjoint equations of the computational e uid dynamics scheme used to discretizetheeulerequations for each objectivefunction e g the amplitude peak of theaeroelastic blade motion theresultingadjointequationsaresolvedusingtheadjointlax wendroffscheme whichisalsoaccelerated using a multigrid technique once the adjoint equations have been solved the computed adjoint variables may be used to compute rapidly the sensitivities of the aeroelastic and aeroacoustic objective functions due to arbitrary changes in geometry the method is computationally efe cient with similar convergence rate histories for both the nominal and the adjoint solutions to demonstrate the utility of the present method we use the sensitivity analysis to redesign the shape of the airfoils of a cascade for increased aeroelastic stability we also redesign the shape of the airfoils of an exit guide vane for reduced downstream radiated noise

on the non hereditary recursion operator and the constraint on the potential associated with the giachetti johnson equation and its gauge equivalent yang equation the recursion operator associated with the giachetti johnson gj equation is shown not to be hereditary restricting the potential to the invariant subspace of the recursion operator leads to a constraint on the potential under the constraint two systems obtained from the gj equation and the related time evolution equation for eigenfunctions are shown to be naturally consistent constants of the motion for former system are given and a solution to this system satisfies a certain higher order stationary equation also similar results are obtained for the yang equation

algorithm developments for discrete adjoint methods this paper presents a number of algorithm developments for adjoint methods using the discrete approach in which the discretisation of the non linear equations is linearised and the resulting matrix is then transposed with a new iterative procedure for solving the adjoint equations exact numerical equivalence is maintained between the linear and adjoint discretisations the incorporation of strong boundary conditions within the discrete approach is discussed as well as a new application of adjoint methods to linear unsteady flow in turbomachinery

on the achievable rate of stationary rayleigh flat fading channels with gaussian inputs in this work a discrete time stationary rayleigh flat fading channel with unknown channel state information at transmitter and receiver side is studied the law of the channel is presumed to be known to the receiver for independent identically distributed i i d zero mean proper gaussian input distributions the achievable rate is investigated the main contribution of this paper is the derivation of two new upper bounds on the achievable rate with gaussian input symbols one of these bounds is based on the one step channel prediction error variance but is not restricted to peak power constrained input symbols like known bounds moreover it is shown that gaussian inputs yield the same pre log as the peak power constrained capacity the derived bounds are compared with a known lower bound on the capacity given by deng and haimovich and with bounds on the peak power constrained capacity given by sethuraman et al finally the achievable rate with i i d gaussian input symbols is compared to the achievable rate using a coherent detection in combination with a solely pilot based channel estimation

on the capacity of a class of signal dependent noise channels in some applications the variance of additive measurement noise depends on the signal that we aim to measure for instance additive signal dependent gaussian noise asdgn channel models are used in molecular and optical communication herein we provide lower and upper bounds on the capacity of additive signal dependent noise asdn channels the first lower bound is based on an extension of majorization inequalities and the second lower bound utilizes the properties of the differential entropy the lower bounds are valid for arbitrary asdn channels the upper bound is based on a previous idea of the authors symmetric relative entropy and is applied to the asdgn channels these bounds indicate that in the asdn channels unlike the classical additive white gaussian noise channels the capacity does not necessarily become larger by reducing the noise variance function we also provide sufficient conditions under which the capacity becomes infinite this is complemented by some conditions implying that the capacity is finite and a unique capacity achieving measure exists in the sense of the output measure

capacity of noncoherent time selective rayleigh fading channels the capacity of noncoherent time selective rayleigh fading channels is studied under various models for the variations in time the study includes both single input and single output siso and multiple input and multiple output mimo systems a block fading model is first considered where the channel changes correlatively over each block period of length t and independently across blocks the predictability of the channel is characterized through the rank q of the correlation matrix of the vector of channel gains in each block this model includes as special cases the standard block fading model where the channel remains constant over block periods q 1 and models where the fading process has finite differential entropy rate q t the capacity is initially studied for long block lengths and some straightforward but interesting asymptotes are established for the case where q is kept fixed as t spl rarr spl infin it is shown that the noncoherent capacity converges to the coherent capacity for the case where both t q spl rarr spl infin with q t being held constant a bound on the capacity loss due to channel unpredictability is established the more interesting scenario of large signal to noise ratio snr is then explored in detail for siso systems useful upper and lower bounds on the large snr asymptotic capacity are derived and it is shown that the capacity grows logarithmically with snr with a slope of t q spl rarr t for q t next in order to facilitate the analysis of mimo systems the rank q block fading model is specialized to the case where each t symbol block consists of q subblocks of length l with the channel remaining constant over each subblock and changing correlatively across subblocks for this model it is shown that the log snr growth behavior of the capacity is the same as that of the standard block fading model with block length l finally the siso and mimo channel models are generalized to allow the fading process to be correlated across blocks in a stationary and ergodic manner it is shown that the log snr growth behavior of the capacity is not affected by the correlation across blocks

convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws part 1 linearized approximations and linearized output functionals this paper analyzes the convergence of discrete approximations to the linearized equations arising from an unsteady one dimensional hyperbolic equation with a convex flux function a simple modified lax friedrichs discretization is used on a uniform grid and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined it is proved that this gives pointwise convergence almost everywhere for the solution to the linearized discrete equations with smooth initial data and also convergence in the discrete approximation of linearized output functionals in part 2 m giles and s ulbrich siam j numer anal 48 2010 pp 905 921 we extend the results to dirac initial data for the linearized equation and will prove the pointwise convergence almost everywhere for the solution of the adjoint discrete equations in addition we present numerical results illustrating the asymptotic behavior which is analyzed

