emergent dynamics of winfree oscillators on locally coupled networks abstract the winfree model is the first mathematical model for synchronization of weakly coupled oscillators compared to the well known kuramoto model the winfree model does not conserve the total phase this leads to rich dynamic features compared to those produced by other phase models in this paper we study the emergent dynamics of the winfree model on a locally coupled static network a randomly chosen phase configuration undergoes several dynamic phase transitions such as incoherence partial locking complete locking partial oscillator death and complete oscillator death as the coupling strength increases we provide several rigorous analytical results on the emergence of these dynamic features we also provide several numerical simulations and compare their results to the analytical results

opinion dynamics of modified hegselmann krause model in a group based population with heterogeneous bounded confidence abstract continuous opinion dynamics in a group based population with heterogeneous bounded confidences is considered in this paper a slightly modified hegselmann krause model is proposed and agents are classified into three categories open minded moderate minded and closed minded agents while the whole population is divided into three subgroups accordingly we study how agents of each category and the population size can affect opinion dynamics it is observed that the number of final opinion clusters is dominated by the closed minded agents open minded agents cannot contribute to forming opinion consensus and the existence of open minded agents may diversify the final opinions instead for the fixed population size and proportion of closed minded agents the relative size of the largest final opinion cluster varies along concave parabola like curve as the proportion of open minded agents increases and there is a tipping point when the number of open minded agents is almost equal to that of moderate minded agents for the fixed proportion of the three categories in the population as the population size becomes larger the number of final opinion clusters will reach a plateau some of the results are different from the previous studies

emergent behaviors of a holonomic particle system on a sphere we study sufficient conditions for the asymptotic emergence of synchronous behaviors in a holonomic particle system on a sphere which was recently introduced by lohe non abelian kuramoto model and synchronization j phys a math theor 42 395101 395126 2009 these conditions depend only on the coupling strength and initial position diameter for identical particles we show that the position diameter approaches zero asymptotically under these sufficient conditions i e all particles approach to the same position for non identical particles the particle positions do not shrink to one point but can be squeezed into some small region whose diameter is inversely proportional to the coupling strength when the coupling strength is large we also provide several numerical results to confirm our analytical findings

colored solutions of the yang baxter equation from representations of uqgl 2 we study the hopf algebra structure and the highest weight representation of a multiparameter version of uqgl 2 the hopf algebra maps of this algebra are explicitly given we show that the multiparameter universal r matrix can be constructed directly as a quantum double intertwiner without using reshetikhin s twisting transformation we find there are two types highest weight representations for this algebra type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity when applying the representation theory to the multi parameter universal r matrix both standard and nonstandard colored solutions of the yang baxter equation are obtained

an eulerian approach to the analysis of krause s consensus models in this paper we analyze a class of multiagent consensus dynamical systems inspired by krause s original model as in krause s model the basic assumption is the so called bounded confidence two agents can influence each other only when their state values are below a given distance threshold r we study the system under an eulerian point of view considering possibly continuous probability distributions of agents and we present original convergence results the limit distribution is always necessarily a convex combination of delta functions at least r far apart from each other in other terms these models are locally aggregating the eulerian perspective provides the natural framework for designing a numerical algorithm by which we obtain several simulations in 1 and 2 dimensions

large scale dynamics of the persistent turning walker model of fish behavior this paper considers a new model of individual displacement based on fish motion the so called persistent turning walker ptw model which involves an ornstein uhlenbeck process on the curvature of the particle trajectory the goal is to show that its large time and space scale dynamics is of diffusive type and to provide an analytic expression of the diffusion coefficient two methods are investigated in the first one we compute the large time asymptotics of the variance of the individual stochastic trajectories the second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories the kinetic model is a fokker planck type equation posed in an extended phase space involving the curvature among the kinetic variables we show that both methods lead to the same value of the diffusion constant we present some numerical simulations to illustrate the theoretical results

