physical optics analysis of multiple interactions in large scatters using current modes an efficient scheme based on physical optics po to analyze the mutual interactions between the parts of large bodies is presented the po current is approximated by current modes defined as complex exponential functions both the body geometry and the current modes are represented by means of nonuniform rational bi spline surfaces functions the current modes are computed by extrapolation considering the current values in a set of sampling points a new interpolation scheme to obtain the phase of the current modes using samples of the spatial frequency is presented the field due to the current modes is calculated efficiently using analytical expressions some results are also presented that show the performances of the method

a novel approach to scatterers localization problem a new approach to find the number and locations of electromagnetic scatterers sources from one view one frequency field data is presented the case of scatterers sources with dimensions comparable to the wavelength is considered first in order to devise an effective technique a new relevant property of the electromagnetic field the point source spectral content is introduced and its relationship with both the sliding windowed fourier transform of the field and the local bandwidth function is discussed to enlighten its usefulness it is also shown that a footprint of the scattering system encoding information on its geometry can be easily extracted from the scattered field by exploiting this new property on this basis the new localization technique is introduced in order to restrict the search region the minimum circular envelope enclosing the scatterers is found by purposely introducing a new technique exploiting the effective bandwidth of the radiated field then the number and locations of scatterers is retrieved by using the field local quantitative feature previously introduced without the complexities of the full inverse problem as it is usually done by the traditional approaches in this way not only a simplified technique is obtained but also the ill posedness of the problem and the noise effects are significantly mitigated the effectiveness of the proposed technique and its overall performance with respect to a singular value decomposition based approach are proved by means of a numerical analysis

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

analysis of numerical errors in large eddy simulation using statistical closure theory this paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large eddy simulation the analysis is based on edqnm closure theory and is applied to the les of decaying isotropic turbulence first the effects of finite differencing truncation error aliasing error and the dynamic smagorinsky model are independently considered the time evolution of kinetic energy and spectra predicted by the analysis are compared to actual les using the navier stokes equations and good agreement is obtained the analysis is then extended to simultaneously consider all sources of error in a second order discretely energy conserving central difference les solver good agreement between the analysis and actual les is obtained the analysis is used to compare the contribution of the subgrid model to that of numerical errors and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors the proposed one dimensional edqnm les model shows potential as a more general tool for the analysis of numerical error and sgs model in simulations of turbulent flow

a new value picking regularization strategy application to the 3 d electromagnetic inverse scattering problem the nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel based data fit cost function because of the ill posedness it is necessary to introduce some form of regularization many authors apply a smoothing constraint on the reconstructed permittivity profile but such regularization smooths away sharp edges in this paper a simple yet effective regularization strategy the value picking vp regularization is proposed this new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges it is based on the knowledge that only a few different permittivity values occur in such profiles the values of which need not be known in advance vp regularization does not impose this a priori information in a strict sense such that it can be applied also to profiles that are only approximately piecewise constant the vp regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem when minimized the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables the vp values which are continuously updated throughout the iterations to minimize the regularized cost function a half quadratic gauss newton optimization technique is presented finally a stepwise relaxed vp regularization scheme is proposed in which the number of vp values is gradually increased this scheme is tested with synthetic and measured scattering data obtained from inhomogeneous 3d targets and is shown to achieve high reconstruction quality

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

alternating adaptive projections in antenna synthesis the projection operator is a basic building block in the application of the alternating projections method to antenna synthesis in general it is a non linear operator that is repeatedly applied in the course of a single synthesis process thus having a considerable impact on the convergence properties of the resulting algorithm a novel approach to the computation of these projections is presented which exploits a simple definition of the relevant spaces particularly that of radiated fields characterization of field mask specification as scale invariant under this definition adds a further degree of freedom namely reference level which impacts on the sensitive to scaling projector in order to compute the optimum reference level an iterative procedure is proposed which is simple to implement easily integrable in standard alternating projection routines and adds negligible computational burden numerical tests confirm an improved performance with respect to the fixed scaling projection operator in terms of convergence rate and robustness against the initial guess supporting our approach as a valid aid in overcoming the drawbacks of the alternating projections based antenna synthesis

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

on the interpolation of electromagnetic near field without prior knowledge of the radiating source a method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available in the absence of a priori knowledge general properties of the electromagnetic field are exploited to estimate the field namely the minimum complexity of the field and the continuity of the first derivatives these properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results respectively the proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas the quality of the interpolation and its robustness to noise are investigated despite its simplicity the interpolation method is able to properly estimate the near field from a random coarse sampling of 2 lambda the quality of the near field interpolation is also confirmed by deriving the far field these promising results pave the way for the development of fast antenna measurement procedures

optimal synthesis of circularly symmetric shaped beams the problem of the optimal power pattern synthesis of circularly symmetric shaped beams is addressed and solved in particular an existence criterion is provided to test a priori i e without solving the overall synthesis problem if a non superdirective source of given size can radiate or not a circularly symmetric power pattern lying in a given arbitrary mask in the affirmative case the proposed approach guarantees the achievement of the optimal solution i e that of maximum directivity or minimum size by using convex optimization techniques in general a number of equivalent source distributions i e radiating the same power pattern do exist which can be explicitly determined in a deterministic way numerical examples concerning applications of actual interest support the given theory and confirm the effectiveness of the developed synthesis procedure

energy preserving turbulent simulations at a reduced computational cost energy conserving discretizations are widely regarded as a fundamental requirement for high fidelity simulations of turbulent flows the skew symmetric splitting of the nonlinear term is a well known approach to obtain semi discrete conservation of energy in the inviscid limit however its computation is roughly twice as expensive as that of the divergence or advective forms alone a novel time advancement strategy that retains the conservation properties of skew symmetric based schemes at a reduced computational cost has been developed this method is based on properly constructed runge kutta schemes in which a different form advective or divergence for the convective term is adopted at each stage a general framework is presented to derive schemes with prescribed accuracy on both solution and energy conservation simulations of homogeneous isotropic turbulence show that the new procedure is effective and can be considerably faster than skew symmetric based techniques

an adaptive implicit explicit scheme for the dns and les of compressible flows on unstructured grids an adaptive implicit explicit scheme for direct numerical simulation dns and large eddy simulation les of compressible turbulent flows on unstructured grids is developed the method uses a node based finite volume discretization with summation by parts sbp property which in conjunction with simultaneous approximation terms sat for imposing boundary conditions leads to a linearly stable semi discrete scheme the solution is marched in time using an implicit explicit runge kutta imex rk time advancement scheme a novel adaptive algorithm for splitting the system into implicit and explicit sets is developed the method is validated using several canonical laminar and turbulent flows load balance for the new scheme is achieved by a dual constraint domain decomposition algorithm the scalability and computational efficiency of the method is investigated and memory savings compared with a fully implicit method is demonstrated a notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

the degrees of freedom of wireless networksvia cut set integrals the problem of determining the number of spatial degrees of freedom d o f of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow physically this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment mathematically this variation is expressed as an integral along the cut which we call cut set integral and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three dimensional 3 d environments presented results shed some new light on the problem of computing the capacity of wireless networks showing a fundamental limitation imposed by the size of the cut through which the information must flow in an attempt to remove what may appear as apparent inconsistencies with previous literature we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop hierarchical cooperation and interference alignment

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

a high order low dispersion symmetry preserving finite volume method for compressible flow on curvilinear grids a new high order finite volume method is presented that preserves the skew symmetry of convection for the compressible flow equations the method is intended for large eddy simulations les of compressible turbulent flows in particular in the context of hybrid rans les computations the method is fourth order accurate and has low numerical dissipation and dispersion due to the finite volume approach mass momentum and total energy are locally conserved furthermore the skew symmetry preservation implies that kinetic energy sound velocity and internal energy are all locally conserved by convection as well the method is unique in that all these properties hold on non uniform curvilinear structured grids due to the conservation of kinetic energy there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection this enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid scale model by minimizing the numerical dispersion the numerical errors are reduced by an order of magnitude compared to a standard fourth order finite volume method

application of the entropically damped artificial compressibility model to direct numerical simulation of turbulent channel flow abstract the feasibility of the entropically damped artificial compressibility edac model for simulation of wall bounded turbulence is examined a favourable feature of edac is the purely parabolic type of governing equations resulting from the introduction of a damping term to the pressure evolution equation this significantly reduces noise in the velocity divergence field when central schemes are applied for the spatial discretisation the method of lines is used for the solution of the edac equations a conservative finite difference method of purely 2nd and mixed 4th 2nd order is applied the explicit 4th order six stage low storage runge kutta method is used for time advancement as expected the mixed scheme is superior to the 2nd order one in terms of both accuracy and computational efficiency for the first time the edac model is assessed for the direct numerical simulation of wall bounded turbulent flow requiring a non uniform mesh as a particular test case we have chosen the channel flow at the friction reynolds numbers r e 180 and 395 a very good agreement with the reference data is obtained as documented by the chosen one point velocity statistics the mean and r m s profiles and the budgets of the reynolds stresses the use of the explicit time discretisation and local rather than compact spatial schemes results in easily and efficiently parallelisable solution algorithm we achieved very high computational performance on a desktop computer when solving the edac equations using a code dedicated for the graphics processing unit gpu the aspects of the gpu implementation are discussed

phaseless antenna measurement on non redundant sample points via leith upatnieks holography a scheme for reducing the number of sample points in phaseless acquisition based on leith upatnieks holography is presented an appropriate choice of the phase of the reference field enables to drastically decrease the sampling rate by acquiring the so called reduced field instead of the real radiated field the reference phase changes are enabled by applying the recent developments on the synthesis of the reference wave moreover optimal sampling interpolation can be applied to the retrieved field so that the real field can be computed at any point on the acquisition surface the method is illustrated by means of multiple simulations for observation domains such as straight lines azimuthal circles as well as for a plane polar acquisition scheme

a complete set of linear phase basis functions for scatterers with flat faces and for planar apertures entire domain basis functions are introduced for the analysis of scattering from bodies with flat portions and of radiation from planar apertures they are defined via the application of the sampling theorem of shannon these basis functions are particularly convenient for polygonal contours however arbitrary contours can be treated in the same framework with a very minor pre processing time a non redundant set of basis functions is determined a priori by explicit approximate formulas either for currents and for radiated field numerical results are presented to shown the accuracy of the method

on the sampling of the electromagnetic field radiated by sparse sources the aim of this paper is to discuss the effectiveness of random sampling of the electromagnetic field in problems involving sparse radiating sources the method adopted in this paper uses an intuitive geometrical approach based on the johnson linderstrauss lemma applied to the epsilon net of the set of the fields radiated by the sparse source the paper shows that a proper non uniform random sampling nurs using some a priori information on the problem allows a significant reduction in the cardinality of the set of the measured data compared to uniform random sampling and to random sampling from a lambda 2 equispaced set of data it is also shown that there is a limiting number of data after which random sampling is not convenient in this case a deterministic sampling strategy called modified non uniform sampling mnus is proposed numerical results on linear sparse arrays confirm the effectiveness of nurs and mnus

comments on fast direct solution of method of moments linear system in the above named work a new algorithm is presented for direct non iterative frequency domain method of moments mom calculations based on block wise compression of the impedance matrix the storage requirements and computational complexity of the algorithm are claimed to be n3 2 and n2 respectively if n is the number of unknowns for a mom surface discretization that is fixed with respect to the wavelength a more rigorous analysis explicitly using the asymptotic expression for the number of degrees of freedom dof in the interaction between groups of scatterers is presented here showing that this should be n3 2log n and n2log2 n respectively the complexity analysis applies to problems that can be formulated as a surface integral equation sie on surfaces in or between homogeneous media such as a ship or an airplane it does not apply to volume discretization mom or multilayer problems the results presented here are also relevant for block wise compression methods using iterative solvers since the compressed impedance matrix is the same consequently the above complexity analysis applies to very large problems well beyond the reach of even the largest existent computers for moderate size problems the measured complexity is lower

an effective deterministic procedure for the synthesis of shaped beams by means of uniform amplitude linear sparse arrays a rigorous deterministic approach is proposed for the mask constrained power pattern synthesis of shaped beams through one dimensional sparse arrays having uniform amplitude excitations and variable phases the approach includes the well known density taper procedure as a special case the corresponding technique which exploits an analytical formulation of the problem and convex programming routines results in fast computation and is able to achieve optimal solutions without recurring to any global optimization numerical results assessing the capabilities of the proposed design method are provided opening the way to the development of an effective approach for the synthesis of circularly symmetric shaped beams via uniformly excited circular ring arrays

on fuzzy almost continuous functions abstract in this paper we redefine the notions of open fuzzy set closed fuzzy set adherent point of a fuzzy set and closure of a fuzzy set all the results pertaining to these notions see velicko 17 are extended to fuzzy setting and several related characterization of fuzzy almost continuous functions are obtained which are the counterparts of the corresponding results in general topological spaces 12 some more properties of fuzzy almost continuous functions are established subsequently a characaterization of normal fuzzy topological spaces is also obtained the notion of fuzzy almost quasi compact mapping is introduced and its characterizations and relationship with fuzzy almost continuous functions are discussed

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

minimum trace norm regularization mtnr in electromagnetic inverse problems this paper discusses a method to regularize linear problems in presence of incomplete and noisy data generated by partially or totally unknown sources the idea is to identify the simplest solution looking for the system having the minimum number of degrees of freedom ndf compatible with the available data it is shown that a normalized version of the trace norm known as 1 schatten norm in functional analysis is a good convex approximation of the ndf of the field this allows to use the trace norm as a convex surrogate of the ndf in the minimization process taking advantage of the recent literature on rank minimization examples regarding mimo beamforming from incomplete channel matrix field interpolation with no a priori information on the sources and land mine identification using the total field are discussed

convergences in fuzzy topological spaces in this paper we introduce the notions of fuzzy upper limit fuzzy lower limit and the fuzzy continuous convergence on the set of fuzzy continuous functions in examining these aforementioned notions in the present paper we find on the one hand many properties of them whilst on the other the following applications take place the characterization of fuzzy compact spaces through the contribution of fuzzy upper limit and the characterization of the fuzzy continuous convergence through the assistance of fuzzy upper limit

efficient sampling of electromagnetic fields via the adaptive cross approximation the adaptive cross approximation method is applied to the problem of efficiently sampling an electromagnetic field across two dimensions the algorithm uses previously collected samples to determine which field samples to take next and reduces the number of samples required to accurately represent the field in this way the field may be sampled faster than it would have been if it had been raster scanned this is achieved without significant changes to the sensor hardware

an effective nf ff transformation technique with planar spiral scanning tailored for quasi planar antennas an effective probe compensated near field far field transformation technique with planar spiral scanning is developed in this paper it makes use of an ellipsoidal modelling of the source instead of the previously adopted spherical one such a modelling tailored for quasi planar antennas allows one to consider measurement planes at a distance smaller than one half the antenna maximum size thus reducing the error related to the truncation of the scanning surface moreover it is quite general containing the spherical modelling as particular case and reduces significantly the number of the needed near field data when dealing with quasi planar antennas some numerical tests assessing the accuracy of the technique and its stability with respect to random errors affecting the data are reported

higher entropy conservation and numerical stability of compressible turbulence simulations we present a numerical formulation for the treatment of nonlinear instabilities in shock free compressible turbulence simulations the formulation is high order and contains no artificial dissipation numerical stability is enhanced through semi discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation the numerical implementation is achieved using a conservative skew symmetric splitting of the nonlinear terms the robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high reynolds number results show the scheme is capable of capturing the statistical equilibrium of low mach number compressible turbulent fluctuations at infinite reynolds number comparisons with the entropy splitting technique j comput phys 162 2000 33 j comput phys 178 2002 307 staggered method j comput phys 191 2 2003 392 and skew symmetric like schemes j comput phys 161 2000 114 confirm the superiority of the current approach we also discuss a flaw in the skew symmetric splitting implemented in the literature very good results are obtained based on the proper splitting

efficient algorithm for the evaluation of the physical optics scattering by nurbs surfaces with relatively general boundary condition an adaptive integration algorithm is presented for the computation of the physical optics po electric and magnetic field scattered by electrically large objects modeled by non uniform rational b splines nurbs the algorithm is the customization of a more general purpose result that has been recently published by using a unique formulation both impenetrable e g impedance surfaces coated conductors as well as transparent thin sheet materials e g thin dielectric panels or frequency selective surfaces are treated via their fresnel reflection and transmission coefficients the po radiation integral is evaluated over the nurbs parametric domain since most of the computer aided geometric design cagd tools are based on nurbs the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description with no need of generating new geometrical models furthermore the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard nyquist based sampling integration algorithms such reduction of the sampling points is achieved by resorting to high frequency technique concepts and allows a significant reduction of the cpu computational burden therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real life electrically large objects

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

large eddy simulation of shock turbulence interaction the approximate deconvolution model adm for large eddy simulation les is adapted for use with a central fourth order finite volume jameson type scheme widely applied for aerodynamics calculations of industrial interest with adm an approximation of the unfiltered solution is obtained by repeated filtering and given a good approximation of the unfiltered solution the nonlinear terms of the filtered navier stokes equation are computed directly the effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation and a relaxation parameter the supersonic turbulent boundary layer along a compression ramp at a freestream mach number of m 3 and a reynolds number based on free stream quantities and the mean momentum thickness at inflow of re 1685 is computed to evaluate the ability of adm to represent discontinuities and turbulent flow regions it was observed that a unified modeling of discontinuities and turbulence required a local adaptation of the secondary filter used for the relaxation regularization the les results are compared with corresponding filtered direct numerical simulation dns data very good agreement between the filtered dns and the les is observed for the mean fluctuating and averaged wall quantities

generalized conservative approximations of split convective derivative operators we propose a strategy to design locally conservative finite difference approximations of convective derivatives for shock free compressible flows with arbitrary order of accuracy that generalizes the approach of ducros et al 2000 1 and that can be applied as a building block of low dissipative hybrid shock capturing methods the approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible euler equations which guarantee strong numerical stability and near energy preservation in the inviscid limit a convenient implementation of the high order fluxes is suggested which guarantees improved computational efficiency over existing methods numerical tests performed for isotropic turbulence at zero viscosity show stability of schemes with order of accuracy up to ten and effectiveness of convective splitting of kennedy and gruber 2008 2 in providing extra stability in the presence of strong density variations numerical simulations of compressible turbulent boundary layer flow indicate suitability of the method for non uniform grids and overall support superior computational efficiency of high order schemes

split form nodal discontinuous galerkin schemes with summation by parts property for the compressible euler equations fisher and carpenter 2013 12 found a remarkable equivalence of general diagonal norm high order summation by parts operators to a subcell based high order finite volume formulation this equivalence enables the construction of provably entropy stable schemes by a specific choice of the subcell finite volume flux we show that besides the construction of entropy stable high order schemes a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms thus by changing the subcell finite volume flux to a specific choice we are able to generate in a systematic way all common split forms of the compressible euler advection terms such as the ducros splitting and the kennedy and gruber splitting although these split forms are not entropy stable we present a systematic way to prove which of those split forms are at least kinetic energy preserving with this we construct a unified high order split form dg framework we investigate with three dimensional numerical simulations of the inviscid taylorgreen vortex and show that the new split forms enhance the robustness of high order simulations in comparison to the standard scheme when solving turbulent vortex dominated flows in fact we show that for certain test cases the novel split form discontinuous galerkin schemes are more robust than the discontinuous galerkin scheme with over integration

fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets abstract we introduce the notions of fuzzy almost continuity and fuzzy weak continuity at a fuzzy point following the pointwise approach we investigate their fuzzy topological properties we also obtain a pointwise characterization of fuzzy almost continuous functions by dual points and fuzzy nets the main idea behind this work is to establish a local theory in the study of continuity and its weaker forms in general fuzzy topological spaces

advanced field interpolation from plane polar samples experimental verification a new and advanced sampling technique far field interpolation with a nonredundant number of samples on plane polar geometry has been experimentally validated for cases of both complex and only amplitude measurements experimental results show good stability of the interpolation algorithm with respect to noise and the lack of samples in the case of a limited scanning area

fuzzy closed and fuzzy perfect mappings abstract it is shown that a fuzzy continuous map f is fuzzy perfect iff f i z is fuzzy closed for every fuzzy topological space z

computational design for long term numerical integration of the equations of fluid motion the integral constraints on quadratic quantities of physical importance such as conservation of mean kinetic energy and mean square vorticity will not be maintained in finite difference analogues of the equation of motion for two dimensional incompressible flow unless the finite difference jacobian expression for the advection term is restricted to a form which properly represents the interaction between grid points as derived in this paper it is shown that the derived form of the finite difference jacobian prevents nonlinear computational instability and thereby permits long term numerical integrations

fuzzy sets and functions on fuzzy spaces abstract we generally follow the terminology of azad j math anal appl 82 1981 14 32 and ming j math anal appl 76 1980 571 599 in addition to the fundamental concepts for fuzzy sets we emphasize the usefulness of the concepts of fuzzy point fuzzy elementhood for fuzzy sets a and b a new characterization is given for relations a b and a b this knowledge permits us to combine the two definitions of fuzzy point fuzzy elementhood in the third section some results are given concerning various special types of fuzzy sets in fuzzy topological spaces and the fuzzy semi regular fuzzy regular spaces defined by azad in the last section the definitions of h almost continuous w almost open functions urysohn space which are defined by hussain wilansky and noiri respectively are extended to fuzzy sets furthermore some results are obtained in the functions of the fuzzy topological spaces defined by azad and those are defined here

on separation axioms and ti fuzzy continuity abstract we introduce and generalise concepts of t continuous functions in a fuzzy setting and study them in connection with the fuzzy continuity and fuzzy separation axioms some fuzzy topological properties are also investigated under such functions

the compressible hybrid rans les formulation using an additive operator in this work the compressible governing equations for the hybrid reynolds averaged large eddy simulations are formally derived by applying a hybrid filter to the navier stokes equations this filter is constructed by linearly combining the reynolds average rans and large eddy simulation les operators with a continuous blending function the derived hybrid equations include additional terms that represent the interactions between rans and les formulations the relevance of these terms is investigated in flat plate turbulent boundary layer simulations and indicate that these additional terms play a fundamental role in compensating for the turbulence that is neither modeled nor resolved in the transition region between rans and les results also show that when the additional terms are included the calculations are not very sensitive to the blending function implemented in the hybrid filter in the contrary when these terms are neglected and a step function is implemented in the hybrid filter nonphysical discontinuities are predicted in the flow statistics

an effective near field far field transformation technique from truncated and inaccurate amplitude only data a general approach to the near field far field transformation from amplitude only near field data is presented the estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional the difficulties related to the possible trapping of the algorithm by a false solution common to any nonlinear inverse problem are mitigated by setting the problem in the space of the squared field amplitudes as already done in a number of existing papers and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem accordingly the a priori information concerning the far field the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional the intrinsic ill conditioning of the problem is managed by adopting a general flexible and nonredundant sampling representation of the field which takes into account the geometrical characteristics of the source as a consequence the number of unknowns is minimized and a technique is obtained which easily matches the available knowledge concerning the behavior of the field the effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis as well as an experimental validation performed by using a very low cost near field facility available at the electronic engineering department university of napoli italy

discretely conservative finite difference formulations for nonlinear conservation laws in split form theory and boundary conditions the lax wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities the discrete operator however need not be derived from the divergence form of the continuous equations indeed conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal norm skew symmetric summation by parts sbp spatial operator yield discrete operators that are conservative furthermore split form discretely conservation operators can be derived for periodic or finite domain sbp spatial operators of any order examples are presented of a fourth order sbp finite difference operator with second order boundary closures sixth and eighth order constructions are derived and are supplied in an accompanying text file

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

electromagnetic field synthesis by hierarchical plane wave based field transformation an optimization based field synthesis approach is presented that employs a hierarchical plane wave based field transformation concept for efficient evaluation of the inverse problem forward operator irregular transmit antenna array configurations can be used to synthesize a target field distribution in an arbitrarily shaped test volume with full consideration of the antenna element radiation characteristics for this purpose a triangular mesh forms the test zone boundary surface on which rao wilton glisson rwg vector basis functions perform electric and magnetic field testing an iterative krylov subspace solver is employed to solve the ill posed inverse problem for the transmit antenna coefficients the effectiveness accuracy and efficiency of the proposed field synthesis algorithm are demonstrated for configurations with test zone extents of up to one hundred wavelengths moreover the approach is utilized for antenna measurements where antenna near fields are transformed into far fields

fast antenna diagnosis algorithm using oblate spheroidal nonuniform grids a fast algorithm for the diagnosis of large antennas is developed the algorithm is based on the rayleigh sommerfeld rs backpropagation method accelerated by a multilevel nonuniform grid algorithm comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions the optimal performance is obtained by using oblate spheroidal grids which are tailored to both the measurement and antenna surfaces further acceleration can be achieved for particular cases via optimal sampling on the antenna surface the algorithm s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions and compared to that achieved with spherical grids the accuracy and error controllability are studied in comparison to the direct rs integral computation

kinetic energy and entropy preserving schemes for compressible flows by split convective forms abstract this study proposes a kinetic energy and entropy preserving scheme to achieve stable and non dissipative compressible flow simulations the proposed scheme is built in such a way that the numerical formulations satisfy the analytical relations among the governing equations at the discrete level the mass and momentum convective terms are recast into split convective forms once the mass and momentum equations are discretized the constraints given by the analytical relations subsequently determine the formulations of the numerical fluxes solved in the total energy equation an analysis reveals that satisfying the analytical relations at the discrete level is essential for solving the energy exchange between the kinetic energy and internal energy correctly in the total energy equation and therefore important for entropy conservation taylor green vortex and euler isotropic turbulence simulations at infinite reynolds number are conducted to verify the analysis given in this paper the proposed scheme achieves both kinetic energy conservation in the incompressible limit and entropy conservation as well as convergences of thermodynamic variable fluctuations whereas existing kinetic energy preserving schemes fail entropy conservation and the thermodynamic variable fluctuations diverge

various fuzzy topological notions and fuzzy almost continuity abstract we extend the notion of almost continuity in the sense of husain 1966 to the fuzzy setting we obtain a pointwise characterization of the notion by dual point and fuzzy net also we formulate conditions under which the two notions of fuzzy almost continuity the one defined in this paper and the one defined by ajmal and azad 1990 turn out to be equivalent the main idea behind this work is to show that using the localized approach developed in earlier papers the study of fuzzy almost continuity can be carried out as successfully as that of its counterpart in general topology in the process we exhibit the compatibility of various existing fuzzy topological notions such as fuzzy regularity c i connectedness i 3 4 c i local connectedness i 3 4 fuzzy t 1 axiom fuzzy t 2 axiom etc

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

on electromagnetics and information theory some connections are described between electromagnetic theory and information theory identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems starting from this result the role of the degrees of freedom of the field in radiating systems is investigated different classes of antennas use the available degrees of freedom in different ways in particular a multiple input multiple output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field applications of the theory to antenna synthesis and antenna characterization in complex environments are shown

a new formulation for the radiation operator application to the fast computation of the singular value decomposition this paper proposes a new formula for the operator mathcal k given by the product of the radiation operator by its adjoint the formula expresses mathcal k by means of a surface integral extended to the boundary of the source domain rather than a volume integral extended to the whole source domain as entailed by its mathematical definition as a result the computation of mathcal k becomes much less onerous than the computation based on its mathematical definition an immediate application of the derived formula is the fast computation of the singular value decomposition of the radiation operator through to the fast computation of mathcal k some possible implications of the derived formula for mathcal k are also discussed finally numerical examples are provided as proof of the validity and effectiveness of the formula

open maps closed maps and local compactness in fuzzy topological spaces on donne des caracterisations des applications floues ouvertes et fermees et on montre que la normalite definie par hutton est invariante sous des applications f fermees f continues

mass momentum and energy conserving mamec discretizations on general grids for the compressible euler and shallow water equations the paper explains a method by which discretizations of the continuity and momentum equations can be designed such that they can be combined with an equation of state into a discrete energy equation the resulting mamec discretizations conserve mass momentum as well as energy although no explicit conservation law for the total energy is present essential ingredients are i discrete convection that leaves the discrete energy invariant and ii discrete consistency between the thermodynamic terms of particular relevance is the way in which finite volume fluxes are related to nodal values the method is an extension of existing methods based on skew symmetry of discrete operators because it allows arbitrary equations of state and a larger class of grids than earlier methods the method is first illustrated with a one dimensional example on a highly stretched staggered grid in which the mamec method calculates qualitatively correct results and a non skew symmetric finite volume method becomes unstable a further example is a two dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid the conservation of mass momentum and energy is checked and losses are found negligible up to machine accuracy

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

high order fluxes for conservative skew symmetric like schemes in structured meshes developing high order non dissipative schemes is an important research task for both steady and unsteady flow computations we take as a starting point the built in de aliasing property of the discretized skew symmetric form for the non linear terms of the navier stokes equations recalled in kravchenko and moin 1 two families of high order locally conservative schemes matching this discretized skew symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible flows the jameson s scheme 2 is shown to be the second order member of larger families of skew symmetric like centered schemes the fourth order finite volume and finite difference and the sixth order finite difference schemes which belong to this family are provided the proposed schemes are extended to shock capturing schemes either by modifying the jameson s artificial viscosity or by hybriding the centered flux with weno 3 fluxes an adapted interpolation is proposed to extend the use of the proposed schemes to non regular grids several tests are provided showing that the conjectured order is properly recovered even with irregular meshes and that the shock capturing properties allow us to improve the second order results for standard test cases the improvement due to fourth order is then confirmed for the estimation of the growth of two ts waves and three crow instability dimensional unstable modes for both confined and free shear flows the last application concerns the steady computation using the spalart allmaras model of a separated boundary layer it confirms that the use of a high order scheme improves the results even in this type of steady applications

an entropy stable nodal discontinuous galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry we design an arbitrary high order accurate nodal discontinuous galerkin spectral element approximation for the non linear two dimensional shallow water equations with non constant possibly discontinuous bathymetry on unstructured possibly curved quadrilateral meshes the scheme is derived from an equivalent flux differencing formulation of the split form of the equations we prove that this discretization exactly preserves the local mass and momentum furthermore combined with a special numerical interface flux function the method exactly preserves the mathematical entropy which is the total energy for the shallow water equations by adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme that is the numerical scheme discretely satisfies the second law of thermodynamics finally with a particular discretization of the bathymetry source term we prove that the numerical approximation is well balanced we provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

on fuzzy compactness in this paper we characterize well known fuzzy compactness see 3 4 9 and 10 using the notion of fuzzy upper limit see 5 also we give and study new fuzzy compactness in fuzzy topological spaces

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

on fuzzy t convergences abstract in this paper we introduce and study the notions of fuzzy convergence and weakly convergence on a fuzzy topological space these notions can be considered as generalizations of the convergence defined in georgiou and papadopoulos 1998 also the forementioned convergence does not coincide with the one defined in chen and chenn 1997 the importance of these convergences relies on the fact that they behave equally well as the convergence defined in georgiou and papadopoulos 1998

fast and accurate near field far field transformation by sampling interpolation of plane polar measurements an optimal sampling interpolation algorithm which allows the accurate recovery of plane rectangular near field samples from the knowledge of the plane polar ones is developed this enables the standard near field far field nf ff transformation which takes full advantage of the fast fourier transform fft algorithm to be applied to plane polar scanning the maximum allowable sample spacing is also rigorously derived and it is shown that it can be significantly greater than lambda 2 as the measurement place moves away from the source this allows a remarkable reduction of both measurement time and memory storage requirements the sampling approach is compared with that based on the bivariate lagrange interpolation bli method the sampling reconstruction agrees with the exact results significantly better than the bli in spite of the significantly lower number of required measurements

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort

on the optimal synthesis of sum or difference patterns of centrosymmetric arrays under arbitrary sidelobe constraints this paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry the aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem extending and completing previous results regarding uniformly spaced linear and planar arrays it is shown that such a class consists of the centrosymmetric arrays whose element patterns are either equal or hermitian symmetric with respect to the center of symmetry the optimal solutions are also hermitian symmetric and the corresponding patterns are real furthermore it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage