on multiscale entropy analysis for physiological data abstract we perform an analysis of cardiac data using multiscale entropy as proposed in costa et al multiscale entropy analysis of complex physiological time series phys rev lett 89 2002 068102 we reproduce the signatures of the multiscale entropy for the three cases of young healthy hearts atrial fibrillation and congestive heart failure we show that one has to be cautious how to interpret these signatures in terms of the underlying dynamics in particular we show that different dynamical systems can exhibit the same signatures depending on the sampling time and that similar systems may have different signatures depending on the time scales involved besides the total amount of data we identify the sampling time the correlation time and the period of possible nonlinear oscillations as important time scales which have to be involved in a detailed analysis of the signatures of multiscale entropies we illustrate our ideas with the lorenz equation as a simple deterministic chaotic system

passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

complete aggregation of the lohe tensor model with the same free flow the lohe tensor model is a first order tensor valued continuous time dynamical system for the aggregation of tensors with the same rank and size it reduces to the well known aggregation models such as the kuramoto model the lohe sphere model and the lohe matrix model as special cases for low rank tensors we present conditions for the solution splitting property asymptotic convergence toward a set of equilibria and analyze two possible asymptotic states completely aggregate state and bi polar state which can emerge from a set of initial data moreover we provide a sufficient framework leading to the aforementioned two asymptotic states in terms of initial data and system parameters

contraction analysis for a class of nondifferentiable systems with applications to stability and network synchronization in this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems contraction theory we focus on switched nondifferentiable systems satisfying caratheodory conditions for the existence and uniqueness of a solution after generalizing the classical definition of contraction to this class of dynamical systems we give sufficient conditions for global convergence of their trajectories the theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems giving conditions for incremental stability of piecewise smooth systems and analyzing the convergence of networked switched systems

robustness and asymptotic stability for the winfree model on a general network under the effect of time delay we study the robustness and asymptotic stability of the unique equilibrium for the winfree model on a general network under the effect of small time delay time delay is a ubiquitous mechanism in classical and quantum many body systems and it is due to the finite speed of communication in this paper we further investigate the robustness of the equilibrium under the effects of small time delay and general network topology for this we present several sufficient frameworks formulated in terms of the network topology coupling strength time delay and initial configuration in the proposed framework we present a positively invariant arc which contains the unique equilibrium independent of strength of time delay by using energy estimates we show that the unique equilibrium in the invariant arc is asymptotically stable we also provide several numerical simulations and compare them with analytical results we study the robustness and asymptotic stability of the unique equilibrium for the winfree model on a general network under the effect of small time delay time delay is a ubiquitous mechanism in classical and quantum many body systems and it is due to the finite speed of communication in this paper we further investigate the robustness of the equilibrium under the effects of small time delay and general network topology for this we present several sufficient frameworks formulated in terms of the network topology coupling strength time delay and initial configuration in the proposed framework we present a positively invariant arc which contains the unique equilibrium independent of strength of time delay by using energy estimates we show that the unique equilibrium in the invariant arc is asymptotically stable we also provide several numerical simulations and compare them with analytical results

on the global well posedness of bv weak solutions to the kuramoto sakaguchi equation abstract the kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit cycle oscillators when the number of oscillators is sufficiently large the dynamics of kuramoto ensemble can be effectively approximated by the corresponding mean field equation namely the kuramoto sakaguchi ks equation this ks equation is a kind of scalar conservation law with a nonlocal flux function due to the mean field interactions among oscillators in this paper we provide a unique global solvability of bounded variation bv weak solutions to the kinetic ks equation for identical oscillators using the method of front tracking in hyperbolic conservation laws moreover we also show that our bv weak solutions satisfy local in time l 1 stability with respect to bv initial data for the ensemble of identical kuramoto oscillators we explicitly construct an exponentially growing bv weak solution generated from bv perturbation of incoherent state for any positive coupling strength this implies the nonlinear instability of incoherent state in a positive coupling strength regime we provide several numerical examples and compare them with our analytical results

low design cost fuzzy controllers for robust stabilization of nonlinear partial differential systems in general the design cost of a fuzzy controller for nonlinear partial differential systems pdss is very expensive in this paper a new approach for robust fuzzy h infty stabilization design is developed for a class of n dimensional nonlinear parabolic pdss further two low design cost robust fuzzy controllers called the robust fuzzy area controller and point controller as well as a normal design cost robust fuzzy full controller are proposed for this problem the difference between the three control designs lies in their controller placement in the spatial domain first we present the n dimensional parabolic takagi sugeno t s fuzzy pds based on the knowledge based fuzzy system technique next these three robust fuzzy controllers are constructed via solving diffusion matrix inequality dmi problems with the proposed simple but general method using the poincare inequality the linear matrix inequality problems are provided to replace dmi problems for the robust fuzzy h infty stabilization designs for computational simplicity further the comparison of these three robust fuzzy controllers are demonstrated to enable a designer to select a low cost option finally a simulation example is provided to illustrate the design procedure and verify the performance of the proposed designs

