using automatic differentiation to create a nonlinear reduced order model aerodynamic solver a novel nonlinear reduced order modeling technique for computational aerodynamics and aeroelasticity is presented the method is based on a taylor series expansion of a frequency domain harmonic balance computational fluid dynamicsolver residual the first andsecond order gradientmatrices andtensorsof the taylorseries expansion are computed using automatic differentiation via fortran 90 95 operator overloading a ritz type expansion using proper orthogonal decomposition shapes is then used in the taylor series expansion to create the nonlinearreduced order model the nonlinear reduced order modeling technique is applied to a viscous flow about anaeroelastic nlr 7301 airfoil modelto determine limit cycle oscillations computational times are decreased from hours to seconds using the nonlinear reduced order model

linearly equivalent actions of solvable groups abstract we determine the positive integers n for which there exist a solvable group g and two non conjugate subgroups of index n in g that induce the same permutation character

high dimensional harmonic balance dealiasing techniques for a duffing oscillator a dealiasing study of the high dimensional harmonic balance method is conducted using a duffing oscillator as a prototypical nonlinear dynamical system previous study has shown that aliasing can occur when the high dimensional harmonic balance method is used to solve systems that contain nonlinearities we demonstrate that frequency filtering techniques such as the fourier smoothing method can sufficiently reduce or eliminate the effects of aliasing the drawback is that fourier filtering requires redundant coordinate transformations between the time and frequency domains resulting in unnecessary computational expense as an alternative temporal filters are constructed based upon compact finite difference schemes with spectral like resolution it is shown that the temporal filtering schemes successfully replicate the performance of the fourier smoothing method with improved computational economy

nonlinear analysis of unsteady flows in multistage turbomachines using harmonic balance a harmonic balance technique for the analysis of two dimensional linear small disturbance and nonlinear unsteady flows in multistage turbomachines is presented the present method uses a mixed time domain frequency domain approach that allows one to compute the unsteady aerodynamic response of multistage machines to both blade vibration the flutter problem and wake interaction the forced response problem in general the flowfield may have multiple excitation frequencies that are not integer multiples of each other so that the unsteady flow is sometimes aperiodic in time using our approach we model each blade row using a computational grid spanning a single blade passage in each blade row we store several subtime level solutions for flows that are periodic in time these subtime levels span a single time period for aperiodic flows the temporal period spanned by these subtime level solutions is sufficiently long to sample the relevant discrete frequencies contained in the aperiodic flow in both cases these subtime level solutions are related to each other through the time derivative terms in the euler or navier stokes equations and boundary conditions complex periodicity conditions connect the subtime levels within a blade passage and interrow boundary conditions connect the solutions among blade rows the resulting discretized equations which are mathematically steady because time derivatives have been replaced by a pseudospectral operator in which the excitation frequencies appear as parameters can be solved very efficiently using multigrid acceleration techniques in this paper we apply the technique to both flutter and wake interaction problems and illustrate the influence of neighboring blade rows on the unsteady aerodynamic response of a blade row

asymmetric flow networks abstract this paper provides a new model of network formation that bridges the gap between the two benchmark game theoretic models by bala and goyal 2000a the one way flow model and the two way flow model and includes both as limiting cases as in both the said models a link can be initiated unilaterally by any player with any other in what we call an asymmetric flow network and the flow through a link towards the player who supports it is perfect unlike those models there is friction or decay in the opposite direction when this decay is complete there is no flow and this corresponds to the one way flow model the limit case when the decay in the opposite direction and asymmetry disappears corresponds to the two way flow model we characterize stable and strictly stable architectures for the whole range of parameters of this intermediate and more general model a study of the efficiency of these architectures shows that in general stability and efficiency do not go together we also prove the convergence of bala and goyal s dynamic model in this context

small linearly equivalent g sets and a construction of beaulieu abstract two g sets g a finite group are called linearly equivalent over a commutative ring k if the permutation representations k x and k y are isomorphic as modules over the group algebra kg pairs of linearly equivalent non isomorphic g sets have applications in number theory and geometry we characterize the groups g for which such pairs exist for any field and give a simple construction of these pairs if k is q these are precisely the non cyclic groups for any non cyclic group we prove that there exist g sets which are non isomorphic and linearly equivalent over q of cardinality 3 g 2 also we investigate a construction of p beaulieu which allows us to construct pairs of transitive linearly equivalent s n sets from arbitrary g sets for an arbitrary group g we show that this construction works over all fields and use it construct for each finite set p of primes s n sets linearly equivalent over a field k if and only if the characteristic of k lies in p

application of proper orthogonal decomposition to the discrete euler equations the response of a fluid moving above a panel to localized oscillation of the panel is predicted using reduced order modelling rom with the proper orthogonal decomposition technique the flow is assumed to be inviscid and is modelled with the euler equations these non linear equations are discretized with a total variation diminishing algorithm and are projected onto an energy optimal subspace defined by an energy threshold criterion applied to a modal representation of time series data results are obtained for a bump oscillating in a mach 1 2 flow rom is found to reduce the degrees of freedom necessary to simulate the flowfield by three orders of magnitude while preserving solution accuracy other observed benefits of rom include increased allowable time step and robustness to variation of oscillation amplitude published in 2002 by john wiley sons ltd

an axiomatic characterization of some locations in trees abstract we describe axioms that uniquely characterize the absolute median and the squared median the point that minimizes the sum of squared distances of a tree a common feature of these characterizations is a consistency axiom of the type first used by h p young to characterize a voting procedure called borda s rule these results make it possible to argue in favor of or against a particular location in terms of principles satisfied or violated

efficient reduced order system identification for linear systems with multiple inputs a new efficient discrete time domain system identification and model reduction method for a large scaled linear dynamic system with multiple inputs is presented the method is based on a modification of the classical eigensystem realization algorithm and a simultaneous injection of multiple inputs so called the single composite input method because the system response is sampled almost exclusively for the single representative input this technique can significantly reduce the model construction time as well as the amount of the sampled data for derivation of the new algorithm the singular value decomposition is performed using output measurements that are not necessarily attributed to pulse inputs application to general computational fluid dynamic systems and formulation of reduced order aeroelastic models are also presented the efficiency and accuracy of the method is demonstrated via a simple aeroelastic system which is modeled by the three dimensional vortex lattice and a six degrees of freedom plate like structure

on the mumford tate group of an abelian variety with complex multiplication let k be a primitive cm type with k o 2n for definitions and previous results see section 1 1 fix n and consider the collection s n rank where rank counts the number of independent translates of qi under the galois action and k ranges over all primitive types the smallest element of s n denoted by b n is referred to as the sharp lower bound for the rank in dimension n as was brought to the author s attention by ribet bounds on b n of the form p 1 for p a prime dividing n follow directly from the proof of ribet s nondegeneracy theorem 21 this is recorded as theorem 1 4 ribet s method also gives bounds of the form 2q for q a prime with q2 dividing n as is observed in theorem 1 12 when combined with the author s constructions of abelian varieties in s 91 we obtain the precise value of b n for many values of n corollaries 1 5 to 1 8 and 1 13 we recall that these constructions use the analytic method of weil and shimura together with new results on the reflex field from an investigation suggested to the author by shim ura the interest of the rank comes from the theory of complex multiplication if a is an abelian variety of cm type k then the kubota rank of a is rank and controls properties of the classfields constructed from a as in kubota 161 and ribet 20 this is connected with the fact that the rank of is also the dimension of the mumford tate group of a and with the relation of this group to the i adic representations of a as in serre 24 251 the main body of the paper contains results that provide information on s n the main result theorem 2 5 asserts that when n is odd there is a computable subset s n of s n that accounts for the ranks of many cm types on most cm fields more precisely let k be the maximal totally real subfield of k and kg be the galois closure of k we consider the per

from local to global stability in stochastic processing networks through quadratic lyapunov functions we construct a generic simple and efficient scheduling policy for stochastic processing networks and provide a general framework to establish its stability our policy is randomized and prioritized with high probability it prioritizes jobs that have been least routed through the network we show that the network is globally stable under this policy if there exists an appropriate quadratic local lyapunov function that provides a negative drift with respect to nominal loads at servers applying this generic framework we obtain stability results for our policy in many important examples of stochastic processing networks open multiclass queueing networks parallel server networks networks of input queued switches and a variety of wireless network models with interference constraints our main novelty is the construction of an appropriate global lyapunov function from quadratic local lyapunov functions which we believe to be of broader interest

new criteria for the solvability of finite groups see 6 or 7 p 291 it has been conjectured that a group is solvable if and only if it has a hall 2 subgroup and a hall 3 subgroup see 11 we verify this conjecture for groups whose composition factors are known simple groups along the way we also verify for groups whose composition factors are known simple groups a conjecture of hall s that if a group has a hall

contrasting the harmonic balance and linearized methods for oscillating flap simulations doi 10 2514 1 43401 in the framework of unsteady aerodynamics forced harmonic motion simulations can be used to compute unsteady loads in this context the present paper assesses two alternatives to the unsteady reynolds averaged navier stokes approach the linearized unsteady reynolds averaged navier stokes equations method and the harmonic balance approach the test case is a naca 64a006 airfoil with an oscillating flap mounted at 75 of the chord emphasis is put on examining the performances of the methods in terms of accuracy and computational cost over a range of physical conditions it is found that for a subsonic flow the linearized unsteady reynolds averaged navier stokes method is the most efficient one in the transonic regime the linearized unsteady reynolds averaged navier stokes method remains the fastest approach but with limited accuracy around shocks whereas a oneharmonic harmonic balance solution is in closer agreement with the unsteady reynolds averaged navier stokes solution inthecaseofseparationinthetransonicregime thelinearizedunsteadyreynolds averagednavier stokes method fails to converge whereas the harmonic balance remains robust and accurate