first order aggregation models with alignment abstract we include alignment interactions in a well studied first order attractive repulsive macroscopic model for aggregation the distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density becomes implicit and can have non unique solutions we investigate the well posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second order kinetic equation we work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as essential tools in the analysis a discretization procedure that parallels the analysis is formulated and implemented numerically in one and two dimensions

q analogues of verma representations of quantum algebras for q a root of unity the case of uq sl 3 verma representation theory for classical lie algebra is extended to study the representation of quantum universal enveloping algebra quantum algebra for the nongeneric case that q is a root of unity on certain subspaces and quotient spaces of the verma space finite and infinite dimensional irreducible or indecomposable representations of slq 3 uq sl 3 are obtained in explicit matrix forms

gradient and passive circuit structure in a class of non linear dynamics on a graph we consider a class of non linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods in particular under the assumption of detailed balance we provide a method to formulate the governing ode system in gradient descent form of sum separable energy functions which thus represent a class of lyapunov functions this class coincides with csiszar s information divergences our approach bases on a transformation of the original problem to a mass preserving transport problem and it reflects a little noticed general structure result for passive network synthesis obtained by b d o anderson and p j moylan in 1975 the proposed gradient formulation extends known gradient results in dynamical systems obtained recently by m erbar and j maas in the context of porous medium equations furthermore we exhibit a novel relationship between inhomogeneous markov chains and passive non linear circuits through gradient systems and show that passivity of resistor elements is equivalent to strict convexity of sum separable stored energy eventually we discuss our results at the intersection of markov chains and network systems under sinusoidal coupling

cucker smale flocking under hierarchical leadership a mathematical theory on flocking serves the foundation for several ubiquitous multiagent phenomena in biology ecology sensor networks and economics as well as social behavior like language emergence and evolution directly inspired by the recent fundamental works of cucker and smale on the construction and analysis of a generic flocking model we study the emergent behavior of cucker smale flocking under hierarchical leadership the rates of convergence towards asymptotically coherent group patterns in different scenarios are established the consistent convergence towards coherent patterns may well reveal the advantages and necessities of having leaders and leadership in a complex biological technological economic or social system with sufficient intelligence

swarming on random graphs ii we consider an individual based model where agents interact over a random network via first order dynamics that involve both attraction and repulsion in the case of all to all coupling of agents in mathbb r d this system has a lowest energy state in which an equal number of agents occupy the vertices of the d dimensional simplex the purpose of this paper is to sharpen and extend a line of work initiated in 56 which studies the behavior of this model when the interaction between the n agents occurs according to an erd s renyi random graph mathcal g n p instead of all to all coupling in particular we study the effect of randomness on the stability of these simplicial solutions and provide rigorous results to demonstrate that stability of these solutions persists for probabilities greater than np o log n in other words only a relatively small number of interactions are required to maintain stability of the state the results rely on basic probability arguments together with spectral properties of random graphs

adaptive discontinuous galerkin finite element methods for nonlinear hyperbolic conservation laws we consider the a posteriori error analysis and adaptive mesh design for discontinuous galerkin finite element approximations to systems of nonlinear hyperbolic conservation laws in particular we discuss the question of error estimation for general target functionals of the solution typical examples include the outflow flux local average and pointwise value as well as the lift and drag coefficients of a body immersed in an inviscid fluid by employing a duality argument we derive so called weighted or type i a posteriori error bounds these error estimates include the product of the finite element residuals with local weighting terms involving the solution of a certain dual or adjoint problem that must be numerically approximated based on the resulting approximate type i bound we design and implement an adaptive algorithm that produces meshes specifically tailored to the efficient computation of the given target functional of practical interest the performance of the proposed adaptive strategy and the quality of the approximate type i a posteriori error bound is illustrated by a series of numerical experiments in particular we demonstrate the superiority of this approach over standard mesh refinement algorithms which employ type ii error indicators

