adaptive mesh finite volume calculation of 2d lid cavity corner vortices abstract an anisotropic refinement criterion suitable for finite volume methods is presented and navier stokes solutions are reported for the lid driven cavity flow configuration at re 1000 with adaptive anisotropic meshes h refinement the a posteriori error estimation criterion is based on the assessment of the goodness of fit of the least squares regression used to perform the variables profile reconstruction and it is capable of detecting both large scale and small scale flow phenomena the criterion allowed to capture in detail the large scale flow structure and also the sequence of creeping flow small sharp corner s 1 eddies up to the fourth corner vortex in addition to the primary cavity vortex the smallest corner vortex detected is o 10 16 smaller in velocity magnitude compared with the cavity primary recirculation flow

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

boundedness preserving implicit correction of mesh induced errors for vof based heat and mass transfer abstract spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for computational fluid dynamics cfd mesh skewness is then typically encountered causing severe deterioration of the formal order of accuracy of the discretisation or boundedness of the solution or both particularly methods inherently relying on the accurate and bounded transport of sharp fields suffer from all types of mesh induced skewness errors namely both non orthogonality and non conjunctionality errors this work is devoted to a boundedness preserving strategy to correct for skewness errors arising from discretisation of advection and diffusion terms within the context of interfacial heat and mass transfer based on the volume of fluid methodology the implementation has been accomplished using a second order finite volume method with support for unstructured meshes of general topology we examine and advance suitable corrections for the finite volume discretisation of a consistent single field model where both accurate and bounded transport due to diffusion and advection is crucial in order to ensure consistency of both the volume fraction and the species concentration transport i e to avoid artificial heat or species transfer corrections are studied for both cases using distorted 2d meshes the cross interfacial jump and adjacent sharp gradients of species concentration render the correction for skewness induced diffusion and advection errors additionally demanding and has not so far been addressed in the literature

performance analysis of derivative constraint adaptive arrays with pointing errors the performance of adaptive arrays with arbitrary order derivative constraints to avoid the signal nulling caused by the error in the steering angle is investigated the generalized sidelobe canceller gsc is used to evaluate the bearing responses of adaptive arrays with pointing errors under the assumption of equispaced linear arrays the legendre polynomial is used to derive a closed form formula for the sidelobe leakage factor the ratio in which the signal leaks into the gsc sidelobe cancelling branch moreover the effective beamwidth the maximum range of pointing inaccuracy allowable to keep the signal loss in array output less than a given value is derived for the gsc with a delay and sum quiescent beamformer such adaptive arrays can achieve the maximum output signal to noise ratio when the presteering is perfect and the performance is independent of the location of the phase origin numerical results are presented to confirm the analysis

causal input output representation of 2d systems in the behavioral approach in this paper the concept of causal input output representation of two dimensional 2d systems in the behavioral approach is introduced these representations provide an interesting connection between classical 2d systems theory and 2d systems theory in the behavioral approach some characterizations of such representations are presented finally a technique that allows us to obtain causal input output representations is proposed

minimum variance beamforming with phase independent derivative constraints a set of first and second order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented efficient algorithms are derived for the implementation of these constraints in contrast to conventional derivative constraint methods which constrain both the magnitude power and phase responses of the beamformer the method only constrains the magnitude response the unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions this phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience as a direct sequence of the phase constraint an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes the problem is avoided through the use of phase independent derivative constraints

a solution of the cauchy problem for multidimensional discrete linear shift invariant systems abstract we propose a solution of the cauchy problem for multidimensional linear shift invariant systems over z r that can be described by a set of multidimensional difference equations we give a method for finding an initial condition structure it consists in finding subsets of z r where the signals can be given arbitrarily and where they fix the trajectory on the whole grid moreover we develop an efficient algorithm computing the whole trajectory once given the initial conditions for this purpose we develop some constructive techniques for laurent polynomial modules

derivative constrained optimum broad band antenna arrays the optimization problem corresponding to the design of a presteered broadband processor with maximally flat second order spatial response in the look direction is discussed the constraints corresponding to necessary and sufficient conditions for second order flatness are presented the nonlinearly constrained optimization approach is unable to consistently locate the global minimum an approach to solving this problem that essentially converts the nonconvex optimization problem into a parameterized set of convex problems is presented in the case of 2 d scenarios the global optimum is determined by finding the roots of a cubic function the characteristics of the constraints including the minimum number required and the dependence on the choice of coordinate systems are examined

adaptive array beamforming based on an efficient technique this paper presents a new processing technique for adaptive array beamforming we first properly decompose the optimal weight vector associated with the original array beamformer into several adaptive weight subvectors an adaptive algorithm based on the conventional rls algorithm is derived to update the weight subvectors the required computational complexity is also evaluated for the proposed technique the convergence rate of the proposed technique is mainly affected by the size of the largest weight subvector faster convergence speed and less array sensitivity to the pointing errors can be achieved by using the proposed technique several simulation results are included for illustration and comparison

generalized eigenspace beamformer based on cg lanczos algorithm the generalized eigenspace beamformer geib has been presented as an efficient way to build a beamformer robust to calibration and pointing errors its main drawback is the great computational cost needed to develop the whole structure mainly associated to obtaining the projection matrix in this paper the relation between conjugate gradient and lanczos algorithm is used to modify the conjugate gradient algorithm robust conjugate gradient method rcgm so the eigenstructure of the correlation matrix can be obtained directly the numerical problems associated to the loss of orthogonality in successive gradient vectors have also been overcome via selective orthogonalization so in this way the proposed rcgm is also robust to numerical problems the overall computational cost in the construction of the geib has been reduced from o n sup 3 n sup 2 to o 3n sup 2 by using the rcgm instead of a conventional projection algorithm computer simulations are also presented to demonstrate the merits of the algorithm

a novel adaptive beamformer based on semidefinite programming sdp with magnitude response constraints a novel robust adaptive beamformer formulated as a semidefinite programming sdp problem is proposed in this paper with new constraints on the magnitude response the beamwidth and response ripple of the robust response region can be well controlled moreover only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom dofs of the adaptive beamformer are consumed consequently the resultant beamformer has significant improvement on signal to interference plus noise ratio sinr an important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix in this paper a method utilizing the extended spectral factorization method is proposed to solve this problem simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed method

a subband selective broadband gsc with cosine modulated blocking matrix a novel subband selective generalized sidelobe canceller gsc for partially adaptive broadband beamforming is proposed the columns of the blocking matrix are derived from a prototype vector by cosine modulation and the broadside constraint is incorporated by imposing zeros on the prototype vector appropriately these columns constitute a series of bandpass filters which select signals with specific directions of arrival and frequencies this results in a high pass type bandlimited spectra of the blocking matrix outputs which is further exploited by subband decomposition and suitably discarding the low pass subbands prior to running independent unconstrained adaptive filters in each nonredundant subband by these steps the computational complexity of a gsc implementation is greatly reduced compared to fully adaptive gsc schemes while performance is comparable or even enhanced due to subband decorrelation in both spatial and temporal domains

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

compressive vof method with skewness correction to capture sharp interfaces on arbitrary meshes the accurate and efficient modelling of two phase flows is at present mostly limited to structured unskewed meshes due to the additional topological and numerical complexity of arbitrary unstructured meshes compressive vof methods which discretize the interface advection with algebraic differencing schemes are computationally efficient and inherently applicable to arbitrary meshes however compressive vof methods evidently suffer severely from numerical diffusion on meshes with topological skewness in this paper we present a compressive vof method using a state of the art donor acceptor advection scheme which includes novel modifications to substantially reduce numerical diffusion on arbitrary meshes without adding computational complexity the new methodology accurately captures evolving interfaces on any arbitrary non overlapping mesh and conserves mass within the limits of the applied solver tolerance a thorough validation of the presented methods is conducted examining the pure advection of the interface indicator function as well as the application to evolving interfaces with surface tension crucially the results on equidistant cartesian and arbitrary tetrahedral meshes are shown to be comparable and accurate