reduced order nonlinear system identification methodology a new method is presented which enables the identification of a reduced order nonlinear ordinary differential equation ode which can be used to model the behavior of nonlinear fluid dynamics the method uses a harmonic balance technique and proper orthogonal decomposition to compute reduced order training datawhich is then used to compute the unknown coefficients of the nonlinear ode the method is used to compute the euler compressible flow solutions for the supercritical two dimensional nlr 7301 airfoil undergoing both small and large pitch oscillationsatthreedifferentreducedfrequenciesandatamachnumberof0 764 steadyanddynamicliftcoefficient datacomputedusingathreeequationreducedordersystemidentificationmodelcomparedwellwithdatacomputed using the full cfd harmonic balance solution the system identification model accurately predicted a nonlinear trend in the lift coefficient results steady and dynamic for pitch oscillation magnitudes greater than 1 deg overall the reduction in the number of nonlinear differential equations was 5 orders of magnitude which corresponded to a 3 order of magnitude reduction in the total computational time

subgroups of finite soluble groups inducing the same permutation character in this paper there are found necessary and sufficient conditions that a pair of solvable finite groups say g and k must satisfy for the existence of a solvable finite group l containing two isomorphic copies of g and h inducing the same permutation character also a construction of l is given as an iterated wreath product with respect to their actions on their natural modules of finite one dimensional affine groups

reduced order subscales for pod models in this work the reduced order subscales for proper orthogonal decomposition models are presented the basic idea consists in splitting the full order solution into the part which can be captured by the reduced order model and the part which cannot the subscales for which a model is required the proposed model for the subscales is defined as a linear function of the solution of the reduced order model the coefficients of this linear function are obtained by comparing the solution of the full order model with the solution of the reduced order model for the same initial conditions which for convenience are evaluated in the snapshots used to train the original reduced order model the difference between both solutions are the subscales for which a model can be built using a least squares procedure the subscales are then introduced as a correction in the reduced order model resulting in an important improvement in accuracy the enhanced reduced order model is tested in several numerical examples these practical cases show that the use of the subscales leads to more accurate solutions successfully corrects errors introduced by hyper reduction and allows to solve complex flow problems using a reduced number of degrees of freedom

nonlinear frequency domain analysis of unsteady flows in turbomachinery with multiple excitation frequencies a harmonic balance technique for the analysis of nonlinear unsteady flows in turbomachiney arising from several excitation sources possibly with frequencies with irrational ratios is presented in this paper this method uses a mixed time domain frequencydomain approach that allows one to model the blade row on a computational grid spanning just a single blade passage no matter the interblade phase angles of the original disturbances using this approach we compute several solutions each one corresponding to one of several times over one period for periodic flows or over a representative time interval for aperiodic flows these time levels are coupled to each other through a spectral time derivative operator in the interior of the computational domain and through the far field and periodic boundary conditions around the boundary of the domain in this paper we apply the method to the two dimensional euler equations although the method can be applied to three dimensional and viscous flows and examine the nonlinear interaction of wake passing with blade vibration

transonic limit cycle oscillation analysis using aerodynamic describing functions and superposition principle limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied transonic nonlinear aerodynamic forces are calculated by solving euler equations or navier stokes equations with respect to harmonic airfoil plunging pitching motion and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in the frequency domain hence the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method the procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail four examples are adopted to verify the accuracy of the present method the isogai wing model with naca 64a010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method another naca 64a010 airfoil model with different structural parameters is then adopt

airfoil motion in subsonic flow with strong cubic nonlinear restoring forces limit cycle oscillations of a two degree of freedom airfoil motion with cubic nonlinearity in the restoring forces are investigated the harmonic balance method is used to derive a frequency relation that depends only on airfoil parameters the amplitudes of the pitch and plunge motions can be computed from analytical expressions once the frequency is known the method is extended to higher harmonics illustrative examples are given and the results are compared with numerical computations

h adaptive stabilized finite element solver for calculation of generalized aerodynamic forces a finite element method based on the streamline upwind petrov galerkin stabilization technique is developed to solve the compressible euler equations the method is extended for computing unsteady small disturbances in the flow domain as a result of boundary motion which is applied through the linearized solid wall boundary condition the method is able to calculate the frequency dependent generalized aerodynamic forces without any need for deformation of mesh inside the flow domain error estimates are used to drive automated h refinement of mesh for steady state and frequency domain calculations steady state solutions and generalized aerodynamic forces are compared to benchmark data for transonic and supersonic mach numbers the results show that the presence of shocks in the flow makes it difficult to use a single mesh for all computations including the linearized flow the h refinement procedure is shown to be an effective way of ensuring reliable computations for the nonlinear and linearized solve

reduced order model development using proper orthogonal decomposition and volterra theory a new approach for generating reduced order models of fluid systems was developed using proper orthogonal decomposition in combination with volterra theory the method involves identifying fluid basis functions with proper orthogonal decomposition and applying systems realization theory to generate a low dimensional model for the scalar coefficients the method was tested on a two dimensional inviscid flow over a bump with forcing eight fluid basis functions were identified and the eigensystem realization algorithm was used to identify an eight state reduced order model time histories of both the reduced order coefficients and the expanded flowfield data accurately tracked the full order results in both amplitude and phase average error less than 5 the reduced order model demonstrated four orders of magnitude reduction in compute time relative to the full system which represents a computational improvement on the same order as the reduction in degrees of freedom

a nonlinear modeling approach using weighted piecewise series and its applications to predict unsteady flows to preserve nonlinearity of a full order system over a range of parameters of interest we propose an accurate and robust nonlinear modeling approach by assembling a set of piecewise linear local solutions expanded about some sampling states the work by rewienski and white 1 on micromachined devices inspired our use of piecewise linear local solutions to study nonlinear unsteady aerodynamics these local approximations are assembled via nonlinear weights of radial basis functions the efficacy of the proposed procedure is validated for a two dimensional airfoil moving with different pitching motions specifically agard s ct2 and ct5 problems 27 in which the flows exhibit different nonlinear behaviors furthermore application of the developed aerodynamic model to a two dimensional aero elastic system proves the approach is capable of predicting limit cycle oscillations lcos by using agard s ct6 28 as a benchmark test all results based on inviscid solutions confirm that our nonlinear model is stable and accurate against the full model solutions and measurements and for predicting not only aerodynamic forces but also detailed flowfields moreover the model is robust for inputs that considerably depart from the base trajectory in form and magnitude this modeling provides a very efficient way for predicting unsteady flowfields with varying parameters because it needs only a tiny fraction of the cost of a full order modeling for each new condition the more cases studied the more savings rendered hence the present approach is especially useful for parametric studies such as in the case of design optimization and exploration of flow phenomena

limit cycle oscillations of delta wing models in low subsonic flow a nonlinear aeroelastic analysis of a low aspect delta wing modeled as a plate of constant thickness demonstrates that limit cycle oscillations lco of the order of the plate thickness are possible the structural nonlinearity arises from double bending in both the chordwise and spanwise directions the present results using a vortex lattice aerodynamic model for a low mach number flow complement earlier studies for rectangular wing platforms that showed similar qualitative results the theoretical results for the flutter boundary beyond which lco occurs have been validated by comparison to the experimental data reported by other investigators for low aspect ratio delta wings also the limit cycle oscillations found experimentally by previous investigators but not previously quantified prior to the present work are consistent with the theoretical results reported here reduced order aerodynamic and structural models are used to substantially decrease computational cost with no loss in accuracy without the use of reduced order models calculations of the lco would be impractical a wind tunnel model is tested to provide a quantitative experimental correlation with the theoretical results for the lco response itself

a comparison of classical and high dimensional harmonic balance approaches for a duffing oscillator the present study focuses on a novel harmonic balance formulation which is much easier to implement than the standard classical harmonic balance method for complex nonlinear mathematical models and algorithms both harmonic balance approaches are applied to duffing s oscillator to demonstrate the advantages and disadvantages of the two approaches a fundamental understanding of the difference between these two methods is achieved and the properties of each method are analyzed in detail

adaptive harmonic balance solutions to euler s equation a new adaptive harmonic balance method is presented and applied to a variety of subsonic and supersonic onedimensional e owe elds containing strong moving shocks the adaptive method augments the frequency content in each cell as required to capture the local e ow physics augmentation automatically adjusts with grid density resulting in lower frequency content on coarse grids that cannot adequately resolve high frequency terms a study of the effect of augmentation thresholds increments and scheduling on the performance and accuracy of the adaptive method is presented and optimal parameters identie ed when optimal parameters are used the new adaptive harmonic balancemethod produces solutions equivalent to a nonadapted harmonic balance solution but with up to a 50 reduction in run time

prediction of aeroelastic limit cycle oscillations based on harmonic forced motion oscillations aeroelastic limit cycle oscillations due to aerodynamic nonlinearities are usually investigated using coupled fluid structure interaction simulations in the time domain these simulations are compu

projection methods for reduced order models of compressible flows two different projection methods galerkin projection and direct projection are developed for reduced order modeling applications the projection methods are used to identify low dimensional systems of ordinary differential equations to represent the dynamics of a compressible two dimensional inviscid flow field under oscillatory forcing proper orthogonal decomposition is used to identify a small number of fluid modes to serve as the basis functions for the projections performance is evaluated relative to a high order numerical model in terms of accuracy order reduction and computational efficiency the treatment of boundary conditions and stability of the reduced order model are addressed in detail the methods developed in this paper are suitable for general application to the euler equations with the addition of dissipation parameters both the galerkin projection and direct projection methods are tractable stable and properly treat the boundary conditions

frequency domain karhunen loeve method and its application to linear dynamic systems forthee rsttime thekarhunen loeve kl procedureisderivedinthefrequencydomainasatoolforcalculating eigenmodes of linear systems the new derivation is based on the discrete fourier transform representation of a time average of proe le energy including a proper system response and a proe le function taking the variational problem posed as such with respect to the proe le function leads to an eigenformulation in the frequency domain choice of a system response for efe cient kl mode calculation and construction of reduced order systems using the kl eigenmodes are also discussed to demonstrate themethod both mechanical and e uid dynamic models are considered the method is equally useful in extracting eigenmodes of an experimentally generated database nomenclature c wing chord length f snapshot matrix as dee ned in eq 13 f fourier operator gik impulse response for the kth input gsk step response for the kth input i

compact implementation strategy for a harmonic balance method within implicit flow solvers a two step approximate factorization technique for implementing a computationally stable nonlinear unsteady frequency domain harmonic balance solution method within existing implicit computational fluid dynamic flow solver codes is presented the approach uses an explicit discretization of the harmonic balance source term and no new implicit code development is required both of these features enable the harmonic balance method to be implemented within existing implicit flow solver codes with minimal modification necessary to the underlying flow solver code the resulting harmonic balance solver can then be used for modeling nonlinear periodic unsteady flows the methodology is applied to the nasa overflow flow solver code and results are presented for transonic viscous flow past an unsteady pitching airfoil section

nonlinear inviscid aerodynamic effects on transonic divergence flutter and limit cycle oscillations by the use of a state of the art computational e uid dynamic cfd method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model an investigationismadeinto how nonlinear aerodynamics can effect the divergence e utter and limit cycle oscillation lco characteristics of a transonic airfoil cone guration a single degree of freedom dof model is studied for divergence and one and two dof models are studied for e utter and lco a harmonicbalancemethod in conjunction with the cfd solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency a procedure for determining the lco solution is also presented for the cone guration investigated nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable lco solutions respectively for the one and two dof e utter models nomenclature a nondimensional location of airfoil elastic axis e b b c semichord and chord respectively cl cm coefe cients of lift and moment about elastic axis respectively e location of airfoil elastic axis measured positive aft of airfoil midchord h airfoil plunge and pitch degrees of freedom i second moment of inertia of airfoil about elastic axis

centers in connected undirected graphs an axiomatic approach a center is a function that associates with every finite connected and undirected graph a nonempty subset of its vertices these functions play an important role in networks such as social or interorganizational networks centers capture notions like being a focal point of communication being strategically located ability and willingness to participate in strategic alliances and the like we focus on the conceptual issue of what makes a position in a graph a central one and investigate some possible concepts of centrality in relation to various properties characterizations of the uncovered center the median and degree center are presented where each of these centers is defined for arbitrary connected undirected simple and possibly cyclic graphs

opinion fluctuations and disagreement in social networks we study a tractable opinion dynamics model that generates long run disagreements and persistent opinion fluctuations our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents 1 regular agents who update their beliefs according to information that they receive from their social neighbors and 2 stubborn agents who never update their opinions and might represent leaders political parties or media sources attempting to influence the beliefs in the rest of the society when the society contains stubborn agents with different opinions the belief dynamics never lead to a consensus among the regular agents instead beliefs in the society fail to converge almost surely the belief profile keeps on fluctuating in an ergodic fashion and it converges in law to a nondegenerate random vector the structure of the graph describing the social network and the location of the stubborn agents within it shape the opinion dynamics the expected belief vector is proved to evolve according to an ordinary differential equation coinciding with the kolmogorov backward equation of a continuous time markov chain on the graph with absorbing states corresponding to the stubborn agents and hence to converge to a harmonic vector with every regular agent s value being the weighted average of its neighbors values and boundary conditions corresponding to the stubborn agents beliefs expected cross products of the agents beliefs allow for a similar characterization in terms of coupled markov chains on the graph describing the social network we prove that in large scale societies which are highly fluid meaning that the product of the mixing time of the markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large a condition of homogeneous influence emerges whereby the stationary beliefs marginal distributions of most of the regular agents have approximately equal first and second moments

adaptive harmonic balance method for nonlinear time periodic flows an adaptive harmonic balance approach is developed and applied to a supersonic subsonic diverging nozzle subject to unsteady periodic outflow conditions the adaptive method minimizes the computational work required to obtain the harmonic balance solution by augmenting the frequency content in each cell as required to capture the local flow physics augmentation automatically adjusts with grid density resulting in lower frequency content on coarse grids the new adaptive harmonic balance method produces solutions equivalent to a non adapted harmonic balance solutions but with up to an 86 reduction in computational effort

a reduced order method for simulation and control of fluid flows this article presents a reduced order modeling approach for simulation and control of viscous incompressible flows the reduced order models suitable for control and which capture the essential physics are developed using the reduced basis method the so called lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall bounded channel flows control action is effected through boundary surface movement on a part of the solid wall our formulation of the reduced order method applied to flow control problems leads to a constrained minimization problem and is solved by applying newton like methods to the necessary conditions of optimality through our computational experiments we demonstrate the feasibility and applicability of the reduced order method for simulation and control of fluid flows

on maximal entries in the principal eigenvector of graphs abstract for an undirected connected graph it is well known that an eigenvector belonging to the principal eigenvalue of g can be given such that all entries are positive we ask whether this vector carries information on the structure of the graph and approach this question by investigating the values that can occur in its maximal entry

investigations and improvement of robustness of reduced order models of reacting flow the impact of chemical reactions on the robustness and accuracy of projection based reduced order models roms of fluid flows is investigated both galerkin and least squares petrov galerkin roms

unipotent subgroups of groups of lie type let g g be either a simple algebraic group over an algebraically closed field k or a finite chevalley group normal or twisted over k f with q 4 for the case of an algebraic group all groups discussed are taken to be closed subgroups of g in this paper we prove results that parallel those in 141 where we deterined those subgroups of g containing a maximal torus given restrictions on k here we study the overgroups of a certain type of unipotent subgroup of g which like the maximal tori are of particular importance to the understanding of the subgroup structure of g as applications we establish results about overgroups of local subgroups of g and results concerning generation by centralizers of unipotent elements a unipotent group i g is said to be full provided i contains each unipotent element of its centralizer such subgroups occur quite often for example let v be an arbitrary unipotent subgroup of g and v a maximal unipotent subgroup of either ng v or v c v then v v and v is full before stating the results we introduce the following notation and terminology let p char k a subgroup x of g is quasisimple if it is a perfect central extension of a simple group connected in case g is an algebraic group x is semisimple if it is a commuting product of quasisimple groups let r x denote the unipotent radical of x which we interpret as o x in case g is finite if k if or f4 let o x denote the group generated by all unipotent elements i e p elements of x

system identification and proper orthogonal decomposition method applied to unsteady aerodynamics the representation of unsteady aerodynamic e owe elds in terms of global aerodynamic modes has proven to be a useful method for reducing the size of the aerodynamic model over those representations that use local variables at discrete grid points in the e ow e eld eigenmodes and proper orthogonal decomposition modes have been used for this purpose with good effect this suggests that system identie cation models may also be used to represent the aerodynamic e owe eld implicit in the use of a systems identie cation technique is the notion that a relative small state space model can be useful in describing a dynamical system the proper orthogonal decomposition model is e rst used to show that indeed a reduced order model can be obtained from a much larger numerical aerodynamical model the vortex lattice method is used for illustrative purposes and the results from the proper orthogonal decomposition model and the system identie cation methods are then compared for the example considered the two methods are shown to give comparable results in terms of accuracy and reduced model size theadvantagesand limitationsofeachapproacharebriee y discussed both appearpromisingandcomplementary in their characteristics

harmonic balance analysis of limit cycle oscillations in turbomachinery a harmonic balance technique for the analysis of limit cycle oscillations of turbomachinery blades is presented this method couples a computational fluid dynamics model to a single degree of freedom structural dynamic model of the turbomachinery blades the computational fluid dynamics solver uses a nonlinear frequency domain harmonic balance approach that allows one to model the blade row of a turbomachine on a computational grid spanning a single blade passage using the harmonic balance approach several solutions each one corresponding to a different subtime level of the periodic unsteady flow are computed simultaneously these subtime level solutions are coupled to each other in the computational field by a spectral approximation of the time derivative term in the navier stokes equation and also by application of far field and periodic boundary conditions the structural dynamic model is based on a similar approach in which a single vibratory mode of interest is modeled using the harmonic balance technique the two solvers are coupled together through the upwash condition on the surface of the blade and the resulting generalized aerodynamic forces in the proposed approach the limit cycle oscillation frequency is treated as another unknown which is solved iteratively together with the governing equations of fluid flow and structural dynamics thereby driving the residual of the aeroelastic problem to convergence in a single computational fluid dynamics run the accuracy of the new method is compared with two other techniques and it is shown to offer significant computational savings

discrete adjoint approach for modeling unsteady aerodynamic design sensitivities a discrete adjoint approach is presented for computing steady and unsteady aerodynamic design sensitivities for compressible viscous flows about airfoil configurations the nominal flow solver method is based on a harmonic balance solution technique which is capable of modeling both steady and nonlinear periodic unsteady flows the computer code for the discrete adjoint solver which is derived from the nominal harmonic balance solver has been generated with the aid of the advanced automatic differentiation software tool known as taf transformation of algorithms in fortran

an axiomatic characterization of a class of locations in tree networks in this paper we describe four axioms that uniquely characterize the class of locations in tree networks that are obtained by minimizing an additively separable nonnegative nondecreasing differentiable and strictly convex function of distances this result is analogous to results that have been obtained in the theory of bargaining social choice and fair resource allocation

atlas of finite groups maximal subgroups and ordinary characters for simple groups this atlas covers groups from the families of the classification of finite simple groups recently updated incorporating corrections

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

a domain decomposition strategy for reduced order models application to the incompressible navier stokes equations abstract in this work a domain decomposition strategy for non linear hyper reduced order models is presented the basic idea consists of restricting the reduced order basis functions to the nodes belonging to each of the subdomains into which the physical domain is partitioned an extension of the proposed domain decomposition strategy to a hybrid full order reduced order model is then described the general domain decomposition approach is particularized for the reduced order finite element approximation of the incompressible navier stokes equations with hyper reduction when solving the reduced incompressible navier stokes equations instabilities in the form of large gradients of the recovered reduced order unknown at the subdomain interfaces may appear which is the motivation for the design of additional stability terms giving rise to penalty matrices numerical examples illustrate the behavior of the proposed method for the simulation of the reduced order systems showing the capability of the approach to adapt to configurations which are not present in the original snapshot set

geometric filtration using proper orthogonal decomposition for aerodynamic design optimization when carrying out design searches traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables this is particularly true when only a small number of simulations is combined with a parameterization which results in a large number of variables of seemingly equal importance here the authors present a variable reduction technique which employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process unlike traditional screening techniques the presented method operates at the geometric level instead of the variable level the filtering process uses the designs which result from a geometry parameterization instead of the variables which control the parameterization the method is shown to perform well in the optimization of a two dimensional airfoil for the minimization of drag to lift ratio producing designs better than those resulting from traditional kriging based surrogate model optimization and with a significant reduction in surrogate tuning cost

block jacobi implicit algorithms for the time spectral method many industrial applications involve flows periodic in time such flows are not simulated with enough efficiency when using classical unsteady techniques as a transient regime must be bypassed new techniques dedicated to time periodic flows and based on fourier analysis have been developed recently among these the time spectral method casts a time periodic flow computation in several coupled steady computations corresponding to a uniform sampling of the period up until now the steady states were reached using an explicit pseudotime algorithm thus very small time steps were needed and the convergence rate slowed down when increasing the number of harmonics in this paper a block jacobi approach is presented to solve the stationary problems with an implicit algorithm numerical simulations show on one hand the good quality of the results and on the other hand the interest of the proposed method to reduce the sensitivity of computations to a large number of harmonics

optimization of nonlinear structural resonance using the incremental harmonic balance method abstract we present an optimization procedure for tailoring the nonlinear structural resonant response with time harmonic loads a nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinear vibration analysis an optimization procedure based on a gradient based algorithm is developed and we use the adjoint method for efficient computation of design sensitivities we consider several examples in which we find optimized beam width distributions that minimize or maximize fundamental or super harmonic resonant responses

characterizations of the 3 cycle count and backward length of a tournament measures of inconsistency or difference between a set of pairwise comparisons and the final ranking of alternatives give valuable and useful information in this paper we present characterizations of two such measures the 3 cycle count and the backward length the characterizations provide insight into what exactly is measured and how measures differ in processing adjustments in a tournament

eigenanalysis of unsteady flow about airfoils cascades and wings a general technique for constructing reduced order models of unsteady aerodynamic flows about two dimensional isolated airfoils cascades of airfoils and three dimensional wings is developed the starting point is a the domain computational model of the unsteady small disturbance flow for illustration purposes we apply the technique to an unsteady incompressible vortex lattice model the eigenmodes of the system which may be thought of as aerodynamic states are computed and subsequently used to construct computationally efficient reduced order models of the unsteady flowfield only a handful of the most dominant eigenmodes are retained in the reduced order model the effect of the remaining eigenmodes is included approximately using a static correction technique an important advantage of the present method is that once the eigenmode information has been computed reduced order models can be constructed for any number of arbitrary modes of airfold motion very inexpensively numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method finally we show how the reduced order model may be incorporated into an aeroelastic flutter model

reduced order models for computational fluid dynamics based nonlinear aeroelastic problems in this work a nonlinear state space based identification method is proposed to describe compactly unsteady aerodynamic responses such a reduced order model is trained on a series of signals that implicitly represent the relationship between the structural motion and the aerodynamic loads the determination of the model parameters is obtained through a two level training procedure where in the first stage the matrices associated to the linear part of the model are computed by a robust subspace projection technique whereas the remaining nonlinear terms are determined by an output error minimization procedure in the second stage the present approach is tested on two different problems proving the convergence toward the reference results obtained by a computational fluid dynamics solver in linear and nonlinear aerodynamic and aeroelastic applications whereas the aerodynamic reduced order models are coupled with the related structural mechanical systems demonstrating the ability of capturing the ma

wavelength assignment for reducing in band crosstalk attack propagation in optical networks ilp formulations and heuristic algorithms abstract today s transparent optical networks tons are highly vulnerable to various physical layer attacks such as high power jamming which can cause severe service disruption or even service denial the transparency of tons enables certain attacks to propagate through the network not only increasing their damage proportions but also making source identification and attack localization more difficult high power jamming attacks causing in band crosstalk in switches are amongst the most malicious of such attacks in this paper we propose a wavelength assignment scheme to reduce their damage assuming limited attack propagation capabilities this complements our previous work in furdek et al m furdek n skorin kapov m grbac attack aware wavelength assignment for localization of in band crosstalk attack propagation ieee osa journal of optical communications and networking 2 11 2010 1000 1009 where we investigated infinite jamming attack propagation to find an upper bound on the network vulnerability to such attacks here we consider a more realistic scenario where crosstalk attacks can spread only via primary and or secondary attackers and define new objective criteria for wavelength assignment called the par primary attack radius and sar secondary attack radius accordingly we formulate the problem variants as integer linear programs ilps with the objectives of minimizing the par and sar values due to the intractability of the ilp formulations for larger instances we propose grasp greedy randomized adaptive search procedure heuristic algorithms to find suboptimal solutions in reasonable time results show that these approaches can obtain solutions using the same number of wavelengths as classical wavelength assignment while significantly reducing jamming attack damage proportions in optical networks

nonlinear model reduction for unsteady discontinuous flows abstract we develop a new nonlinear reduced order model rom based on proper orthogonal decomposition pod which can be used for quantitative simulation of not only smooth flows but also flows with strong discontinuities the new model is derived using a galerkin projection of the fully conservative nonlinear discretized 2 d euler equations onto the pod basis constructed for each conservative variable this approach can be interpreted as a variant of the spectral method with a truncated set of basis functions a system of ordinary differential equations odes derived using this model reduction technique resembles the major nonlinear and conservation properties of the original discretized euler equations the new reduced order model also preserves the stability properties of the discrete full order model equations so that no additional stabilization is required unlike conventional pod based models that are susceptible to numerical instabilities the performance of the new pod rom is evaluated for 2 d compressible unsteady inviscid flows over a wide range of mach numbers including trans and supersonic flows with strong shock waves

a framework for optimal temporal reduced order modeling of nonlinear dynamical systems abstract an optimal temporal reduced order modeling framework is proposed for nonlinear dynamical systems the governing equations are modified for an under resolved simulation with an arbitrary scheme and a coarse temporal grid subgrid scale models are developed to account for the unresolved temporal structure via inclusion of statistical information on a multi point temporal stencil these models are based upon principles of mean square error minimization conditional expectations and stochastic estimation in order to validate the proposed framework we investigate time periodic solutions for a canonical duffing oscillator using a coarse harmonic balance scheme in order to demonstrate application of the proposed framework to a high dimensional nonlinear dynamical system we also investigate a simply supported geometrically nonlinear beam under the influence of time periodic external forcing for both problems the subgrid scale models are shown to significantly improve the accuracy of coarse grained solutions

element boundary terms in reduced order models for flow problems domain decomposition and adaptive coarse mesh hyper reduction abstract in this paper we present a finite element based reduced order model and in particular we consider two aspects related to the introduction of inter element boundary terms in the formulation the first is a domain decomposition strategy in which the transmission conditions involve boundary terms to account for non matching meshes and discontinuous physical properties the second is a coarse mesh hyper reduction for which we propose an adaptive refinement driven by an a posteriori error estimator that contains element boundary terms as the finite element full order model the reduced order model is based on the variational multi scale framework with sub grid scales defined not only in the element interiors but also on the inter element boundaries we present some examples of application using the incompressible navier stokes equations and the boussinesq approximation

stable network topologies using the notion of covering abstract an alternative perspective to evaluate networks and network evolution is introduced based on the notion of covering for a particular node in a network covering captures the idea of being outperformed by another node in terms of for example visibility and possibility of information gathering in this paper we focus on networks where these subdued network positions do not exist we call these networks stable within this set we identify the minimal stable networks which frequently have a bubble like structure severing a link in such a network results in at least one of the nodes being covered in a minimal stable network therefore all nodes cooperate to avoid that one of the nodes ends up in a subdued position our results can be applied to for example the design of covert communication networks and the dynamics of social and information networks

aeroelastic modeling using geometrically nonlinear solid shell elements an aeroelastic model is developed by using multivariable solid shell elements geometrical nonlinearity and the elimination of corresponding locking phenomena are considered accurately in the modeling unsteady aerodynamic forces are addressed by solving euler flow dynamic equations the computational structural dynamics solver is loosely coupled to the computational fluid dynamics solver and the full match of the computational structural dynamics and computational fluid dynamics interfaces is achieved by three dimensional modeling an interpolation method using finite element shape functions is developed to transform forces from aerodynamic grids to structural grids the aerodynamic mesh deformation is obtained by using radial basis functions combined with the transfinite interpolation method the aeroelastic model is validated through the study of the flutter and the limit cycle oscillation of a cropped delta wing in transonic flow moreover the establishment of the aeroelastic model using multivariab

an axiomatic approach to location on networks the problem under consideration is that of locating a facility on a tree network given data specifying the locations of the users on the network the approach taken is to formulate axioms that require consistent response of the solution to variations in the users location data it is shown that three independent axioms determine together a unique solution located at the point that minimizes the sum of the squares of the distances to the users