opinion dynamics in heterogeneous networks convergence conjectures and theorems recently significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers and agents update their opinions synchronously by averaging their neighbors opinions the neighbors of each agent can be defined as either 1 those agents whose opinions are in its confidence range or 2 those agents whose influence range contain the agent s opinion the former definition is employed in hegselmann and krause s bounded confidence model and the latter is novel here as the confidence and influence ranges are distinct for each agent the heterogeneous state dependent interconnection topology leads to a poorly understood complex dynamic behavior in both models we classify the agents via their interconnection topology and accordingly compute the equilibria of the system then we define a positive invariant set centered at each equilibrium opinion vector we show that if a trajectory enters one such set then it converges to a steady state with consta

broadband time domain impedance models the modeling of a set of impedance values given either experimentally or heuristically for implementation as a time domain impedance equivalent boundary condition tdibc is discussed it is shown that impedance as defined by the reflection of plane harmonic waves when extended for broadband time domain applications can correspond to mathematically feasible but physically unacceptable noncausal reflection processes given a set of impedance data on a finite positive and real frequency range it is possible to construct causal time domain models that render efficient implementation of tdibc for broadband reflections however these models defined by measurement of harmonic waves may not be valid for the reflection of impulses for which measurement of transient reflections is warranted

inertial hegselmann krause systems we derive an energy bound for inertial hegselmann krause hk systems which are a variant of the classic hk model that allows agents to change weights as they please at each step we use the bound to prove the convergence of hk systems with static agents which settles a widely believed conjecture this paper also introduces anchored hk systems and show their equivalence to the symmetric heterogeneous model

a generalized recursive convolution method for time domain propagation in porous media an efficient numerical method referred to as the auxiliary differential equation ade method is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media for this purpose the relaxation functions are approximated in the frequency domain by rational functions the time variation of the convolution is thus governed by first order differential equations which can be straightforwardly solved the accuracy of the method is first investigated and compared to that of recursive convolution methods it is shown that while recursive convolution methods are first or second order accurate in time the ade method does not introduce any additional error the ade method is then applied for outdoor sound propagation using the equations proposed by wilson et al in the ground 2007 appl acoust 68 173 200 a first one dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications finally the ade method is used to compute sound propagation in a three dimensional geometry over an absorbing ground results obtained with wilson s equations are compared to those obtained with zwikker and kosten s equations and with an impedance surface for different flow resistivities

existence and stability of entire solutions to a semilinear fourth order elliptic problem for a semilinear biharmonic equation with exponential nonlinearity we study the existence and the asymptotic behavior of entire solutions furthermore their stability and stability outside a compact set of rn n 2 is discussed in any space dimension n

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

a stabilization theorem for dynamics of continuous opinions abstract a stabilization theorem for processes of opinion dynamics is presented the theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging like the models of hegselmann krause and weisbuch deffuant the analysis detects self confidence as a driving force of stabilization

time domain numerical simulation of a flow impedance tube an efficient method has been developed for the application of the surface acoustic impedance condition in time domain solutions of aeroacoustic problems such as the broadband frequency simulation of a flow impedance tube the basis for this method is the standard impedance condition stated in the frequency domain as the particle displacement continuity equation the development of the time domain impedance condition follows the relations among the frequency z and discrete time domains and a rational function representation of the impedance in thez domain the resultant impedance condition consists of finite infinite impulse response type digital filter operations in the time domain which is very suitable to computational aeroacoustics algorithms this paper describes the present approach and discusses the time domain numerical simulations of the nasa langley flow impedance tube with a constant depth ceramic tubular liner both single and broadband frequency simulations are performed excellent agreement is shown with experimental data at various frequencies and flow conditions

towards perfectly absorbing boundary conditions for euler equations in this paper we examine the effectiveness of absorbing layers as non reflecting computational boundaries for the euler equations the absorbing layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation this methodology is similar to that used by berenger for the numerical solutions of maxwell s equations specifically we apply this methodology to three physical problems shock vortex interactions a plane free shear flow and an axisymmetric jet with emphasis on acoustic wave propagation our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

time domain impedance boundary conditions for computational aeroacoustics it is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance impedance is a complex quantity as such it is designed primarily for frequency domain analysis time domain boundary conditions that are the equivalent of the frequency domain impedance boundary condition are proposed both single frequency and model broadband time domain impedance boundary conditions are provided it is shown that the proposed boundary conditions together with the linearized euler equations form well posed initial boundary value problems unlike ill posed problems they are free from spurious instabilities that would render time marching computational solutions impossible

on synchronous robotic networks part ii time complexity of rendezvous and deployment algorithms this paper analyzes a number of basic coordination algorithms running on synchronous robotic networks we provide upper and lower bounds on the time complexity of the move toward average and circumcenter laws both achieving rendezvous and of the centroid law achieving deployment over a region of interest the results are derived via novel analysis methods including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal toeplitz and circulant matrices

the total s energy of a multiagent system we introduce the total s energy of a multiagent system with time dependent links this provides a new analytical perspective on bidirectional agreement dynamics which we use to bound the convergence rates of dynamical systems for synchronization flocking opinion dynamics and social epistemology

ground parameter information for propagation modeling the relative success of various simplified ground impedance models at fitting data obtained from direct and indirect measurements is reviewed a new two parameter approximation for the normal surface impedance of a nonhard backed layer structure is introduced a two parameter model of this form is shown to have wide success in fitting recent ground impedance and excess attenuation data obtained by a variety of techniques further evidence is produced of the unreliability that would be associated with extrapolation of fits based on the single parameter semiempirical model widely used at present outside the frequency range of the fitted data by refitting classical ground impedance data and tabulating resulting parameters along with those obtained more recently a menu of ground types best fit models associated parameter values and frequency ranges of fits has been compiled

low dispersion finite difference methods for acoustic waves in a pipe a new algorithm for computing one dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial boundary value problem conventional dissipation free second order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength using the signal generated by a piston in a duct as an example transient acoustic computations are presented using a new compact three point algorithm which allows about 60 fewer mesh points per wave length both pulse and harmonic excitation are considered coupling of the acoustic signal with the pipe resonant modes are shown to generate a complex transient wave with rich harmonic content

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

the gel fand problem for the biharmonic operator we study stable and finite morse index solutions of the equation delta 2 u e u if the equation is posed in mathbb r n we classify radial stable solutions we then construct nonradial stable solutions and we prove that unlike the corresponding second order problem no liouville type theorem holds unless additional information is available on the asymptotics of solutions at infinity thanks to this analysis we prove that stable solutions of the equation on a smoothly bounded domain supplemented with navier boundary conditions are smooth if and only if n leqq 12 we find an upper bound for the hausdorff dimension of their singular set in higher dimensions and conclude with an a priori estimate for solutions of bounded morse index provided they are controlled in a suitable morrey norm

energy analysis and discretization of nonlinear impedance boundary conditions for the time domain linearized euler equations time domain impedance boundary conditions tdibcs can be enforced using the impeda nce the admittance or the scattering operator this article demonstrates the computational advantage of the last even for nonlinear tdibcs with the linearized euler equations this is achieved by a systematic semi discrete energy analysis of the weak enforcement of a generic nonlinear tdibc in a discontinuous galerkin finite element method in particular the analysis highlights that the sole definition of a discrete model is not enough to fully define a tdibc to support the analysis an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube then the derivation of time delayed broadband tdibcs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners a high order discretization of the derived time local formulation which consists in composing a set of ordinary differential equations with a transport equation is applied to two flow ducts

diffusive influence systems influence systems seek to model how influence broadly defined spreads across a dynamic network we build a general analytical framework which we then use to prove that while turing complete influence dynamics of the diffusive type is almost surely asymptotically periodic in addition to resolving the dynamics of a widely used family of multiagent systems we introduce a general renormalization method for the bifurcation analysis of multiagent systems

interaction ruling animal collective behavior depends on topological rather than metric distance evidence from a field study numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals however very little is known about the nature of such interaction so that models and theories mostly rely on aprioristic assumptions by reconstructing the three dimensional positions of individual birds in airborne flocks of a few thousand members we show that the interaction does not depend on the metric distance as most current models and theories assume but rather on the topological distance in fact we discovered that each bird interacts on average with a fixed number of neighbors six to seven rather than with all neighbors within a fixed metric distance we argue that a topological interaction is indispensable to maintain a flock s cohesion against the large density changes caused by external perturbations typically predation we support this hypothesis by numerical simulations showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one

synchronization in oscillator networks with delayed coupling a stability criterion we derive a stability criterion for the synchronous state in networks of identical phase oscillators with delayed coupling the criterion applies to any network whether regular or random low dimensional or high dimensional directed or undirected in which each oscillator receives delayed signals from k others where k is uniform for all oscillators

an exact laplace transform formulation for a point source above a ground surface an exact analysis is given for a point source in air above a ground surface by representing the plane wave reflection coefficient as the laplace transform of an image source distribution a well behaved image integral instead of the usual sommerfeld integral is obtained the approach is valid for both locally and extended reacting surfaces for a locally reacting ground surface the image integral is an especially simple rapidly convergent integral the integral for local reaction is investigated analytically for a number of limiting cases the resulting analytic solutions are compared with analytic solutions obtained from more standard approaches finally the image integral for local reaction is analyzed numerically and an upper limit on the numerical integration is given it is shown that with realistic values of ground impedance the prescribed integration limit allows the image integral to be easily and accurately computed numerically

well posedness of the limiting equation of a noisy consensus model in opinion dynamics abstract this paper establishes the global well posedness of the nonlinear fokker planck equation for a noisy version of the hegselmann krause model the equation captures the mean field behavior of a classic multiagent system for opinion dynamics we prove the global existence uniqueness nonnegativity and regularity of the weak solution we also exhibit a global stability condition which delineates a forbidden region for consensus formation this is the first nonlinear stability result derived for the hegselmann krause model

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

existence of stable solutions to δ mu eu in rn with m 3 and n 2m abstract we consider the polyharmonic equation m u e u in r n with m 3 and n 2 m we prove the existence of many entire stable solutions this answers some questions raised by farina and ferrero in 7

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

broadband impedance boundary conditions for the simulation of sound propagation in the time domain an accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband frequency simulation in aeroacoustic problems to show the capability of this method two kinds of numerical simulations are performed and compared with the analytical experimental results one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall both single frequency and broadband frequency simulations are performed within the framework of linearized euler equations a high order dispersion relation preserving finite difference method and a low dissipation low dispersion runge kutta method are used for spatial discretization and time integration respectively the results show excellent agreement with the analytical experimental results at various frequencies the method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well posedness of the broadband time domain impedance boundary condition