mean field fluid behavior of the gaussian core model we show that the gaussian core model of particles interacting via a penetrable repulsive gaussian potential first considered by stillinger j chem phys 65 3968 1976 behaves as a weakly correlated mean field fluid over a surprisingly wide density and temperature range in the bulk the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function and by the more sophisticated hypernetted chain integral equation the resulting pressure deviates very little from a simple mean field like quadratic form in the density while the low density virial expansion turns out to have an extremely small radius of convergence density profiles near a hard wall are also very accurately described by the corresponding mean field free energy functional the binary version of the model exhibits a spinodal instability against demixing at high densities possible implications for semidilute polymer solutions are discussed

fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

chaotic component obscured by strong periodicity in voice production system the effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two mass model the two mass model assumes the glottal airflow to be laminar nonviscous and incompressible in this model when the asymmetric factor is decreased from 0 65 to 0 35 only 1 1 and 1 2 modes are detectable however with the same parameters four vibratory modes 1 1 1 2 2 4 2 6 are found in the asymmetric composite model using the navier stokes equations to describe the complex aerodynamics in the glottis moreover the amplitude of the waveform is modulated by a small amplitude noiselike series the nonlinear detection method reveals that this noiselike modulation is not random but rather it is deterministic chaos this result agrees with the phenomenon often seen in voice in which the voice signal is strongly periodic but modulated by a small amplitude chaotic component the only difference between the two mass model and the composite model is in their descriptions of glottal airflow therefore the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production including bifurcation and a small amplitude chaotic component obscured by strong periodicity

bifurcations in an asymmetric vocal fold model a two mass model of vocal fold vibrations is analyzed with methods from nonlinear dynamics bifurcations are located in parameter planes of physiological interest subglottal pressure stiffness of the folds it is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes toroidal oscillations and chaos the corresponding attractors are characterized by phase portraits spectra and next maximum maps the relevance of these simulations for voice disorders such as laryngeal paralysis is discussed

phase separation of penetrable core mixtures a two component system of penetrable particles interacting via a gaussian core potential is considered which may serve as a crude model for binary polymer solutions the pair structure and thermodynamic properties are calculated within the random phase approximation rpa and the hypernetted chain hnc integral equation the analytical rpa predictions are in semi quantitative agreement with the numerical solutions of the hnc approximation which itself is very accurate for gaussian core systems a fluid fluid phase separation is predicted to occur for a broad range of potential parameters the pair structure exhibits a nontrivial clustering behaviour of the minority component similiar conclusions hold for the related model of parabolic core mixtures which is frequently used in dissipative particle dynamics dpd simulations

reachability analysis of dynamical systems having piecewise constant derivatives abstract in this paper we consider a class of hybrid systems namely dynamical systems with piecewise constant derivatives pcd systems such systems consist of a partition of the euclidean space into a finite set of polyhedral sets regions within each region the dynamics is defined by a constant vector field hence discrete transitions occur only on the boundaries between regions where the trajectories change their direction with respect to such systems we investigate the reachability question given an effective description of the systems and of two polyhedral subsets p and q of the state space is there a trajectory starting at some x p and reaching some point in q our main results are a decision procedure for two dimensional systems and an undecidability result for three or more dimensions

reachability analysis of linear dynamic systems with constant arbitrary and lipschitz continuous inputs abstract this paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute time domain bounds of states and outputs with floating point precision the focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time inputs can be constant arbitrary or lipschitz continuous waveforms uncertainties in initial conditions and inputs are modeled using zonotopes the calculations exploit the definition of zonotopes and the modal information of the linear system dynamics

theoretical and experimental study of quasisteady flow separation within the glottis during phonation application to a modified two mass model most flow models used in numerical simulation of voiced sound production rely for the sake of simplicity upon a certain number of assumptions while most of these assumptions constitute reasonable first approximations others appear more doubtful in particular it is implicitly assumed that the air flow through the glottal channel separates from the walls at a fixed point since this assumption appears quite unrealistic and considering that the position of the separation point is an important parameter in phonation models in this paper a revised fluid mechanical description of the air flow through the glottis is proposed in which the separation point is allowed to move this theoretical model as well as the assumptions made are validated using steady and unsteady flow measurements combined with flow visualizations in order to evaluate the effective impact of the revised theory we then present an application to a simple mechanical model of the vocal cords derived from the classical two mass model as expected implementation of a moving separation point appears to be of great importance for the modeling of glottal signals it is further shown that the numerical model coupled with a more realistic description of the vocal cord collision can lead to signals surprisingly close to those observed in real speech by inverse filtering