lie algebraic structure for the akns system a new approach is proposed to construct the master symmetry and to prove its lie algebraic structure for the akns system

symmetries and constants of motion for new akns hierarchies two sets of infinite number of symmetries their lie algebra properties and constants of motion for a class of non linear evolution equations associated with non isospectral deformations of the akns spectral problem are constructed

euler calculations with embedded cartesian grids and small perturbation boundary conditions this study examines the use of stationary cartesian mesh for steady and unsteady flow computations the surface boundary conditions are imposed by reflected points a cloud of nodes in the vicinity of the surface is used to get a weighted average of the flow properties via a gridless least squares technique if the displacement of the moving surface from the original position is typically small a small perturbation boundary condition method can be used to ensure computational efficiency multigrid solution is made via a framework of embedded grids for local grid refinement computations of airfoil wing and wing body test cases show the practical usefulness of the embedded cartesian grids with the small perturbation boundary conditions approach

the constraints of potentials and the finite dimensional integrable systems restricting potential to the space spanned by the eigenvectors of the recursion operator leads to a natural constraint of potential and a finite dimensional integrable hamiltonian system the general method for proving the consistency of the two systems stemming from the lax pair and obtaining the constants of the motion for the hamiltonian system is illustrated by the classical boussinesq and akns hierarchies by using gauge transformation similar results for the jaulent miodek and kaup newell hierarchies are presented

the behavior of flux difference splitting schemes near slowly moving shock waves abstract an investigation of the behavior of shock capturing schemes which compute the numerical flux from a solution of riemann s problem is performed the schemes of godunov roe and osher are examined for a one dimensional model problem consisting of a nearly stationary shock both scalar and systems of equations are examined it is found that for slow shocks there is a significant error generated when solving systems of equations while the scalar results are well behaved this error consists of a long wavelength noise in the downstream running wave families that is not effectively damped by the dissipation of the scheme the source of this error is shown and the implications for the performance of these schemes are considered this error may contribute to the slow convergence to steady state reported by many researchers

calculation of airfoil flutter by an euler method with approximate boundary conditions a numerical method is demonstrated for solving the steady and unsteady euler equations on stationary cartersian grids for the purpose of time domain simulation of aeroelastic problems wall boundary conditions are implemented on nonmoving mean chord positions by assuming the airfoil being thin and undergoing small deformation whereas the full nonlinear euler equations are used in the flowfield for accurate resolution of shock waves and vorticity the method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body the first order wall boundary conditions are used in solving the full euler equations and the results are compared with the euler solutions using the exact boundary conditions and known experimental data it is shown that the first order boundary conditions are adequate to represent airfoils of typical thicknesses with small deformation for both steady and unsteady calculations flutter boundaries are accurately predicted by this method for the isogai wing model test case

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

the capacity of discrete time memoryless rayleigh fading channels we consider transmission over a discrete time rayleigh fading channel in which successive symbols face independent fading and where neither the transmitter nor the receiver has channel state information subject to an average power constraint we study the capacity achieving distribution of this channel and prove it to be discrete with a finite number of mass points one of them located at the origin we numerically compute the capacity and the corresponding optimal distribution as a function of the signal to noise ratio snr the behavior of the channel at low snr is studied and finally a comparison is drawn with the ideal additive white gaussian noise channel

on the use of isospectral eigenvalue problems for obtaining hereditary symmetries for hamiltonian systems we present an algorithmic method for obtaining an hereditary symmetry the generalized squared eigenfunction operator from a given isospectral eigenvalue problem this method is applied to the n n eigenvalue problem considered by ablowitz and haberman and to the eigenvalue problem considered by alonso the relevant hamiltonian formulations are also determined finally an alternative method is presented in the case two evolution equations are related by a miura type transformation and their hamiltonian formulations are known

hamiltonian structure of discrete soliton systems we describe an approach for investigating the hamiltonian structures of the lattice isospectral evolution equations associated with a general discrete spectral problem by using the so called implicit representations of the isospectral flows we demonstrate the existence of the recursion operator l which is a strong and hereditary symmetry of the flows it is then proven that every equation in the isospectral hierarchy possesses the hamiltonian structure if l has a skew symmetric factorization and the first equation ut k 0 in the hierarchy satisfies some simple condition we obtain related properties such as the implectic symplectic factorization of l the liouville complete integrability and the multi hamiltonian structures of the isospectral hierarchy four examples are given

generalization of sturm liouville theory to a system of ordinary differential equations with dirac type spectrum the sturm liouville theory is generalized to dirac equation like systems of ordinary differential equations it is shown how the comparison theorem and conversion to integral equations can be generalized

unsteady flow calculations with a multigrid navier stokes method a multigrid navier stokes method with a two equation k u turbulence model is developed for calculating unsteady flows the method uses a staggered finite volume scheme to discretize the navier stokes and the turbulence model equations in space a fully implicit time accurate scheme is reformulated so that an efficient explicit multistage method with local time stepping residual smoothing and multigrid can be used to accelerate convergence within each unsteady time step the method combines the advantages of implicit and explicit schemes for unsteady flow calculations solutions for the forced oscillation of an airfoil are obtained with the euler and the navier stokes equations results are compared with experimental data