mode interaction in rayleigh be nard convection abstract a long wave model for two dimensional thermal convection is examined this model contains both quadratic and cubic nonlinearity unless the problem is symmetrical about the horizontal mid plane in which case only the cubic nonlinearity is present in the asymmetrical case a strong interaction between modes with wavenumbers k and 2k is responsible for wavenumber gaps regions in parameter space where steady states of a given spatial period cease to exist in both the symmetrical and asymmetrical cases a 1 3 resonance generates multiple steady solutions of a given spatial period we calculate steady states and determine their stability for the asymmetrical case we also solve the initial value problem and find stable travelling waves stable modulated travelling waves and stable heteroclinic cycles as predicted by an analysis of the 1 2 resonance

parameter estimation problems with singular information matrices the case of a singular fisher information matrix fim represents a significant complication for the theory of the cramer rao lower bound crb that is usually handled by resorting to the pseudoinverse of the fisher matrix we take a different approach in which the crb is derived as the solution to an unconstrained quadratic maximization problem which enables us to handle the singular case in a simple yet rigorous manner when the fisher matrix is singular except under unusual circumstances any estimator having the specified bias derivatives that figure in the crb must have infinite variance

exploring estimator bias variance tradeoffs using the uniform cr bound we introduce a plane which we call the delta sigma plane that is indexed by the norm of the estimator bias gradient and the variance of the estimator the norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space using a uniform cramer rao cr bound on estimator variance a delta sigma tradeoff curve is specified that defines an unachievable region of the delta sigma plane for a specified statistical model in order to place an estimator on this plane for comparison with the delta sigma tradeoff curve the estimator variance bias gradient and bias gradient norm must be evaluated we present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log likelihood we demonstrate the methods developed in this paper for linear gaussian and nonlinear poisson inverse problems

resonant interactions in thermosolutal convection when convection occurs in a finite box successive modes become unstable as the rayleigh number is increased giving rise to branches of nonlinear solutions that are linked by mixed mode branches emerging from hopf transcritical or pitchfork bifurcations the fundamental mode in particular gives rise to resonant interactions several specific examples of these generic features have already been described here we study resonant interactions in two dimensional thermosolutal convection with point symmetry imposed where behaviour is enriched by the presence of oscillations and of subcritical steady convection steady m roll solutions are obtained numerically and their stability properties are investigated by computing the leading real and complex eigenvalues we find that the branch of fundamental m 1 solutions for a box with aspect ratio 1 5 develops loops that touch the m 3 branch in transcritical bifurcations as is reduced these loops detach themselves from the m 1 branch and eventually join the stacked m 2 branch increasing on the other hand leads to complicated triple resonances involving m 1 m 3 and m 5 solutions these resonant interactions are associated with pattern selection and the transfer of stability from single roll to multiple roll solutions in wider boxes

singular higher order divergence conforming bases of additive kind and moments method applications to 3d sharp wedge structures we present new subsectional singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges the bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood singular bases of this kind complete to arbitrarily high order are described in a unified and consistent manner for curved quadrilateral and triangular elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components adequate modelling of the divergence and removal of spurious solutions these singular high order bases provide more accurate and efficient numerical solutions of surface integral problems several test case problems are considered in the paper thereby obtaining highly accurate numerical results for the current and charge density induced on 3d sharp wedge structures the results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problems

gradient singular hierarchical finite elements for vector electromagnetics new tetrahedral finite elements are described for the analysis of vector electromagnetic fields they are singular elements that are more accurate than conventional polynomial based elements near sharp edges and corners they are hierarchical meaning that elements of different orders accuracies are available and may be placed together in the same mesh without violating continuity of the field the elements are formed from a series of scalar singular elements by taking the gradient and are therefore called gradient singular results using the new elements in p adaptive analysis orders 1 to 3 demonstrate that when they are used in place of conventional elements the scattering parameters are as much as 10 times more accurate for the same number of unknowns