distributed robust adaptive equilibrium computation for generalized convex games this paper considers a class of generalized convex games where each player is associated with a convex objective function a convex inequality constraint and a convex constraint set the players aim to compute a nash equilibrium through communicating with neighboring players the particular challenge we consider is that the component functions are unknown a priori to associated players we study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies the algorithm performance is verified through demand response on the ieee 30 bus test system our technical tools integrate convex analysis variational inequalities and simultaneous perturbation stochastic approximation

nonlinear analysis of irregular animal vocalizations animal vocalizations range from almost periodic vocal fold vibration to completely atonal turbulent noise between these two extremes a variety of nonlinear dynamics such as limit cycles subharmonics biphonation and chaotic episodes have been recently observed these observations imply possible functional roles of nonlinear dynamics in animal acoustic communication nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves so far nonlinear dynamical structures of animal voices have been mainly studied with spectrograms in this study the deterministic versus stochastic dvs prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations macaque screams piglet screams and dog barks results showed that in vocalizations with pronounced harmonic components adult macaque screams certain piglet screams and dog barks deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction the difference termed low dimensional nonlinearity measure lnm indicates the presence of a low dimensional attractor in highly irregular signals such as juvenile macaque screams piglet screams and some dog barks the detectable amount of nonlinearity was comparatively small analyzing 120 samples of dog barks it was further shown that the harmonic to noise ratio hnr was positively correlated with lnm it is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components including subharmonics and biphonation or low dimensional chaos

a theorem on the absence of phase transitions in one dimensional growth models with on site periodic potentials we rigorously prove that a wide class of one dimensional growth models with on site periodic potential such as the discrete sine gordon model have no phase transition at any temperature t 0 the proof relies on the spectral analysis of the transfer operator associated with the models we show that this operator is hilbert schmidt and that its maximum eigenvalue is an analytical function of temperature

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

estimating model parameters by chaos synchronization using chaos synchronization and a proposed iterative method of parameter adaptation we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters this parameter adaptation method can be applied to a spatiotemporal chaotic system with a one way coupled map lattice as a biomedical application this method is capable of estimating the asymmetric tension parameter of a vocal fold model

criterion for determining clustering versus reentrant melting behavior for bounded interaction potentials we examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials that do not diverge at the origin are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity by employing a mean field density functional theory which is shown to become exact at high temperatures and or densities we establish a criterion that determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

computation of maximal safe sets for switching systems the problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models given the practical and theoretical relevance of the problem finding implementable procedures that could at least approximate the maximal safe set is important to this end we begin by restricting our attention to a special class of hybrid systems switching systems we exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set this procedure requires the computation of a maximal controlled invariant set we then restrict our attention to linear discrete time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets however even for this class of systems the computation may not converge in a finite number of steps we then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained a tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set our procedure is applied to the idle speed regulation problem in engine control to demonstrate its efficiency

a constraint satisfaction approach for enclosing solutions to parametric ordinary differential equations this paper considers initial value problems for ordinary differential equations odes where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs this work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ode the relaxation uses hermite interpolation polynomials and enclosures of their error terms to approximate the ode our work also shows how to find an evaluation time for the relaxation that minimizes its local error theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs the results also indicate that the new algorithm should be significantly faster when the ode contains many operations

reachability analysis of nonlinear differential algebraic systems this paper presents a numerical procedure for the reachability analysis of systems with nonlinear semi explicit index 1 differential algebraic equations the procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way i e it is guaranteed that all possible trajectories of the system are enclosed thus the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them the presented approach scales favorably with the number of state variables this makes it possible to solve problems of industry relevant size as demonstrated by a transient stability analysis of the ieee 14 bus benchmark problem for power systems

validated solutions of initial value problems for ordinary differential equations compared to standard numerical methods for initial value problems ivps for ordinary differential equations odes validated methods for ivps for odes have two important advantages if they return a solution to a problem then 1 the problem is guaranteed to have a unique solution and 2 an enclosure of the true solution is produced the authors survey taylor series methods for validated solutions of ivps for odes describe several such methods in a common framework and identify areas for future research

a dynamic game approach to distributionally robust safety specifications for stochastic systems abstract this paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times subject to the worst possible disturbance distribution in an ambiguity set we propose a dynamic game formulation of constructing such policies and identify conditions under which a non randomized markov policy is optimal based on this existence result we develop a practical design approach to safety oriented stochastic controllers with limited information about disturbance distributions however an associated bellman equation involves infinite dimensional minimax optimization problems since the disturbance distribution may have a continuous density to alleviate computational issues we propose a duality based reformulation method that converts the infinite dimensional minimax problem into a semi infinite program that can be solved using existing convergent algorithms we prove that there is no duality gap and that this approach thus preserves optimality the results of numerical tests confirm that the proposed method is robust against distributional errors in disturbances while a standard stochastic safety verification tool is not

monotone piecewise affine systems piecewise affine pwa systems are autonomous systems with discontinuous vector fields which are affine ordinary differential equations at the points of continuity these systems have applications to many fields of engineering including systems biology and traffic engineering we define what it means for a pwa system to be monotone and we provide a set of sufficient conditions for monotonicity of pwa systems with hyperrectangular invariants such sufficient conditions are useful for understanding the dynamics of such pwa systems and for designing controllers for qualitative reference tracking we apply these results towards the drug discovery problem for the cancer related p53 pathway

a time dependent hamilton jacobi formulation of reachable sets for continuous dynamic games we describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game the algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time dependent hamilton jacobi isaacs partial differential equation while alternative techniques for computing the reachable set have been proposed the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters because the time dependent equation s solution is continuous and defined throughout the state space methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions a numerical implementation of our formulation is described and has been released on the web its correctness is verified through a two vehicle three dimensional collision avoidance example for which an analytic solution is available

nonlinear dynamical analysis of speech this paper reports results of the estimation of dynamical invariants namely lyapunov exponents dimension and metric entropy for speech signals two optimality criteria from dynamical systems literature namely singular value decomposition method and the redundancy method are used to reconstruct state space trajectories of speech and make observations the positive values of the largest lyapunov exponent of speech signals in the form of phoneme articulations show the average exponential divergence of nearby trajectories in the reconstructed state space the dimension of a time series is a measure of its complexity and gives bounds on the number of state space variables needed to model it it is found that most speech signals in the form of phoneme articulations are low dimensional for comparison a statistical model of a speech time series is also used to estimate the correlation dimension the second order dynamical entropy which is a lower bound of metric entropy of speech time series is found to

recurrence plot analysis of nonstationary data the understanding of curved patterns recurrence plots of the calls of the nomascus concolor western black crested gibbon and hylobates lar white handed gibbon show characteristic circular curved and hyperbolic patterns superimposed to the main temporal scale of the signal it is shown that these patterns are related to particular nonstationarities in the signal some of them can be reproduced by artificial signals like frequency modulated sinusoids and sinusoids with time divergent frequency these modulations are too faint to be resolved by conventional time frequency analysis with similar precision therefore recurrence plots act as a magnifying glass for the detection of multiple temporal scales in slightly modulated signals the detected phenomena in these acoustic signals can be explained in the biomechanical context by taking in account the role of the muscles controlling the vocal folds

noise can delay and advance the collapse of spatiotemporal chaos spatiotemporal chaos on a regular ring network of excitable gray scott dynamical elements collapses to a stable asymptotic state we find that the addition of dynamical noise clearly influences the spatiotemporal pattern and the transient lifetime of spatiotemporal chaos spatially uniform noise significantly decreases the average lifetime of spatiotemporal chaos due to an enlargement of regions of local collapse for spatially inhomogeneous noise the collapse is maximally delayed at an intermediate noise level but drastically advanced for larger noise levels

modeling of chaotic vibrations in symmetric vocal folds the chaos mechanism of above range phonation was examined in symmetrically modeled vocal folds by using the traditional two mass model assumption the poincare map technique was used to display chaotic attractors this method provided an effective description of irregular vocal fold movements the power spectrum lyapunov exponent and kaplan yorke dimension were employed to describe chaotic vibrations in the vocal fold model these nonlinear dynamic analyses suggested that for the positive lyapunov exponent chaotic attractors contribute to irregular vocal fold vibrations descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos to investigate the effects of independent parameters such as subglottal pressure coupling stiffness and phonation neutral area bifurcation diagrams based on the poincare map were discussed the results confirmed that the dynamics of the two mass model was strongly influenced by independent parameters nonlinear dynamic methods were expecte

the algorithmic analysis of hybrid systems we present a general framework for the formal specification and algorithmic analysis of hybrid systems a hybrid system consists of a discrete program with an analog environment we model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws for verification purposes we restrict ourselves to linear hybrid systems where all variables follow piecewise linear trajectories we provide decidability and undecidability results for classes of linear hybrid systems and we show that standard program analysis techniques can be adapted to linear hybrid systems in particular we consider symbolic model checking and minimization procedures that are based on the reachability analysis of an infinite state space the procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space we also present approximation techniques for dealing with systems for which the iterative procedures do not converge

lagrangian methods for approximating the viability kernel in high dimensional systems abstract while a number of lagrangian algorithms to approximate reachability in dozens or even hundreds of dimensions for systems with linear dynamics have recently appeared in the literature no similarly scalable algorithms for approximating viable sets have been developed in this paper we describe a connection between reachability and viability that enables us to compute the viability kernel using reach sets this connection applies to any type of system such as those with nonlinear dynamics and or non convex state constraints however here we take advantage of it to construct three viability kernel approximation algorithms for linear systems with convex input and state constraint sets we compare the performance of the three algorithms and demonstrate that the two based on highly scalable lagrangian reachability those using ellipsoidal and support vector set representations are able to compute the viability kernel for linear systems of larger state dimension than was previously feasible using traditional eulerian methods our results are illustrated on a 6 dimensional pharmacokinetic model and a 20 dimensional model of heat conduction on a lattice

computational techniques for reachability analysis of max plus linear systems this work discusses a computational approach to reachability analysis of max plus linear mpl systems a class of discrete event systems widely used in synchronization and scheduling applications given a set of initial states we characterize and compute its reach tube namely the collection of set of reachable states regarded step wise as reach sets by an alternative characterization of the mpl dynamics we show that the exact computation of the reach sets can be performed quickly and compactly by manipulations of difference bound matrices and further derive worst case bounds on the complexity of these operations the approach is also extended to backward reachability analysis the concepts and results are elucidated by a running example and we further illustrate the performance of the approach by a numerical benchmark the technique comfortably handles twenty dimensional mpl systems i e with twenty continuous state variables and as such it outperforms the state of the art alternative approaches in the literature

experiments based parameter identification on the gpu for cooperative systems abstract in this paper we describe how to enhance experimental parameter identification for cooperative systems using the gpu this kind of identification is necessary for example in the area of developing robust controllers and observers based on available measurement data first we point out which parts of the general global optimization based parameter identification procedure can be parallelized and compare it to the experiments based technique after that we illustrate the principle and its implementation with the help of a close to life textbook example finally we demonstrate how the gpu based experimental parameter identification works for identifying experimentally the parameters of the reduced order temperature model for the distributed heating system this is an important step towards working with uncertain models in the context of solid oxide fuel cells

on reachability and minimum cost optimal control questions of reachability for continuous and hybrid systems can be formulated as optimal control or game theory problems whose solution can be characterized using variants of the hamilton jacobi bellman or isaacs partial differential equations the formal link between the solution to the partial differential equation and the reachability problem is usually established in the framework of viscosity solutions this paper establishes such a link between reachability viability and invariance problems and viscosity solutions of a special form of the hamilton jacobi equation this equation is developed to address optimal control problems where the cost function is the minimum of a function of the state over a specified horizon the main advantage of the proposed approach is that the properties of the value function uniform continuity and the form of the partial differential equation standard hamilton jacobi form continuity of the hamiltonian and simple boundary conditions make the numerical solution of the problem much simpler than other approaches proposed in the literature this fact is demonstrated by applying our approach to a reachability problem that arises in flight control and using numerical tools to compute the solution

underapproximating backward reachable sets by semialgebraic sets underapproximations uas of backward reachable sets play an important role in controller synthesis and trajectory analysis for constrained nonlinear dynamical systems but there are few methods available to compute them given a nonlinear system a target region of simply connected compact type and a time duration we present a method using boundary analysis to compute an ua of the backward reachable set the ua is represented as a semialgebraic set formed by what we term polynomial mathtt level set functions the polynomial mathtt level set function is a semidefinite positive function with one real root such that the interior and closure of a semialgebraic set formed by it are both simply connected and have the same boundary the function can be computed by solving a convex program which is constructed based on sum of squares decomposition and linear interval inequalities we test our method on several examples and compare them with existing methods the results show that our method can obtain better estimations more efficiently in terms of time for these special examples

on barriers in state and input constrained nonlinear systems in this paper the problem of state and input constrained control is addressed with multidimensional constraints we obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied for all times this boundary is made of two disjoint parts the subset of the state constraint boundary on which there are trajectories pointing toward the interior of the admissible set or tangentially to it and a barrier namely a semipermeable surface which is constructed via a minimum like principle

lax hopf based incorporation of internal boundary conditions into hamilton jacobi equation part ii computational methods this article presents a new method for explicitly computing solutions to a hamilton jacobi partial differential equation for which initial boundary and internal conditions are prescribed as piecewise affine functions based on viability theory a lax hopf formula is used to construct analytical solutions for the individual contribution of each affine condition to the solution of the problem the results are assembled into a lax hopf algorithm which can be used to compute the solution to the partial differential equation at any arbitrary time at no other cost than evaluating a semi analytical expression numerically the method being semi analytical it performs at machine accuracy compared to the discretization error inherent to finite difference schemes the performance of the method is assessed with benchmark analytical examples the running time of the algorithm is compared with the running time of a godunov scheme

glottal flow through a two mass model comparison of navier stokes solutions with simplified models a new numerical model of the vocal folds is presented based on the well known two mass models of the vocal folds the two mass model is coupled to a model of glottal airflow based on the incompressible navier stokes equations glottal waves are produced using different initial glottal gaps and different subglottal pressures fundamental frequency glottal peak flow and closed phase of the glottal waves have been compared with values known from the literature the phonation threshold pressure was determined for different initial glottal gaps the phonation threshold pressure obtained using the flow model with navier stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the bernoulli equation using the navier stokes equations an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase whereas the fundamental frequency in the bernoulli based model does not change with increasing pressure

inner approximating reachable sets for polynomial systems with time varying uncertainties in this paper we propose a convex programming based method to address a long standing problem of inner approximating backward reachable sets of state constrained polynomial systems subject to time varying uncertainties the backward reachable set is a set of states from which all trajectories starting will surely enter a target region at the end of a given time horizon without violating a set of state constraints in spite of the actions of uncertainties it is equal to the zero sublevel set of the unique lipschitz viscosity solution to a hamilton jacobi partial differential equation hje we show that inner approximations of the backward reachable set can be formed by zero sublevel sets of its viscosity supersolutions consequently we reduce the inner approximation problem to a problem of synthesizing polynomial viscosity supersolutions to this hje such a polynomial solution in our method is synthesized by solving a single semidefinite program we also prove that polynomial solutions to the formulated semidefinite program exist and can produce a convergent sequence of inner approximations to the interior of the backward reachable set in measure under appropriate assumptions this is the main contribution of this paper several illustrative examples demonstrate the merits of our approach

structure of hard hypersphere fluids in odd dimensions the structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard sphere fluids s b yuste and a santos phys rev a 43 5418 1991 the theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in laplace space the coefficients being determined by simple physical requirements fourier transform in terms of reverse bessel polynomials constitute the mathematical framework of this approximation from which an analytical expression for the static structure factor is obtained in its most elementary form the method recovers the solution of the percus yevick closure to the ornstein zernike equation for hyperspheres at odd dimensions the present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state excellent agreement with available computer simulation data at d 5 and d 7 is obtained

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

interval bounds on the solutions of semi explicit index one daes part 1 analysis this article presents two methods for computing interval bounds on the solutions of nonlinear semi explicit index one differential algebraic equations daes part 1 presents theoretical developments while part 2 discusses implementation and numerical examples the primary theoretical contributions are 1 an interval inclusion test for existence and uniqueness of a solution and 2 sufficient conditions in terms of differential inequalities for two functions to describe componentwise upper and lower bounds on this solution point wise in the independent variable the first proposed method applies these results sequentially in a two phase algorithm analogous to validated integration methods for ordinary differential equations the second method unifies these steps to characterize bounds as the solutions of an auxiliary system of daes efficient implementations of both are described using interval computations and demonstrated on numerical examples

routes to spatiotemporal chaos in the rheology of nematogenic fluids with a view to understanding the rheochaos observed in recent experiments in a variety of orientable fluids we study numerically the equations of motion of the spatiotemporal evolution of the traceless symmetric order parameter of a sheared nematogenic fluid in particular we establish by decisive numerical tests that the irregular oscillatory behavior seen in a region of parameter space where the nematic is not stably flow aligning is in fact spatiotemporal chaos we outline the dynamical phase diagram of the model and study the route to the chaotic state we find that spatiotemporal chaos in this system sets in via a regime of spatiotemporal intermittency with a power law distribution of the widths of laminar regions as in h chate and p manneville phys rev lett 58 112 1987 further the evolution of the histogram of band sizes shows a growing length scale as one moves from the chaotic towards the flow aligned phase finally we suggest possible experiments in which one can observe the intriguing behaviors discussed here

intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees human phonation does not always involve symmetric motions of the two vocal folds asymmetric motions can create slanted or oblique glottal angles this study reports intraglottal pressure profiles for a plexiglas model of the larynx with a glottis having a 10 degree divergence angle and either a symmetric orientation or an oblique angle of 15 degrees for the oblique glottis one side was divergent and the other convergent the vocal fold surfaces had 14 pressure taps the minimal glottal diameter was held constant at 0 04 cm results indicated that for either the symmetric or oblique case the pressure profiles were different on the two sides of the glottis except for the symmetric geometry for a transglottal pressure of 3 cm h2o for the symmetric case flow separation created lower pressures on the side where the flow stayed attached to the wall and the largest pressure differences between the two sides of the channel were 5 6 of the transglottal pressure for the oblique case pressures were lower

linear functional state bounding for positive systems with disturbances varying within a bounded set in most of the existing works on state bounding for perturbed dynamical systems the disturbance vector is only considered under the assumption that its norms components are bounded by known constant bounds this paper considers a more general case where the disturbance vector is assumed to vary within a known bounded set furthermore instead of finding bounds of the full system state vector this paper focuses on finding the smallest componentwise bound of a given linear function of the system state vector a class of perturbed positive systems is considered and a new method for deriving the smallest bound is presented our presented method is also extended to positive systems with time delays and to nonlinear systems which are bounded by positive systems a numerical example is given to illustrate the effectiveness of the obtained results

stable interval observers in bbc for linear systems with time varying input bounds this technical note deals with the design of stable interval observers and estimators for continuous time linear dynamic systems under uncertain initial states and uncertain inputs enclosed within time varying zonotopic bounds no monotony assumption such as cooperativity is required in the vector field the interval observer stability directly derives from the stability of the observer state matrix where any poles real or complex single or multiple are handled in the same way

reach avoid verification for nonlinear systems based on boundary analysis in this technical note we propose a set boundary based method to verify reach avoid properties of non linear dynamical systems with parametric uncertainty which works under the assumption that the initial set is a compact set in comparison to the conventional approach employing safely overapproximating state extrapolation on the full volume of the initial set our boundary based method applies such state extrapolation only to the initial set s boundary and thus to a set of significantly smaller volume this can help enhance precision and reduce computational burden when solving reach avoid verification problems especially for cases with large initial sets and or large time horizons furthermore our boundary based method lifts existing reachability analysis techniques with their often confined geometric representations of reachable sets like interval boxes zonotopes polyhedra ellipsoids to considerably more complex geometric shapes where the boundary of the set is representable as a finite union of such shapes the resulting benefits brought by our boundary based method in reach avoid verification are illustrated through several examples

unsteady behavior of flow in a scaled up vocal folds model measurements of the fluid flow through a scaled up model of the human glottis are presented to determine whether glottal flow may be approximated as unsteady time and space resolved velocity vector fields from digital particle image velocimetry dpiv measurements of the flow through the gap between two moving rigid walls are presented in four cases over a range of strouhal numbers 0 010 0 018 0 035 0 040 corresponding to life scale f0 of 30 58 109 and 126hz respectively at a reynolds number of 8000 it is observed that 1 glottal flow onset is delayed after glottal opening and 2 glottal flow shutoff occurs prior to closure a comparison between flow through a fully open nonmoving glottis and that through the moving vocal folds shows a marked difference in spatial structure of the glottal jet the following features of the flow are seen to exhibit strong dependence on cycle frequency a glottal exit plane velocity b volume flow c vortex shedding rates and d vortex amplitude v

complexity reduction through a schur based decomposition for reachability analysis of linear time invariant systems this article presents a method for complexity reduction in reachability analysis and safety preserving controller synthesis via schur based decomposition the decomposition results in either decoupled or weakly coupled lower dimensional subsystems reachable sets computed independently for each subsystem are back projected and intersected to yield an overapproximation of the actual reachable set moreover applying this technique to a class of unstable lti systems we show that when certain eigenvalue and state constraint conditions are satisfied further reduction of complexity is possible evaluating our method for a variety of examples we demonstrate that significant reduction in the computational costs can be achieved this technique has considerable potential utility for use in conjunction with computationally intensive reachability tools

a hybrid bounding method for computing an over approximation for the reachable set of uncertain nonlinear systems in this paper we show how to compute an over approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration we introduce two ways to do so the first one is a full interval method which handles whole domains for set computation and relies on state of the art validated numerical integration methods the second one relies on comparison theorems for differential inequalities in order to bracket the uncertain dynamics between two dynamical systems where there is no uncertainty since the derived bracketing systems are piecewise ck differentiable functions validated numerical integration methods cannot be used directly hence our contribution resides in the use of hybrid automata to model the bounding systems we give a rule for building these automata and we show how to run them and address mode switching in a guaranteed way in order to compute the over approximation for the reachable set the computational cost of our method is also analyzed and shown to be smaller that the one of classical interval techniques sufficient conditions are given which ensure the epsiv practical stability of the enclosures given by our hybrid bounding method two examples are also given which show that the performance of our method is very promising

hamilton jacobi formulation for reach avoid differential games a new framework for formulating reachability problems with competing inputs nonlinear dynamics and state constraints as optimal control problems is developed such reach avoid problems arise in among others the study of safety problems in hybrid systems earlier approaches to reach avoid computations are either restricted to linear systems or face numerical difficulties due to possible discontinuities in the hamiltonian of the optimal control problem the main advantage of the approach proposed in this paper is that it can be applied to a general class of target hitting continuous dynamic games with nonlinear dynamics and has very good properties in terms of its numerical solution since the value function and the hamiltonian of the system are both continuous the performance of the proposed method is demonstrated by applying it to a case study which involves the target hitting problem of an underactuated underwater vehicle in the presence of obstacles

a differential game with two players and one target we study a two player differential game in which one of the players wants the state of the system to reach an open target while the other player wants the state of the system to avoid this target we show that the victory domains of the players form a partition of the complement of the target one of them can be characterized by the mean of geometrical conditions as a discriminating domain finally we show that the common boundary of the victory domains enjoys a semipermeability property

low temperature and high temperature approximations for penetrable sphere fluids comparison with monte carlo simulations and integral equation theories the two body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials the simplest of which being that of penetrable spheres pss in this paper we construct two simple analytical theories for the structural properties of ps fluids a low temperature lt approximation that can be seen as an extension to pss of the well known solution of the percus yevick py equation for hard spheres and a high temperature ht approximation based on the exact asymptotic behavior in the limit of infinite temperature monte carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories it is found that despite their simplicity the ht and lt approximations exhibit a fair agreement with the simulation data within their respective domains of applicability so that they complement each other a comparison with numerical solutions of the py and the hypernetted chain approximations is also carried out the latter showing a very good performance except inside the core at low temperatures

a new method of reachable set estimation for time delay systems with polytopic uncertainties we address the reachable set bounding problem of linear systems subject to both time varying delay and polytopic uncertainties a novel criterion is established to give a more accurate description of the set which bounds the states starting from the origin by inputs with peak values by combining the maximal lyapunov functional and the reciprocally convex approach we obtain a tighter reachable set estimation with lower computational complexity the corresponding reachable set condition for the common lyapunov functional can be obtained naturally as a special case of the above result finally two examples illustrate the advantages of our proposed method

on maximal robust positively invariant sets in constrained nonlinear systems abstract in this technical communique we study the maximal robust positively invariant set for state constrained continuous time nonlinear systems subjected to a bounded disturbance extending results from the theory of barriers we show that this set is closed and that its boundary consists of two complementary parts one of which we name the invariance barrier which consists of trajectories that satisfy the maximum principle

approximate reduction of heterogenous nonlinear models with differential hulls we present a model reduction technique for a class of nonlinear ordinary differential equation ode models of heterogeneous systems where heterogeneity is expressed in terms of classes of state variables having the same dynamics structurally but which are characterized by distinct parameters to this end we first build a system of differential inequalities that provides lower and upper bounds for each original state variable but such that it is homogeneous in its parameters then we use two methods for exact aggregation of odes to exploit this homogeneity yielding a smaller model of size independent of the number of heterogeneous classes we apply this technique to two case studies a multiclass queuing network and a model of epidemics spread

bounds on the reachable sets of nonlinear control systems the computation of rigorous enclosures of the reachable sets of nonlinear control systems is considered with a focus on applications for which speed is crucial low computational costs make interval methods based on differential inequalities an attractive option unfortunately such methods are prone to large overestimation and often produce useless results in practice from physical considerations however it is common that some crude set is known to contain the reachable set we establish a general bounding result based on differential inequalities which enables the effective use of such sets during the bounding procedure in the case where this set is a convex polyhedron an efficient implementation using interval computations is developed using readily available physical information from practical examples this method is shown to provide significant advantages over alternative methods in terms of both efficiency and accuracy

reachability analysis of nonlinear systems using matrix measures matrix measures also known as logarithmic norms have historically been used to provide bounds on the divergence of trajectories of a system of ordinary differential equations in this technical note we use them to compute guaranteed overapproximations of reachable sets for nonlinear continuous time systems using numerically simulated trajectories and to bound the accumulation of numerical simulation errors along simulation traces our method employs a user supplied bound on the matrix measure of the system s jacobian matrix to compute bounds on the behavior of nearby trajectories leading to efficient computation of reachable sets when such bounds are available we demonstrate that the proposed technique scales well to systems with a large number of states

radial distribution function of penetrable sphere fluids to the second order in density the simplest bounded potential is that of penetrable spheres which takes a positive finite value if the two spheres are overlapped being zero otherwise in this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of t ensuremath equiv k b t where k b is the boltzmann constant and t is the temperature for penetrable sphere fluids the expressions are exact except for the function represented by an elementary diagram inside the core which is approximated by a polynomial form in excellent agreement with accurate results obtained by monte carlo integration comparison with the hypernetted chain hnc and percus yevick py theories shows that the latter is better than the former for t ensuremath lesssim 1 only however even at zero temperature hard sphere limit the py solution is not accurate inside the overlapping region where no practical cancellation of the neglected diagrams takes place the exact fourth virial coefficient is positive for t ensuremath lesssim 0 73 reaches a minimum negative value at t ensuremath approx 1 1 and then goes to zero from below as 1 t 4 for high temperatures these features are captured qualitatively but not quantitatively by the hnc and py predictions in addition in both theories the compressibility route is the best one for t ensuremath lesssim 0 7 while the virial route is preferable if t ensuremath gtrsim 0 7

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

spatio temporal analysis of irregular vocal fold oscillations biphonation due to desynchronization of spatial modes this report is on direct observation and modal analysis of irregular spatio temporal vibration patterns of vocal fold pathologies in vivo the observed oscillation patterns are described quantitatively with multiline kymograms spectral analysis and spatio temporal plots the complex spatio temporal vibration patterns are decomposed by empirical orthogonal functions into independent vibratory modes it is shown quantitatively that biphonation can be induced either by left right asymmetry or by desynchronized anterior posterior vibratory modes and the term ap anterior posterior biphonation is introduced the presented phonation examples show that for normal phonation the first two modes sufficiently explain the glottal dynamics the spatio temporal oscillation pattern associated with biphonation due to left right asymmetry can be explained by the first three modes higher order modes are required to describe the pattern for biphonation induced by anterior posterior vibrations spatial irregularity is

a comprehensive method for reachability analysis of uncertain nonlinear hybrid systems reachability analysis of nonlinear uncertain hybrid systems i e continuous discrete dynamical systems whose continuous dynamics guard sets and reset functions are defined by nonlinear functions can be decomposed in three algorithmic steps computing the reachable set when the system is in a given operation mode computing the discrete transitions i e detecting and localizing when and where the continuous flowpipe intersects the guard sets and aggregating the multiple trajectories that result from an uncertain transition once the whole flow pipe has transitioned so that the algorithm can resume this paper proposes a comprehensive method that provides a nicely integrated solution to the hybrid reachability problem at the core of the method is the concept of mspb i e geometrical object obtained as the minkowski sum of a parallelotope and an axes aligned box mspb are a way to control the over approximation of the taylor s interval integration method as they happen to be a specific type of zonotope they articulate perfectly with the zonotope bounding method that we propose to enclose in an optimal way the set of flowpipe trajectories generated by the transition process the method is evaluated both theoretically by analyzing its complexity and empirically by applying it to well chosen hybrid nonlinear examples

interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations for normal phonation two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1 1 entrainment the eigenfunctions show some correspondence to theoretical low order normal modes of a simplified three dimensional elastic continuum and to the normal modes of a linearized two mass model the eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations these chaotic oscillations might be understood in terms of a desynchronization of a few of the low order modes and may be related to mechanisms of creaky voice or vocal fry furthermore some of the empirical eigenfunctions captured during complex oscillations correspond to higher order normal modes described in earlier theoretical work the empirical eigenfunctions may also be useful in the design of lower order models valid over the range for which the empirical eigenfunctions remain more or less constant and may help facilitate bifurcation analyses of the biomechanical simulation

hybrid abstractions of affine systems abstract this paper considers the problem of building a set of hybrid abstractions for affine systems in order to compute over approximations of the reachable space each abstraction is based on a decomposition of the continuous state space that is defined by hyperplanes generated by linear combinations of two vectors the choice of these vectors is based on consideration of the dynamics of the system and uses for example the left eigenvectors of the matrix that defines these dynamics we show that the reachability calculus can then be performed on a combination of such abstractions and how its accuracy depends on the choice of hyperplanes that define the decomposition

cooperative pursuit with voronoi partitions this work considers a pursuit evasion game in which a number of pursuers are attempting to capture a single evader cooperation among multiple agents can be difficult to achieve as it may require the selection of actions in the joint input space of all agents this work presents a decentralized real time algorithm for cooperative pursuit of a single evader by multiple pursuers in bounded simply connected planar domains the algorithm is based on minimizing the area of the generalized voronoi partition of the evader the pursuers share state information but compute their inputs independently no assumptions are made about the evader s control strategies other than requiring the evader control inputs to conform to a speed limit proof of guaranteed capture is shown when the domain is convex and the players motion models are kinematic simulation results are presented showing the efficiency and effectiveness of this strategy

interval quadratic programming for day ahead dispatch of uncertain predicted demand in this paper we propose an interval quadratic programming method for the day ahead scheduling of power generation and battery charge cycles where the prediction uncertainty of power consumption and photovoltaic power generation is described as a parameter vector lying in an interval box the interval quadratic programming is formulated as the problem of finding the tightest box i e interval hull that encloses the image of a function of the minimizer in parametric quadratic programming to solve this problem in a computationally efficient manner we take a novel approach based on a monotonicity analysis of the minimizer in the parametric quadratic programming in particular giving a tractable parameterization of the minimizer on the basis of the karush kuhn tucker condition we show that the monotonicity analysis with respect to the parameter vector can be relaxed to the sign pattern analysis of an oblique projection matrix the monotonicity of the minimizer is found to be essential in the day ahead dispatch problem where uncertain predicted demand described by a parameter vector is dispatched to power generation and battery charge cycles while the economic cost is minimized finally we verify the efficiency of the proposed method numerically using experimental and predicted data for power consumption and photovoltaic power generation