adaptive array beamforming with robust capabilities under random phase perturbations the problem of adaptive array beamforming with multiple beam constraints in the presence of steering error caused by random phase perturbations is considered we first construct a cost function consisting of terms that utilize a posteriori information due to the received array data and a priori information due to the probabilistic distribution of phase perturbation respectively then an appropriate estimate of the actual phase angle vector associated with each of the desired signals can be obtained by performing a nonlinear optimization problem based on the cost function an implementation algorithm is further presented to iteratively solve the problem theoretical analysis regarding the convergence property of the iterative procedure is also investigated finally several computer simulation examples are provided for illustration

numerical method for coupled fluid flow heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology abstract a numerical method is presented that can be used for both solid body stress analysis and fluid flow predictions independently as well as in a coupled manner the method uses an integral form of equations governing mass energy and momentum balance for an arbitrary control volume a detailed description is provided of a novel second order accurate spatial discretisation technique which can accommodate unstructured moving meshes with cells of arbitrary topology this is accompanied by a fully implicit temporal discretisation which makes the method stable for any time step size the resulting set of coupled non linear algebraic equations is solved by employing a segregated approach leading to a decoupled set of linear algebraic equations for each dependent variable with a sparse diagonally dominant coefficient matrix these equations are solved by an iterative conjugate gradient solver which retains the sparsity of the coefficient matrix thus achieving a very efficient use of computer resources the method has been tested on a number of fluid flow and stress analysis problems and numerical calculations show favourable agreement with analytical and or experimental results in order to demonstrate the full capabilities of the present method an example of numerically complex coupled fluid flow stress analysis and heat transfer calculations is presented

generalized eigenspace based beamformers the generalized eigenspace based beamformer geib is presented here which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer lcmvb the weight vector of the geib is found by projecting the lcmvb weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix the geib and the lcmvb have the same responses to the desired signal and the interferers however the weight vector of the geib has a smaller norm and generates a lower output noise power an additional advantage of the geib is that the linear constraints can be treated flexibly i e each linear constraint can be chosen to be preserved or not preserved the cost of preserving a linear constraint is to get more output noise power in addition to developing the geib we discuss the effects of imposing linear constraints on the output noise powers of the geib and the lcmvb computer simulations are also presented that demonstrate the merits of the geib

improved adaptive nulling of coherent interference without spatial smoothing a new scheme for adaptive nulling in the presence of coherent interference is proposed that finds the weight vector using a nonsquare correlation matrix without spatial smoothing conventional schemes which use square matrices correspond to specific cases of the new method it allows us to increase the dimension of the weight vector such that the nulling capability is enhanced theoretic performance analysis is made showing that the output signal to interference ratio sinr of such a beamformer is proportional to the weight dimension for sidelobe interference simulation results confirm this

adaptive beamforming with real valued coefficients based on uniform linear arrays a class of adaptive beamforming algorithms with real valued coefficients is proposed based on the uniform linear array structure by introducing a preprocessing transformation matrix it is derived from the beamformer with a minimum mean square error mse or a maximum output signal to interference plus noise ratio sinr depending on the specific design criteria the key parameter of the transformation matrix takes different values for different beamforming scenarios and three representative examples are studied the linearly constrained minimum variance beamformer and the generalized sidelobe canceller the reference signal based beamformer and the class of blind beamformers based on the constant modulus algorithm its advantage is twofold 1 with real valued coefficients the computational complexity of the overall system is reduced significantly 2 a faster convergence speed is achieved and given the same stepsize the system arrives at a lower mse or a higher output sinr

robust wideband beamforming with frequency response variation constraint subject to arbitrary norm bounded error traditional robust wideband beamforming is mainly achieved by extending the narrowband robust beamforming methods to the wideband case through frequency sampling with robust constraints imposed on different frequency points separately the resultant beamformer may have different responses at different frequencies causing intolerable distortion to the desired signal to improve the frequency response consistency of the beamformer against arbitrary array manifold errors a novel robust beamformer is proposed with a closed form solution a previously proposed robust beamformer can be considered as its special case

spatial blocking filter derivative constraints for the generalized sidelobe canceller and music the paper presents a new approach to spatial derivative constraints for the generalized sidelobe canceller gsc spatial derivative constraints have been applied to linearly constrained minimum variance beamformers to reduce the sensitivity to steering error earlier approaches to this problem constrained derivatives of the beamformer power and phase response leading to beamformer performance that depended on the coordinate reference location of the array current approaches constrain only the beamformer power response eliminating the problem with phase dependence however nonlinear minimization is required in order to solve for the linear constraint equations an alternative approach for the gsc which is presented in the paper is to use derivative constraints to flatten the null of the spatial blocking filter power response thus for a small steering error the desired signal is still blocked from the noise cancelling filter and the gsc output is unaffected by the steering error these derivative constraints can be used with wideband array calibration leading to effective performance in the presence of array errors this same approach to derivative constraints can be used in other applications involving spatial blocking filters such as the constrained music direction finding algorithm to give robustness against direction error of the known signal subspace

robust adaptive beamformers based on worst case optimization and constraints on magnitude response in this paper novel robust adaptive beamformers are proposed with constraints on array magnitude response with the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight the optimization of an adaptive beamformer which is often described as a quadratic optimization problem in conventional beamforming methods is then reformulated as a linear programming lp problem unlike conventional robust beamformers the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple in practice an array has many imperfections besides steering direction error in order to make the adaptive beamformer robust against all kinds of imperfections worst case optimization is exploited to reconstruct the robust beamformer by minimizing array output power with the existence of the worst case array imperfections the robust beamforming can be expressed as a second order cone programming socp problem the resultant beamformer possesses superior robustness against arbitrary array imperfections with the proposed methods a large robust response region and a high signal to interference plus noise ratio sinr enhancement can be achieved readily simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed methods

two dimensional proper rational matrices and causal input output representations of two dimensional behavioral systems the concept of proper rational matrix is strictly connected with the representation of causal transfer matrices in the two dimensional 2d case there is much freedom in defining proper rational matrices this freedom is connected to the fact that past and future in the 2d case can be determined by a 2d cone in this way the concept of rational matrix which is proper with respect to a cone can be introduced moreover an algorithm that checks the properness of a rational matrix is proposed finally this algorithm is used for determining all possible causal input output i o representations of a behavior given by a kernel representation

controllability of 2 d systems the concept of controllability of 2 d systems is introduced in a behavioral framework this property is defined as a systems concept and is characterized in terms of system representations state space realizations for controllable 2 d systems are presented the structure of state space systems is analyzed and the notions of trimness reachability and observability are introduced and characterized these realizations do not depend on any assumptions concerning causality

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables

constraints for maximally flat optimum broadband antenna arrays frequency response shaping for the direct form pre steered broadband pb antenna array processor is often achieved by imposing look direction constraints on the weights of the processor this results in a linearly constrained optimization problem to ensure a maximally flat spatial response of a specified order in the look direction of the pb processor additional constraints known as derivative constraints can be further imposed on the weights in general derivative constraints corresponding to necessary and sufficient ns conditions for a maximally flat spatial power response can result in a quadratic equality constrained optimization problem we transform the quadratic ns derivative constraints to parameterized linear forms these parameterized linear forms allow the global optimum of the quadratic equality constrained optimization problem to be obtained easily they also provide a general framework for deriving new sets of derivative constraints which correspond only to sufficient conditions for a maximally flat spatial power response these sufficient derivative constraints are useful for real time processing because of their reduced computational requirements and because they ran deliver performance comparable to the ns derivative constraints