robust target localization in the absence of signal propagation models this paper considers a problem of target or source localization based on the measurements from a mobile sensor or a network of sensors the assumption is that the received signal strength is strictly monotonic with the distance between the target and the sensor no explicit signal propagation model neither the structure nor the mathematical description is assumed or used in localization the contribution of the paper is to show that this mere knowledge of monotonicity suffices in locating the unknown target in the absence of noise further in the presence of noise robust localization algorithms are developed and analyzed by exploiting various forms of angular temporal and spatial averages the asymptotic convergence results have been established in the presence of noise and further the finite step performance results are developed

resonant mode interactions in rayleigh benard convection department of physics university of california berkeley california 94720 received 5 february 1998 in systems with midplane re ection symmetry the dominant spatial resonance is the 1 3 resonance numeri cal continuation is used to study this and other 1 2k11 resonances in two dimensional convection betweenno slip perfectly conducting horizontal plates periodic boundary conditions are imposed in the horizontal these resonances in uence the process of wave number selection at moderate rayleigh numbers through thegeneration of hybrid solutions and thereby modify the eckhaus picture of wave number selection unlike thebetter known mixed modes the hybrid solutions have the same symmetry as a pair of primary rolls both hybridand symmetry breaking mixed modes are computed and their linear stability properties with respect to pertur bations preserving different spatial periods are determined a complete description of the effects of midplanere ection on wave number selection emerges only steady solutions are considered and the prandtl number is xed ats510 s1063 651x 98 05709 2 pacs number s 47 20 ky 05 45 1bi introduction

robust tracking of piecewise linear trajectories with binary sensor networks we present a novel approach to the problem of tracking objects moving along smooth trajectories using a network of simple inexpensive binary sensors specifically we consider object trajectories that can be well approximated by piecewise linear curves and sensors that can only detect whether an object is in their sensing range we start by considering objects moving along straight line trajectories with an unknown speed and show that such objects can be tracked using the measurements of just three generically placed binary sensors whose sensing ranges intersect the trajectory next we present an asymptotic analysis that shows that a trajectory consisting of a finite number of straight line segments can be recovered with high probability using an arbitrarily low spatial density of sensors in the limit when the area to be covered gets larger and larger we also present efficient algorithms that effectively recover piecewise linear trajectories finally we present analysis and simulations to demonstrate the high tracking accuracy of our approach and its robustness to sensing errors

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

optimization with few violated constraints for linear bounded error parameter estimation in the context of linear constrained optimization we study the problem of finding an optimal solution satisfying all but k of the given n constraints a solution is obtained by means of an algorithm of the complexity min o n spl middot k sup d o n spl middot d sup k 1 where d is the dimension of the problem we then use these results to solve the problem of robust identification in the presence of outliers in the setting of bounded error parameter identification finally we show that the estimate obtained converges to the true but unknown parameter in the presence of outliers

elliptic localization performance study and optimum receiver placement range based localization often relies on toa that creates a circular contour or tdoa that yields hyperbolic surface to determine the position of an emitting object another approach that has gained attention recently is elliptic localization elliptic localization uses an active transmitter to send out a signal and several receivers to acquire the reflected or relayed signal from an object to obtain its location this paper performs a fundamental investigation on the performance of elliptic localization for both the synchronous and asynchronous cases between the transmitter and the receivers their performance is also characterized with respect to the hyperbolic localization the study is based on the cramer rao lower bound crlb for the object location under gaussian measurement noise as well as gaussian errors in the transmitter and receiver positions when the receiver positions are controllable we derive the optimum receiver placement for elliptic positioning to improve the localization accuracy we conclude the study with simulation results to demonstrate the elliptic localization performance using the crlbs and the maximum likelihood estimators