toward synchronization in networks with nonlinear dynamics a submodular optimization framework synchronization underlies phenomena including memory and perception in the brain coordinated motion of animal flocks and stability of the power grid these synchronization phenomena are often modeled through networks of phase coupled oscillating nodes heterogeneity in the node dynamics however may prevent such networks from achieving the required level of synchronization in order to guarantee synchronization external inputs can be used to pin a subset of nodes to a reference frequency while the remaining nodes are steered toward synchronization via local coupling in this paper we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from a desired set of initial states we derive threshold based sufficient conditions for synchronization and then prove that these conditions are equivalent to constraints on monotone submodular functions over partition matroids based on this connection we map the sufficient conditions for synchronization to constraints on submodular functions leading to efficient algorithms with provable optimality bounds for selecting input nodes we illustrate our approach via numerical studies of synchronization in power systems

on the schrodinger lohe hierarchy for aggregation and its emergent dynamics the lohe hierarchy is a hierarchy of finite dimensional aggregation models consisting of the kuramoto model the complex lohe sphere model the lohe matrix model and the lohe tensor model in contrast the schrodinger lohe model is the only known infinite dimensional lohe aggregation model in literature in this paper we provide an explicit connection between the schrodinger lohe model and the complex lohe sphere model and then by exploiting this explicit relation we construct infinite dimensional liftings of the lohe matrix and the lohe tensor models in this way we establish the schrodinger lohe hierarchy which corresponds to the infinite dimensional extensions of the lohe hierarchy for the proposed hierarchy we provide sufficient frameworks leading to the complete aggregation in terms of coupling strengths and initial configurations

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

unified cooperative control of multiple agents on a sphere for different spherical patterns in this technical note we consider the cooperative control of multiple agents on a sphere provide the appropriate attraction repulsion interactions between agents with introduction of the state dependent repulsive coefficients and design the unified control laws for agents to achieve three fundamental spherical configurations or patterns rendezvous uniform deployment and formation using both the first and second order models we present the analysis of the stability scaling and geometric patterns of the models on the sphere under different attraction repulsion parameters with illustration of the geometrical patterns and the geometrical isomerism by simulations the closed loop dynamics of agents are invariant with respect to group rotation actions on the sphere

frequency synchronization and phase agreement in kuramoto oscillator networks with delays we investigate frequency synchronization and phase agreement in networks of non identical kuramoto oscillators with delayed coupling we provide delay dependent lower bounds for the coupling gain so that a network with all to all coupling and constant heterogeneous delays achieves synchronization the given bounds are determined explicitly by the system parameters furthermore we show that frequency synchronization and phase agreement are possible in general directed networks of non identical oscillators which contain a spanning tree if the delays satisfy a self consistency condition networks with delays differ at this point notably from networks without delays because phase agreement is not possible in undelayed non identical kuramoto oscillator networks in addition to the sufficient conditions for synchronization we investigate the connection between phase agreement and the existence of solutions of a necessary self consistency condition

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

on approximating contractive systems we consider approximating the trajectories of a contractive system using a simpler system e g an lti system we derive bounds on the approximation error that depend on the trajectories of the simpler system and demonstrate their usefulness using several models from systems biology

parameterization of computational domain in isogeometric analysis methods and comparison parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis in this paper we investigate this problem in the 2d case i e how to parametrize the computational domains by planar b spline surface from the given cad objects four boundary planar b spline curves firstly two kinds of sufficient conditions for injective b spline parameterization are derived with respect to the control points then we show how to find good parameterization of computational domain by solving a constraint optimization problem in which the constraint condition is the injectivity sufficient conditions of planar b spline parametrization and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of planar b spline parameterization by using this method the resulted parameterization has no self intersections and the isoparametric net has good uniformity and orthogonality after introducing a posteriori error estimation for isogeometric analysis we propose r refinement method to optimize the parameterization by repositioning the inner control points such that the estimated error is minimized several examples are tested on isogeometric heat conduction problem to show the effectiveness of the proposed methods and the impact of the parameterization on the quality of the approximation solution comparison examples with known exact solutions are also presented

from nurbs to nurps geometries abstract quadratic powell sabin splines and their rational extension the so called nurps surfaces are an interesting alternative for classical tensor product nurbs in the context of isogeometric analysis because they allow the use of local refinements while retaining a b spline like representation and exact description of conic sections in this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic nurbs representation into a nurps representation suitable for the analysis

generalized b splines as a tool in isogeometric analysis the concept of isogeometric analysis has been proposed in 13 where nurbs are considered as basis of the analysis thanks to their ability to construct an exact geometric model in several practical applications and to their popularity in commercial cad systems in this paper we propose an alternative to the rational model presenting an isogeometric analysis approach based on generalized b splines geometric models exactly represented by generalized b splines include those generated by nurbs moreover generalized b splines possess all fundamental properties of algebraic b splines and nurbs including classical refinement processes as h p k refinements finally since generalized b splines are not confined to rational functions they behave completely similar to algebraic b splines with respect to differentiation and integration this seems to be of interest in the treatment of some relevant problems

a two dimensional isogeometric boundary element method for elastostatic analysis the concept of isogeometric analysis where functions that are used to describe geometry in cad software are used to approximate the unknown fields in numerical simulations has received great attention in recent years the method has the potential to have profound impact on engineering design since the task of meshing which in some cases can add significant overhead has been circumvented much of the research effort has been focused on finite element implementations of the isogeometric concept but at present little has been seen on the application to the boundary element method the current paper proposes an isogeometric boundary element method bem which we term igabem applied to two dimensional elastostatic problems using non uniform rational b splines nurbs we find it is a natural fit with the isogeometric concept since both the nurbs approximation and bem deal with quantities entirely on the boundary the method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric bem implementation

a passivity based approach to stability of spatially distributed systems with a cyclic interconnection structure a class of distributed systems with a cyclic interconnection structure is considered these systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns in this paper a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified for these systems global stability results hold if the ldquosecantrdquo criterion is satisfied in the linear case it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic lyapunov function which extends a recent diagonal stability result to partial differential equations for reaction diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established all of the derived results remain true for both linear and nonlinear positive diffusion terms similar results are shown for compartmental systems

logarithmic lipschitz norms and diffusion induced instability abstract this paper proves that ordinary differential equation systems that are contractive with respect to l p norms remain so when diffusion is added thus diffusive instabilities in the sense of the turing phenomenon cannot arise for such systems and in fact any two solutions converge exponentially to each other the key tools are semi inner products and logarithmic lipschitz constants in banach spaces an example from biochemistry is discussed which shows the necessity of considering non hilbert spaces an analogous result for graph defined interconnections of systems defined by ordinary differential equations is given as well

formation of phase locked states in a population of locally interacting kuramoto oscillators abstract in this paper we present an asymptotic formation of phase locked states from the ensemble of kuramoto oscillators with a symmetric and connected interaction topology for a limited interaction topology that does not have an all to all interaction lyapunov type approaches based on phase and frequency diameters do not work due to the lack of completeness thus we employ an energy method together with the connectedness of underlying interaction topologies to determine the complete synchronization estimates our synchronization estimation method consists of two parts first we establish that the uniform boundedness of fluctuations yields the asymptotic formation of phase locked states using ojasiewicz gradient inequality second we show that for the initial configurations lying in the half circle the uniform boundedness of fluctuations can be derived by a comparison with solutions to the linear gronwall s differential inequality for the total phase variance

isogeometric analysis using t splines on two patch geometries we develop optimal approximation estimates for t splines in the case of geometries obtained by gluing two standard tensor product patches we derive results both for the t spline space in the parametric domain and the mapped t nurbs in the physical one a set of numerical tests in complete accordance with the theoretical developments is also presented

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

on the łojasiewicz exponent of kuramoto model the ojasiewicz inequality and ojasiewicz exponent reveal a fundamental relation between a potential function and its gradient in this paper we explore the ojasiewicz exponent of kuramoto model and prove that the exponent is exactly 12 for equilibria located inside a quarter of circle this implies that the convergence towards such a phase locked state must be exponentially fast in contrast we give an example to see the exponent can be less than 12 for other equilibriums more precisely we prove that the exponent for the bi cluster equilibrium which is located on the boundary of a quarter of circle is 13 this gives an insight for the occurrence of exponential and algebraic convergence of kuramoto model we also present a general theorem for exponential convergence of second order gradient like system by which a criterion for the kuramoto model with inertia is established

hamiltonian perspective on compartmental reaction diffusion networks inspired by the recent developments in modeling and analysis of reaction networks we provide a geometric formulation of the reversible reaction networks under the influence of diffusion using the graph knowledge of the underlying reaction network the obtained reaction diffusion system is a distributed parameter port hamiltonian system on a compact spatial domain motivated by the need for computer based design we offer a spatially consistent discretization of the pde system and in a systematic manner recover a compartmental ode model on a simplicial triangulation of the spatial domain exploring the properties of a balanced weighted laplacian matrix of the reaction network and the laplacian of the simplicial complex we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points the paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction diffusion networks

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

synchronization of interconnected systems with applications to biochemical networks an input output approach this paper provides synchronization conditions for networks of nonlinear systems the components of the network referred to as compartments in this paper are made up of an identical interconnection of subsystems each represented as an operator in an extended l2 space and referred to as a species the compartments are in turn coupled through a diffusion like term among the respective species the synchronization conditions are provided by combining the input output properties of the subsystems with information about the structure of the network the paper also explores results for state space models as well as biochemical applications the work is motivated by cellular networks where signaling occurs both internally through interactions of species and externally through intercellular signaling the theory is illustrated by providing synchronization conditions for networks of goodwin oscillators

synchronization of diffusively coupled limit cycle oscillators we develop analytical and numerical conditions to determine whether limit cycle oscillations synchronize in diffusively coupled systems we examine two classes of systems reaction diffusion pdes with neumann boundary conditions and compartmental odes where compartments are interconnected through diffusion terms with adjacent compartments in both cases the uncoupled dynamics are governed by a nonlinear system that admits an asymptotically stable limit cycle we provide two time scale averaging methods for certifying stability of spatially homogeneous time periodic trajectories in the presence of sufficiently small or large diffusion and develop methods using the structured singular value for the case of intermediate diffusion we highlight cases where diffusion stabilizes or destabilizes such trajectories

complex dynamics of the biological rhythms gallbladder and heart cases abstract a theoretical analysis of the mechanisms underlying the dynamics of gallbladder and heart pulsation could clarify the question regarding the classification as chaotic of the associated behaviour eventually related to a normal and healthy beat this analysis is particularly relevant in view of the control of dynamic bifurcations arising in situations of disease in this work a summary of the dfa method applied to gallbladder volume data for a modest number of healthy and ill patients is presented the presence of signal correlation is found in both cases but the fit shapes differ from some critical values

a performance study of nurbs based isogeometric analysis for interior two dimensional time harmonic acoustics abstract this work evaluates the performance of a nurbs based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions an initial assessment is made by studying eigenvalue problems for a square and a circular domain the spectral approximation properties of nurbs functions of varying order are compared to those of conventional polynomials and are found to be superior yielding more accurate representations of eigenvalues as well as eigenmodes the higher smoothness of nurbs shape functions yields better approximations over an extended frequency range when compared to conventional polynomials two numerical case studies including a geometrically complex domain are used to benchmark the method versus the traditional finite element method a convergence analysis confirms the higher efficiency of the isogeometric method on a per degree of freedom basis simulations over a wider frequency range also illustrate that the method suffers less from the dispersion effects that deteriorate the acoustic response towards higher frequencies the tensor product structure of nurbs however also imposes practical considerations when modelling a complex geometry consisting of multiple patches

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

approximating the steady state periodic solutions of contractive systems we consider contractive systems whose trajectories evolve on a compact and convex state space it is well known that if the time varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications we develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system e g an lti system the approximation includes an error bound that is based on the input to state stability property of contractive systems we show that in some cases this error bound can be computed explicitly we also use the bound to derive a new theoretical result namely that a contractive system with an additive periodic input behaves like a low pass filter we demonstrate our results using several examples from systems biology

certifying spatially uniform behavior in reaction diffusion pde and compartmental ode systems we present a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction diffusion pde with neumann boundary conditions this condition makes use of the jacobian matrix of the reaction terms and the second neumann eigenvalue of the laplacian operator on the given spatial domain and eliminates the global lipschitz assumptions commonly used in mathematical biology literature we then derive numerical procedures that employ linear matrix inequalities to certify this condition and illustrate these procedures on models of several biochemical reaction networks finally we present an analog of this pde result for the synchronization of a network of identical ode models coupled by diffusion terms from a systems biology perspective the main contribution of the paper is to blend analytical and numerical tools from nonlinear systems and control theory to derive a relaxed and verifiable condition for spatial uniformity of biological processes

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

analysis suitable t splines are dual compatible abstract in this paper we define dual compatible dc t splines and we prove that analysis suitable as t splines are dual compatible we show that the classical construction of a dual basis for tensor product t splines easily generalizes to dc t spline spaces and we discuss in the last section of the paper how it paves the way to a mathematical theory of as t splines

on synchronous steady states and internal models of diffusively coupled systems we investigate the problem of synchronizing nonidentical nonlinear dynamical systems by means of generalized diffusive couplings the focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing nonidentical models we show that for the problem to be solvable a synchronous steady state needs to exist this condition leads to the requirement that all individual system models need to embed an internal model of some common endosystem the latter condition is expressed in terms of nonlinear partial differential equations the conditions derived in this paper are related to those known from the theory of output regulation

evidence for determinism in ventricular fibrillation using a recently formulated technique for in vivo cardiac transmembrane current estimation we examined ventricular fibrillation for evidence of deterministic linear and nonlinear structure both unstable fixed point analysis and a newly formulated measure of nonlinear determinism indicated that ventricular fibrillation in vivo exhibits deterministic dynamics similar to those previously used in chaos control

selective pattern formation control autonomous pattern formation phenomena are ubiquitous throughout nature the goal of this paper is to show the possibility to effectively generate various desired spatial patterns by guiding such phenomena suitably to this end we employ a reaction diffusion system as a mathematical model and formulate and solve a novel pattern formation control problem first we describe the control objective in terms of spatial spectrum consensus which enables utilize recent advances on networked control system theory next the effectiveness of the proposed control law is evaluated theoretically by exploiting the center manifold theorem and also numerically by simulation the turing instabilities play a crucial role throughout the paper

stability of phase locking in a ring of unidirectionally coupled oscillators we discuss the dynamic behaviour of a finite group of phase oscillators unidirectionally coupled in a ring the dynamics are based on the kuramoto model in the case of identical oscillators all phase locking solutions and their stability properties are obtained for nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling an algorithm to obtain all phase locking solutions is proposed these solutions can be classified into classes each with its own stability properties the stability properties are obtained by means of a novel extension of gershgorin s theorem one class of stable solutions has the property that all phase differences between neighbouring cells are contained in contrary to intuition a second class of stable solutions is established with exactly one of the phase differences contained in the stability results are extended from sinusoidal interconnections to a class of odd functions to conclude a connection with the field of active antenna arrays is made generalizing some results earlier obtained in this field

contraction after small transients contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation we consider three generalizations of contraction with respect to a norm that allow contraction to take place after small transients in time and or amplitude these generalized contractive systems gcss are useful for several reasons first we show that there exist simple and checkable conditions guaranteeing that a system is a gcs and demonstrate their usefulness using several models from systems biology second allowing small transients does not destroy the important asymptotic properties of contractive systems like convergence to a unique equilibrium point if it exists and entrainment to a periodic excitation third in some cases as we change the parameters in a contractive system it becomes a gcs just before it looses contractivity with respect to a norm in this respect generalized contractivity is the analogue of marginal stability in lyapunov stability theory

brief paper distributed adaptive control for synchronization of unknown nonlinear networked systems this paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics a design method is presented for adaptive synchronization controllers for distributed systems having non identical unknown nonlinear dynamics and for a target dynamics to be tracked that is also nonlinear and unknown the development is for strongly connected digraph communication structures a lyapunov technique is presented for designing a robust adaptive synchronization control protocol the proper selection of the lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the frobenius norm the resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node singular value analysis is used it is shown that the singular values of certain key matrices are intimately related to structural properties of the graph

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

analysis of interconnected oscillators by dissipativity theory this paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension oscillators are regarded as open systems that satisfy a particular dissipation inequality it is shown that this characterization has implications for the global stability analysis of limit cycle oscillations i in isolated oscillators ii in interconnections of oscillators and iii for the global synchrony analysis in interconnections of identical oscillators

adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations this paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays mixed delays as well as uncertain nonlinear external and stochastic perturbations hybrid perturbations a simple but robust adaptive controller is designed such that the response system can lag synchronize with a drive system based on the lyapunov stability theory and some suitable lyapunov krasovskii functionals several sufficient conditions ensuring the lag synchronization are developed our synchronization criteria are easily verified and do not need to solve any linear matrix inequality some existing results are improved and extended moreover the designed adaptive controller has better anti interference capacity and is more practical than the usual adaptive controller numerical simulations are exploited to show the effectiveness of the theoretical results

isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

asymptotic formation and orbital stability of phase locked states for the kuramoto model abstract we discuss the asymptotic formation and nonlinear orbital stability of phase locked states arising from the ensemble of non identical kuramoto oscillators we provide an explicit lower bound for a coupling strength on the formation of phase locked states which only depends on the diameters of natural frequencies and initial phase configurations we show that when the phases of non identical oscillators are distributed over the half circle and the coupling strength is sufficiently large the dynamics of kuramoto oscillators exhibits two stages transition and relaxation stages in a transition stage initial configurations shrink to configurations whose diameters are strictly less than 2 in a finite time and then the configurations tend to phase locked states asymptotically this improves previous results on the formation of phase locked states by chopra spong 2009 26 and ha ha kim 2010 27 where their attention were focused only on the latter relaxation stage we also show that the kuramoto model is l 1 contractive in the sense that the l 1 distance along two smooth kuramoto flows is less than or equal to that of initial configurations in particular when two initial configurations have the same averaged phases the l 1 distance between them decays to zero exponentially fast for the configurations with different phase averages we use the method of average adjustment and translation invariant of the kuramoto model to show that one solution converges to the translation of the other solution exponentially fast this establishes the orbital stability of the phase locked states our stability analysis does not employ any standard linearization technique around the given phase locked states but instead we use a robust l 1 metric functional as a lyapunov functional in the formation process of phase locked states we estimate the number of collisions between oscillators and lower upper bounds of the transversal phase differences