clustering and asymptotic behavior in opinion formation abstract we investigate the long time behavior of models of opinion formation we consider the case of compactly supported interactions between agents which are also non symmetric including for instance the so called krause model because of the finite range of interaction convergence to a unique consensus is not expected in general we are nevertheless able to prove the convergence to a final equilibrium state composed of possibly several local consensus this result had so far only been conjectured through numerical evidence because of the non symmetry in the model the analysis is delicate and is performed in two steps first using entropy estimates to prove the formation of stable clusters and then studying the evolution in each cluster we study both discrete and continuous in time models and give rates of convergence when those are available

flocking dynamics and mean field limit in the cucker smale type model with topological interactions abstract we introduce a cucker smale type model for flocking where the strength of interaction between two agents depends on their relative separation called topological distance in previous works which is the number of intermediate individuals separating them this makes the model scale free and is motivated by recent extensive observations of starling flocks suggesting that the interaction ruling animal collective behavior depends on topological rather than the metric distance we study the conditions leading to asymptotic flocking in the topological model defined as the convergence of the agents velocities to a common vector the shift from metric to topological interactions requires development of new analytical methods taking into account the graph theoretical nature of the problem moreover we provide a rigorous derivation of the mean field limit of large populations recovering kinetic and hydrodynamic descriptions in particular we introduce the novel concept of relative separation in continuum descriptions which is applicable to a broad variety of models of collective behavior as an example we shortly discuss a topological modification of the attraction repulsion model and illustrate with numerical simulations that the modified model produces interesting new pattern dynamics

sparse jurdjevic quinn stabilization of dissipative systems abstract for control affine systems with a proper lyapunov function the classical jurdjevic quinn procedure see jurdjevic and quinn 1978 gives a well known and widely used method for the design of feedback controls that asymptotically stabilize the system to some invariant set in this procedure all controls are in general required to be activated i e nonzero at the same time in this paper we give sufficient conditions under which this stabilization can be achieved by means of sparse feedback controls i e feedback controls having the smallest possible number of nonzero components we thus obtain a sparse version of the classical jurdjevic quinn theorem we propose three different explicit stabilizing control strategies depending on the method used to handle possible discontinuities arising from the definition of the feedback a time varying periodic feedback a sampled feedback and a hybrid hysteresis we illustrate our results by applying them to opinion formation models thus recovering and generalizing former results for such models

quantum chains with glq 2 symmetry usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras uq g here we propose a method for constructing quantum chains with cq g global symmetry where cq g is the algebra of functions on the quantum group in particular we will construct a quantum chain with glq 2 symmetry which interpolates between two classical ising chains it is shown that the hamiltonian of this chain satisfies the generalized braid group algebra

a new model for self organized dynamics and its flocking behavior we introduce a model for self organized dynamics which we argue addresses several drawbacks of the celebrated cucker smale c s model the proposed model does not only take into account the distance between agents but instead the influence between agents is scaled in term of their relative distance consequently our model does not involve any explicit dependence on the number of agents only their geometry in phase space is taken into account the use of relative distances destroys the symmetry property of the original c s model which was the key for the various recent studies of c s flocking behavior to this end we introduce here a new framework to analyze the phenomenon of flocking for a rather general class of dynamical systems which covers systems with non symmetric influence matrices in particular we analyze the flocking behavior of the proposed model as well as other strongly asymmetric models with leaders

flocking estimates for the cucker smale model with time lag and hierarchical leadership abstract we analyze the cucker smale model under hierarchical leadership in presence of a time delay by using a lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay we also prove a flocking estimate in the case of a free will leader these results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations

flocking and asymptotic velocity of the cucker smale model with processing delay abstract the processing delay is incorporated into the influence function of the well known cucker smale model for self organized systems with multiple agents both symmetric and non symmetric pairwise influence functions are considered and a lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed cucker smale model an analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval

energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators in this paper a hanging node discontinuous galerkin isogeometric discretisation of the multigroup discrete ordinates sn equations is presented in which each energy group has its own mesh the equations are discretised using non uniform rational b splines nurbs which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest this would not be the case using straight sided finite elements information is transferred between meshes via the construction of a supermesh this is a non trivial task for two arbitrary meshes but is significantly simplified here by deriving every mesh from a common coarsest initial mesh in order to take full advantage of this flexible discretisation goal based error estimators are derived for the multigroup discrete ordinates equations with both fixed extraneous and fission sources and these estimators are used to drive an adaptive mesh refinement amr procedure the method is applied to a variety of test cases for both fixed and fission source problems the error estimators are found to be extremely accurate for linear nurbs discretisations with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the exact adjoint solution required to calculate the estimators nevertheless the method seems to produce optimal meshes in the amr process for both linear and quadratic discretisations and is 100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

discontinuous isogeometric analysis methods for the first order form of the neutron transport equation with discrete ordinate sn angular discretisation in this paper two discontinuous galerkin isogeometric analysis methods are developed and applied to the first order form of the neutron transport equation with a discrete ordinate s n angular discretisation the discontinuous galerkin projection approach was taken on both an element level and the patch level for a given non uniform rational b spline nurbs patch this paper describes the detailed dispersion analysis that has been used to analyse the numerical stability of both of these schemes the convergence of the schemes for both smooth and non smooth solutions was also investigated using the method of manufactured solutions mms for multidimensional problems and a 1d semi analytical benchmark whose solution contains a strongly discontinuous first derivative this paper also investigates the challenges posed by strongly curved boundaries at both the nurbs element and patch level with several algorithms developed to deal with such cases finally numerical results are presented both for a simple pincell test problem as well as the c5g7 quarter core mox uox small light water reactor lwr benchmark problem these numerical results produced by the isogeometric analysis iga methods are compared and contrasted against linear and quadratic discontinuous galerkin finite element dgfem s n based methods

an ode model of the motion of pelagic fish a system of ordinary differential equations odes is derived from a discrete system of vicsek czirok et al phys rev lett 75 6 1226 1229 1995 describing the motion of a school of fish classes of linear and stationary solutions of the odes are found and their stability explored using equivariant bifurcation theory the existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found applications of the model to the migration of the capelin a pelagic fish that undertakes an extensive migration in the north atlantic are discussed and simulation of the odes presented

the bond based peridynamic system with dirichlet type volume constraint in this paper the bond based peridynamic system is analysed as a non local boundary value problem with volume constraint the study extends earlier works in the literature on non local diffusion and non local peridynamic models to include non positive definite kernels we prove the well posedness of both linear and nonlinear variational problems with volume constraints the analysis is based on some non local poincare type inequalities and the compactness of the associated non local operators it also offers careful characterizations of the associated solution spaces such as compact embedding separability and completeness in the limit of vanishing non locality the convergence of the peridynamic system to the classical navier equations of elasticity with poisson ratio is demonstrated

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

time delay effect on the flocking in an ensemble of thermomechanical cucker smale particles abstract we study the communication time delay effect on the emergent dynamics of thermodynamic cucker smale tcs ensemble with temperature as an internal state in the presence of time delay conservation laws for momentum and energy do not hold so that the analytic tool based on the energy method cannot be applied for the tcs model as it is we show that temperature stays positive in the presence of small time delay as long as temperatures stay positive the tcs model is well posed by direct application of cauchy lipschitz theory when the size of time delay and initial data are sufficiently small we can derive differential inequalities for velocity and temperature diameters using these differential inequalities we show that temperature and velocity diameters tend to zero exponentially fast whereas the position diameter is uniformly bounded we also present several numerical simulations and compare them with analytic results

dual consistency and functional accuracy consider the discretization of a partial differential equation pde and an integral functional that depends on the pde solution the discretization is dual consistent if it leads to a discrete dual problem that is a consistent approximation of the corresponding continuous dual problem consequently a dual consistent discretization is a synthesis of the so called discrete adjoint and continuous adjoint approaches we highlight the impact of dual consistency on summation by parts sbp finite difference discretizations of steady state pdes specifically superconvergent functionals and accurate functional error estimates in the case of functional superconvergence the discrete adjoint variables do not need to be computed since dual consistency on its own is sufficient numerical examples demonstrate that dual consistent schemes significantly outperform dual inconsistent schemes in terms of functional accuracy and error estimate effectiveness the dual consistent and dual inconsistent discretizations have similar computational costs so dual consistency leads to improved efficiency to illustrate the dual consistency analysis of sbp schemes we thoroughly examine a discretization of the euler equations of gas dynamics including the treatment of the boundary conditions numerical dissipation interface penalties and quadrature by sbp norms

adjoint consistency analysis of discontinuous galerkin discretizations this paper is concerned with the adjoint consistency of discontinuous galerkin dg discretizations adjoint consistency in addition to consistency is the key requirement for dg discretizations to be of optimal order in l 2 as well as measured in terms of target functionals we provide a general framework for analyzing the adjoint consistency of dg discretizations which is also useful for the derivation of adjoint consistent methods this analysis will be performed for the dg discretizations of the linear advection equation the interior penalty dg method for elliptic problems and the dg discretization of the compressible euler equations this framework is then used to derive an adjoint consistent dg discretization of the compressible navier stokes equations numerical experiments demonstrate the link of adjoint consistency to the accuracy of numerical flow solutions and the smoothness of discrete adjoint solutions

a local sensitivity analysis for the hydrodynamic cucker smale model with random inputs abstract we present a local sensitivity analysis for the hydrodynamic cucker smale hcs model with random inputs in the absence of random inputs the hcs model was derived as a macroscopic model for the emergent dynamics of the cs flocking ensemble from the kinetic cs model via the moment method and mono kinetic ansatz for a closure condition in this paper we incorporate the uncertain effects together with the hcs model to result in the random hcs model for definiteness we consider the uncertainties in initial data and communication weight function for this random hcs model we perform local sensitivity estimates such as the propagation of pathwise well posedness pathwise l 2 stability and flocking estimates of solution process

from discrete cucker smale model to continuous cucker smale model in a temperature field we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results

a cucker smale model with noise and delay a generalization of the cucker smale model for collective animal behavior is investigated the model is formulated as a system of delayed stochastic differential equations it incorporates two additional processes which are present in animal decision making but are often neglected in modeling i stochasticity imperfections of individual behavior and ii delayed responses of individuals to signals in their environment sufficient conditions for flocking for the generalized cucker smale model are derived by using a suitable lyapunov functional as a by product a new result regarding the asymptotic behavior of delayed geometric brownian motion is obtained in the second part of the paper results of systematic numerical simulations are presented they not only illustrate the analytical results but hint at a somehow surprising behavior of the system namely that the introduction of an intermediate time delay may facilitate flocking

kinetic models for topological nearest neighbor interactions we consider systems of agents interacting through topological interactions these have been shown to play an important part in animal and human behavior precisely the system consists of a finite number of particles characterized by their positions and velocities at random times a randomly chosen particle the follower adopts the velocity of its closest neighbor the leader we study the limit of a system size going to infinity and under the assumption of propagation of chaos show that the limit kinetic equation is a non standard spatial diffusion equation for the particle distribution function we also study the case wherein the particles interact with their k closest neighbors and show that the corresponding kinetic equation is the same finally we prove that these models can be seen as a singular limit of the smooth rank based model previously studied in 10 the proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments

some weak flocking models and its application to target tracking abstract in this paper we introduce a new concept named the weak flocking behavior that is if the complex system has the weak flocking property the agents do not need have the same velocities to keep together when t this shows the biggest difference between weak flocking behavior and the flocking behavior the advantage of this concept is that its practical significance the agents don t need always keep in step in lots of the complex systems but they still keep together then we propose a weak flocking model with two agents and study two different mechanisms for this model moreover we also consider a system with n agents under the weak link mechanism the system with n agents can keep weak flocking

collective behavior models with vision geometrical constraints truncated noises and propagation of chaos abstract we consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains we rigorously derive a vlasov fokker planck type of kinetic mean field equation from the corresponding stochastic integral inclusion system more specifically we construct a global in time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1 wasserstein distance

eulerian dynamics with a commutator forcing iii fractional diffusion of order 0 α 1 abstract we continue our study of hydrodynamic models of self organized evolution of agents with singular interaction kernel x x 1 following our works shvydkoy and tadmor 2017 1 2 which focused on the range 1 2 and do et al 2017 which covered the range 0 1 in this paper we revisit the latter case and give a short er proof of global in time existence of smooth solutions together with a full description of their long time dynamics specifically we prove that starting from any initial condition in 0 u 0 h 2 h 3 the solution approaches exponentially fast to a flocking state solution consisting of a wave x t u traveling with a constant velocity determined by the conserved average velocity u the convergence is accompanied by exponential decay of all higher order derivatives of u

a space angle dgfem approach for the boltzmann radiation transport equation with local angular refinement in this paper a new method for the discretization of the radiation transport equation is presented based on a discontinuous galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization to cope with the discontinuous spatial nature of the solution a generalized riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes a new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem the resulting numerical fluxes for the various possible cases where neighboring elements have an equal higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation the choice of discontinuous trial functions not only has the advantage of easing local refinement it also facilitates the use of efficient sweep based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution the approach is illustrated by a series of numerical experiments results show high orders of convergence for the scalar flux on angular refinement the generalized riemann upwinding procedure leads to stable and consistent solutions further the sweep based solver performs well when used as a preconditioner for a krylov method

continuous time average preserving opinion dynamics with opinion dependent communications we study a simple continuous time multiagent system related to krause s model of opinion dynamics each agent holds a real value and this value is continuously attracted by every other value differing from it by less than 1 with an intensity proportional to the difference we prove convergence to a set of clusters with the agents in each cluster sharing a common value and provide a lower bound on the distance between clusters at a stable equilibrium under a suitable notion of multiagent system stability to better understand the behavior of the system for a large number of agents we introduce a variant involving a continuum of agents we prove under some conditions the existence of a solution to the system dynamics convergence to clusters and a nontrivial lower bound on the distance between clusters finally we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents

discontinuous galerkin method for krause s consensus models and pressureless euler equations in this paper we apply discontinuous galerkin dg methods to solve two model equations email protected s consensus models and pressureless euler equations these two models are used to describe the collisions of particles and the distributions can be identified as density functions if the particles are placed at a single point then the density function turns out to be a d function and is difficult to be well approximated numerically in this paper we use dg method to approximate such a singularity and demonstrate the good performance of the scheme since the density functions are always positive we apply a positivity preserving limiter to them moreover for pressureless euler equations the velocity satisfies the maximum principle we also construct special limiters to fulfill this requirement

a continuous model for ratings we study rating systems such as the famous elo system applied to a large number of players we assume that each player is characterized by an intrinsic inner strength and follow the evolution of their rating evaluations by deriving a new continuous model a kinetic like equation we then investigate the validity of the rating systems by looking at their large time behavior as one would ideally expect the rating of each player to converge to their actual strength the simplistic case when all players interact indeed yields an exponential convergence of the ratings however the behavior in the more realistic cases with only local interactions is more complex with several possible equilibria depending on the exact initial distribution of initial ratings and possibly very slow convergence

contagion shocks in one dimension we consider an agent based model of emotional contagion coupled with motion in one dimension that has recently been studied in the computer science community the model involves movement with a speed proportional to a fear variable that undergoes a temporal consensus averaging based on distance to other agents we study the effect of riemann initial data for this problem leading to shock dynamics that are studied both within the agent based model as well as in a continuum limit we examine the behavior of the model under distinguished limits as the characteristic contagion interaction distance and the interaction timescale both approach zero the limiting behavior is related to a classical model for pressureless gas dynamics with sticky particles in comparison we observe a threshold for the interaction distance vs interaction timescale that produce qualitatively different behavior for the system in one case particle paths do not cross and there is a natural eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit

local phase synchronization and clustering for the delayed phase coupled oscillators with plastic coupling abstract in this paper we investigate the local synchronization problem for delayed phase coupled oscillators with plastic coupling also referred as a generalized kuramoto model by linearizing the phase coupled oscillators system at a special solution an approximation phase coupled system with delay effects is deduced moreover we find the multiplicity of semisimple zero eigenvalue for coupling strength coefficients matrix and the rank of vandermonde matrix associated initial values are two sensitive factors the former is closely related to the maximum number of clusters phase of linear coupled system and the latter determines clusters phase synchronization as results both frequency synchronization criteria and phase synchronization criteria are established in this literature also the final synchronization frequency and phase are formulated in terms of coupling strength initial values and time delay

a kinetic description for the herding behavior in financial market as a continuation of the study of the herding model proposed in bae et al in arxiv 1712 01085 2017 we consider in this paper the derivation of the kinetic version of the herding model the existence of the measure valued solution and the corresponding herding behavior at the kinetic level we first consider the mean field limit of the particle herding model and derive the existence of the measure valued solutions for the kinetic herding model we then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals first we derive a herding phenomena of the measure valued solutions under virtually no restrictions on the parameter sets using the barbalat s lemma we however don t get any herding rate in this case on the other hand we also establish a gronwall type estimate for another herding functional leading to the exponential herding rate under comparatively strict conditions these results are then extended to smooth solutions

an exact rescaling velocity method for some kinetic flocking models in this work we discuss kinetic descriptions of flocking models of the so called cucker smale ieee trans automat control 52 2007 pp 852 862 and motsch tadmor j statist phys 144 2011 pp 923 947 types these models are given by vlasov type equations where the interactions taken into account are only given long range bi particles interaction potentials we introduce a new exact rescaling velocity method inspired by the recent work f filbet and t rey j comput phys 248 2013 pp 177 199 allowing us to observe numerically the flocking behavior of the solutions to these equations without a need of remeshing or taking a very fine grid in the velocity space to stabilize the exact method we also introduce a modification of the classical upwind finite volume scheme which preserves the physical properties of the solution such as momentum conservation

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

some remarks on the gauss decomposition for quantum group glq n with application to q bosonization the gauss decomposition of quantum group glq n is defined purely algebraically the entries of the upper triangular matrix commutes with those of the lower triangular one the quantum determinant is the product of the diagonal matrix elements this decomposition gives rise to a new bosonization of the glq n in terms of 2n q oscillators

a local sensitivity analysis for the kinetic cucker smale equation with random inputs abstract we present a local sensitivity analysis for the kinetic cucker smale c s equation with random inputs this is a companion work to our previous local sensitivity analysis for the particle c s model random inputs in the coefficients of the kinetic c s equation can be caused by diverse sources such as the incomplete measurement and interactions with unknown environments and will enter the problem through the communication function or initial data for the proposed random kinetic c s equation we present sufficient conditions for the pathwise well posedness and flocking estimates for the local sensitivity analysis we study the propagation of regularity of the kinetic density function in random space

flocking with short range interactions we study the large time behavior of continuum alignment dynamics based on cucker smale cs type interactions which involve short range kernels that is communication kernels with support much smaller than the diameter of the crowd we show that if the amplitude of the interactions is larger than a finite threshold then unconditional hydrodynamic flocking follows since we do not impose any regularity nor do we require the kernels to be bounded the result covers both regular and singular interaction kernels moreover we treat initial densities in the general class of compactly supported measures which are required to have positive mass on average over balls at small enough scale but otherwise vacuum is allowed at smaller scales consequently our arguments of hydrodynamic flocking apply mutatis mutandis to the agent based cs model with finitely many dirac masses in particular discrete flocking threshold is shown to depend on the number of dense clusters of communication but otherwise does not grow with the number of agents

an adaptive hanging node discontinuous isogeometric analysis method for the first order form of the neutron transport equation with discrete ordinate sn angular discretisation abstract in this paper a discontinuous hanging node isogeometric analysis iga method is developed and applied to the first order form of the neutron transport equation with a discrete ordinate s n angular discretisation in two dimensional space the complexities involved in upwinding across curved element boundaries that contain hanging nodes have been addressed to ensure that the scheme remains conservative a robust algorithm for cycle breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction the convergence rate of the scheme has been verified using the method of manufactured solutions mms with a smooth solution heuristic error indicators have been used to drive an adaptive mesh refinement amr algorithm to take advantage of the hanging node discretisation the effectiveness of this method is demonstrated for three test cases the first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source the second test case is a radiation shielding problem and the third is a 3 3 supercell featuring a burnable absorber in the final test case comparisons are made to the discontinuous galerkin finite element method dgfem using both straight sided and curved quadratic finite elements

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

a geometry preserving conservative mesh to mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup second order even parity form of the neutron transport equation abstract in this paper a method is presented for the application of energy dependent spatial meshes applied to the multigroup second order even parity form of the neutron transport equation using isogeometric analysis iga the computation of the inter group regenerative source terms is based on conservative interpolation by galerkin projection the use of non uniform rational b splines nurbs from the original computer aided design cad model allows for efficient implementation and calculation of the spatial projection operations while avoiding the complications of matching different geometric approximations faced by traditional finite element methods fem the rate of convergence was verified using the method of manufactured solutions mms and found to preserve the theoretical rates when interpolating between spatial meshes of different refinements the scheme s numerical efficiency was then studied using a series of two energy group pincell test cases where a significant saving in the number of degrees of freedom can be found if the energy group with a complex variation in the solution is refined more than an energy group with a simpler solution function finally the method was applied to a heterogeneous seven group reactor pincell where the spatial meshes for each energy group were adaptively selected for refinement it was observed that by refining selected energy groups a reduction in the total number of degrees of freedom for the same total l 2 error can be obtained

complete classification of the asymptotical behavior for singular c s model on the real line abstract in this paper we study the singular cucker smale c s model on the real line for long range case i e 1 we prove the uniqueness of the solution in the sense of definition 2 1 and the unconditional flocking emergence moreover the sufficient and necessary condition for collision and sticking phenomenon will be provided for short range case i e 1 we construct the uniform in time lower bound of the relative distance between particles and provide the sufficient and necessary condition for the emergence of multi cluster formation for critical case i e 1 we show the uniform lower bound of the relative distance and unconditional flocking emergence these results provide a complete classification of the collective behavior for c s model on the real line

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

minimising the error in eigenvalue calculations involving the boltzmann transport equation using goal based adaptivity on unstructured meshes this article presents a method for goal based anisotropic adaptive methods for the finite element method applied to the boltzmann transport equation the neutron multiplication factor k e f f is used as the goal of the adaptive procedure the anisotropic adaptive algorithm requires error measures for k e f f with directional dependence general error estimators are derived for any given functional of the flux and applied to k e f f to acquire the driving force for the adaptive procedure the error estimators require the solution of an appropriately formed dual equation forward and dual error indicators are calculated by weighting the hessian of each solution with the dual and forward residual respectively the hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence the two indicators are combined to form a single error metric that is used to adapt the finite element mesh the residual is approximated using a novel technique arising from the sub grid scale finite element discretisation two adaptive routes are demonstrated i a single mesh is used to solve all energy groups and ii a different mesh is used to solve each energy group the second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh the k e f f goal based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained

representations of quantum matrix algebra mq 2 and its q boson realization in this paper it is proved that the nontrivial finite dimensional irreducible representations of the quantum matrix algebra mq 2 or the coordinate ring of the quantum group glq 2 exist only when q is a root of unity and thereby construct such representations for mq 2 some finite dimensional indecomposable representations of mq 2 are also explicitly presented finally the q boson realization of mq 2 is discussed and it is shown that it works in this case as well as in the quantum algebra case

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