optimal sensor scheduling for multiple linear dynamical systems we consider the design of an optimal collision free sensor schedule for a number of sensors which monitor different linear dynamical systems correspondingly at each time only one of all the sensors can send its local estimate to the remote estimator a preliminary work for the two sensor scheduling case has been studied in the literature the generalization into multiple sensor scheduling case is shown to be nontrivial we first find a necessary condition of the optimal solution which can significantly reduce the feasible optimal solution space without loss of performance by modelling a finite state markov decision process mdp problem we can numerically search an asymptotic periodic schedule which is proven to be optimal some simple but effective suboptimal schedules for any systems are proposed we also find a lower bound of the optimal cost which enables us to quantify the performance gap between any suboptimal schedule and an optimal one

mono implicit runge kutta formulae for the numerical solution of second order nonlinear two point boundary value problems mono implicit runge kutta mirk formulae are widely used for the numerical solution of first order systems of nonlinear two point boundary value problems in order to avoid costly matrix multiplications mirk formulae are usually implemented in a deferred correction framework and this is the basis of the well known boundary value code twpbvp however many two point boundary value problems occur naturally as second or higher order equations or systems and for such problems there are significant savings in computational effort to be made if the mirk methods are tailored for these higher order forms in this paper we describe mirk algorithms for second order equations and report numerical results that illustrate the substantial savings that are possible particularly for second order systems of equations where the first derivative is absent

higher order hybrid fem mom technique for analysis of antennas and scatterers a novel higher order large domain hybrid computational electromagnetic technique based on the finite element method fem and method of moments mom is proposed for three dimensional analysis of antennas and scatterers in the frequency domain the geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders the fields and currents on elements are modeled using curl and divergence conforming hierarchical polynomial vector basis functions of arbitrary approximation orders and the galerkin method is used for testing the elements can be as large as about two wavelengths in each dimension as multiple mom objects are possible in a global exterior region the mom part provides much greater modeling versatility and potential for applications especially in antenna problems than just as a boundary integral closure to the fem part the examples demonstrate excellent accuracy convergence efficiency and versatility of the new fem mom technique and very effective large domain meshes that consist of a very small number of large flat and curved fem and mom elements with p refined field and current distributions of high approximation orders the reduction in the number of unknowns is by two orders of magnitude when compared to available data for low order fem mom modeling

guaranteeing practical convergence in algorithms for sensor and source localization this paper considers localization of a source or a sensor from distance measurements we argue that linear algorithms proposed for this purpose are susceptible to poor noise performance instead given a set of sensors anchors of known positions and measured distances of the source sensor to be localized from them we propose a potentially nonconvex weighted cost function whose global minimum estimates the location of the source sensor one seeks the contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors anchors of known positions such that if the object to be localized is in this region localization occurs by globally exponentially convergent gradient descent in the noise free case exponential convergence in the noise free case represents practical convergence as it ensures graceful performance degradation in the presence of noise these results guide the deployment of sensors anchors so that small subsets can be made responsible for practical localization in geographical areas determined by our approach

sensor network localization with imprecise distances an approach to formulate geometric relations among distances between nodes as equality constraints is introduced in this paper to study the localization problem with imprecise distance information in sensor networks these constraints can be further used to formulate optimization problems for distance estimation the optimization solutions correspond to a set of distances that are consistent with the fact that sensor nodes live in the same plane or 3d space as the anchor nodes these techniques serve as the foundation for most of the existing localization algorithms that depend on the sensors distances to anchors to compute each sensor s location 2006 elsevier b v all rights reserved

fundamental properties and performance of conventional bearings only target motion analysis this paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform the process is inherently nonlinear and exhibits unusual observability properties that are geometry dependent a maximum likelihood estimate mle of the target motion analysis solution is developed and its performance analyzed a comparison is drawn between the mle and two previously reported methods a nonlinear modified instrumental variable estimate miv and the pseudo linear estimate ple both the miv and ple are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the mle the limits on performance that can be expected from processing bearing data are detailed specifically for long range to baseline geometries approximate expressions for the cramer rao bound are derived extension of the results to the practical filters approximately predicts numerically observed behavior for less restrictive geometries bounds are presented incorporation of a target speed constraint on the mle results in a transition to a lower dimensional problem as noise level and range increases monte carlo experimental results are presented and the improvements realized by the mle techniques are evident