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

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

geometry independent field approximation cad analysis integration geometrical exactness and adaptivity in isogeometric analysis iga the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain this identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper 20 as a key advantage on the way to the integration of computer aided design cad and subsequent analysis in computer aided engineering cae 20 claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables without requiring the regeneration of the mesh at each change of the domain geometry yet in finite element versions of iga a parameterization of the interior of the domain must still be constructed since cad only provides information about the boundary the identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately in particular when the solution is not smooth we propose here a new paradigm called geometry independent field approximation gift where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight cad integration gift has the following features 1 it is possible to flexibly

an isogeometric analysis approach for the study of the gyrokinetic quasi neutrality equation in this work a new discretization scheme for the gyrokinetic quasi neutrality equation is proposed it is based on isogeometric analysis the iga which relies on nurbs functions accommodates arbitrary coordinates and the use of complicated computation domains moreover arbitrary high order degree of basis functions can be used and their regularity enables the use of a low number of elements here this approach is successfully tested on elliptic problems like the quasi neutrality equation arising in gyrokinetic models in this last application when polar coordinates are considered a fast solver can be used and the non locality is dealt with a suitable decomposition which reduces the resolution of the gyrokinetic quasi neutrality equation to a sequence of local 2d elliptic problems

brief paper diagonal stability of a class of cyclic systems and its connection with the secant criterion we consider a class of systems with a cyclic interconnection structure that arises among other examples in dynamic models for certain biochemical reactions we first show that a secant criterion for local stability derived earlier in the literature is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices we then revisit a recent generalization of this criterion to output strictly passive systems and recover the same stability condition using our diagonal stability result as a tool for constructing a lyapunov function using this procedure for lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

emergent behaviors of lohe tensor flocks we present a new aggregation model on the space of rank m tensors with the same size and study emergent dynamics of the proposed model our proposed new aggregation model is general enough to encompass lohe type models such as the kuramoto model the lohe sphere model and the lohe matrix models for the ensemble of real rank 0 rank 1 and rank 2 tensors respectively in this regard we call our proposed model as the lohe tensor model for rank m tensors with the same size for emergent dynamics of the proposed model we employ the ensemble diameter as a lyapunov functional to derive a riccati type differential inequality as a direct application of these differential inequalities we provide two sufficient frameworks leading to the emergent dynamics for homogeneous and heterogeneous ensembles in terms of system parameters and initial data

on the finiteness of collisions and phase locked states for the kuramoto model synchronization phenomenon is ubiquitous in our complex systems and many phenomenological models have been proposed and studied analytically and numerically among them the kuramoto model serves as a prototype model for the phase synchronization of weakly coupled oscillators in this paper we study the finiteness of collisions crossings among kuramoto oscillators in the relaxation process toward the phase locked states and the total number of phase locked states with positive kuramoto order parameters for identical oscillators it is well known that collisions between distinct oscillators cannot occur in finite time and we show that there are only a finite number of phase locked states with positive order parameters however for non identical oscillators oscillators with different natural frequencies can cross each other in their relaxation process and estimating the total number of phase locked states is a nontrivial matter we show that for the non identical case asymptotic phase locking is equivalent to the finiteness of collisions and the total number of phase locked states with positive order parameters is bounded above by 2 n where n is the number of oscillators

reproducing kernel triangular b spline based fem for solving pdes abstract we propose a reproducing kernel triangular b spline based finite element method fem as an improvement to the conventional triangular b spline element for solving partial differential equations pdes in the latter unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the b spline the performance therefore becomes unstable and cannot be controlled in a desirable way to address this issue the proposed improvement adopts the reproducing kernel approximation in the calculation of b spline kernel function three types of pde problems are tested to validate the present element and compare against the conventional triangular b spline it has been shown that the improved triangular b spline satisfies the partition of unity condition even for extreme conditions including corners and holes

on the synchronization theory of kuramoto oscillators under the effect of inertia abstract we investigate the synchronized collective behavior of the kuramoto oscillators with inertia effect both the frequency synchronization for nonidentical case and the phase synchronization for identical case are in view as an application of our general theory we show the global frequency synchronization for the three nonidentical oscillator case

on the relaxation dynamics of lohe oscillators on some riemannian manifolds we study the collective relaxation dynamics appearing in weakly coupled lohe oscillators in a large coupling regime the lohe models on the unit sphere and unitary group were proposed as a nonabelian generalization of the kuramoto model on the unit circle and their emergent dynamics has been extensively studied in previous literature for some restricted class of initial data based on the lyapunov functional approach and order parameter approach in this paper we extend the previous partial results to cover a generic initial configuration via the detailed analysis on the order parameter measuring the modulus of the centroid in particular we present a detailed relaxation dynamics and structure of the resulting asymptotic states for the lohe sphere model we also present new gradient flow formulations for the lohe matrix models with the same one body hamiltonians on some group manifolds as a direct application of this new formulation we show that every bounded lohe flow which originated from any initial configuration converges asymptotically

brief paper an internal model principle is necessary and sufficient for linear output synchronization output synchronization of a network of heterogeneous linear state space models under time varying and directed interconnection structures is investigated it is shown that assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories the resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

complete entrainment of kuramoto oscillators with inertia on networks via gradient like flow abstract we study the asymptotic complete entrainment of kuramoto oscillators with inertia on symmetric and connected network we provide several sufficient conditions for the asymptotic complete entrainment in terms of initial phase frequency configurations strengths of inertia and coupling and natural frequency distributions for this purpose we reinterpret the kuramoto oscillators with inertia as a second order gradient like flow and adopt analytical methods based on several lyapunov functions to apply the convergence estimate studied by haraux and jendoubi 21 our approach does not require any spectral information of the graph associated with the given network structure

some remarks on spatial uniformity of solutions of reaction diffusion pdes abstract in this paper we present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction diffusion partial differential equation pde with neumann boundary conditions in one dimension using the jacobian matrix of the reaction term and the first dirichlet eigenvalue of the laplacian operator on the given spatial domain the estimates are based on logarithmic norms in non hilbert spaces which allow in particular for a class of examples of interest in biology tighter estimates than other previously proposed methods

contractivity of transport distances for the kinetic kuramoto equation we present synchronization and contractivity estimates for the kinetic kuramoto model obtained from the kuramoto phase model in the mean field limit for identical kuramoto oscillators we present an admissible class of initial data leading to time asymptotic complete synchronization that is all measure valued solutions converge to the traveling dirac measure concentrated on the initial averaged phase in the case of non identical oscillators we show that the velocity field converges to the average natural frequency proving that the oscillators move asymptotically with the same frequency under suitable assumptions on the initial configuration if two initial radon measures have the same natural frequency density function and strength of coupling we show that the wasserstein p distance between corresponding measure valued solutions is exponentially decreasing in time this contraction principle is more general than previous l 1 contraction properties of the kuramoto phase model

existence and robustness of phase locking in coupled kuramoto oscillators under mean field feedback motivated by the recent development of deep brain stimulation dbs for neurological diseases we study a network of interconnected oscillators under the influence of mean field feedback and analyze the robustness of its phase locking with respect to general inputs under standard assumptions this system can be reduced to a modified version of the kuramoto model of coupled nonlinear oscillators in the first part of the paper we present an analytical study on the existence of phase locked solutions under generic interconnection and feedback configurations in particular we show that in general no oscillating phase locked solutions can co exist with any non zero proportional mean field feedback in the second part we prove some robustness properties of phase locked solutions namely total stability this general result allows in particular to justify the persistence of practically phase locked states if sufficiently small feedback gains are applied and to give explicit necessary conditions on the intensity of a desynchronizing mean field feedback furthermore the lyapunov function used in the analysis provides a new characterization of the robust phase locked configurations in the kuramoto system with symmetric interconnections

the spectrum of the locked state for the kuramoto model of coupled oscillators we analyze the linear stability of the phase locked state in the kuramoto model of coupled oscillators the main result is the first rigorous characterization of the spectrum and its associated eigenvectors for any finite number of oscillators all but two of the eigenvalues are negative and merge into a continuous spectrum as the number of oscillators tends to infinity one eigenvalue is always zero by rotational invariance the final eigenvalue corresponding to a collective mode determines the stability of the locked state

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures

an isogeometric method for the reissner mindlin plate bending problem we present a new isogeometric method for the discretization of the reissner mindlin plate bending problem the proposed scheme follows a recent theoretical framework that makes possible the construction of a space of smooth discrete deflections wh and a space of smooth discrete rotations h such that the kirchhoff constraint is exactly satisfied at the limit therefore we obtain a formulation which is natural from the theoretical mechanical viewpoint and locking free by construction we prove that the method is uniformly stable and satisfies optimal convergence estimates finally the theoretical results are fully supported by numerical tests

lyapunov function for the kuramoto model of nonlinearly coupled oscillators a lyapunov function for the phase locked state of the kuramoto model of non linearly coupled oscillators is presented it is also valid for finite range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes for the kuramoto model a minimum of the lyapunov function corresponds to a ground state of a system with frustration the interaction between the oscillators xy spins is ferromagnetic whereas the random frequencies induce random fields which try to break the ferromagnetic order i e global phase locking the ensuing arguments imply asymptotic stability of the phase locked state up to degeneracy and hold for any probability distribution of the frequencies special attention is given to discrete distribution functions we argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results but that a partial locking of some but not all sublattices is not to be expected the order parameter of the phase locked state is shown to have a strictly positive lower bound r 1 2 so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded

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

emergent dynamics of a generalized lohe model on some class of lie groups we introduce a lohe group which is a new class of matrix lie groups and present a continuous dynamical system for the synchronization of group elements in a lohe group the lohe group includes classical lie groups such as the orthogonal unitary and symplectic groups and since lohe groups need not be compact global existence of odes may fail the proposed dynamical system generalizes the lohe model lohe in j phys a 43 465301 2010 lohe in j phys a 42 395101 395126 2009 itself a nonabelian generalization of the kuramoto model and alongside we also generalize the analytical framework ha and ryoo in j stat phys 163 411 439 2016 of emergent and unique phase locked states for the construction of the phase locked states we introduce lyapunov functions measuring the ensemble diameter and the dissimilarity between two lohe flows and derive gronwall type differential inequalities for them the global existence of solutions then become a consequence of the boundedness of these lyapunov functions our sufficient framework for the emergent dynamics is formulated in terms of coupling strength and initial states and it leads to the global existence of solutions and the formation and uniqueness of a phase locked asymptotic state as a concrete example we demonstrate how our theory can show emergent phenomenon on the heisenberg group where all initial configurations tend to a unique phase locked state exponentially fast

oscillations in i o monotone systems under negative feedback oscillatory behavior is a key property of many biological systems the small gain theorem sgt for input output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a necessary condition for the existence of periodic solutions one advantage of the use of the monotone sgt technique is its robustness with respect to all perturbations that preserve monotonicity and stability properties of a very low dimensional in many interesting examples just one dimensional model reduction this robustness makes the technique useful in the analysis of molecular biological models in which there is large uncertainty regarding the values of kinetic and other parameters however verifying the conditions needed in order to apply the sgt is not always easy this paper provides an approach to the verification of the needed properties and illustrates the approach through an application to a classical model of circadian oscillations as a nontrivial case study and provides a theorem in the converse direction of predicting oscillations when the sgt conditions fail

isogeometric analysis using lr b splines abstract the recently proposed locally refined b splines denoted lr b splines by dokken et al 2013 6 may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis in this paper we propose local refinement strategies for adaptive isogeometric analysis using lr b splines and investigate its performance by doing numerical tests on well known benchmark cases the theory behind lr b spline is not presented in full details but the main conceptual ingredients are explained and illustrated by a number of examples

synchronization under space and time dependent heterogeneities we study output synchronization of nonlinear systems subject to a class of spatially and temporally varying heterogeneities we begin by addressing reaction diffusion pdes and show that an incremental passivity property in the nominal reaction dynamics is fundamental in guaranteeing spatial homogenization of trajectories our distributed control achieves homogenization by defining an internal model subsystem for each output corresponding to the respective heterogeneity we also design a similar distributed internal model control that achieves output synchronization of a network of incrementally passive nonlinear ode systems in the presence of heterogeneities we prove that our control laws effectively compensate for desynchronizing effects due to the differences between the heterogeneous inputs we illustrate our algorithms on ring oscillators and bistable systems the main contribution of the paper is a constructive and unified approach to guaranteeing homogenization under heterogeneities for both reaction diffusion pde and diffusively coupled ode systems

consensus of high order multi agent systems with switching topologies abstract in this paper a consensus problem is investigated for high order multi agent systems with switching communication networks through which only output information instead of full state information can be transmitted to neighbors based on self state feedback and neighbor output feedback a new consensus protocol is proposed which can realize arbitrary convergence rate furthermore as an application a nonlinear heading consensus protocol is designed for a multi vehicle model finally numerical simulations are given to illustrate the theoretical results

local maximum entropy approximation schemes a seamless bridge between finite elements and meshfree methods we present a one parameter family of approximation schemes which we refer to as local maximum entropy approximation schemes that bridges continuously two important limits delaunay triangulation and maximum entropy max ent statistical inference local max ent approximation schemes represent a compromise in the sense of pareto optimality between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width local max ent approximation schemes are entirely defined by the node set and the domain of analysis and the shape functions are positive interpolate affine functions exactly and have a weak kronecker delta property at the boundary local max ent approximation may be regarded as a regularization or thermalization of delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation local max ent approximation schemes can be taken as a convenient basis for the numerical solution of pdes in the style of meshfree galerkin methods in test cases characterized by smooth solutions we find that the accuracy of local max ent approximation schemes is vastly superior to that of finite elements

stabilization and synchronization for a heterogeneous multi agent system via harmonic control abstract in this paper a class of heterogeneous multi agent systems with directed cycle graphs is investigated the stabilization and synchronization problems via harmonic control are solved under some conditions and the feedback control gains are constructively designed several numerical examples are presented to demonstrate the effectiveness of the proposed method