Performance Variability and Project Dynamics

We present a dynamical model of complex cooperative projects such as large engineering design or software development efforts, comprised of concurrent and interrelated tasks. The model contains a stochastic component to account for temporal fluctuations both in task performance and in the interactions between related tasks. We show that as the system size increases, so does the average completion time. Also, for fixed system size, the dynamics of individual project realizations can exhibit large deviations from the average when fluctuations increase past a threshold, causing long delays in completion times. These effects are in agreement with empirical observation. We also show that the negative effects of both large groups and long delays caused by fluctuations may be mitigated by arranging projects in a hierarchical or modular structure. Our model is applicable to any arrangement of interdependent tasks, providing an analytical prediction for the average completion time as well as a numerical threshold for the fluctuation strength beyond which long delays are likely. In conjunction with previous modeling techniques, it thus provides managers with a predictive tool to be used in the design of a project's architecture. Bernardo A. Huberman is a Senior HP Fellow and Director of the Information Dynamics Laboratory. He is also a Consulting Professor of Physics at Stanford University. For the past ten years he has concentrated on understanding distributed processes and on the design of mechanisms for information aggregation and the protection of privacy as well as market-based distributed resource allocation systems. Dennis Wilkinson is a recent graduate of Stanford University with a doctorate in Physics, and has accepted a position in the Department of Defense. His research interests include dynamics of social networks and other stochastic systems, information extraction from large, complex networks, and techniques in distributed computing.     

Filtering,Smoothing and M-ary Detection with Discrete Time Poisson Observations

Abstract

In this article, we solve a class of estimation problems, namely, filtering smoothing and detection for a discrete time dynamical system with integer-valued observations. The observation processes we consider are Poisson random variables observed at discrete times. Here, the distribution parameter for each Poisson observation is determined by the state of a Markov chain. By appealing to a duality between forward (in time) filter and its corresponding backward processes, we compute dynamics satisfied by the unnormalized form of the smoother probability. These dynamics can be applied to construct algorithms typically referred to as fixed point smoothers, fixed lag smoothers, and fixed interval smoothers. M-ary detection filters are computed for two scenarios: one for the standard model parameter detection problem and the other for a jump Markov system.     

Nonlinear dynamic analysis of a hybrid squeeze-film damper-mounted rigid rotor lubricated with couple stress fluid and active control

The hybrid squeeze-film damper bearing with active control is proposed in this paper and the lubricating with couple stress fluid is also taken into consideration. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincaré maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the non-dimensional speed ratio s = 3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action. Besides, the rotor dynamic responses of the system will be more stable by using couple stress fluid.     

Long-term dynamics of discrete-time predator–prey models: stability of equilibria,cycles and chaos

ABSTRACT

In [A.S. Ackleh, M.I. Hossain, A. Veprauskas, and A. Zhang, Persistence and stability analysis of discrete-time predator-prey models: A study of population and evolutionary dynamics, J. Differ. Equ. Appl. 25 (2019), pp. 1568–1603.], we established conditions for the persistence and local asymptotic stability of the interior equilibrium for two discrete-time predator–prey models (one without and with evolution to resist toxicants). In the current paper, we provide a more in-depth analysis of these models, including global stability of equilibria, existence of cycles and chaos. Our main focus is to examine how the speed of evolution ν may impact population dynamics. For both models, we establish conditions under which the interior equilibrium is global asymptotically stable using perturbation analysis together with the construction of Lyapunov functions. For small ν, we show that the global dynamics of the evolutionary system are nothing but a continuous perturbation of the non-evolutionary system. However, when the speed of evolution is increased, we perform numerical studies which demonstrate that evolution may introduce rich dynamics including cyclic and chaotic behaviour that are not observed when evolution is absent.     

Allee effects in a discrete-time SIS epidemic model with infected newborns

We extend the framework of Rios-Soto et al. (Contemporary Mathematics, 2006, 410, 297) to include both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number ?₀, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This is in contrast to the recent observations of Franke and Yakubu, that the demographic dynamics can be chaotic while the infective dynamics are oscillatory and non-chaotic in periodically-forced SIS epidemic models (Mathematical Biosciences, 2006, 204, 68).     

Finite-Dimensional Filtering and Control for Continuous-Time Nonlinear Systems

Abstract

A partially observed stochastic control problem is considered in continuous time where both the state and observation processes are given by non-linear dynamics. Measure change techniques applied to the cost process allow both state and observation processes to be thought of as linear. If the cost is given a special form, this transformation changes the original non-linear problem into a linear one.     

Noise-Induced Resonance in Bistable Systems Caused by Delay Feedback

Abstract

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one-dimensional parametrized stochastic differential equation with point delay; the basic properties of which we check.

With a view to capturing the effective dynamics and, in particular, the resonance-like behavior of the reference model, we construct a simplified or reduced model, the two-state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance.

Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two-state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.     

Multiphysics finite element model for the computation of the electro-mechanical dynamics of a hybrid reluctance actuator

ABSTRACT

In hybrid reluctance actuators, the achievable closed-loop system bandwidth is affected by the eddy currents and hysteresis in the ferromagnetic components and the mechanical resonance modes. Such effects must be accurately predicted to achieve high performance via feedback control. Therefore, a multiphysics electro-mechanical finite element model is proposed in this paper to compute the dynamics of a 2-DoF hybrid reluctance actuator. An electromagnetic simulation is adopted to compute the electromagnetic dynamics and the actuation torque, which is employed as input for a structural dynamic simulation computing the electro-mechanical frequency response function. For model validation, the simulated and measured frequency response plots are compared for two actuators with solid and laminated outer yoke, respectively. In both cases, the model accurately predicts the measurement results, with a maximum relative phase error of 1.7% between the first resonance frequency and 1 kHz and a relative error of 1.5% for the second resonance frequency..     

The Emergence of Racial Segregation in an Agent-Based Model of Residential Location: The Role of Competing Preferences

Models of segregation dynamics have examined how individual preferences over neighborhood racial composition determine macroscopic patterns of segregation. Many fewer models have considered the role of household preferences over other location attributes, which may compete with preferences over racial composition. We hypothesize that household preferences over location characteristics other than racial composition affect segregation dynamics in nonlinear ways and that, for a critical range of parameter values, these competing preferences can qualitatively affect segregation outcomes. To test this hypothesis, we develop a dynamic agent-based model that examines macro-level patterns of segregation as the result of interdependent household location choices. The model incorporates household preferences over multiple neighborhood features, some of which are endogenous to residential location patterns, and allows for income heterogeneity across races and among households of the same race. Preliminary findings indicate that patterns of segregation can emerge even when individuals are wholly indifferent to neighborhood racial composition, due to competing preferences over neighborhood density. Further, the model shows a strong tendency to concentrate affluent families in a small number of suburbs, potentially mimicking recent empirical findings on favored quarters in metropolitan areas. This paper was the first runner-up for the 2004 NAACSOS best paper award. Kan Chen is an associate professor in the Department of Computational Science at the National University of Singapore. His recent research interests include spatial and temporal scaling in driven, dissipative systems, applications of self-organized criticality, dynamics of earthquakes, and computational finance. He received a B.Sc. in physics from the University of Science and Technology of China (1983) and a Ph.D. in physics from Ohio State University (1988). Elena Irwin is an associate professor in the Department of Agricultural, Environmental, and Development Economics at Ohio State University. Her research interests include land use change, urban sprawl, household location decisions, and the value of open space. This research applies theory and modeling techniques from the fields of spatial and regional economics, including the application of spatial econometrics and geographic information systems (GIS). She received a B.A. in German and History from Washington University in St. Louis (1988) and a Ph.D. in Agricultural and Resource Economics from the University of Maryland (1998). Ciriyam Jayaprakash is a Professor in the Department of Physics at the Ohio State University. His recent research interests include spatially extended nonlinear systems including fully-developed turbulence, genetic regulatory networks, and applications of statistical mechanical techniques to financial and social sciences. He received an M.S. in Physics from the Indian Institute of Technology, Kanpur (1973), an M.S. in Physics from Caltech (1975) and a Ph.D in Physics from the University of Illinois at Urbana-Champaign (1979). Keith Warren is an assistant professor in the College of Social Work at Ohio State University. His research interests focus on interpersonal interactions in the development and solution of social problems, particularly those of urban areas such as segregation, substance abuse and increased interpersonal violence. He received a B.A in Behavioral Science from Warren Wilson College (1984), and a Ph.D. in Social Work from the University of Texas at Austin (1998)     

Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions

Abstract

A coupled system of the two-dimensional Navier–Stokes equations and the salinity transport equation with spatially correlated white noise on the boundary as well as in fluid is investigated. The noise affects the system through a dynamical boundary condition. This system may be considered as a model for gravity currents in oceanic fluids. The noise is due to uncertainty in salinity flux on fluid boundary. After transforming this system into a random dynamical system, we first obtain asymptotic estimates on system evolution, and then show that the long time dynamics is captured by a random attractor.     

Uniformity,Bipolarization and Pluriformity Captured as Generic Stylized Behavior with an Agent-Based Simulation Model of Attitude Change

This paper focuses at the dynamics of attitude change in large groups. A multi-agent computer simulation has been developed as a tool to study hypothesis we take to study these dynamics. A major extension in comparison to earlier models is that Social Judgment Theory is being formalized to incorporate processes of assimilation and contrast in persuasion processes. Results demonstrate that the attitude structure of agents determines the occurrence of assimilation and contrast effects, which in turn cause a group of agents to reach consensus, to bipolarize, or to develop a number of subgroups sharing the same position. Subsequent experiments demonstrate the robustness of these effects for a different formalization of the social network, and the susceptibility for population size.This paper won the best paper award at NAACSOS 2004, Pittsburgh PA. NAACSOS is the main conference of the North American Association for Computational Social and Organizational Science.Wander Jager received his Ph.D. degree in Social Sciences in 2000 from the University of Groningen, the Netherlands. Dr. Jager is currently Associate Professor at the University of Groningen. His current application domain concerns marketing, innovation diffusion and social simulation. Dr. Jager has authored or co-authored various papers on market dynamics, diffusion processes, resource use and sustainable consumption.Frédéric Amblard received his Ph.D. degree in Multi-Agent Simulation in 2003 from Blaise Pascal University, Clermont-Ferrand, France. Dr. Amblard is currently Associate Professor at the University of Social Sciences in Toulouse and researcher associated to the CNRS-IRIT, Institute of Research in Computer Sciences in Toulouse. His current application domain now concerns Agent-Based Social Simulation. Dr. Amblard has authored or coauthored various research papers either in computer sciences, in physics or in sociology.A preceding version of this paper has been presented to the 2004 Conference of the North American Association for Computational Social and Organization Science, Pittsburgh, USA and received the best paper award from this conference.     

Selected experimental methods for determining droplet parameters from the intensity distribution of scattered light: A review

The present paper summarizes some experimental methods, which have been developed using the results of calculations based on the theory of Gustav Mie. As examples two regions of the scattered light are considered in more detail. The intensity distribution in the forward hemisphere for scattering angles 30 ≤ θ ≤ 60 shows maxima, which can be identified as regular fringes on a screen. The spacing between the fringes is a measure for the droplet size. In the intensity distribution of the backward hemisphere the region of the first rainbow can be found. In the rainbow region a main maximum, subsidiary maxima and a ripple structure can be identified. The angular position of the main maximum is a measure for the refractive index of the droplet. The angular distance between the subsidiary maxima and the angular distance between the ripples both are a function of droplet size. A comparison with other size measurement methods gives information about the sphericity of the droplet. An evaporating droplet shows for instance oscillations of the rainbow position due to morphology dependent resonances. The oscillation frequency is proportional to the evaporation rate.     

An Impact of Stochastic Dynamic Boundary Conditions on the Evolution of the Cahn-Hilliard System

Abstract

Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition involves the time derivative as well as spatial derivatives for the system state variables on the boundary. Although stochastic static (Neumann or Dirichet type) boundary conditions have been applied for stochastic partial differential equations, not much is known about the dynamical impact of stochastic dynamic boundary conditions. The purpose of this article is to study possible impacts of stochastic dynamic boundary conditions on the long term dynamics of the Cahn-Hilliard equation arising in the materials science. We show that the dimension estimation of the random attractor increases as the coefficient for the dynamic term in the stochastic dynamic boundary condition decreases. However, the dimension of the random attractor is not affected by the corresponding stochastic static boundary condition.     

The Initial Drift of a 2D Droplet at Zero Temperature

We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. We compute the explicit value of this coefficient.      

Numerical analysis of a rigid rotor supported by aerodynamic four-lobe journal bearing system with mass unbalance

This paper presents the effect of rotor mass on the nonlinear dynamic behavior of a rigid rotor-bearing system excited by mass unbalance. Aerodynamic four-lobe journal bearing is used to support a rigid rotor. A finite element method is employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using Runge-Kutta method. To analyze the behavior of the rotor center in the horizontal and vertical directions under different operating conditions, the dynamic trajectory, the power spectra, the Poincare maps and the bifurcation diagrams are used. From this study, results show how the complex dynamic behavior of this type of system comprising periodic, KT-periodic and quasi-periodic responses of the rotor center varies with changes in rotor mass values by considering two bearing aspect ratios. Results of this study contribute a better understanding of the nonlinear dynamics of an aerodynamic four-lobe journal bearing system.     

Identification of harmful time harmonic interactions in a high power squirrel-cage traction machine

The paper offers a methodology for the identification the time harmonic interactions with a strong negative impact on the rotor of a high power induction machine. These potentially dangerous pulsating torques may be effectively reduced by carefully setting the machine’s drive control. A novel approach based on a complex finite element model and further post-processing is used. Results obtained from electromagnetic calculations in the form of pulsating torques are used as mechanical loading of a structural dynamic model. This complex model intended for rotor vibration analysis is described in brief in the mechanical part of the paper. The proposed methodology is applied to the machine used as a propulsion unit for multisystem locomotives of 1600 kW power.     

Sanov results for Glauber spin-glass dynamics

Summary. In this paper we prove a Sanov result, i.e. a Large Deviation Principle (LDP) for the distribution of the empirical measure, for the annealed Glauber dynamics of the Sherrington-Kirkpatrick spin-glass. Without restrictions on time or temperature we prove a full LDP for the asymmetric dynamics and the crucial upper large deviations bound for the symmetric dynamics. In the symmetric model a new order-parameter arises corresponding to the response function in [SoZi83]. In the asymmetric case we show that the corresponding rate function has a unique minimum, given as the solution of a self-consistent equation. The key argument used in the proofs is a general result for mixing of what is known as Large Deviation Systems (LDS) with measures obeying an independent LDP. Received: 18 May 1995 / In revised form: 14 March 1996     

On the oil-whipping of a rotor-bearing system by a continuum model

The nonlinear dynamic behavior of a rotor-bearing system is analyzed based on a continuum model. The finite element method is adopted in the analysis. Emphasis is placed on the so-called “oil-whip phenomena” which might lead to the failure of the rotor system. The dynamic response of the system in unbalanced conditions is approached by a direct integration method. It is found that a typical “oil-whip phenomenon” is successfully simulated, and the effect of the refinement of the finite element mesh is also checked. Furthermore, the bifurcation behavior of the oil-whip phenomenon that is of much concern in recent nonlinear dynamics research is analyzed. The rotor-bearing system is also examined by a simple discrete model. Significant differences are found between these two models. It is suggested that a careful examination should be made in modeling the nonlinear dynamic behavior of a rotor system.     

The asymptotic distribution of Frobenius numbers

The Frobenius number F(a) of an integer vector a with positive coprime coefficients is defined as the largest number that does not have a representation as a positive integer linear combination of the coefficients of a. We show that if a is taken to be random in an expanding d-dimensional domain, then F(a) has a limit distribution, which is given by the probability distribution for the covering radius of a certain simplex with respect to a (d−1)-dimensional random lattice. This result extends recent studies for d=3 by Arnold, Bourgain-Sinai and Shur-Sinai-Ustinov. The key features of our approach are (a) a novel interpretation of the Frobenius number in terms of the dynamics of a certain group action on the space of d-dimensional lattices, and (b) an equidistribution theorem for a multidimensional Farey sequence on closed horospheres.