minimum variance in biased estimation bounds and asymptotically optimal estimators we develop a uniform cramer rao lower bound ucrlb on the total variance of any estimator of an unknown vector of parameters with bias gradient matrix whose norm is bounded by a constant we consider both the frobenius norm and the spectral norm of the bias gradient matrix leading to two corresponding lower bounds we then develop optimal estimators that achieve these lower bounds in the case in which the measurements are related to the unknown parameters through a linear gaussian model tikhonov regularization is shown to achieve the ucrlb when the frobenius norm is considered and the shrunken estimator is shown to achieve the ucrlb when the spectral norm is considered for more general models the penalized maximum likelihood pml estimator with a suitable penalizing function is shown to asymptotically achieve the ucrlb to establish the asymptotic optimality of the pml estimator we first develop the asymptotic mean and variance of the pml estimator for any choice of penalizing function satisfying certain regularity constraints and then derive a general condition on the penalizing function under which the resulting pml estimator asymptotically achieves the ucrlb this then implies that from all linear and nonlinear estimators with bias gradient whose norm is bounded by a constant the proposed pml estimator asymptotically results in the smallest possible variance

optimality analysis of sensor target localization geometries the problem of target localization involves estimating the position of a target from multiple noisy sensor measurements it is well known that the relative sensor target geometry can significantly affect the performance of any particular localization algorithm the localization performance can be explicitly characterized by certain measures for example by the cramer rao lower bound which is equal to the inverse fisher information matrix on the estimator variance in addition the cramer rao lower bound is commonly used to generate a so called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate i e an estimate which achieves the lower bound the aim of this work is to identify those relative sensor target geometries which result in a measure of the uncertainty ellipse being minimized deeming such sensor target geometries to be optimal with respect to the chosen measure the optimal sensor target geometries for range only time of arrival based and bearing only localization are identified and studied in this work the optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor target configuration is not in general unique the importance of understanding the influence of the sensor target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples

non conformal domain decomposition method with mixed true second order transmission condition for solving large finite antenna arrays a non overlapping and non conformal domain decomposition method ddm is presented for modeling large finite antenna arrays two major benefits of the proposed ddm a a mixed true second order transmission condition sotc with corner edge penalty terms is developed to facilitate fast convergence in the ddm iterations numerical experiments indicate that the convergence of ddm with the aforementioned sotc is insensitive to the sizes of arrays and b the non conformal property of the proposed ddm permits the use of completely independent discretization for each of the sub domains we demonstrate the performance of the proposed approach through several large scale problems

multilevel characteristic basis finite element method ml cbfem an efficient version of a domain decomposition algorithm for large scale electromagnetic problems we introduce a memory efficient version of the characteristic basis finite element method cbfem which combines the domain decomposition with the use of characteristic basis functions cbfs that are tailored for each individual subdomain although the conventional cbfem is inherently an efficient approach the final number of unknowns is primarily determined by the size or the number of the subdomains the larger the size of the subdomains or fewer the number the less is the final number of unknowns however if we employ large subdomains it is more difficult to generate cbfs for each subdomain due to the memory bottleneck in utilizing direct solution techniques employed to generate the cbfs in the proposed multilevel approach referred to herein as the multilevel cbfem ml cbfem we first decompose the computational domain into several smaller subdomains and generate the cbfs for each subdomain in a conventional manner then these bases are combined in a multilevel fashion to derive the cbfs for larger subdomains in each level the cbfs are created by using the bases in the lower level this approach also called nested cbfem leads to a considerable reduction in the matrix size and memory and thus makes use of direct solvers efficiently

repeatable extended jacobian inverse kinematics algorithm for mobile manipulators abstract an inverse kinematics algorithm for a robotic system is called repeatable if it transforms closed paths in the task space into closed paths in the configuration space in this paper we assume the endogenous configuration space approach and define a repeatable inverse kinematics algorithm for mobile manipulators patterned on the extended jacobian scheme an examination of a dynamic system associated with this algorithm gives new insight into the mechanism of repeatability as an illustration of the general design strategy an extended jacobian algorithm is applied to a kinematic car type platform carrying the polycrank 7 dof on board manipulator

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

a novel location penalized maximum likelihood estimator for bearing only target localization in this paper we present a location penalized maximum likelihood lpml estimator for bearing only target localization we develop a new penalized maximum likelihood cost function by transforming the variables of target position and bearings the new penalized likelihood function can also be recognized as a posterior distribution under a bayesian framework by penalizing a prior we give analysis of the asymptotic properties and show that both traditional bearing maximum likelihood tbml and lpml estimators are asymptotically efficient estimators to compare the performances of the tbml and lpml estimators we analyze the cramer rao lower bound crlb of the two estimators and show that the bound of the lpml estimator is lower than that of the tbml estimator extensive simulations are performed it is observed that the new lpml algorithm consistently outperforms other well known algorithms field experiments are also conducted by applying this method to localize a vehicle using real world data acquired by an acoustic array sensor network the new lpml algorithm demonstrates superior performance in all the field experiments

singular higher order complete vector bases for finite methods this paper presents new singular curl and divergence conforming vector bases that incorporate the edge conditions singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements the curl divergence conforming singular bases guarantee tangential normal continuity along the edges of the elements allowing for the discontinuity of normal tangential components adequate modeling of the curl divergence and removal of spurious modes solutions these singular high order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems sample numerical results confirm the faster convergence of these bases on wedge problems

uniformly improving the cramer rao bound and maximum likelihood estimation an important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem as well as determining estimators that achieve the optimal performance the traditional cramer rao type bounds provide benchmarks on the variance of any estimator of a deterministic parameter vector under suitable regularity conditions while requiring a priori specification of a desired bias gradient in applications it is often not clear how to choose the required bias a direct measure of the estimation error that takes both the variance and the bias into account is the mean squared error mse which is the sum of the variance and the squared norm of the bias here we develop bounds on the mse in estimating a deterministic parameter vector x0 over all bias vectors that are linear in x0 which includes the traditional unbiased estimation as a special case in some settings it is possible to minimize the mse over all linear bias vectors more generally direct minimization is not possible since the optimal solution depends on the unknown x0 nonetheless we show that in many cases we can find bias vectors that result in an mse bound that is smaller than the cramer rao lower bound crlb for all values of x0 furthermore we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists by performing a simple linear transformation on the standard maximum likelihood ml estimator this leads to estimators that result in a smaller mse than the ml approach for all possible values of x0

amplitude equations for systems with competing instabilities we describe how to derive ordinary differential equations to predict the time dependence of a system governed by partial differential equations when that system is near to the polycritical condition for the onset of several instabilities the method is illustrated for the general case of two competing instabilities and then a specific physical example of this case is worked out in detail the basic idea is to extend the krylov bogolyubov mitropolsky method of nonlinear mechanics to bifurcation problems

finite element analysis of complex antennas and arrays various technical issues are addressed in the frequency and time domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials the paper starts with the finite element formulation of a generic antenna problem formulation for the modeling of general electrically and magnetically dispersive lossy and anisotropic materials in the time domain finite element analysis is presented for the first time this is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions perfectly matched layers and boundary integral equations it then describes the modeling of antenna feeds using a current probe including an improved model a voltage gap and a waveguide port boundary condition after that numerical approaches to modeling infinite phased arrays large finite arrays and antenna platform interaction are presented including two novel domain decomposition algorithms in both the frequency and time domains numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays