A discrete mechanics framework for real time virtual surgical simulations with application to virtual laparoscopic nephrectomy.

PubMed

Zhou, Xiangmin; Zhang, Nan; Sha, Desong; Shen, Yunhe; Tamma, Kumar K; Sweet, Robert

2009-01-01

The inability to render realistic soft-tissue behavior in real time has remained a barrier to face and content aspects of validity for many virtual reality surgical training systems. Biophysically based models are not only suitable for training purposes but also for patient-specific clinical applications, physiological modeling and surgical planning. When considering the existing approaches for modeling soft tissue for virtual reality surgical simulation, the computer graphics-based approach lacks predictive capability; the mass-spring model (MSM) based approach lacks biophysically realistic soft-tissue dynamic behavior; and the finite element method (FEM) approaches fail to meet the real-time requirement. The present development stems from physics fundamental thermodynamic first law; for a space discrete dynamic system directly formulates the space discrete but time continuous governing equation with embedded material constitutive relation and results in a discrete mechanics framework which possesses a unique balance between the computational efforts and the physically realistic soft-tissue dynamic behavior. We describe the development of the discrete mechanics framework with focused attention towards a virtual laparoscopic nephrectomy application.

Noise Propagation and Uncertainty Quantification in Hybrid Multiphysics Models: Initiation and Reaction Propagation in Energetic Materials

DTIC Science & Technology

2016-05-23

general model for heterogeneous granular media under compaction and (ii) the lack of a reliable multiscale discrete -to-continuum framework for...dynamics. These include a continuum- discrete model of heat dissipation/diffusion and a continuum- discrete model of compaction of a granular material with...the lack of a general model for het- erogeneous granular media under compac- tion and (ii) the lack of a reliable multi- scale discrete -to-continuum

On the relationship of steady states of continuous and discrete models arising from biology.

PubMed

Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka

2012-12-01

For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.

General method to find the attractors of discrete dynamic models of biological systems.

PubMed

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

General method to find the attractors of discrete dynamic models of biological systems

NASA Astrophysics Data System (ADS)

Gan, Xiao; Albert, Réka

2018-04-01

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

Discrete virus infection model of hepatitis B virus.

PubMed

Zhang, Pengfei; Min, Lequan; Pian, Jianwei

2015-01-01

In 1996 Nowak and his colleagues proposed a differential equation virus infection model, which has been widely applied in the study for the dynamics of hepatitis B virus (HBV) infection. Biological dynamics may be described more practically by discrete events rather than continuous ones. Using discrete systems to describe biological dynamics should be reasonable. Based on one revised Nowak et al's virus infection model, this study introduces a discrete virus infection model (DVIM). Two equilibriums of this model, E1 and E2, represents infection free and infection persistent, respectively. Similar to the case of the basic virus infection model, this study deduces a basic virus reproductive number R0 independing on the number of total cells of an infected target organ. A proposed theorem proves that if the basic virus reproductive number R0<1 then the virus free equilibrium E1 is locally stable. The DVIM is more reasonable than an abstract discrete susceptible-infected-recovered model (SIRS) whose basic virus reproductive number R0 is relevant to the number of total cells of the infected target organ. As an application, this study models the clinic HBV DNA data of a patient who was accepted via anti-HBV infection therapy with drug lamivudine. The results show that the numerical simulation is good in agreement with the clinic data.

A discrete geometric approach for simulating the dynamics of thin viscous threads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Audoly, B., E-mail: audoly@lmm.jussieu.fr; Clauvelin, N.; Brun, P.-T.

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistencymore » of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.« less

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

PubMed

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Nonlinear Maps for Design of Discrete Time Models of Neuronal Network Dynamics

DTIC Science & Technology

2016-02-29

Performance/Technic~ 02-01-2016- 02-29-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete -Time Models of Neuronal...neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this approach, time step can be made...propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete -time models for studies of large-scale neuronal

Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics

DTIC Science & Technology

2016-03-31

2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete -Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this...responsive tiring patterns. We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete -time models for

Stability analysis of the Euler discretization for SIR epidemic model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

A Stochastic Dynamic Programming Model With Fuzzy Storage States Applied to Reservoir Operation Optimization

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Jamshid; Mahdizadeh, Kourosh; Afshar, Abbas

2004-08-01

Application of stochastic dynamic programming (SDP) models to reservoir optimization calls for state variables discretization. As an important variable discretization of reservoir storage volume has a pronounced effect on the computational efforts. The error caused by storage volume discretization is examined by considering it as a fuzzy state variable. In this approach, the point-to-point transitions between storage volumes at the beginning and end of each period are replaced by transitions between storage intervals. This is achieved by using fuzzy arithmetic operations with fuzzy numbers. In this approach, instead of aggregating single-valued crisp numbers, the membership functions of fuzzy numbers are combined. Running a simulated model with optimal release policies derived from fuzzy and non-fuzzy SDP models shows that a fuzzy SDP with a coarse discretization scheme performs as well as a classical SDP having much finer discretized space. It is believed that this advantage in the fuzzy SDP model is due to the smooth transitions between storage intervals which benefit from soft boundaries.

Estimation of Dynamic Discrete Choice Models by Maximum Likelihood and the Simulated Method of Moments

PubMed Central

Eisenhauer, Philipp; Heckman, James J.; Mosso, Stefano

2015-01-01

We compare the performance of maximum likelihood (ML) and simulated method of moments (SMM) estimation for dynamic discrete choice models. We construct and estimate a simplified dynamic structural model of education that captures some basic features of educational choices in the United States in the 1980s and early 1990s. We use estimates from our model to simulate a synthetic dataset and assess the ability of ML and SMM to recover the model parameters on this sample. We investigate the performance of alternative tuning parameters for SMM. PMID:26494926

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

PubMed

Brocklehurst, Paul; Ni, Haibo; Zhang, Henggui; Ye, Jianqiao

2017-01-01

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation.

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue

PubMed Central

Zhang, Henggui

2017-01-01

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation. PMID:28510575

A Discrete Events Delay Differential System Model for Transmission of Vancomycin-Resistant Enterococcus (VRE) in Hospitals

DTIC Science & Technology

2010-09-19

estimated directly form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after...hospital infections , is used to motivate possibilities of modeling nosocomial infec- tion dynamics. This is done in the context of hospital monitoring and...model development. Key Words: Delay equations, discrete events, nosocomial infection dynamics, surveil- lance data, inverse problems, parameter

Assessing the importance of self-regulating mechanisms in diamondback moth population dynamics: application of discrete mathematical models.

PubMed

Nedorezov, Lev V; Löhr, Bernhard L; Sadykova, Dinara L

2008-10-07

The applicability of discrete mathematical models for the description of diamondback moth (DBM) (Plutella xylostella L.) population dynamics was investigated. The parameter values for several well-known discrete time models (Skellam, Moran-Ricker, Hassell, Maynard Smith-Slatkin, and discrete logistic models) were estimated for an experimental time series from a highland cabbage-growing area in eastern Kenya. For all sets of parameters, boundaries of confidence domains were determined. Maximum calculated birth rates varied between 1.086 and 1.359 when empirical values were used for parameter estimation. After fitting of the models to the empirical trajectory, all birth rate values resulted considerably higher (1.742-3.526). The carrying capacity was determined between 13.0 and 39.9DBM/plant, after fitting of the models these values declined to 6.48-9.3, all values well within the range encountered empirically. The application of the Durbin-Watson criteria for comparison of theoretical and experimental population trajectories produced negative correlations with all models. A test of residual value groupings for randomness showed that their distribution is non-stochastic. In consequence, we conclude that DBM dynamics cannot be explained as a result of intra-population self-regulative mechanisms only (=by any of the models tested) and that more comprehensive models are required for the explanation of DBM population dynamics.

Comparing the Discrete and Continuous Logistic Models

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

Cross Coursing in Mathematics: Physical Modelling in Differential Equations Crossing to Discrete Dynamical Systems

ERIC Educational Resources Information Center

Winkel, Brian

2012-01-01

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

NASA Astrophysics Data System (ADS)

Ullrich, Paul A.; Jablonowski, Christiane; Kent, James; Lauritzen, Peter H.; Nair, Ramachandran; Reed, Kevin A.; Zarzycki, Colin M.; Hall, David M.; Dazlich, Don; Heikes, Ross; Konor, Celal; Randall, David; Dubos, Thomas; Meurdesoif, Yann; Chen, Xi; Harris, Lucas; Kühnlein, Christian; Lee, Vivian; Qaddouri, Abdessamad; Girard, Claude; Giorgetta, Marco; Reinert, Daniel; Klemp, Joseph; Park, Sang-Hun; Skamarock, William; Miura, Hiroaki; Ohno, Tomoki; Yoshida, Ryuji; Walko, Robert; Reinecke, Alex; Viner, Kevin

2017-12-01

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier-Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

NASA Astrophysics Data System (ADS)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Reducing Neuronal Networks to Discrete Dynamics

PubMed Central

Terman, David; Ahn, Sungwoo; Wang, Xueying; Just, Winfried

2008-01-01

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [1], we analyze the discrete model. PMID:18443649

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

Improved Discretization of Grounding Lines and Calving Fronts using an Embedded-Boundary Approach in BISICLES

NASA Astrophysics Data System (ADS)

Martin, D. F.; Cornford, S. L.; Schwartz, P.; Bhalla, A.; Johansen, H.; Ng, E.

2017-12-01

Correctly representing grounding line and calving-front dynamics is of fundamental importance in modeling marine ice sheets, since the configuration of these interfaces exerts a controlling influence on the dynamics of the ice sheet. Traditional ice sheet models have struggled to correctly represent these regions without very high spatial resolution. We have developed a front-tracking discretization for grounding lines and calving fronts based on the Chombo embedded-boundary cut-cell framework. This promises better representation of these interfaces vs. a traditional stair-step discretization on Cartesian meshes like those currently used in the block-structured AMR BISICLES code. The dynamic adaptivity of the BISICLES model complements the subgrid-scale discretizations of this scheme, producing a robust approach for tracking the evolution of these interfaces. Also, the fundamental discontinuous nature of flow across grounding lines is respected by mathematically treating it as a material phase change. We present examples of this approach to demonstrate its effectiveness.

Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

PubMed

Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

2017-07-01

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

A Neural Dynamic Model Generates Descriptions of Object-Oriented Actions.

PubMed

Richter, Mathis; Lins, Jonas; Schöner, Gregor

2017-01-01

Describing actions entails that relations between objects are discovered. A pervasively neural account of this process requires that fundamental problems are solved: the neural pointer problem, the binding problem, and the problem of generating discrete processing steps from time-continuous neural processes. We present a prototypical solution to these problems in a neural dynamic model that comprises dynamic neural fields holding representations close to sensorimotor surfaces as well as dynamic neural nodes holding discrete, language-like representations. Making the connection between these two types of representations enables the model to describe actions as well as to perceptually ground movement phrases-all based on real visual input. We demonstrate how the dynamic neural processes autonomously generate the processing steps required to describe or ground object-oriented actions. By solving the fundamental problems of neural pointing, binding, and emergent discrete processing, the model may be a first but critical step toward a systematic neural processing account of higher cognition. Copyright © 2017 The Authors. Topics in Cognitive Science published by Wiley Periodicals, Inc. on behalf of Cognitive Science Society.

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

NASA Astrophysics Data System (ADS)

Gong, Zongping; Hamazaki, Ryusuke; Ueda, Masahito

2018-01-01

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

PubMed Central

Elmeligy Abdelhamid, Sherif H.; Kuhlman, Chris J.; Marathe, Madhav V.; Mortveit, Henning S.; Ravi, S. S.

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools. PMID:26263006

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.

PubMed

Elmeligy Abdelhamid, Sherif H; Kuhlman, Chris J; Marathe, Madhav V; Mortveit, Henning S; Ravi, S S

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

Peridynamics with LAMMPS : a user guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.; Silling, Stewart Andrew; Seleson, Pablo

Peridynamics is a nonlocal extension of classical continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamics model. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized within LAMMPS. An example problem is also included.

Principles of Discrete Time Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2014-04-01

1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.

Dynamical systems model and discrete element simulations of a tapped granular column

NASA Astrophysics Data System (ADS)

Rosato, A. D.; Blackmore, D.; Tricoche, X. M.; Urban, K.; Zuo, L.

2013-06-01

We present an approximate dynamical systems model for the mass center trajectory of a tapped column of N uniform, inelastic, spheres (diameter d), in which collisional energy loss is governed by the Walton-Braun linear loading-unloading soft interaction. Rigorous analysis of the model, akin to the equations for the motion of a single bouncing ball on a vibrating plate, reveals a parameter γ≔2aω2(1+e)/g that gauges the dynamical regimes and their transitions. In particular, we find bifurcations from periodic to chaotic dynamics that depend on frequency ω, amplitude a/d of the tap. Dynamics predicted by the model are also qualitatively observed in discrete element simulations carried out over a broad range of the tap parameters.

A Decision Tool that Combines Discrete Event Software Process Models with System Dynamics Pieces for Software Development Cost Estimation and Analysis

NASA Technical Reports Server (NTRS)

Mizell, Carolyn Barrett; Malone, Linda

2007-01-01

The development process for a large software development project is very complex and dependent on many variables that are dynamic and interrelated. Factors such as size, productivity and defect injection rates will have substantial impact on the project in terms of cost and schedule. These factors can be affected by the intricacies of the process itself as well as human behavior because the process is very labor intensive. The complex nature of the development process can be investigated with software development process models that utilize discrete event simulation to analyze the effects of process changes. The organizational environment and its effects on the workforce can be analyzed with system dynamics that utilizes continuous simulation. Each has unique strengths and the benefits of both types can be exploited by combining a system dynamics model and a discrete event process model. This paper will demonstrate how the two types of models can be combined to investigate the impacts of human resource interactions on productivity and ultimately on cost and schedule.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Prediction of Flutter Boundary Using Flutter Margin for The Discrete-Time System

NASA Astrophysics Data System (ADS)

Dwi Saputra, Angga; Wibawa Purabaya, R.

2018-04-01

Flutter testing in a wind tunnel is generally conducted at subcritical speeds to avoid damages. Hence, The flutter speed has to be predicted from the behavior some of its stability criteria estimated against the dynamic pressure or flight speed. Therefore, it is quite important for a reliable flutter prediction method to estimates flutter boundary. This paper summarizes the flutter testing of a wing cantilever model in a wind tunnel. The model has two degree of freedom; they are bending and torsion modes. The flutter test was conducted in a subsonic wind tunnel. The dynamic data responses was measured by two accelerometers that were mounted on leading edge and center of wing tip. The measurement was repeated while the wind speed increased. The dynamic responses were used to determine the parameter flutter margin for the discrete-time system. The flutter boundary of the model was estimated using extrapolation of the parameter flutter margin against the dynamic pressure. The parameter flutter margin for the discrete-time system has a better performance for flutter prediction than the modal parameters. A model with two degree freedom and experiencing classical flutter, the parameter flutter margin for the discrete-time system gives a satisfying result in prediction of flutter boundary on subsonic wind tunnel test.

Local and global dynamics of Ramsey model: From continuous to discrete time.

PubMed

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Local and global dynamics of Ramsey model: From continuous to discrete time

NASA Astrophysics Data System (ADS)

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Quantization of systems with temporally varying discretization. II. Local evolution moves

NASA Astrophysics Data System (ADS)

Höhn, Philipp A.

2014-10-01

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, "Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces," J. Math. Phys. 55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc

Microstructural comparison of the kinematics of discrete and continuum dislocations models

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Po, Giacomo

2015-12-01

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.

Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters

NASA Astrophysics Data System (ADS)

Bischi, G. I.; Tramontana, F.

2010-10-01

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka-Volterra prey-predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka-Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka-Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.

Counting and classifying attractors in high dimensional dynamical systems.

PubMed

Bagley, R J; Glass, L

1996-12-07

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

PubMed

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

PubMed

Mendonça, J Ricardo G; Gevorgyan, Yeva

2017-05-01

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

Discrete Dynamical Modeling.

ERIC Educational Resources Information Center

Sandefur, James T.

1991-01-01

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Prediction of Vehicle Mobility on Large-Scale Soft-Soil Terrain Maps Using Physics-Based Simulation

DTIC Science & Technology

2016-08-04

soil type. The modeling approach is based on (i) a seamless integration of multibody dynamics and discrete element method (DEM) solvers, and (ii...ensure that the vehicle follows a desired path. The soil is modeled as a Discrete Element Model (DEM) with a general cohesive material model that is

From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity

NASA Astrophysics Data System (ADS)

Höhn, P. A.

2012-05-01

In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this thesis, the conundrum of (quantum) gravitational dynamics is approached from two different directions by means of new canonical tools. This thesis is accordingly divided into two parts: In the first part, a general canonical formalism for discrete systems featuring a variational action principle is developed which is equivalent to the covariant formulation following directly from the action. This formalism can handle evolving phase spaces and is thus appropriate for describing evolving lattices. Attention will be devoted to a characterization of the constraints, symmetries and degrees of freedom appearing in such discrete systems which, in the case of evolving phase spaces, is time step dependent. The advantage of this formalism is that it does not depend on the particular discretization and, hence, is suitable for coarse graining procedures. This formalism is applicable to discrete mechanics, lattice field theories and discrete gravity models---underlying some approaches to quantum gravity---and, furthermore, may prove useful for numerical imple mentations. For concreteness, these new tools are employed to formulate Regge Calculus canonically as a theory of the dynamics of discrete hypersurfaces in discrete spacetimes, thereby removing a longstanding obstacle to connecting covariant simplicial gravity models with canonical frameworks. This result is interesting in view of several background independent approaches to quantum gravity. In addition, perturbative expansions around symmetric background solutions of Regge Calculus are studied up to second order. Background gauge modes generically become propagating at second order as a consequence of a symmetry breaking. In the second part of this thesis, the paradigm of relational dynamics is considered. Dynamical observables in gravity are relational. Unfortunately, their construction and evaluation is notoriously difficult, especially in the quantum theory. An effective canonical framework is devised which permits to evaluate the semiclassical relational dynamics of constrained quantum systems by sidestepping technical problems associated with explicit constructions of physical Hilbert spaces. This effective approach is well-geared for addressing the concept of relational evolution in general quantum cosmological models since it (i) allows to depart from idealized relational `clock references’ and, instead, to employ generic degrees of freedom as imperfect relational `clocks’, (ii) enables one to systematically switch between different such `clocks’ and (iii) yields a consistent (temporally) local time evolution with transient observables so long as semiclassicality holds. These techniques are illustrated by toy models and, finally, are applied to a non-integrable cosmological model. It is argued that relational evolution is generically only a transient and semiclassical phenomenon

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

H∞ control of combustion in diesel engines using a discrete dynamics model

NASA Astrophysics Data System (ADS)

Hirata, Mitsuo; Ishizuki, Sota; Suzuki, Masayasu

2016-09-01

This paper proposes a control method for combustion in diesel engines using a discrete dynamics model. The proposed two-degree-of-freedom control scheme achieves not only good feedback properties such as disturbance suppression and robust stability but also a good transient response. The method includes a feedforward controller constructed from the inverse model of the plant, and a feedback controller designed by an Hcontrol method, which reduces the effect of the turbocharger lag. The effectiveness of the proposed method is evaluated via numerical simulations.

A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

NASA Astrophysics Data System (ADS)

Kim, Dae Ho; Kim, Jin Min

2012-09-01

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family-Vicsek dynamic scaling form with growth exponent β ≈ 0.0542, roughness exponent α ≈ 0.240 and dynamic exponent z ≈ 4.42. They satisfy a scaling relation α + z = 2zrw, where zrw is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation \\frac{\\partial h}{\\partial t}={\

Simulation of Healing Threshold in Strain-Induced Inflammation Through a Discrete Informatics Model.

PubMed

Ibrahim, Israr Bin M; Sarma O V, Sanjay; Pidaparti, Ramana M

2018-05-01

Respiratory diseases such as asthma and acute respiratory distress syndrome as well as acute lung injury involve inflammation at the cellular level. The inflammation process is very complex and is characterized by the emergence of cytokines along with other changes in cellular processes. Due to the complexity of the various constituents that makes up the inflammation dynamics, it is necessary to develop models that can complement experiments to fully understand inflammatory diseases. In this study, we developed a discrete informatics model based on cellular automata (CA) approach to investigate the influence of elastic field (stretch/strain) on the dynamics of inflammation and account for probabilistic adaptation based on statistical interpretation of existing experimental data. Our simulation model investigated the effects of low, medium, and high strain conditions on inflammation dynamics. Results suggest that the model is able to indicate the threshold of innate healing of tissue as a response to strain experienced by the tissue. When strain is under the threshold, the tissue is still capable of adapting its structure to heal the damaged part. However, there exists a strain threshold where healing capability breaks down. The results obtained demonstrate that the developed discrete informatics based CA model is capable of modeling and giving insights into inflammation dynamics parameters under various mechanical strain/stretch environments.

Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models

NASA Astrophysics Data System (ADS)

Steinhaus, Sebastian

2015-09-01

The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretization. However, extracting these mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories. Therefore, we introduce a simple two-dimensional toy model for Yang-Mills coupled to spin foams, namely an Ising model coupled to so-called intertwiner models defined for SU (2 )k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretization. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Partition-based discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo

2018-04-01

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

Cross-Paradigm Simulation Modeling: Challenges and Successes

DTIC Science & Technology

2011-12-01

is also highlighted. 2.1 Discrete-Event Simulation Discrete-event simulation ( DES ) is a modeling method for stochastic, dynamic models where...which almost anything can be coded; models can be incredibly detailed. Most commercial DES software has a graphical interface which allows the user to...results. Although the above definition is the commonly accepted definition of DES , there are two different worldviews that dominate DES modeling today: a

A discrete control model of PLANT

NASA Technical Reports Server (NTRS)

Mitchell, C. M.

1985-01-01

A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.

Evolution of specialization under non-equilibrium population dynamics.

PubMed

Nurmi, Tuomas; Parvinen, Kalle

2013-03-21

We analyze the evolution of specialization in resource utilization in a mechanistically underpinned discrete-time model using the adaptive dynamics approach. We assume two nutritionally equivalent resources that in the absence of consumers grow sigmoidally towards a resource-specific carrying capacity. The consumers use resources according to the law of mass-action with rates involving trade-off. The resulting discrete-time model for the consumer population has over-compensatory dynamics. We illuminate the way non-equilibrium population dynamics affect the evolutionary dynamics of the resource consumption rates, and show that evolution to the trimorphic coexistence of a generalist and two specialists is possible due to asynchronous non-equilibrium population dynamics of the specialists. In addition, various forms of cyclic evolutionary dynamics are possible. Furthermore, evolutionary suicide may occur even without Allee effects and demographic stochasticity. Copyright © 2013 Elsevier Ltd. All rights reserved.

Age or stage structure? A comparison of dynamic outcomes from discrete age- and stage-structured population models.

PubMed

Wikan, Arild

2012-06-01

Discrete stage-structured density-dependent and discrete age-structured density-dependent population models are considered. Regarding the former, we prove that the model at hand is permanent (i.e., that the population will neither go extinct nor exhibit explosive oscillations) and given density dependent fecundity terms we also show that species with delayed semelparous life histories tend to be more stable than species which possess precocious semelparous life histories. Moreover, our findings together with results obtained from other stage-structured models seem to illustrate a fairly general ecological principle, namely that iteroparous species are more stable than semelparous species. Our analysis of various age-structured models does not necessarily support the conclusions above. In fact, species with precocious life histories now appear to possess better stability properties than species with delayed life histories, especially in the iteroparous case. We also show that there are dynamical outcomes from semelparous age-structured models which we are not able to capture in corresponding stage-structured cases. Finally, both age- and stage-structured population models may generate periodic dynamics of low period (either exact or approximate). The important prerequisite is to assume density-dependent survival probabilities.

Discrete-state representation of ion permeation coupled to fast gating in a model of ClC chloride channels: comparison to multi-ion continuous space Brownian dynamics simulations.

PubMed

Coalson, Rob D; Cheng, Mary Hongying

2010-01-28

A discrete-state model of chloride ion motion in a ClC chloride channel is constructed, following a previously developed multi-ion continuous space model of the same system (Cheng, M. H.; Mamonov, A. B.; Dukes, J. W.; Coalson, R. D. J. Phys. Chem. B 2007, 111, 5956) that included a simplistic representation of the fast gate in this channel. The reducibility of the many-body continuous space to the eight discrete-state model considered in the present work is examined in detail by performing three-dimensional Brownian dynamics simulations of each allowed state-to-state transition in order to extract the appropriate rate constant for this process, and then inserting the pairwise rate constants thereby obtained into an appropriate set of kinetic master equations. Experimental properties of interest, including the rate of Cl(-) ion permeation through the open channel and the average rate of closing of the fast gate as a function of bulk Cl(-) ion concentrations in the intracellular and extracellular electrolyte reservoirs are computed. Good agreement is found between the results obtained via the eight discrete-state model versus the multi-ion continuous space model, thereby encouraging continued development of the discrete-state model to include more complex behaviors observed experimentally in these channels.

Effective Hamiltonian for travelling discrete breathers

NASA Astrophysics Data System (ADS)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Polynomial algebra of discrete models in systems biology.

PubMed

Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2010-07-01

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces

NASA Astrophysics Data System (ADS)

Tal, Yuval; Hager, Bradford H.

2017-09-01

This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal-dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate.

Variational Algorithms for Test Particle Trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. Leland; Finn, John M.; Qin, Hong; Tang, William M.

2015-11-01

The theory of variational integration provides a novel framework for constructing conservative numerical methods for magnetized test particle dynamics. The retention of conservation laws in the numerical time advance captures the correct qualitative behavior of the long time dynamics. For modeling the Lorentz force system, new variational integrators have been developed that are both symplectic and electromagnetically gauge invariant. For guiding center test particle dynamics, discretization of the phase-space action principle yields multistep variational algorithms, in general. Obtaining the desired long-term numerical fidelity requires mitigation of the multistep method's parasitic modes or applying a discretization scheme that possesses a discrete degeneracy to yield a one-step method. Dissipative effects may be modeled using Lagrange-D'Alembert variational principles. Numerical results will be presented using a new numerical platform that interfaces with popular equilibrium codes and utilizes parallel hardware to achieve reduced times to solution. This work was supported by DOE Contract DE-AC02-09CH11466.

The discrete-time compensated Kalman filter

NASA Technical Reports Server (NTRS)

Lee, W. H.; Athans, M.

1978-01-01

A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.

Dynamics of embryonic stem cell differentiation inferred from single-cell transcriptomics show a series of transitions through discrete cell states

PubMed Central

Jang, Sumin; Choubey, Sandeep; Furchtgott, Leon; Zou, Ling-Nan; Doyle, Adele; Menon, Vilas; Loew, Ethan B; Krostag, Anne-Rachel; Martinez, Refugio A; Madisen, Linda; Levi, Boaz P; Ramanathan, Sharad

2017-01-01

The complexity of gene regulatory networks that lead multipotent cells to acquire different cell fates makes a quantitative understanding of differentiation challenging. Using a statistical framework to analyze single-cell transcriptomics data, we infer the gene expression dynamics of early mouse embryonic stem (mES) cell differentiation, uncovering discrete transitions across nine cell states. We validate the predicted transitions across discrete states using flow cytometry. Moreover, using live-cell microscopy, we show that individual cells undergo abrupt transitions from a naïve to primed pluripotent state. Using the inferred discrete cell states to build a probabilistic model for the underlying gene regulatory network, we further predict and experimentally verify that these states have unique response to perturbations, thus defining them functionally. Our study provides a framework to infer the dynamics of differentiation from single cell transcriptomics data and to build predictive models of the gene regulatory networks that drive the sequence of cell fate decisions during development. DOI: http://dx.doi.org/10.7554/eLife.20487.001 PMID:28296635

Single-crossover recombination in discrete time.

PubMed

von Wangenheim, Ute; Baake, Ellen; Baake, Michael

2010-05-01

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.

Dynamic thermal-time model of cold hardiness for dormant grapevine buds

USDA-ARS?s Scientific Manuscript database

Grapevine (Vitis spp.) cold hardiness varies dynamically throughout the dormant season, primarily in response to changes in temperature. We describe development and possible uses of a discrete-dynamic model of bud cold hardiness for three Vitis genotypes. Iterative methods were used to optimize and ...

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Equation-free and variable free modeling for complex/multiscale systems. Coarse-grained computation in science and engineering using fine-grained models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kevrekidis, Ioannis G.

The work explored the linking of modern developing machine learning techniques (manifold learning and in particular diffusion maps) with traditional PDE modeling/discretization/scientific computation techniques via the equation-free methodology developed by the PI. The result (in addition to several PhD degrees, two of them by CSGF Fellows) was a sequence of strong developments - in part on the algorithmic side, linking data mining with scientific computing, and in part on applications, ranging from PDE discretizations to molecular dynamics and complex network dynamics.

Modeling and Control of the Cobelli Model as a Personalized Prescriptive Tool for Diabetes Treatment

DTIC Science & Technology

2016-11-05

within the body allow for a more quantified approach in medicine prescription as well as a deeper understanding of the discrete operations of...dynamics within the body allow for a more quantified approach in medicine prescription as well as a deeper understanding of the discrete operations of... discrete value) of the desired output (healthy blood glucose concentration in this project), yi is the ith sample of the measured output, ui is

2D discontinuous piecewise linear map: Emergence of fashion cycles.

PubMed

Gardini, L; Sushko, I; Matsuyama, K

2018-05-01

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Simulation Model for Scenario Optimization of the Ready-Mix Concrete Delivery Problem

NASA Astrophysics Data System (ADS)

Galić, Mario; Kraus, Ivan

2016-12-01

This paper introduces a discrete simulation model for solving routing and network material flow problems in construction projects. Before the description of the model a detailed literature review is provided. The model is verified using a case study of solving the ready-mix concrete network flow and routing problem in metropolitan area in Croatia. Within this study real-time input parameters were taken into account. Simulation model is structured in Enterprise Dynamics simulation software and Microsoft Excel linked with Google Maps. The model is dynamic, easily managed and adjustable, but also provides good estimation for minimization of costs and realization time in solving discrete routing and material network flow problems.

Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong

2018-02-01

To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu-Eckhaus equation is derived from the reduction in an extended Ablowitz-Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu-Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.

Optimal region of latching activity in an adaptive Potts model for networks of neurons

NASA Astrophysics Data System (ADS)

Abdollah-nia, Mohammad-Farshad; Saeedghalati, Mohammadkarim; Abbassian, Abdolhossein

2012-02-01

In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A spontaneous behavior of hopping from one discrete attractor state to another (referred to as latching) has been proposed to be associated with higher cognitive functions. Here we propose a model in which both the stochastic dynamics of Potts models and an adaptive potential function are present. A latching dynamics is observed in a limited region of the noise(temperature)-adaptation parameter space. We hence suggest noise as a fundamental factor in such alternations alongside adaptation. From a dynamical systems point of view, the noise-adaptation alternations may be the underlying mechanism for multi-stability in attractor-based models. An optimality criterion for realistic models is finally inferred.

Modeling and control of operator functional state in a unified framework of fuzzy inference petri nets.

PubMed

Zhang, Jian-Hua; Xia, Jia-Jun; Garibaldi, Jonathan M; Groumpos, Petros P; Wang, Ru-Bin

2017-06-01

In human-machine (HM) hybrid control systems, human operator and machine cooperate to achieve the control objectives. To enhance the overall HM system performance, the discrete manual control task-load by the operator must be dynamically allocated in accordance with continuous-time fluctuation of psychophysiological functional status of the operator, so-called operator functional state (OFS). The behavior of the HM system is hybrid in nature due to the co-existence of discrete task-load (control) variable and continuous operator performance (system output) variable. Petri net is an effective tool for modeling discrete event systems, but for hybrid system involving discrete dynamics, generally Petri net model has to be extended. Instead of using different tools to represent continuous and discrete components of a hybrid system, this paper proposed a method of fuzzy inference Petri nets (FIPN) to represent the HM hybrid system comprising a Mamdani-type fuzzy model of OFS and a logical switching controller in a unified framework, in which the task-load level is dynamically reallocated between the operator and machine based on the model-predicted OFS. Furthermore, this paper used a multi-model approach to predict the operator performance based on three electroencephalographic (EEG) input variables (features) via the Wang-Mendel (WM) fuzzy modeling method. The membership function parameters of fuzzy OFS model for each experimental participant were optimized using artificial bee colony (ABC) evolutionary algorithm. Three performance indices, RMSE, MRE, and EPR, were computed to evaluate the overall modeling accuracy. Experiment data from six participants are analyzed. The results show that the proposed method (FIPN with adaptive task allocation) yields lower breakdown rate (from 14.8% to 3.27%) and higher human performance (from 90.30% to 91.99%). The simulation results of the FIPN-based adaptive HM (AHM) system on six experimental participants demonstrate that the FIPN framework provides an effective way to model and regulate/optimize the OFS in HM hybrid systems composed of continuous-time OFS model and discrete-event switching controller. Copyright © 2017 Elsevier B.V. All rights reserved.

GPU accelerated Discrete Element Method (DEM) molecular dynamics for conservative, faceted particle simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spellings, Matthew; Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109; Marson, Ryan L.

Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method ismore » a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.« less

Qualitative analysis of a discrete thermostatted kinetic framework modeling complex adaptive systems

NASA Astrophysics Data System (ADS)

Bianca, Carlo; Mogno, Caterina

2018-01-01

This paper deals with the derivation of a new discrete thermostatted kinetic framework for the modeling of complex adaptive systems subjected to external force fields (nonequilibrium system). Specifically, in order to model nonequilibrium stationary states of the system, the external force field is coupled to a dissipative term (thermostat). The well-posedness of the related Cauchy problem is investigated thus allowing the new discrete thermostatted framework to be suitable for the derivation of specific models and the related computational analysis. Applications to crowd dynamics and future research directions are also discussed within the paper.

Study on a discrete-time dynamic control model to enhance nitrogen removal with fluctuation of influent in oxidation ditches.

PubMed

Liu, Yanchen; Shi, Hanchang; Shi, Huiming; Wang, Zhiqiang

2010-10-01

The aim of study was proposed a new control model feasible on-line implemented by Programmable Logic Controller (PLC) to enhance nitrogen removal against the fluctuation of influent in Carrousel oxidation ditch. The discrete-time control model was established by confirmation model of operational conditions based on a expert access, which was obtained by a simulation using Activated Sludge Model 2-D (ASM2-D) and Computation Fluid Dynamics (CFD), and discrete-time control model to switch between different operational stages. A full-scale example is provided to demonstrate the feasibility of the proposed operation and the procedure of the control design. The effluent quality was substantially improved, to the extent that it met the new wastewater discharge standards of NH(3)-N<5mg/L and TN<15 mg/L enacted in China throughout a one-day period with fluctuation of influent. Copyright © 2010 Elsevier Ltd. All rights reserved.

Dynamic Models of Insurgent Activity

DTIC Science & Technology

2014-05-19

Martin Short, P. Jeffrey Brantingham, Frederick Schoenberg, George Tita . Self-Exciting Point Process Modeling of Crime, Journal of the American...Mohler, P. J. Brantingham, G. E. Tita . Gang rivalry dynamics via coupled point process networks, Discrete and Continuous Dynamical Systems - Series...8532-2-1 Laura Smith, Andrea Bertozzi, P. Jeffrey Brantingham, George Tita , Matthew Valasik. ADAPTATION OF AN ECOLOGICAL TERRITORIAL MODEL TOSTREET

A large-signal dynamic simulation for the series resonant converter

NASA Technical Reports Server (NTRS)

King, R. J.; Stuart, T. A.

1983-01-01

A simple nonlinear discrete-time dynamic model for the series resonant dc-dc converter is derived using approximations appropriate to most power converters. This model is useful for the dynamic simulation of a series resonant converter using only a desktop calculator. The model is compared with a laboratory converter for a large transient event.

Experiments of reconstructing discrete atmospheric dynamic models from data (I)

NASA Astrophysics Data System (ADS)

Lin, Zhenshan; Zhu, Yanyu; Deng, Ziwang

1995-03-01

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, x n + 1 = 1- μx {2/n}, could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

A hierarchical dislocation-grain boundary interaction model based on 3D discrete dislocation dynamics and molecular dynamics

NASA Astrophysics Data System (ADS)

Gao, Yuan; Zhuang, Zhuo; You, XiaoChuan

2011-04-01

We develop a new hierarchical dislocation-grain boundary (GB) interaction model to predict the mechanical behavior of polycrystalline metals at micro and submicro scales by coupling 3D Discrete Dislocation Dynamics (DDD) simulation with the Molecular Dynamics (MD) simulation. At the microscales, the DDD simulations are responsible for capturing the evolution of dislocation structures; at the nanoscales, the MD simulations are responsible for obtaining the GB energy and ISF energy which are then transferred hierarchically to the DDD level. In the present model, four kinds of dislocation-GB interactions, i.e. transmission, absorption, re-emission and reflection, are all considered. By this methodology, the compression of a Cu micro-sized bi-crystal pillar is studied. We investigate the characteristic mechanical behavior of the bi-crystal compared with that of the single-crystal. Moreover, the comparison between the present penetrable model of GB and the conventional impenetrable model also shows the accuracy and efficiency of the present model.

An extension of the OpenModelica compiler for using Modelica models in a discrete event simulation

DOE PAGES

Nutaro, James

2014-11-03

In this article, a new back-end and run-time system is described for the OpenModelica compiler. This new back-end transforms a Modelica model into a module for the adevs discrete event simulation package, thereby extending adevs to encompass complex, hybrid dynamical systems. The new run-time system that has been built within the adevs simulation package supports models with state-events and time-events and that comprise differential-algebraic systems with high index. Finally, although the procedure for effecting this transformation is based on adevs and the Discrete Event System Specification, it can be adapted to any discrete event simulation package.

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops

NASA Astrophysics Data System (ADS)

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops.

PubMed

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

An opinion-driven behavioral dynamics model for addictive behaviors

NASA Astrophysics Data System (ADS)

Moore, Thomas W.; Finley, Patrick D.; Apelberg, Benjamin J.; Ambrose, Bridget K.; Brodsky, Nancy S.; Brown, Theresa J.; Husten, Corinne; Glass, Robert J.

2015-04-01

We present a model of behavioral dynamics that combines a social network-based opinion dynamics model with behavioral mapping. The behavioral component is discrete and history-dependent to represent situations in which an individual's behavior is initially driven by opinion and later constrained by physiological or psychological conditions that serve to maintain the behavior. Individuals are modeled as nodes in a social network connected by directed edges. Parameter sweeps illustrate model behavior and the effects of individual parameters and parameter interactions on model results. Mapping a continuous opinion variable into a discrete behavioral space induces clustering on directed networks. Clusters provide targets of opportunity for influencing the network state; however, the smaller the network the greater the stochasticity and potential variability in outcomes. This has implications both for behaviors that are influenced by close relationships verses those influenced by societal norms and for the effectiveness of strategies for influencing those behaviors.

Optimal Estimation with Two Process Models and No Measurements

DTIC Science & Technology

2015-08-01

models will be lost if either of the models includes deterministic modeling errors. 12 5. References and Notes 1. Brown RG, Hwang PYC. Introduction to...independent process models when no measurements are present. The observer follows a derivation similar to that of the discrete time Kalman filter. A simulation...discrete time Kalman filter. A simulation example is provided in which a process model based on the dynamics of a ballistic projectile is blended with an

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue.

PubMed

Saleem, M; Agrawal, Tanuja; Anees, Afzal

2014-01-01

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K (+))-limited environment. Our both continuous and discrete models illustrate 'cancer immunoediting' as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202-206].

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue

PubMed Central

Saleem, M.; Agrawal, Tanuja; Anees, Afzal

2014-01-01

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K +)-limited environment. Our both continuous and discrete models illustrate ‘cancer immunoediting’ as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202–206]. PMID:24963981

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann

2003-01-01

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Discrete model of the olivo-cerebellar system: structure and dynamics

NASA Astrophysics Data System (ADS)

Maslennikov, O. V.; Nekorkin, V. I.

2012-08-01

We propose a discrete model of the olivo-cerebellar system. The model consists of three layers of interacting elements, namely, inferior olive neurons, Purkinje cells, and deep cerebellar nuclear neurons combined into a structure by axonal connections. Each element of the structure is described by a two-dimensional map with an individual set of parameters for each type of neurons. Dynamic properties of different types of neurons are described and spontaneous and stimulusinduced dynamics of the system is explored. Unlike the previously proposed models, this study takes into account the axonal interaction of neurons of different layers, as well as the interaction of the inferior olive neurons through electrical synapses with the property of plasticity. It is shown that the inclusion of these factors plays a significant role in the formation of spatio-temporal activity of the inferior olive neurons.

Solutions of burnt-bridge models for molecular motor transport.

PubMed

Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B; Artyomov, Maxim N

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called "bridges"), is investigated theoretically by analyzing discrete-state stochastic "burnt-bridge" models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed ("burned") with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander; Pronina, Ekaterina; Kolomeisky, Anatoly; Artyomov, Maxim

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability p, creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of p<1 a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Solutions of burnt-bridge models for molecular motor transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander Yu.; Pronina, Ekaterina; Kolomeisky, Anatoly B.; Artyomov, Maxim N.

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called “bridges”), is investigated theoretically by analyzing discrete-state stochastic “burnt-bridge” models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (“burned”) with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ng, B

This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.

DEVS representation of dynamical systems - Event-based intelligent control. [Discrete Event System Specification

NASA Technical Reports Server (NTRS)

Zeigler, Bernard P.

1989-01-01

It is shown how systems can be advantageously represented as discrete-event models by using DEVS (discrete-event system specification), a set-theoretic formalism. Such DEVS models provide a basis for the design of event-based logic control. In this control paradigm, the controller expects to receive confirming sensor responses to its control commands within definite time windows determined by its DEVS model of the system under control. The event-based contral paradigm is applied in advanced robotic and intelligent automation, showing how classical process control can be readily interfaced with rule-based symbolic reasoning systems.

Transfer of dipolar gas through the discrete localized mode.

PubMed

Bai, Xiao-Dong; Zhang, Ai-Xia; Xue, Ju-Kui

2013-12-01

By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates.

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

PubMed

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

Modeling the spatially dynamic distribution of humans in the Oregon (USA) coast range.

Treesearch

Jeffrey D. Kline; David L. Azuma; Alissa Moses

2003-01-01

A common approach to land use change analyses in multidisciplinary landscape-level studies is to delineate discrete forest and non-forest or urban and non-urban land use categories to serve as inputs into sets of integrated sub-models describing socioeconomic and ecological processes. Such discrete land use categories, however, may be inappropriate when the...

Parallel Discrete Molecular Dynamics Simulation With Speculation and In-Order Commitment*†

PubMed Central

Khan, Md. Ashfaquzzaman; Herbordt, Martin C.

2011-01-01

Discrete molecular dynamics simulation (DMD) uses simplified and discretized models enabling simulations to advance by event rather than by timestep. DMD is an instance of discrete event simulation and so is difficult to scale: even in this multi-core era, all reported DMD codes are serial. In this paper we discuss the inherent difficulties of scaling DMD and present our method of parallelizing DMD through event-based decomposition. Our method is microarchitecture inspired: speculative processing of events exposes parallelism, while in-order commitment ensures correctness. We analyze the potential of this parallelization method for shared-memory multiprocessors. Achieving scalability required extensive experimentation with scheduling and synchronization methods to mitigate serialization. The speed-up achieved for a variety of system sizes and complexities is nearly 6× on an 8-core and over 9× on a 12-core processor. We present and verify analytical models that account for the achieved performance as a function of available concurrency and architectural limitations. PMID:21822327

Parallel Discrete Molecular Dynamics Simulation With Speculation and In-Order Commitment.

PubMed

Khan, Md Ashfaquzzaman; Herbordt, Martin C

2011-07-20

Discrete molecular dynamics simulation (DMD) uses simplified and discretized models enabling simulations to advance by event rather than by timestep. DMD is an instance of discrete event simulation and so is difficult to scale: even in this multi-core era, all reported DMD codes are serial. In this paper we discuss the inherent difficulties of scaling DMD and present our method of parallelizing DMD through event-based decomposition. Our method is microarchitecture inspired: speculative processing of events exposes parallelism, while in-order commitment ensures correctness. We analyze the potential of this parallelization method for shared-memory multiprocessors. Achieving scalability required extensive experimentation with scheduling and synchronization methods to mitigate serialization. The speed-up achieved for a variety of system sizes and complexities is nearly 6× on an 8-core and over 9× on a 12-core processor. We present and verify analytical models that account for the achieved performance as a function of available concurrency and architectural limitations.

Nonlinear wave propagation in discrete and continuous systems

NASA Astrophysics Data System (ADS)

Rothos, V. M.

2016-09-01

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

Using Innovative Outliers to Detect Discrete Shifts in Dynamics in Group-Based State-Space Models

ERIC Educational Resources Information Center

Chow, Sy-Miin; Hamaker, Ellen L.; Allaire, Jason C.

2009-01-01

Outliers are typically regarded as data anomalies that should be discarded. However, dynamic or "innovative" outliers can be appropriately utilized to capture unusual but substantively meaningful shifts in a system's dynamics. We extend De Jong and Penzer's 1998 approach for representing outliers in single-subject state-space models to a…

Relating coupled map lattices to integro-difference equations: dispersal-driven instabilities in coupled map lattices.

PubMed

White, Steven M; White, K A Jane

2005-08-21

Recently there has been a great deal of interest within the ecological community about the interactions of local populations that are coupled only by dispersal. Models have been developed to consider such scenarios but the theory needed to validate model outcomes has been somewhat lacking. In this paper, we present theory which can be used to understand these types of interaction when population exhibit discrete time dynamics. In particular, we consider a spatial extension to discrete-time models, known as coupled map lattices (CMLs) which are discrete in space. We introduce a general form of the CML and link this to integro-difference equations via a special redistribution kernel. General conditions are then derived for dispersal-driven instabilities. We then apply this theory to two discrete-time models; a predator-prey model and a host-pathogen model.

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia.

PubMed

Gaudiano, Marcos E; Lenaerts, Tom; Pacheco, Jorge M

2016-12-01

Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can - on average - easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system. Copyright © 2016 Elsevier Inc. All rights reserved.

Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yu, Liping

2016-12-01

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

NASA Astrophysics Data System (ADS)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Modelling heat transfer during flow through a random packed bed of spheres

NASA Astrophysics Data System (ADS)

Burström, Per E. C.; Frishfelds, Vilnis; Ljung, Anna-Lena; Lundström, T. Staffan; Marjavaara, B. Daniel

2018-04-01

Heat transfer in a random packed bed of monosized iron ore pellets is modelled with both a discrete three-dimensional system of spheres and a continuous Computational Fluid Dynamics (CFD) model. Results show a good agreement between the two models for average values over a cross section of the bed for an even temperature profiles at the inlet. The advantage with the discrete model is that it captures local effects such as decreased heat transfer in sections with low speed. The disadvantage is that it is computationally heavy for larger systems of pellets. If averaged values are sufficient, the CFD model is an attractive alternative that is easy to couple to the physics up- and downstream the packed bed. The good agreement between the discrete and continuous model furthermore indicates that the discrete model may be used also on non-Stokian flow in the transitional region between laminar and turbulent flow, as turbulent effects show little influence of the overall heat transfer rates in the continuous model.

An opinion-driven behavioral dynamics model for addictive behaviors

DOE PAGES

Moore, Thomas W.; Finley, Patrick D.; Apelberg, Benjamin J.; ...

2015-04-08

We present a model of behavioral dynamics that combines a social network-based opinion dynamics model with behavioral mapping. The behavioral component is discrete and history-dependent to represent situations in which an individual’s behavior is initially driven by opinion and later constrained by physiological or psychological conditions that serve to maintain the behavior. Additionally, individuals are modeled as nodes in a social network connected by directed edges. Parameter sweeps illustrate model behavior and the effects of individual parameters and parameter interactions on model results. Mapping a continuous opinion variable into a discrete behavioral space induces clustering on directed networks. Clusters providemore » targets of opportunity for influencing the network state; however, the smaller the network the greater the stochasticity and potential variability in outcomes. Furthermore, this has implications both for behaviors that are influenced by close relationships verses those influenced by societal norms and for the effectiveness of strategies for influencing those behaviors.« less

THYME: Toolkit for Hybrid Modeling of Electric Power Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutaro Kalyan Perumalla, James Joseph

2011-01-01

THYME is an object oriented library for building models of wide area control and communications in electric power systems. This software is designed as a module to be used with existing open source simulators for discrete event systems in general and communication systems in particular. THYME consists of a typical model for simulating electro-mechanical transients (e.g., as are used in dynamic stability studies), data handling objects to work with CDF and PTI formatted power flow data, and sample models of discrete sensors and controllers.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

Parameter redundancy in discrete state-space and integrated models.

PubMed

Cole, Diana J; McCrea, Rachel S

2016-09-01

Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant. © 2016 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Gap discrete breathers in strained boron nitride

NASA Astrophysics Data System (ADS)

Barani, Elham; Korznikova, Elena A.; Chetverikov, Alexander P.; Zhou, Kun; Dmitriev, Sergey V.

2017-11-01

Linear and nonlinear dynamics of hexagonal boron nitride (h-BN) lattice is studied by means of molecular dynamics simulations with the use of the Tersoff interatomic potentials. It is found that sufficiently large homogeneous elastic strain along zigzag direction opens a wide gap in the phonon spectrum. Extended vibrational mode with boron and nitrogen sublattices vibrating in-plane as a whole in strained h-BN has frequency within the phonon gap. This fact suggests that a nonlinear spatially localized vibrational mode with frequencies in the phonon gap, called discrete breather (also often termed as intrinsic localized mode), can be excited. Properties of the gap discrete breathers in strained h-BN are contrasted with that for analogous vibrational mode found earlier in strained graphene. It is found that h-BN modeled with the Tersoff potentials does not support transverse discrete breathers.

Modeling discrete and rhythmic movements through motor primitives: a review.

PubMed

Degallier, Sarah; Ijspeert, Auke

2010-10-01

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

The effects of host-feeding on stability of discrete-time host-parasitoid population dynamic models.

PubMed

Emerick, Brooks; Singh, Abhyudai

2016-02-01

Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect host-parasitoid population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact, allowing specific behaviors to be mechanistically incorporated. We use the semi-discrete approach to study the effects of host-feeding, which occurs when a parasitoid consumes a potential host larva without ovipositing. We find that host-feeding by itself cannot stabilize the system, and both populations exhibit behavior similar to the Nicholson-Bailey model. However, when combined with stabilizing mechanisms such as density-dependent host mortality, host-feeding contracts the region of parameter space that allows for a stable host-parasitoid equilibrium. In contrast, when combined with a density-dependent parasitoid attack rate, host-feeding expands the non-zero equilibrium stability region. Our results show that host-feeding causes inefficiency in the parasitoid population, which yields a higher population of hosts per generation. This suggests that host-feeding may have limited long-term impact in terms of suppressing host levels for biological control applications. Copyright © 2015 Elsevier Inc. All rights reserved.

State-and-transition simulation models: a framework for forecasting landscape change

USGS Publications Warehouse

Daniel, Colin; Frid, Leonardo; Sleeter, Benjamin M.; Fortin, Marie-Josée

2016-01-01

SummaryA wide range of spatially explicit simulation models have been developed to forecast landscape dynamics, including models for projecting changes in both vegetation and land use. While these models have generally been developed as separate applications, each with a separate purpose and audience, they share many common features.We present a general framework, called a state-and-transition simulation model (STSM), which captures a number of these common features, accompanied by a software product, called ST-Sim, to build and run such models. The STSM method divides a landscape into a set of discrete spatial units and simulates the discrete state of each cell forward as a discrete-time-inhomogeneous stochastic process. The method differs from a spatially interacting Markov chain in several important ways, including the ability to add discrete counters such as age and time-since-transition as state variables, to specify one-step transition rates as either probabilities or target areas, and to represent multiple types of transitions between pairs of states.We demonstrate the STSM method using a model of land-use/land-cover (LULC) change for the state of Hawai'i, USA. Processes represented in this example include expansion/contraction of agricultural lands, urbanization, wildfire, shrub encroachment into grassland and harvest of tree plantations; the model also projects shifts in moisture zones due to climate change. Key model output includes projections of the future spatial and temporal distribution of LULC classes and moisture zones across the landscape over the next 50 years.State-and-transition simulation models can be applied to a wide range of landscapes, including questions of both land-use change and vegetation dynamics. Because the method is inherently stochastic, it is well suited for characterizing uncertainty in model projections. When combined with the ST-Sim software, STSMs offer a simple yet powerful means for developing a wide range of models of landscape dynamics.

Basal friction evolution and crevasse distribution during the surge of Basin 3, Austfonna ice-cap - offline coupling between a continuum ice dynamic model and a discrete element model

NASA Astrophysics Data System (ADS)

Gong, Yongmei; Zwinger, Thomas; Åström, Jan; Gladstone, Rupert; Schellenberger, Thomas; Altena, Bas; Moore, John

2017-04-01

The outlet glacier at Basin 3, Austfonna ice-cap entered its active surge phase in autumn 2012. We assess the evolution of the basal friction during the surge through inverse modelling of basal friction coefficients using recent velocity observation from 2012 to 2014 in a continuum ice dynamic model Elmer/ice. The obtained basal friction coefficient distributions at different time instances are further used as a boundary condition in a discrete element model (HiDEM) that is capable of computing fracturing of ice. The inverted basal friction coefficient evolution shows a gradual 'unplugging' of the stagnant frontal area and northwards and inland expansion of the fast flowing region in the southern basin. The validation between the modeled crevasses distribution and the satellite observation in August 2013 shows a good agreement in shear zones inland and at the frontal area. Crevasse distributions of the summer before and after the glacier reached its maximum velocity in January 2013 (August 2012 and August 2014, respectively) are also evaluated. Previous studies suggest the triggering and development of the surge are linked to surface melt water penetrating through ice to form an efficient basal hydrology system thereby triggering a hydro- thermodynamic feedback. This preliminary offline coupling between a continuum ice dynamic model and a discrete element model will give a hint on future model development of linking supra-glacial to sub-glacial hydrology system.

Discretization of the total magnetic field by the nuclear spin bath in fluorine-doped ZnSe.

PubMed

Zhukov, E A; Kirstein, E; Kopteva, N E; Heisterkamp, F; Yugova, I A; Korenev, V L; Yakovlev, D R; Pawlis, A; Bayer, M; Greilich, A

2018-05-16

The coherent spin dynamics of fluorine donor-bound electrons in ZnSe induced by pulsed optical excitation is studied in a perpendicular applied magnetic field. The Larmor precession frequency serves as a measure for the total magnetic field exerted onto the electron spins and, surprisingly, does not increase linearly with the applied field, but shows a step-like behavior with pronounced plateaus, given by multiples of the laser repetition rate. This discretization occurs by a feedback mechanism in which the electron spins polarize the nuclear spins, which in turn generate a local Overhauser field adjusting the total magnetic field accordingly. Varying the optical excitation power, we can control the plateaus, in agreement with our theoretical model. From this model, we trace the observed discretization to the optically induced Stark field, which causes the dynamic nuclear polarization.

A hybrid-system model of the coagulation cascade: simulation, sensitivity, and validation.

PubMed

Makin, Joseph G; Narayanan, Srini

2013-10-01

The process of human blood clotting involves a complex interaction of continuous-time/continuous-state processes and discrete-event/discrete-state phenomena, where the former comprise the various chemical rate equations and the latter comprise both threshold-limited behaviors and binary states (presence/absence of a chemical). Whereas previous blood-clotting models used only continuous dynamics and perforce addressed only portions of the coagulation cascade, we capture both continuous and discrete aspects by modeling it as a hybrid dynamical system. The model was implemented as a hybrid Petri net, a graphical modeling language that extends ordinary Petri nets to cover continuous quantities and continuous-time flows. The primary focus is simulation: (1) fidelity to the clinical data in terms of clotting-factor concentrations and elapsed time; (2) reproduction of known clotting pathologies; and (3) fine-grained predictions which may be used to refine clinical understanding of blood clotting. Next we examine sensitivity to rate-constant perturbation. Finally, we propose a method for titrating between reliance on the model and on prior clinical knowledge. For simplicity, we confine these last two analyses to a critical purely-continuous subsystem of the model.

Plane stress problems using hysteretic rigid body spring network models

NASA Astrophysics Data System (ADS)

Christos, Sofianos D.; Vlasis, Koumousis K.

2017-10-01

In this work, a discrete numerical scheme is presented capable of modeling the hysteretic behavior of 2D structures. Rigid Body Spring Network (RBSN) models that were first proposed by Kawai (Nucl Eng Des 48(1):29-207, 1978) are extended to account for hysteretic elastoplastic behavior. Discretization is based on Voronoi tessellation, as proposed specifically for RBSN models to ensure uniformity. As a result, the structure is discretized into convex polygons that form the discrete rigid bodies of the model. These are connected with three zero length, i.e., single-node springs in the middle of their common facets. The springs follow the smooth hysteretic Bouc-Wen model which efficiently incorporates classical plasticity with no direct reference to a yield surface. Numerical results for both static and dynamic loadings are presented, which validate the proposed simplified spring-mass formulation. In addition, they verify the model's applicability on determining primarily the displacement field and plastic zones compared to the standard elastoplastic finite element method.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

PubMed

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

The dynamics and control of large flexible space structures. Part A: Discrete model and modal control

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Sellappan, R.

1978-01-01

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.

The discrete dynamics of symmetric competition in the plane.

PubMed

Jiang, H; Rogers, T D

1987-01-01

We consider the generalized Lotka-Volterra two-species system xn + 1 = xn exp(r1(1 - xn) - s1yn) yn + 1 = yn exp(r2(1 - yn) - s2xn) originally proposed by R. M. May as a model for competitive interaction. In the symmetric case that r1 = r2 and s1 = s2, a region of ultimate confinement is found and the dynamics therein are described in some detail. The bifurcations of periodic points of low period are studied, and a cascade of period-doubling bifurcations is indicated. Within the confinement region, a parameter region is determined for the stable Hopf bifurcation of a pair of symmetrically placed period-two points, which imposes a second component of oscillation near the stable cycles. It is suggested that the symmetric competitive model contains much of the dynamical complexity to be expected in any discrete two-dimensional competitive model.

Dynamic Response-by-Response Models of Matching Behavior in Rhesus Monkeys

ERIC Educational Resources Information Center

Lau, Brian; Glimcher, Paul W.

2005-01-01

We studied the choice behavior of 2 monkeys in a discrete-trial task with reinforcement contingencies similar to those Herrnstein (1961) used when he described the matching law. In each session, the monkeys experienced blocks of discrete trials at different relative-reinforcer frequencies or magnitudes with unsignalled transitions between the…

Coupled dynamics of a viscoelastically supported infinite string and a number of discrete mechanical systems moving with uniform speed

NASA Astrophysics Data System (ADS)

Roy, Soumyajit; Chakraborty, G.; DasGupta, Anirvan

2018-02-01

The mutual interaction between a number of multi degrees of freedom mechanical systems moving with uniform speed along an infinite taut string supported by a viscoelastic layer has been studied using the substructure synthesis method when base excitations of a common frequency are given to the mechanical systems. The mobility or impedance matrices of the string have been calculated analytically by Fourier transform method as well as wave propagation technique. The above matrices are used to calculate the response of the discrete mechanical systems. Special attention is paid to the contact forces between the discrete and the continuous systems which are estimated by numerical simulation. The effects of phase difference, the distance between the systems and different base excitation amplitudes on the collective behaviour of the mechanical systems are also studied. The present study has relevance to the coupled dynamic problem of more than one railway pantographs and an overhead catenary system where the pantographs are modelled as discrete systems and the catenary is modelled as a taut string supported by continuous viscoelastic layer.

Exploring high dimensional data with Butterfly: a novel classification algorithm based on discrete dynamical systems.

PubMed

Geraci, Joseph; Dharsee, Moyez; Nuin, Paulo; Haslehurst, Alexandria; Koti, Madhuri; Feilotter, Harriet E; Evans, Ken

2014-03-01

We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer dataset that comes along with the included Butterfly R package. In the included R script, a univariate feature selection method is used for the dimension reduction step, but in the future we wish to use a more powerful multivariate feature reduction method based on neural networks (Kriesel, 2007). A script written in R (designed to run on R studio) accompanies this article that implements this algorithm and is available at http://butterflygeraci.codeplex.com/. For details on the R package or for help installing the software refer to the accompanying document, Supporting Material and Appendix.

Dynamical Localization for Discrete Anderson Dirac Operators

NASA Astrophysics Data System (ADS)

Prado, Roberto A.; de Oliveira, César R.; Carvalho, Silas L.

2017-04-01

We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d\\in { 1, 2, 3} , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the continuous Dirac operators and consist in the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by different scalar potentials, which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support. We prove the exponential decay of fractional moments of the Green function for such models in each of the above regimes, i.e., (j) throughout the spectrum at larger disorder, (jj) for energies near the band edges at arbitrary disorder and (jjj) in dimension one, for all energies in the spectrum and arbitrary disorder. Dynamical localization in theses regimes follows from the fractional moments method. The result in the one-dimensional regime contrast with one that was previously obtained for 1D Dirac model with Bernoulli potential.

Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

NASA Astrophysics Data System (ADS)

Vanicat, Matthieu

2018-04-01

We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.

Dynamic properties in the four-state haploid coupled discrete-time mutation-selection model with an infinite population limit

NASA Astrophysics Data System (ADS)

Lee, Kyu Sang; Gill, Wonpyong

2017-11-01

The dynamic properties, such as the crossing time and time-dependence of the relative density of the four-state haploid coupled discrete-time mutation-selection model, were calculated with the assumption that μ ij = μ ji , where μ ij denotes the mutation rate between the sequence elements, i and j. The crossing time for s = 0 and r 23 = r 42 = 1 in the four-state model became saturated at a large fitness parameter when r 12 > 1, was scaled as a power law in the fitness parameter when r 12 = 1, and diverged when the fitness parameter approached the critical fitness parameter when r 12 < 1, where r ij = μ ij / μ 14.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

A dynamic model of functioning of a bank

NASA Astrophysics Data System (ADS)

Malafeyev, Oleg; Awasthi, Achal; Zaitseva, Irina; Rezenkov, Denis; Bogdanova, Svetlana

2018-04-01

In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming makes sure that the solutions obtained are globally optimal and numerically stable. The optimization process is set up as a discrete multi-stage decision process and solved with the help of dynamic programming.

Dynamic modeling of brushless dc motors for aerospace actuation

NASA Technical Reports Server (NTRS)

Demerdash, N. A.; Nehl, T. W.

1980-01-01

A discrete time model for simulation of the dynamics of samarium cobalt-type permanent magnet brushless dc machines is presented. The simulation model includes modeling of the interaction between these machines and their attached power conditioners. These are transistorized conditioner units. This model is part of an overall discrete-time analysis of the dynamic performance of electromechanical actuators, which was conducted as part of prototype development of such actuators studied and built for NASA-Johnson Space Center as a prospective alternative to hydraulic actuators presently used in shuttle orbiter applications. The resulting numerical simulations of the various machine and power conditioner current and voltage waveforms gave excellent correlation to the actual waveforms collected from actual hardware experimental testing. These results, numerical and experimental, are presented here for machine motoring, regeneration and dynamic braking modes. Application of the resulting model to the determination of machine current and torque profiles during closed-loop actuator operation were also analyzed and the results are given here. These results are given in light of an overall view of the actuator system components. The applicability of this method of analysis to design optimization and trouble-shooting in such prototype development is also discussed in light of the results at hand.

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

PubMed

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

Ensemble-type numerical uncertainty information from single model integrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

Sampled control stability of the ESA instrument pointing system

NASA Astrophysics Data System (ADS)

Thieme, G.; Rogers, P.; Sciacovelli, D.

Stability analysis and simulation results are presented for the ESA Instrument Pointing System (IPS) that is to be used in Spacelab's second launch. Of the two IPS plant dynamic models used in the ESA and NASA activities, one is based on six interconnected rigid bodies that represent the IPS and plant dynamic models used in the ESA and NASA activities, one is based on six interconnected rigid bodies that represent the IPS and its payload, while the other follows the NASA practice of defining an IPS-Spacelab 2 plant configuration through a structural finite element model, which is then used to generate modal data for various pointing directions. In both cases, the IPS dynamic plant model is truncated, then discretized at the sampling frequency and interfaces to a PID-based control law. A stability analysis has been carried out in discrete domain for various instrument pointing directions, taking into account suitable parameter variation ranges. A number of time simulations are presented.

META 2f: Probabilistic, Compositional, Multi-dimension Model-Based Verification (PROMISE)

DTIC Science & Technology

2011-10-01

Equational Logic, Rewriting Logic, and Maude ................................................ 52  5.3  Results and Discussion...and its discrete transitions are left unchanged. However, the differential equations describing the continuous dynamics (in each mode) are replaced by...by replacing hard-to-analyze differential equations by discrete transitions. In principle, predicate and qualitative abstraction can be used on a

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

PubMed Central

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

NASA Astrophysics Data System (ADS)

Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

2017-11-01

In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing. ?? 2006, The International Biometric Society.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation.

PubMed

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-09-08

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Dynamic modeling and parameter estimation of a radial and loop type distribution system network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jun Qui; Heng Chen; Girgis, A.A.

1993-05-01

This paper presents a new identification approach to three-phase power system modeling and model reduction taking power system network as multi-input, multi-output (MIMO) processes. The model estimate can be obtained in discrete-time input-output form, discrete- or continuous-time state-space variable form, or frequency-domain impedance transfer function matrix form. An algorithm for determining the model structure of this MIMO process is described. The effect of measurement noise on the approach is also discussed. This approach has been applied on a sample system and simulation results are also presented in this paper.

On the Dynamics of an Incursion Describing the Interactions between Functionally Differentiated Subsystems of a Discrete-time Anticipatory System

NASA Astrophysics Data System (ADS)

Burke, Mark E.

2010-11-01

Dubois coined the term incursion, for an inclusive or implicit recursion, to describe a discrete-time anticipatory system which computes its future states by reference to its future states as well as its current and past states. In this paper, we look at a model which has been proposed in the context of a social system which has functionally differentiated subsystems. The model is derived from a discrete-time compartmental SIS epidemic model. We analyse a low order instance of the model both in its form as a recursion with no anticipatory capacity, and also as an incursion with associated anticipatory capacity. The properties of the incursion are compared and contrasted with those of the underlying recursion.

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays.

PubMed

Hu, Jin; Wang, Jun

2015-06-01

In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given. Copyright © 2015 Elsevier Ltd. All rights reserved.

A comparison of the lattice discrete particle method to the finite-element method and the K&C material model for simulating the static and dynamic response of concrete.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Jovanca J.; Bishop, Joseph E.

2013-11-01

This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed atmore » Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.« less

Discrete Model of Opinion Changes Using Knowledge and Emotions as Control Variables

PubMed Central

Sobkowicz, Pawel

2012-01-01

We present a new model of opinion changes dependent on the agents emotional state and their information about the issue in question. Our goal is to construct a simple, yet nontrivial and flexible representation of individual attitude dynamics for agent based simulations, that could be used in a variety of social environments. The model is a discrete version of the cusp catastrophe model of opinion dynamics in which information is treated as the normal factor while emotional arousal (agitation level determining agent receptiveness and rationality) is treated as the splitting factor. Both variables determine the resulting agent opinion, which itself can be in favor of the studied position, against it, or neutral. Thanks to the flexibility of implementing communication between the agents, the model is potentially applicable in a wide range of situations. As an example of the model application, we study the dynamics of a set of agents communicating among themselves via messages. In the example, we chose the simplest, fully connected communication topology, to focus on the effects of the individual opinion dynamics, and to look for stable final distributions of agents with different emotions, information and opinions. Even for such simplified system, the model shows complex behavior, including phase transitions due to symmetry breaking by external propaganda. PMID:22984516

Discrete model of opinion changes using knowledge and emotions as control variables.

PubMed

Sobkowicz, Pawel

2012-01-01

We present a new model of opinion changes dependent on the agents emotional state and their information about the issue in question. Our goal is to construct a simple, yet nontrivial and flexible representation of individual attitude dynamics for agent based simulations, that could be used in a variety of social environments. The model is a discrete version of the cusp catastrophe model of opinion dynamics in which information is treated as the normal factor while emotional arousal (agitation level determining agent receptiveness and rationality) is treated as the splitting factor. Both variables determine the resulting agent opinion, which itself can be in favor of the studied position, against it, or neutral. Thanks to the flexibility of implementing communication between the agents, the model is potentially applicable in a wide range of situations. As an example of the model application, we study the dynamics of a set of agents communicating among themselves via messages. In the example, we chose the simplest, fully connected communication topology, to focus on the effects of the individual opinion dynamics, and to look for stable final distributions of agents with different emotions, information and opinions. Even for such simplified system, the model shows complex behavior, including phase transitions due to symmetry breaking by external propaganda.

Dynamical discrete/continuum linear response shells theory of solvation: convergence test for NH4+ and OH- ions in water solution using DFT and DFTB methods.

PubMed

de Lima, Guilherme Ferreira; Duarte, Hélio Anderson; Pliego, Josefredo R

2010-12-09

A new dynamical discrete/continuum solvation model was tested for NH(4)(+) and OH(-) ions in water solvent. The method is similar to continuum solvation models in a sense that the linear response approximation is used. However, different from pure continuum models, explicit solvent molecules are included in the inner shell, which allows adequate treatment of specific solute-solvent interactions present in the first solvation shell, the main drawback of continuum models. Molecular dynamics calculations coupled with SCC-DFTB method are used to generate the configurations of the solute in a box with 64 water molecules, while the interaction energies are calculated at the DFT level. We have tested the convergence of the method using a variable number of explicit water molecules and it was found that even a small number of waters (as low as 14) are able to produce converged values. Our results also point out that the Born model, often used for long-range correction, is not reliable and our method should be applied for more accurate calculations.

A Global Picture of the Gamma-Ricker Map: A Flexible Discrete-Time Model with Factors of Positive and Negative Density Dependence.

PubMed

Liz, Eduardo

2018-02-01

The gamma-Ricker model is one of the more flexible and general discrete-time population models. It is defined on the basis of the Ricker model, introducing an additional parameter [Formula: see text]. For some values of this parameter ([Formula: see text], population is overcompensatory, and the introduction of an additional parameter gives more flexibility to fit the stock-recruitment curve to field data. For other parameter values ([Formula: see text]), the gamma-Ricker model represents populations whose per-capita growth rate combines both negative density dependence and positive density dependence. The former can lead to overcompensation and dynamic instability, and the latter can lead to a strong Allee effect. We study the impact of the cooperation factor in the dynamics and provide rigorous conditions under which increasing the Allee effect strength stabilizes or destabilizes population dynamics, promotes or prevents population extinction, and increases or decreases population size. Our theoretical results also include new global stability criteria and a description of the possible bifurcations.

Adaptive modeling, identification, and control of dynamic structural systems. I. Theory

USGS Publications Warehouse

Safak, Erdal

1989-01-01

A concise review of the theory of adaptive modeling, identification, and control of dynamic structural systems based on discrete-time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time-varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete-time representation of single-input single-output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is necessary to follow the examples for applications in structural dynamics presented in the second paper.

Analysis and Design of International Emission Trading Markets Applying System Dynamics Techniques

NASA Astrophysics Data System (ADS)

Hu, Bo; Pickl, Stefan

2010-11-01

The design and analysis of international emission trading markets is an important actual challenge. Time-discrete models are needed to understand and optimize these procedures. We give an introduction into this scientific area and present actual modeling approaches. Furthermore, we develop a model which is embedded in a holistic problem solution. Measures for energy efficiency are characterized. The economic time-discrete "cap-and-trade" mechanism is influenced by various underlying anticipatory effects. With a systematic dynamic approach the effects can be examined. First numerical results show that fair international emissions trading can only be conducted with the use of protective export duties. Furthermore a comparatively high price which evokes emission reduction inevitably has an inhibiting effect on economic growth according to our model. As it always has been expected it is not without difficulty to find a balance between economic growth and emission reduction. It can be anticipated using our System Dynamics model simulation that substantial changes must be taken place before international emissions trading markets can contribute to global GHG emissions mitigation.

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

NASA Astrophysics Data System (ADS)

Sánchez-Rey, Bernardo; Quintero, Niurka R.; Cuevas-Maraver, Jesús; Alejo, Miguel A.

2014-10-01

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model.

PubMed

Sánchez-Rey, Bernardo; Quintero, Niurka R; Cuevas-Maraver, Jesús; Alejo, Miguel A

2014-10-01

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

Inhomogeneous point-process entropy: An instantaneous measure of complexity in discrete systems

NASA Astrophysics Data System (ADS)

Valenza, Gaetano; Citi, Luca; Scilingo, Enzo Pasquale; Barbieri, Riccardo

2014-05-01

Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties.

Analysis of discrete and continuous distributions of ventilatory time constants from dynamic computed tomography

NASA Astrophysics Data System (ADS)

Doebrich, Marcus; Markstaller, Klaus; Karmrodt, Jens; Kauczor, Hans-Ulrich; Eberle, Balthasar; Weiler, Norbert; Thelen, Manfred; Schreiber, Wolfgang G.

2005-04-01

In this study, an algorithm was developed to measure the distribution of pulmonary time constants (TCs) from dynamic computed tomography (CT) data sets during a sudden airway pressure step up. Simulations with synthetic data were performed to test the methodology as well as the influence of experimental noise. Furthermore the algorithm was applied to in vivo data. In five pigs sudden changes in airway pressure were imposed during dynamic CT acquisition in healthy lungs and in a saline lavage ARDS model. The fractional gas content in the imaged slice (FGC) was calculated by density measurements for each CT image. Temporal variations of the FGC were analysed assuming a model with a continuous distribution of exponentially decaying time constants. The simulations proved the feasibility of the method. The influence of experimental noise could be well evaluated. Analysis of the in vivo data showed that in healthy lungs ventilation processes can be more likely characterized by discrete TCs whereas in ARDS lungs continuous distributions of TCs are observed. The temporal behaviour of lung inflation and deflation can be characterized objectively using the described new methodology. This study indicates that continuous distributions of TCs reflect lung ventilation mechanics more accurately compared to discrete TCs.

Model predictive control of an air suspension system with damping multi-mode switching damper based on hybrid model

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Yuan, Chaochun; Cai, Yingfeng; Wang, Shaohua; Chen, Long

2017-09-01

This paper presents the hybrid modeling and the model predictive control of an air suspension system with damping multi-mode switching damper. Unlike traditional damper with continuously adjustable damping, in this study, a new damper with four discrete damping modes is applied to vehicle semi-active air suspension. The new damper can achieve different damping modes by just controlling the on-off statuses of two solenoid valves, which makes its damping adjustment more efficient and more reliable. However, since the damping mode switching induces different modes of operation, the air suspension system with the new damper poses challenging hybrid control problem. To model both the continuous/discrete dynamics and the switching between different damping modes, the framework of mixed logical dynamical (MLD) systems is used to establish the system hybrid model. Based on the resulting hybrid dynamical model, the system control problem is recast as a model predictive control (MPC) problem, which allows us to optimize the switching sequences of the damping modes by taking into account the suspension performance requirements. Numerical simulations results demonstrate the efficacy of the proposed control method finally.

Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal

NASA Astrophysics Data System (ADS)

Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun

2013-05-01

Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Macroscopic damping model for structural dynamics with random polycrystalline configurations

NASA Astrophysics Data System (ADS)

Yang, Yantao; Cui, Junzhi; Yu, Yifan; Xiang, Meizhen

2018-06-01

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.

Dust emission modelling around a stockpile by using computational fluid dynamics and discrete element method

NASA Astrophysics Data System (ADS)

Derakhshani, S. M.; Schott, D. L.; Lodewijks, G.

2013-06-01

Dust emissions can have significant effects on the human health, environment and industry equipment. Understanding the dust generation process helps to select a suitable dust preventing approach and also is useful to evaluate the environmental impact of dust emission. To describe these processes, numerical methods such as Computational Fluid Dynamics (CFD) are widely used, however nowadays particle based methods like Discrete Element Method (DEM) allow researchers to model interaction between particles and fluid flow. In this study, air flow over a stockpile, dust emission, erosion and surface deformation of granular material in the form of stockpile are studied by using DEM and CFD as a coupled method. Two and three dimensional simulations are respectively developed for CFD and DEM methods to minimize CPU time. The standard κ-ɛ turbulence model is used in a fully developed turbulent flow. The continuous gas phase and the discrete particle phase link to each other through gas-particle void fractions and momentum transfer. In addition to stockpile deformation, dust dispersion is studied and finally the accuracy of stockpile deformation results obtained by CFD-DEM modelling will be validated by the agreement with the existing experimental data.

Inhibitory neurons promote robust critical firing dynamics in networks of integrate-and-fire neurons.

PubMed

Lu, Zhixin; Squires, Shane; Ott, Edward; Girvan, Michelle

2016-12-01

We study the firing dynamics of a discrete-state and discrete-time version of an integrate-and-fire neuronal network model with both excitatory and inhibitory neurons. When the integer-valued state of a neuron exceeds a threshold value, the neuron fires, sends out state-changing signals to its connected neurons, and returns to the resting state. In this model, a continuous phase transition from non-ceaseless firing to ceaseless firing is observed. At criticality, power-law distributions of avalanche size and duration with the previously derived exponents, -3/2 and -2, respectively, are observed. Using a mean-field approach, we show analytically how the critical point depends on model parameters. Our main result is that the combined presence of both inhibitory neurons and integrate-and-fire dynamics greatly enhances the robustness of critical power-law behavior (i.e., there is an increased range of parameters, including both sub- and supercritical values, for which several decades of power-law behavior occurs).

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

PubMed

Frasca, Mattia; Sharkey, Kieran J

2016-06-21

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation

PubMed Central

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-01-01

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein. PMID:16965175

A discrete-element model for viscoelastic deformation and fracture of glacial ice

NASA Astrophysics Data System (ADS)

Riikilä, T. I.; Tallinen, T.; Åström, J.; Timonen, J.

2015-10-01

A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

Dynamic programming and graph algorithms in computer vision.

PubMed

Felzenszwalb, Pedro F; Zabih, Ramin

2011-04-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting since, by carefully exploiting problem structure, they often provide nontrivial guarantees concerning solution quality. In this paper, we review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo, the mid-level problem of interactive object segmentation, and the high-level problem of model-based recognition.

Discrete Inverse and State Estimation Problems

NASA Astrophysics Data System (ADS)

Wunsch, Carl

2006-06-01

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. Provides a comprehensive introduction to discrete methods of inference from incomplete information Based upon 25 years of practical experience using real data and models Develops sequential and whole-domain analysis methods from simple least-squares Contains many examples and problems, and web-based support through MIT opencourseware

Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: The Discrete-Continuous Model revisited

NASA Astrophysics Data System (ADS)

Vattré, A.; Devincre, B.; Feyel, F.; Gatti, R.; Groh, S.; Jamond, O.; Roos, A.

2014-02-01

A unified model coupling 3D dislocation dynamics (DD) simulations with the finite element (FE) method is revisited. The so-called Discrete-Continuous Model (DCM) aims to predict plastic flow at the (sub-)micron length scale of materials with complex boundary conditions. The evolution of the dislocation microstructure and the short-range dislocation-dislocation interactions are calculated with a DD code. The long-range mechanical fields due to the dislocations are calculated by a FE code, taking into account the boundary conditions. The coupling procedure is based on eigenstrain theory, and the precise manner in which the plastic slip, i.e. the dislocation glide as calculated by the DD code, is transferred to the integration points of the FE mesh is described in full detail. Several test cases are presented, and the DCM is applied to plastic flow in a single-crystal Nickel-based superalloy.

Hemolytic potential of hydrodynamic cavitation.

PubMed

Chambers, S D; Bartlett, R H; Ceccio, S L

2000-08-01

The purpose of this study was to determine the hemolytic potentials of discrete bubble cavitation and attached cavitation. To generate controlled cavitation events, a venturigeometry hydrodynamic device, called a Cavitation Susceptibility Meter (CSM), was constructed. A comparison between the hemolytic potential of discrete bubble cavitation and attached cavitation was investigated with a single-pass flow apparatus and a recirculating flow apparatus, both utilizing the CSM. An analytical model, based on spherical bubble dynamics, was developed for predicting the hemolysis caused by discrete bubble cavitation. Experimentally, discrete bubble cavitation did not correlate with a measurable increase in plasma-free hemoglobin (PFHb), as predicted by the analytical model. However, attached cavitation did result in significant PFHb generation. The rate of PFHb generation scaled inversely with the Cavitation number at a constant flow rate, suggesting that the size of the attached cavity was the dominant hemolytic factor.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Bertin, N.; Upadhyay, M. V.; Pradalier, C.; Capolungo, L.

2015-09-01

In this paper, we propose a novel full-field approach based on the fast Fourier transform (FFT) technique to compute mechanical fields in periodic discrete dislocation dynamics (DDD) simulations for anisotropic materials: the DDD-FFT approach. By coupling the FFT-based approach to the discrete continuous model, the present approach benefits from the high computational efficiency of the FFT algorithm, while allowing for a discrete representation of dislocation lines. It is demonstrated that the computational time associated with the new DDD-FFT approach is significantly lower than that of current DDD approaches when large number of dislocation segments are involved for isotropic and anisotropic elasticity, respectively. Furthermore, for fine Fourier grids, the treatment of anisotropic elasticity comes at a similar computational cost to that of isotropic simulation. Thus, the proposed approach paves the way towards achieving scale transition from DDD to mesoscale plasticity, especially due to the method’s ability to incorporate inhomogeneous elasticity.

Dynamical quantum phase transitions in discrete time crystals

NASA Astrophysics Data System (ADS)

Kosior, Arkadiusz; Sacha, Krzysztof

2018-05-01

Discrete time crystals are related to nonequilibrium dynamics of periodically driven quantum many-body systems where the discrete time-translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry. Recently, the concept of phase transitions has been extended to nonequilibrium dynamics of time-independent systems induced by a quantum quench, i.e., a sudden change of some parameter of the Hamiltonian. There, the return probability of a system to the ground state reveals singularities in time which are dubbed dynamical quantum phase transitions. We show that the quantum quench in a discrete time crystal leads to dynamical quantum phase transitions where the return probability of a periodically driven system to a Floquet eigenstate before the quench reveals singularities in time. It indicates that dynamical quantum phase transitions are not restricted to time-independent systems and can be also observed in systems that are periodically driven. We discuss how the phenomenon can be observed in ultracold atomic gases.

Comparing a discrete and continuum model of the intestinal crypt

PubMed Central

Murray, Philip J.; Walter, Alex; Fletcher, Alex G.; Edwards, Carina M.; Tindall, Marcus J.; Maini, Philip K.

2011-01-01

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalisations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts. PMID:21411869

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

NASA Astrophysics Data System (ADS)

Ramachandran, Nirmal; Ganguli, Ranjan

2018-06-01

A discrete model is introduced to analyze transverse vibration of straight, clamped-free (CF) columns of variable cross-sectional geometry under the influence of gravity and a constant axial force at the tip. The discrete model is used to determine critical combinations of loading parameters - a gravity parameter and a tip force parameter - that cause onset of dynamic instability in the CF column. A methodology, based on matrix-factorization, is described to transform the discrete model into a family of models corresponding to weightless and unloaded clamped-free (WUCF) columns, each with a transverse vibration spectrum isospectral to the original model. Characteristics of models in this isospectral family are dependent on three transformation parameters. A procedure is discussed to convert the isospectral discrete model description into geometric description of realistic columns i.e. from the discrete model, we construct isospectral WUCF columns with rectangular cross-sections varying in width and depth. As part of numerical studies to demonstrate efficacy of techniques presented, frequency parameters of a uniform column and three types of tapered CF columns under different combinations of loading parameters are obtained from the discrete model. Critical combinations of these parameters for a typical tapered column are derived. These results match with published results. Example CF columns, under arbitrarily-chosen combinations of loading parameters are considered and for each combination, isospectral WUCF columns are constructed. Role of transformation parameters in determining characteristics of isospectral columns is discussed and optimum values are deduced. Natural frequencies of these WUCF columns computed using Finite Element Method (FEM) match well with those of the given gravity-loaded CF column with tip force, hence confirming isospectrality.

Determining A Purely Symbolic Transfer Function from Symbol Streams: Theory and Algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

Transfer function modeling is a \\emph{standard technique} in classical Linear Time Invariant and Statistical Process Control. The work of Box and Jenkins was seminal in developing methods for identifying parameters associated with classicalmore » $(r,s,k)$$ transfer functions. Discrete event systems are often \\emph{used} for modeling hybrid control structures and high-level decision problems. \\emph{Examples include} discrete time, discrete strategy repeated games. For these games, a \\emph{discrete transfer function in the form of} an accurate hidden Markov model of input-output relations \\emph{could be used to derive optimal response strategies.} In this paper, we develop an algorithm \\emph{for} creating probabilistic \\textit{Mealy machines} that act as transfer function models for discrete event dynamic systems (DEDS). Our models are defined by three parameters, $$(l_1, l_2, k)$ just as the Box-Jenkins transfer function models. Here $$l_1$$ is the maximal input history lengths to consider, $$l_2$$ is the maximal output history lengths to consider and $k$ is the response lag. Using related results, We show that our Mealy machine transfer functions are optimal in the sense that they maximize the mutual information between the current known state of the DEDS and the next observed input/output pair.« less

Cavity master equation for the continuous time dynamics of discrete-spin models.

PubMed

Aurell, E; Del Ferraro, G; Domínguez, E; Mulet, R

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Cavity master equation for the continuous time dynamics of discrete-spin models

NASA Astrophysics Data System (ADS)

Aurell, E.; Del Ferraro, G.; Domínguez, E.; Mulet, R.

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

Alternative Stable States, Coral Reefs, and Smooth Dynamics with a Kick.

PubMed

Ippolito, Stephen; Naudot, Vincent; Noonburg, Erik G

2016-03-01

We consider a computer simulation, which was found to be faithful to time series data for Caribbean coral reefs, and an analytical model to help understand the dynamics of the simulation. The analytical model is a system of ordinary differential equations (ODE), and the authors claim this model demonstrates the existence of alternative stable states. The existence of an alternative stable state should consider a sudden shift in coral and macroalgae populations, while the grazing rate remains constant. The results of such shifts, however, are often confounded by changes in grazing rate. Although the ODE suggest alternative stable states, the ODE need modification to explicitly account for shifts or discrete events such as hurricanes. The goal of this paper will be to study the simulation dynamics through a simplified analytical representation. We proceed by modifying the original analytical model through incorporating discrete changes into the ODE. We then analyze the resulting dynamics and their bifurcations with respect to changes in grazing rate and hurricane frequency. In particular, a "kick" enabling the ODE to consider impulse events is added. Beyond adding a "kick" we employ the grazing function that is suggested by the simulation. The extended model was fit to the simulation data to support its use and predicts the existence cycles depending nonlinearly on grazing rates and hurricane frequency. These cycles may bring new insights into consideration for reef health, restoration and dynamics.

A toolbox for discrete modelling of cell signalling dynamics.

PubMed

Paterson, Yasmin Z; Shorthouse, David; Pleijzier, Markus W; Piterman, Nir; Bendtsen, Claus; Hall, Benjamin A; Fisher, Jasmin

2018-06-18

In an age where the volume of data regarding biological systems exceeds our ability to analyse it, many researchers are looking towards systems biology and computational modelling to help unravel the complexities of gene and protein regulatory networks. In particular, the use of discrete modelling allows generation of signalling networks in the absence of full quantitative descriptions of systems, which are necessary for ordinary differential equation (ODE) models. In order to make such techniques more accessible to mainstream researchers, tools such as the BioModelAnalyzer (BMA) have been developed to provide a user-friendly graphical interface for discrete modelling of biological systems. Here we use the BMA to build a library of discrete target functions of known canonical molecular interactions, translated from ordinary differential equations (ODEs). We then show that these BMA target functions can be used to reconstruct complex networks, which can correctly predict many known genetic perturbations. This new library supports the accessibility ethos behind the creation of BMA, providing a toolbox for the construction of complex cell signalling models without the need for extensive experience in computer programming or mathematical modelling, and allows for construction and simulation of complex biological systems with only small amounts of quantitative data.

Retrofitted supersymmetric models

NASA Astrophysics Data System (ADS)

Bose, Manatosh

This thesis explores several models of metastable dynamic supersymmetry breaking (MDSB) and a supersymmetric model of hybrid inflation. All of these models possess discrete R-symmetries. We specially focus on the retrofitted models for supersymmetry breaking models. At first we construct retrofitted models of gravity mediation. In these models we explore the genericity of the so-called "split supersymmetry." We show that with the simplest models, where the goldstino multiplet is neutral under the discrete R-symmetry, a split spectrum is not generic. However if the goldstino superfield is charged under some symmetry other than the R-symmetry, then a split spectrum is achievable but not generic. We also present a gravity mediated model where the fine tuning of the Z-boson mass is dictated by a discrete choice rather than a continuous tuning. Then we construct retrofitted models of gauge mediated SUSY breaking. We show that, in these models, if the approximate R-symmetry of the theory is spontaneously broken, the messenger scale is fixed; if explicitly broken by retrofitted couplings, a very small dimensionless number is required; if supergravity corrections are responsible for the symmetry breaking, at least two moderately small couplings are required, and that there is a large range of possible messenger scales. Finally we switch our attention to small field hybrid inflation. We construct a model that yields a spectral index ns = 0.96. Here, we also briefly discuss the possibility of relating the scale of inflation with the dynamics responsible for supersymmetry breaking.

Ecological monitoring in a discrete-time prey-predator model.

PubMed

Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J

2017-09-21

The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Understanding water column and streambed thermal refugia for endangered mussels in the Delaware River

USGS Publications Warehouse

Briggs, Martin A.; Voytek, Emily B.; Day-Lewis, Frederick D.; Rosenberry, Donald O.; Lane, John W.

2013-01-01

Groundwater discharge locations along the upper Delaware River, both discrete bank seeps and diffuse streambed upwelling, may create thermal niche environments that benefit the endangered dwarf wedgemussel (Alasmidonta heterodon). We seek to identify whether discrete or diffuse groundwater inflow is the dominant control on refugia. Numerous springs and seeps were identified at all locations where dwarf wedgemussels still can be found. Infrared imagery and custom high spatial resolution fiber-optic distributed temperature sensors reveal complex thermal dynamics at one of the seeps with a relatively stable, cold groundwater plume extending along the streambed/water-column interface during mid-summer. This plume, primarily fed by a discrete bank seep, was shown through analytical and numerical heat-transport modeling to dominate temperature dynamics in the region of potential habitation by the adult dwarf wedgemussel.

A discrete mathematical model of the dynamic evolution of a transportation network

NASA Astrophysics Data System (ADS)

Malinetskii, G. G.; Stepantsov, M. E.

2009-09-01

A dynamic model of the evolution of a transportation network is proposed. The main feature of this model is that the evolution of the transportation network is not a process of centralized transportation optimization. Rather, its dynamic behavior is a result of the system self-organization that occurs in the course of the satisfaction of needs in goods transportation and the evolution of the infrastructure of the network nodes. Nonetheless, the possibility of soft control of the network evolution direction is taken into account.

Analysis, simulation and visualization of 1D tapping via reduced dynamical models

NASA Astrophysics Data System (ADS)

Blackmore, Denis; Rosato, Anthony; Tricoche, Xavier; Urban, Kevin; Zou, Luo

2014-04-01

A low-dimensional center-of-mass dynamical model is devised as a simplified means of approximately predicting some important aspects of the motion of a vertical column comprised of a large number of particles subjected to gravity and periodic vertical tapping. This model is investigated first as a continuous dynamical system using analytical, simulation and visualization techniques. Then, by employing an approach analogous to that used to approximate the dynamics of a bouncing ball on an oscillating flat plate, it is modeled as a discrete dynamical system and analyzed to determine bifurcations and transitions to chaotic motion along with other properties. The predictions of the analysis are then compared-primarily qualitatively-with visualization and simulation results of the reduced continuous model, and ultimately with simulations of the complete system dynamics.

Perfect discretization of reparametrization invariant path integrals

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

2011-05-01

To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

Dynamics of a Tapped Granular Column

NASA Astrophysics Data System (ADS)

Rosato, Anthony; Blackmore, Denis; Zuo, Luo; Hao, Wu; Horntrop, David

2015-11-01

We consider the behavior of a column of spheres subjected to a time-dependent vertical taps. Of interest are various dynamical properties, such as the motion of its mass center, its response to taps of different intensities and forms, and the effect of system size and material properties. The interplay between diverse time and length scales are the key contributors to the column's evolving dynamics. Soft sphere discrete element simulations were conducted over a very wide parameter space to obtain a portrait of column behavior as embodied by the collective dynamics of the mass center motion. Results compared favorably with a derived reduced-order paradigm of the mass center motion (surprisingly analogous to that for a single bouncing ball on an oscillating plate) with respect to dynamical regimes and their transitions. A continuum model obtained from a system of Newtonian equations, as a locally averaged limit in the transport mode along trajectories is described, and a numerical solution protocol for a one-dimensional system is outlined. Typical trajectories and density evolution profiles are shown. We conclude with a discussion of our investigations to relate predictions of the continuum and reduced dynamical systems models with discrete simulations.

A discrete mathematical model for the aggregation of β-Amyloid.

PubMed

Dayeh, Maher A; Livadiotis, George; Elaydi, Saber

2018-01-01

Dementia associated with the Alzheimer's disease is thought to be correlated with the conversion of the β - Amyloid (Aβ) peptides from soluble monomers to aggregated oligomers and insoluble fibrils. We present a discrete-time mathematical model for the aggregation of Aβ monomers into oligomers using concepts from chemical kinetics and population dynamics. Conditions for the stability and instability of the equilibria of the model are established. A formula for the number of monomers that is required for producing oligomers is also given. This may provide compound designers a mechanism to inhibit the Aβ aggregation.

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

NASA Astrophysics Data System (ADS)

Li, Chong; Yuan, Juyun; Yu, Haitao; Yuan, Yong

2018-01-01

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for one-dimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom (MDOF) system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom (DOFs) in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

Modeling Epidemics with Dynamic Small-World Networks

NASA Astrophysics Data System (ADS)

Kaski, Kimmo; Saramäki, Jari

2005-06-01

In this presentation a minimal model for describing the spreading of an infectious disease, such as influenza, is discussed. Here it is assumed that spreading takes place on a dynamic small-world network comprising short- and long-range infection events. Approximate equations for the epidemic threshold as well as the spreading dynamics are derived and they agree well with numerical discrete time-step simulations. Also the dependence of the epidemic saturation time on the initial conditions is analysed and a comparison with real-world data is made.

Discrete Dynamics Model for the Speract-Activated Ca2+ Signaling Network Relevant to Sperm Motility

PubMed Central

Espinal, Jesús; Aldana, Maximino; Guerrero, Adán; Wood, Christopher

2011-01-01

Understanding how spermatozoa approach the egg is a central biological issue. Recently a considerable amount of experimental evidence has accumulated on the relation between oscillations in intracellular calcium ion concentration ([Ca]) in the sea urchin sperm flagellum, triggered by peptides secreted from the egg, and sperm motility. Determination of the structure and dynamics of the signaling pathway leading to these oscillations is a fundamental problem. However, a biochemically based formulation for the comprehension of the molecular mechanisms operating in the axoneme as a response to external stimulus is still lacking. Based on experiments on the S. purpuratus sea urchin spermatozoa, we propose a signaling network model where nodes are discrete variables corresponding to the pathway elements and the signal transmission takes place at discrete time intervals according to logical rules. The validity of this model is corroborated by reproducing previous empirically determined signaling features. Prompted by the model predictions we performed experiments which identified novel characteristics of the signaling pathway. We uncovered the role of a high voltage-activated channel as a regulator of the delay in the onset of fluctuations after activation of the signaling cascade. This delay time has recently been shown to be an important regulatory factor for sea urchin sperm reorientation. Another finding is the participation of a voltage-dependent calcium-activated channel in the determination of the period of the fluctuations. Furthermore, by analyzing the spread of network perturbations we find that it operates in a dynamically critical regime. Our work demonstrates that a coarse-grained approach to the dynamics of the signaling pathway is capable of revealing regulatory sperm navigation elements and provides insight, in terms of criticality, on the concurrence of the high robustness and adaptability that the reproduction processes are predicted to have developed throughout evolution. PMID:21857937

DISCRETE VOLUME-ELEMENT METHOD FOR NETWORK WATER- QUALITY MODELS

EPA Science Inventory

An explicit dynamic water-quality modeling algorithm is developed for tracking dissolved substances in water-distribution networks. The algorithm is based on a mass-balance relation within pipes that considers both advective transport and reaction kinetics. Complete mixing of m...

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

PubMed

Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A

2017-01-20

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction

NASA Astrophysics Data System (ADS)

Kaewunruen, S.; Mirza, O.

2017-10-01

At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.

A Discrete Electromechanical Model for Human Cardiac Tissue: Effects of Stretch-Activated Currents and Stretch Conditions on Restitution Properties and Spiral Wave Dynamics

PubMed Central

Weise, Louis D.; Panfilov, Alexander V.

2013-01-01

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning. PMID:23527160

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics.

PubMed

Weise, Louis D; Panfilov, Alexander V

2013-01-01

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.

Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS.

PubMed

Brackley, C A; Morozov, A N; Marenduzzo, D

2014-04-07

An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Discrete dynamical system modelling for gene regulatory networks of 5-hydroxymethylfurfural tolerance for ethanologenic yeast.

PubMed

Song, M; Ouyang, Z; Liu, Z L

2009-05-01

Composed of linear difference equations, a discrete dynamical system (DDS) model was designed to reconstruct transcriptional regulations in gene regulatory networks (GRNs) for ethanologenic yeast Saccharomyces cerevisiae in response to 5-hydroxymethylfurfural (HMF), a bioethanol conversion inhibitor. The modelling aims at identification of a system of linear difference equations to represent temporal interactions among significantly expressed genes. Power stability is imposed on a system model under the normal condition in the absence of the inhibitor. Non-uniform sampling, typical in a time-course experimental design, is addressed by a log-time domain interpolation. A statistically significant DDS model of the yeast GRN derived from time-course gene expression measurements by exposure to HMF, revealed several verified transcriptional regulation events. These events implicate Yap1 and Pdr3, transcription factors consistently known for their regulatory roles by other studies or postulated by independent sequence motif analysis, suggesting their involvement in yeast tolerance and detoxification of the inhibitor.

Hybrid Modeling for Testing Intelligent Software for Lunar-Mars Closed Life Support

NASA Technical Reports Server (NTRS)

Malin, Jane T.; Nicholson, Leonard S. (Technical Monitor)

1999-01-01

Intelligent software is being developed for closed life support systems with biological components, for human exploration of the Moon and Mars. The intelligent software functions include planning/scheduling, reactive discrete control and sequencing, management of continuous control, and fault detection, diagnosis, and management of failures and errors. Four types of modeling information have been essential to system modeling and simulation to develop and test the software and to provide operational model-based what-if analyses: discrete component operational and failure modes; continuous dynamic performance within component modes, modeled qualitatively or quantitatively; configuration of flows and power among components in the system; and operations activities and scenarios. CONFIG, a multi-purpose discrete event simulation tool that integrates all four types of models for use throughout the engineering and operations life cycle, has been used to model components and systems involved in the production and transfer of oxygen and carbon dioxide in a plant-growth chamber and between that chamber and a habitation chamber with physicochemical systems for gas processing.

NasoNet, modeling the spread of nasopharyngeal cancer with networks of probabilistic events in discrete time.

PubMed

Galán, S F; Aguado, F; Díez, F J; Mira, J

2002-07-01

The spread of cancer is a non-deterministic dynamic process. As a consequence, the design of an assistant system for the diagnosis and prognosis of the extent of a cancer should be based on a representation method that deals with both uncertainty and time. The ultimate goal is to know the stage of development of a cancer in a patient before selecting the appropriate treatment. A network of probabilistic events in discrete time (NPEDT) is a type of Bayesian network for temporal reasoning that models the causal mechanisms associated with the time evolution of a process. This paper describes NasoNet, a system that applies NPEDTs to the diagnosis and prognosis of nasopharyngeal cancer. We have made use of temporal noisy gates to model the dynamic causal interactions that take place in the domain. The methodology we describe is general enough to be applied to any other type of cancer.

Nucleation and growth of Y2O3 nanoparticles in a RF-ICTP reactor: a discrete sectional study based on CFD simulation supported with experiments

NASA Astrophysics Data System (ADS)

Dhamale, G. D.; Tak, A. K.; Mathe, V. L.; Ghorui, S.

2018-06-01

Synthesis of yttria (Y2O3) nanoparticles in an atmospheric pressure radiofrequency inductively coupled thermal plasma (RF-ICTP) reactor has been investigated using the discrete-sectional (DS) model of particle nucleation and growth with argon as the plasma gas. Thermal and fluid dynamic information necessary for the investigation have been extracted through rigorous computational fluid dynamic (CFD) study of the system with coupled electromagnetic equations under the extended field approach. The theoretical framework has been benchmarked against published data first, and then applied to investigate the nucleation and growth process of yttrium oxide nanoparticles in the plasma reactor using the discrete-sectional (DS) model. While a variety of nucleation and growth mechanisms are suggested in literature, the study finds that the theory of homogeneous nucleation fits well with the features observed experimentally. Significant influences of the feed rate and quench rate on the distribution of particles sizes are observed. Theoretically obtained size distribution of the particles agrees well with that observed in the experiment. Different thermo-fluid dynamic environments with varied quench rates, encountered by the propagating vapor front inside the reactor under different operating conditions are found to be primarily responsible for variations in the width of the size distribution.

Dynamic discrete tomography

NASA Astrophysics Data System (ADS)

Alpers, Andreas; Gritzmann, Peter

2018-03-01

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their x-rays. This particular particle tracking problem, with applications, e.g. in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.

Dynamic Programming and Graph Algorithms in Computer Vision*

PubMed Central

Felzenszwalb, Pedro F.; Zabih, Ramin

2013-01-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950

Discrete epidemic models with arbitrary stage distributions and applications to disease control.

PubMed

Hernandez-Ceron, Nancy; Feng, Zhilan; Castillo-Chavez, Carlos

2013-10-01

W.O. Kermack and A.G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack–McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of epidemics, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures.

Multiscale Analysis of Structurally-Graded Microstructures Using Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Crystal Plasticity

NASA Technical Reports Server (NTRS)

Saether, Erik; Hochhalter, Jacob D.; Glaessgen, Edward H.; Mishin, Yuri

2014-01-01

A multiscale modeling methodology is developed for structurally-graded material microstructures. Molecular dynamic (MD) simulations are performed at the nanoscale to determine fundamental failure mechanisms and quantify material constitutive parameters. These parameters are used to calibrate material processes at the mesoscale using discrete dislocation dynamics (DD). Different grain boundary interactions with dislocations are analyzed using DD to predict grain-size dependent stress-strain behavior. These relationships are mapped into crystal plasticity (CP) parameters to develop a computationally efficient finite element-based DD/CP model for continuum-level simulations and complete the multiscale analysis by predicting the behavior of macroscopic physical specimens. The present analysis is focused on simulating the behavior of a graded microstructure in which grain sizes are on the order of nanometers in the exterior region and transition to larger, multi-micron size in the interior domain. This microstructural configuration has been shown to offer improved mechanical properties over homogeneous coarse-grained materials by increasing yield stress while maintaining ductility. Various mesoscopic polycrystal models of structurally-graded microstructures are generated, analyzed and used as a benchmark for comparison between multiscale DD/CP model and DD predictions. A final series of simulations utilize the DD/CP analysis method exclusively to study macroscopic models that cannot be analyzed by MD or DD methods alone due to the model size.

Continuous and discrete extreme climatic events affecting the dynamics of a high-arctic reindeer population.

PubMed

Chan, Kung-Sik; Mysterud, Atle; Øritsland, Nils Are; Severinsen, Torbjørn; Stenseth, Nils Chr

2005-10-01

Climate at northern latitudes are currently changing both with regard to the mean and the temporal variability at any given site, increasing the frequency of extreme events such as cold and warm spells. Here we use a conceptually new modelling approach with two different dynamic terms of the climatic effects on a Svalbard reindeer population (the Brøggerhalvøya population) which underwent an extreme icing event ("locked pastures") with 80% reduction in population size during one winter (1993/94). One term captures the continuous and linear effect depending upon the Arctic Oscillation and another the discrete (rare) "event" process. The introduction of an "event" parameter describing the discrete extreme winter resulted in a more parsimonious model. Such an approach may be useful in strongly age-structured ungulate populations, with young and very old individuals being particularly prone to mortality factors during adverse conditions (resulting in a population structure that differs before and after extreme climatic events). A simulation study demonstrates that our approach is able to properly detect the ecological effects of such extreme climate events.

Beverton-Holt discrete pest management models with pulsed chemical control and evolution of pesticide resistance

NASA Astrophysics Data System (ADS)

Liang, Juhua; Tang, Sanyi; Cheke, Robert A.

2016-07-01

Pest resistance to pesticides is usually managed by switching between different types of pesticides. The optimal switching time, which depends on the dynamics of the pest population and on the evolution of the pesticide resistance, is critical. Here we address how the dynamic complexity of the pest population, the development of resistance and the spraying frequency of pulsed chemical control affect optimal switching strategies given different control aims. To do this, we developed novel discrete pest population growth models with both impulsive chemical control and the evolution of pesticide resistance. Strong and weak threshold conditions which guarantee the extinction of the pest population, based on the threshold values of the analytical formula for the optimal switching time, were derived. Further, we addressed switching strategies in the light of chosen economic injury levels. Moreover, the effects of the complex dynamical behaviour of the pest population on the pesticide switching times were also studied. The pesticide application period, the evolution of pesticide resistance and the dynamic complexity of the pest population may result in complex outbreak patterns, with consequent effects on the pesticide switching strategies.

High-Efficiency High-Resolution Global Model Developments at the NASA Goddard Data Assimilation Office

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; Atlas, Robert (Technical Monitor)

2002-01-01

The Data Assimilation Office (DAO) has been developing a new generation of ultra-high resolution General Circulation Model (GCM) that is suitable for 4-D data assimilation, numerical weather predictions, and climate simulations. These three applications have conflicting requirements. For 4-D data assimilation and weather predictions, it is highly desirable to run the model at the highest possible spatial resolution (e.g., 55 km or finer) so as to be able to resolve and predict socially and economically important weather phenomena such as tropical cyclones, hurricanes, and severe winter storms. For climate change applications, the model simulations need to be carried out for decades, if not centuries. To reduce uncertainty in climate change assessments, the next generation model would also need to be run at a fine enough spatial resolution that can at least marginally simulate the effects of intense tropical cyclones. Scientific problems (e.g., parameterization of subgrid scale moist processes) aside, all three areas of application require the model's computational performance to be dramatically improved as compared to the previous generation. In this talk, I will present the current and future developments of the "finite-volume dynamical core" at the Data Assimilation Office. This dynamical core applies modem monotonicity preserving algorithms and is genuinely conservative by construction, not by an ad hoc fixer. The "discretization" of the conservation laws is purely local, which is clearly advantageous for resolving sharp gradient flow features. In addition, the local nature of the finite-volume discretization also has a significant advantage on distributed memory parallel computers. Together with a unique vertically Lagrangian control volume discretization that essentially reduces the dimension of the computational problem from three to two, the finite-volume dynamical core is very efficient, particularly at high resolutions. I will also present the computational design of the dynamical core using a hybrid distributed-shared memory programming paradigm that is portable to virtually any of today's high-end parallel super-computing clusters.

High-Efficiency High-Resolution Global Model Developments at the NASA Goddard Data Assimilation Office

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; Atlas, Robert (Technical Monitor)

2002-01-01

The Data Assimilation Office (DAO) has been developing a new generation of ultra-high resolution General Circulation Model (GCM) that is suitable for 4-D data assimilation, numerical weather predictions, and climate simulations. These three applications have conflicting requirements. For 4-D data assimilation and weather predictions, it is highly desirable to run the model at the highest possible spatial resolution (e.g., 55 kin or finer) so as to be able to resolve and predict socially and economically important weather phenomena such as tropical cyclones, hurricanes, and severe winter storms. For climate change applications, the model simulations need to be carried out for decades, if not centuries. To reduce uncertainty in climate change assessments, the next generation model would also need to be run at a fine enough spatial resolution that can at least marginally simulate the effects of intense tropical cyclones. Scientific problems (e.g., parameterization of subgrid scale moist processes) aside, all three areas of application require the model's computational performance to be dramatically improved as compared to the previous generation. In this talk, I will present the current and future developments of the "finite-volume dynamical core" at the Data Assimilation Office. This dynamical core applies modem monotonicity preserving algorithms and is genuinely conservative by construction, not by an ad hoc fixer. The "discretization" of the conservation laws is purely local, which is clearly advantageous for resolving sharp gradient flow features. In addition, the local nature of the finite-volume discretization also has a significant advantage on distributed memory parallel computers. Together with a unique vertically Lagrangian control volume discretization that essentially reduces the dimension of the computational problem from three to two, the finite-volume dynamical core is very efficient, particularly at high resolutions. I will also present the computational design of the dynamical core using a hybrid distributed- shared memory programming paradigm that is portable to virtually any of today's high-end parallel super-computing clusters.

State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

PubMed

Elenchezhiyan, M; Prakash, J

2015-09-01

In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Improved treatment of optics in the Lindquist-Wheeler models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Ferreira, Pedro G.; O'Donnell, Kane

2012-01-01

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state physics, and result in a dynamical description of the large-scale Universe in which the global expansion is given by a Friedmann-like equation. We show that if these models are constructed in a particular way then the redshifts of distant objects, as well as the dynamics of the global space-time, can be made to be in good agreement with the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) solutions of Einstein’s equations, at the level of ≲3% out to z≃2. Angular diameter and luminosity distances, on the other hand, differ from those found in the corresponding FLRW models, while being consistent with the “empty beam” approximation, together with the shearing effects due to the nearest masses. This can be compared with the large deviations found from the corresponding FLRW values obtained in a previous study that considered LW models constructed in a different way. We therefore advocate the improved LW models we consider here as useful constructions that appear to faithfully reproduce both the dynamical and observational properties of space-times containing discrete masses.

When to be discrete: the importance of time formulation in understanding animal movement.

PubMed

McClintock, Brett T; Johnson, Devin S; Hooten, Mevin B; Ver Hoef, Jay M; Morales, Juan M

2014-01-01

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

When to be discrete: The importance of time formulation in understanding animal movement

USGS Publications Warehouse

McClintock, Brett T.; Johnson, Devin S.; Hooten, Mevin B.; Ver Hoef, Jay M.; Morales, Juan M.

2014-01-01

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.

Effect of discrete track support by sleepers on rail corrugation at a curved track

NASA Astrophysics Data System (ADS)

Jin, X. S.; Wen, Z. F.

2008-08-01

The paper investigates into the effect of discrete track support by sleepers on the initiation and development of rail corrugation at a curved track when a railway vehicle passes through using a numerical method. The numerical method considers a combination of Kalker's rolling contact theory with non-Hertzian form, a linear frictional work model and a dynamics model of a half railway vehicle coupled with the curved track. The half-vehicle has a two-axle bogie and doubled suspension systems. It is treated as a full dynamic rigid multi-body model. In the track model, an Euler beam is used to model the rail, and the discrete track support by sleepers moving backward with respect to the vehicle running direction is considered to simulate the effect of the discrete sleeper support on the wheels/rails in rolling contact when the vehicle moves on the track. The sleeper is treated as a rigid body and the ballast bed is replaced with equivalent mass bodies. The numerical analysis exams in detail the variations of wheel/rail normal loads, the creepages, and the rail wear volume along the curved track. Their variations are much concerned with the discrete track support. The numerical results show that the discrete track support causes the fluctuating of the normal loads and creepages at a few frequencies. These frequencies comprise the passing frequency of the sleepers and the excited track resonant frequencies, which are higher than the sleeper passing frequency. Consequently, rail corrugation with several wavelengths initiates and develops. Also the results show that the contact vibrating between the curved rails and the four wheels of the same bogie has different frequencies. In this way, the different key frequencies to be excited play an important role in the initiation and development of curved rail corrugation. Therefore, the corrugations caused by the four wheels of the same bogie present different wavelengths. The paper shows and discusses the depths of the initial corrugations caused by the four wheels of the same bogie, at the entering transition curve, the circle curve and the exit transition curve of the curved track, respectively.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Discrete stochastic charging of aggregate grains

NASA Astrophysics Data System (ADS)

Matthews, Lorin S.; Shotorban, Babak; Hyde, Truell W.

2018-05-01

Dust particles immersed in a plasma environment become charged through the collection of electrons and ions at random times, causing the dust charge to fluctuate about an equilibrium value. Small grains (with radii less than 1 μm) or grains in a tenuous plasma environment are sensitive to single additions of electrons or ions. Here we present a numerical model that allows examination of discrete stochastic charge fluctuations on the surface of aggregate grains and determines the effect of these fluctuations on the dynamics of grain aggregation. We show that the mean and standard deviation of charge on aggregate grains follow the same trends as those predicted for spheres having an equivalent radius, though aggregates exhibit larger variations from the predicted values. In some plasma environments, these charge fluctuations occur on timescales which are relevant for dynamics of aggregate growth. Coupled dynamics and charging models show that charge fluctuations tend to produce aggregates which are much more linear or filamentary than aggregates formed in an environment where the charge is stationary.

The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay

PubMed Central

Muthoni, Mutei Damaris; Pang, Jianhua

2017-01-01

This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with discrete delays. The properties of the bifurcated periodic solutions are studied by using the normal form on the center manifold. Numerical examples and simulations are given to illustrate the bifurcation analysis and the obtained results. PMID:29312457

Metapopulation dynamics and the evolution of dispersal

NASA Astrophysics Data System (ADS)

Parvinen, Kalle

A metapopulation consists of local populations living in habitat patches. In this chapter metapopulation dynamics and the evolution of dispersal is studied in two metapopulation models defined in discrete time. In the first model there are finitely many patches, and in the other one there are infinitely many patches, which allows to incorporate catastrophes into the model. In the first model, cyclic local population dynamics can be either synchronized or not, and increasing dispersal both synchronizes and stabilizes metapopulation dynamics. On the other hand, the type of dynamics has a strong effect on the evolution of dispersal. In case of non-synchronized metapopulation dynamics, dispersal is much more beneficial than in the case of synchronized metapopulation dynamics. Local dynamics has a substantial effect also on the possibility of evolutionary branching in both models. Furthermore, with an Allee effect in the local dynamics of the second model, even evolutionary suicide can occur. It is an evolutionary process in which a viable population adapts in such a way that it can no longer persist.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khrennikov, Andrei; Volovich, Yaroslav

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (butmore » discrete time{exclamation_point}) dynamics is compatible with discrete energy levels.« less

Dynamic characterization, monitoring and control of rotating flexible beam-mass structures via piezo-embedded techniques

NASA Technical Reports Server (NTRS)

Lai, Steven H.-Y.

1992-01-01

A variational principle and a finite element discretization technique were used to derive the dynamic equations for a high speed rotating flexible beam-mass system embedded with piezo-electric materials. The dynamic equation thus obtained allows the development of finite element models which accommodate both the original structural element and the piezoelectric element. The solutions of finite element models provide system dynamics needed to design a sensing system. The characterization of gyroscopic effect and damping capacity of smart rotating devices are addressed. Several simulation examples are presented to validate the analytical solution.

Time-domain simulation of flute-like instruments: comparison of jet-drive and discrete-vortex models.

PubMed

Auvray, Roman; Ernoult, Augustin; Fabre, Benoît; Lagrée, Pierre-Yves

2014-07-01

This paper presents two models of sound production in flute-like instruments that allow time-domain simulations. The models are based on different descriptions of the jet flow within the window of the instrument. The jet-drive model depicts the jet by its transverse perturbation that interacts with the labium to produce sound. The discrete-vortex model depicts the jet as two independent shear layers along which vortices are convected and interact with the acoustic field within the window. The limit of validity between both models is usually discussed according to the aspect ratio of the jet W/h, with W the window length and h the flue channel height. The present simulations, compared with experimental data gathered on a recorder, allow to extend the aspect ratio criterion to the notion of dynamic aspect ratio defined as λ/h where λ is the hydrodynamic wavelength that now accounts for geometrical properties, such as W/h, as well as for dynamic properties, such as the Strouhal number. The two models are found to be applicable over neighboring values of geometry and blowing pressure.

A discrete mesoscopic particle model of the mechanics of a multi-constituent arterial wall.

PubMed

Witthoft, Alexandra; Yazdani, Alireza; Peng, Zhangli; Bellini, Chiara; Humphrey, Jay D; Karniadakis, George Em

2016-01-01

Blood vessels have unique properties that allow them to function together within a complex, self-regulating network. The contractile capacity of the wall combined with complex mechanical properties of the extracellular matrix enables vessels to adapt to changes in haemodynamic loading. Homogenized phenomenological and multi-constituent, structurally motivated continuum models have successfully captured these mechanical properties, but truly describing intricate microstructural details of the arterial wall may require a discrete framework. Such an approach would facilitate modelling interactions between or the separation of layers of the wall and would offer the advantage of seamless integration with discrete models of complex blood flow. We present a discrete particle model of a multi-constituent, nonlinearly elastic, anisotropic arterial wall, which we develop using the dissipative particle dynamics method. Mimicking basic features of the microstructure of the arterial wall, the model comprises an elastin matrix having isotropic nonlinear elastic properties plus anisotropic fibre reinforcement that represents the stiffer collagen fibres of the wall. These collagen fibres are distributed evenly and are oriented in four directions, symmetric to the vessel axis. Experimental results from biaxial mechanical tests of an artery are used for model validation, and a delamination test is simulated to demonstrate the new capabilities of the model. © 2016 The Author(s).

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Disaggregation and Refinement of System Dynamics Models via Agent-based Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutaro, James J; Ozmen, Ozgur; Schryver, Jack C

System dynamics models are usually used to investigate aggregate level behavior, but these models can be decomposed into agents that have more realistic individual behaviors. Here we develop a simple model of the STEM workforce to illuminate the impacts that arise from the disaggregation and refinement of system dynamics models via agent-based modeling. Particularly, alteration of Poisson assumptions, adding heterogeneity to decision-making processes of agents, and discrete-time formulation are investigated and their impacts are illustrated. The goal is to demonstrate both the promise and danger of agent-based modeling in the context of a relatively simple model and to delineate themore » importance of modeling decisions that are often overlooked.« less

Investigation of the effects of sleeper-passing impacts on the high-speed train

NASA Astrophysics Data System (ADS)

Wu, Xingwen; Cai, Wubin; Chi, Maoru; Wei, Lai; Shi, Huailong; Zhu, Minhao

2015-12-01

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.

Identification of cascade water tanks using a PWARX model

NASA Astrophysics Data System (ADS)

Mattsson, Per; Zachariah, Dave; Stoica, Petre

2018-06-01

In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

Viewing hybrid systems as products of control systems and automata

NASA Technical Reports Server (NTRS)

Grossman, R. L.; Larson, R. G.

1992-01-01

The purpose of this note is to show how hybrid systems may be modeled as products of nonlinear control systems and finite state automata. By a hybrid system, we mean a network of consisting of continuous, nonlinear control system connected to discrete, finite state automata. Our point of view is that the automata switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. We show how a nonlinear control system may be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. We also show that a finite automata has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces.

Discrete Event Simulation Models for CT Examination Queuing in West China Hospital.

PubMed

Luo, Li; Liu, Hangjiang; Liao, Huchang; Tang, Shijun; Shi, Yingkang; Guo, Huili

2016-01-01

In CT examination, the emergency patients (EPs) have highest priorities in the queuing system and thus the general patients (GPs) have to wait for a long time. This leads to a low degree of satisfaction of the whole patients. The aim of this study is to improve the patients' satisfaction by designing new queuing strategies for CT examination. We divide the EPs into urgent type and emergency type and then design two queuing strategies: one is that the urgent patients (UPs) wedge into the GPs' queue with fixed interval (fixed priority model) and the other is that the patients have dynamic priorities for queuing (dynamic priority model). Based on the data from Radiology Information Database (RID) of West China Hospital (WCH), we develop some discrete event simulation models for CT examination according to the designed strategies. We compare the performance of different strategies on the basis of the simulation results. The strategy that patients have dynamic priorities for queuing makes the waiting time of GPs decrease by 13 minutes and the degree of satisfaction increase by 40.6%. We design a more reasonable CT examination queuing strategy to decrease patients' waiting time and increase their satisfaction degrees.

Discrete Event Simulation Models for CT Examination Queuing in West China Hospital

PubMed Central

Luo, Li; Tang, Shijun; Shi, Yingkang; Guo, Huili

2016-01-01

In CT examination, the emergency patients (EPs) have highest priorities in the queuing system and thus the general patients (GPs) have to wait for a long time. This leads to a low degree of satisfaction of the whole patients. The aim of this study is to improve the patients' satisfaction by designing new queuing strategies for CT examination. We divide the EPs into urgent type and emergency type and then design two queuing strategies: one is that the urgent patients (UPs) wedge into the GPs' queue with fixed interval (fixed priority model) and the other is that the patients have dynamic priorities for queuing (dynamic priority model). Based on the data from Radiology Information Database (RID) of West China Hospital (WCH), we develop some discrete event simulation models for CT examination according to the designed strategies. We compare the performance of different strategies on the basis of the simulation results. The strategy that patients have dynamic priorities for queuing makes the waiting time of GPs decrease by 13 minutes and the degree of satisfaction increase by 40.6%. We design a more reasonable CT examination queuing strategy to decrease patients' waiting time and increase their satisfaction degrees. PMID:27547237

Discrete time modeling and stability analysis of TCP Vegas

NASA Astrophysics Data System (ADS)

You, Byungyong; Koo, Kyungmo; Lee, Jin S.

2007-12-01

This paper presents an analysis method for TCP Vegas network model with single link and single source. Some papers showed global stability of several network models, but those models are not a dual problem where dynamics both exist in sources and links such as TCP Vegas. Other papers studied TCP Vegas as a dual problem, but it did not fully derive an asymptotic stability region. Therefore we analyze TCP Vegas with Jury's criterion which is necessary and sufficient condition. So we use state space model in discrete time and by using Jury's criterion, we could find an asymptotic stability region of TCP Vegas network model. This result is verified by ns-2 simulation. And by comparing with other results, we could know our method performed well.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Global Sensitivity Applied to Dynamic Combined Finite Discrete Element Methods for Fracture Simulation

NASA Astrophysics Data System (ADS)

Godinez, H. C.; Rougier, E.; Osthus, D.; Srinivasan, G.

2017-12-01

Fracture propagation play a key role for a number of application of interest to the scientific community. From dynamic fracture processes like spall and fragmentation in metals and detection of gas flow in static fractures in rock and the subsurface, the dynamics of fracture propagation is important to various engineering and scientific disciplines. In this work we implement a global sensitivity analysis test to the Hybrid Optimization Software Suite (HOSS), a multi-physics software tool based on the combined finite-discrete element method, that is used to describe material deformation and failure (i.e., fracture and fragmentation) under a number of user-prescribed boundary conditions. We explore the sensitivity of HOSS for various model parameters that influence how fracture are propagated through a material of interest. The parameters control the softening curve that the model relies to determine fractures within each element in the mesh, as well a other internal parameters which influence fracture behavior. The sensitivity method we apply is the Fourier Amplitude Sensitivity Test (FAST), which is a global sensitivity method to explore how each parameter influence the model fracture and to determine the key model parameters that have the most impact on the model. We present several sensitivity experiments for different combination of model parameters and compare against experimental data for verification.

Landau-Zener transitions and Dykhne formula in a simple continuum model

NASA Astrophysics Data System (ADS)

Dunham, Yujin; Garmon, Savannah

The Landau-Zener model describing the interaction between two linearly driven discrete levels is useful in describing many simple dynamical systems; however, no system is completely isolated from the surrounding environment. Here we examine a generalizations of the original Landau-Zener model to study simple environmental influences. We consider a model in which one of the discrete levels is replaced with a energy continuum, in which we find that the survival probability for the initially occupied diabatic level is unaffected by the presence of the continuum. This result can be predicted by assuming that each step in the evolution for the diabatic state evolves independently according to the Landau-Zener formula, even in the continuum limit. We also show that, at least for the simplest model, this result can also be predicted with the natural generalization of the Dykhne formula for open systems. We also observe dissipation as the non-escape probability from the discrete levels is no longer equal to one.

Solving a discrete model of the lac operon using Z3

NASA Astrophysics Data System (ADS)

Gutierrez, Natalia A.

2014-05-01

A discrete model for the Lcac Operon is solved using the SMT-solver Z3. Traditionally the Lac Operon is formulated in a continuous math model. This model is a system of ordinary differential equations. Here, it was considerated as a discrete model, based on a Boolean red. The biological problem of Lac Operon is enunciated as a problem of Boolean satisfiability, and it is solved using an STM-solver named Z3. Z3 is a powerful solver that allows understanding the basic dynamic of the Lac Operon in an easier and more efficient way. The multi-stability of the Lac Operon can be easily computed with Z3. The code that solves the Boolean red can be written in Python language or SMT-Lib language. Both languages were used in local version of the program as online version of Z3. For future investigations it is proposed to solve the Boolean red of Lac Operon using others SMT-solvers as cvc4, alt-ergo, mathsat and yices.

Spatiotemporal pattern in somitogenesis: a non-Turing scenario with wave propagation.

PubMed

Nagahara, Hiroki; Ma, Yue; Takenaka, Yoshiko; Kageyama, Ryoichiro; Yoshikawa, Kenichi

2009-08-01

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

One-Dimensional Collision Carts Computer Model and Its Design Ideas for Productive Experiential Learning

ERIC Educational Resources Information Center

Wee, Loo Kang

2012-01-01

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a…

Dynamical clustering of red blood cells in capillary vessels.

PubMed

Boryczko, Krzysztof; Dzwinel, Witold; Yuen, David A

2003-02-01

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.

A comparison of dynamic and static economic models of uneven-aged stand management

Treesearch

Robert G. Haight

1985-01-01

Numerical techniques have been used to compute the discrete-time sequence of residual diameter distributions that maximize the present net worth (PNW) of harvestable volume from an uneven-aged stand. Results contradicted optimal steady-state diameter distributions determined with static analysis. In this paper, optimality conditions for solutions to dynamic and static...

Dynamical Localization for Discrete and Continuous Random Schrödinger Operators

NASA Astrophysics Data System (ADS)

Germinet, F.; De Bièvre, S.

We show for a large class of random Schrödinger operators Ho on and on that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real, Here ψ is a function of sufficiently rapid decrease, and PI(Ho) is the spectral projector of Ho corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of Ho and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.

Solving protein structures using short-distance cross-linking constraints as a guide for discrete molecular dynamics simulations

PubMed Central

Brodie, Nicholas I.; Popov, Konstantin I.; Petrotchenko, Evgeniy V.; Dokholyan, Nikolay V.; Borchers, Christoph H.

2017-01-01

We present an integrated experimental and computational approach for de novo protein structure determination in which short-distance cross-linking data are incorporated into rapid discrete molecular dynamics (DMD) simulations as constraints, reducing the conformational space and achieving the correct protein folding on practical time scales. We tested our approach on myoglobin and FK506 binding protein—models for α helix–rich and β sheet–rich proteins, respectively—and found that the lowest-energy structures obtained were in agreement with the crystal structure, hydrogen-deuterium exchange, surface modification, and long-distance cross-linking validation data. Our approach is readily applicable to other proteins with unknown structures. PMID:28695211

Solving protein structures using short-distance cross-linking constraints as a guide for discrete molecular dynamics simulations.

PubMed

Brodie, Nicholas I; Popov, Konstantin I; Petrotchenko, Evgeniy V; Dokholyan, Nikolay V; Borchers, Christoph H

2017-07-01

We present an integrated experimental and computational approach for de novo protein structure determination in which short-distance cross-linking data are incorporated into rapid discrete molecular dynamics (DMD) simulations as constraints, reducing the conformational space and achieving the correct protein folding on practical time scales. We tested our approach on myoglobin and FK506 binding protein-models for α helix-rich and β sheet-rich proteins, respectively-and found that the lowest-energy structures obtained were in agreement with the crystal structure, hydrogen-deuterium exchange, surface modification, and long-distance cross-linking validation data. Our approach is readily applicable to other proteins with unknown structures.

Domain decomposition methods in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gropp, William D.; Keyes, David E.

1991-01-01

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Modelling and simulation techniques for membrane biology.

PubMed

Burrage, Kevin; Hancock, John; Leier, André; Nicolau, Dan V

2007-07-01

One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics. On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes.

Stochastic hybrid delay population dynamics: well-posed models and extinction.

PubMed

Yuan, Chenggui; Mao, Xuerong; Lygeros, John

2009-01-01

Nonlinear differential equations have been used for decades for studying fluctuations in the populations of species, interactions of species with the environment, and competition and symbiosis between species. Over the years, the original non-linear models have been embellished with delay terms, stochastic terms and more recently discrete dynamics. In this paper, we investigate stochastic hybrid delay population dynamics (SHDPD), a very general class of population dynamics that comprises all of these phenomena. For this class of systems, we provide sufficient conditions to ensure that SHDPD have global positive, ultimately bounded solutions, a minimum requirement for a realistic, well-posed model. We then study the question of extinction and establish conditions under which an ecosystem modelled by SHDPD is doomed.

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, Charles E.

1990-01-01

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

A mathematical model of the structure and evolution of small scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, C. E.

1990-01-01

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Deep Brain Stimulation Frequency—A Divining Rod for New and Novel Concepts of Nervous System Function and Therapy

PubMed Central

Montgomery, Erwin B.; He, Huang

2016-01-01

The efficacy of Deep Brain Stimulation (DBS) for an expanding array of neurological and psychiatric disorders demonstrates directly that DBS affects the basic electroneurophysiological mechanisms of the brain. The increasing array of active electrode configurations, stimulation currents, pulse widths, frequencies, and pulse patterns provides valuable tools to probe electroneurophysiological mechanisms. The extension of basic electroneurophysiological and anatomical concepts using sophisticated computational modeling and simulation has provided relatively straightforward explanations of all the DBS parameters except frequency. This article summarizes current thought about frequency and relevant observations. Current methodological and conceptual errors are critically examined in the hope that future work will not replicate these errors. One possible alternative theory is presented to provide a contrast to many current theories. DBS, conceptually, is a noisy discrete oscillator interacting with the basal ganglia–thalamic–cortical system of multiple re-entrant, discrete oscillators. Implications for positive and negative resonance, stochastic resonance and coherence, noisy synchronization, and holographic memory (related to movement generation) are presented. The time course of DBS neuronal responses demonstrates evolution of the DBS response consistent with the dynamics of re-entrant mechanisms. Finally, computational modeling demonstrates identical dynamics as seen by neuronal activities recorded from human and nonhuman primates, illustrating the differences of discrete from continuous harmonic oscillators and the power of conceptualizing the nervous system as composed on interacting discrete nonlinear oscillators. PMID:27548234

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

Tuning Fractures With Dynamic Data

NASA Astrophysics Data System (ADS)

Yao, Mengbi; Chang, Haibin; Li, Xiang; Zhang, Dongxiao

2018-02-01

Flow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non-Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough-transform method is employed to parameterize non-Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is capable of dealing with strongly nonlinear problems. A series of numerical case studies with increasing complexity are set up to examine the performance of the proposed approach.

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

NASA Technical Reports Server (NTRS)

Heyliger, P. R.; Ramirez, G.; Pei, K. C.

1994-01-01

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Model-Based Prognostics of Hybrid Systems

NASA Technical Reports Server (NTRS)

Daigle, Matthew; Roychoudhury, Indranil; Bregon, Anibal

2015-01-01

Model-based prognostics has become a popular approach to solving the prognostics problem. However, almost all work has focused on prognostics of systems with continuous dynamics. In this paper, we extend the model-based prognostics framework to hybrid systems models that combine both continuous and discrete dynamics. In general, most systems are hybrid in nature, including those that combine physical processes with software. We generalize the model-based prognostics formulation to hybrid systems, and describe the challenges involved. We present a general approach for modeling hybrid systems, and overview methods for solving estimation and prediction in hybrid systems. As a case study, we consider the problem of conflict (i.e., loss of separation) prediction in the National Airspace System, in which the aircraft models are hybrid dynamical systems.

Adjustable Autonomy Testbed

NASA Technical Reports Server (NTRS)

Malin, Jane T.; Schrenkenghost, Debra K.

2001-01-01

The Adjustable Autonomy Testbed (AAT) is a simulation-based testbed located in the Intelligent Systems Laboratory in the Automation, Robotics and Simulation Division at NASA Johnson Space Center. The purpose of the testbed is to support evaluation and validation of prototypes of adjustable autonomous agent software for control and fault management for complex systems. The AA T project has developed prototype adjustable autonomous agent software and human interfaces for cooperative fault management. This software builds on current autonomous agent technology by altering the architecture, components and interfaces for effective teamwork between autonomous systems and human experts. Autonomous agents include a planner, flexible executive, low level control and deductive model-based fault isolation. Adjustable autonomy is intended to increase the flexibility and effectiveness of fault management with an autonomous system. The test domain for this work is control of advanced life support systems for habitats for planetary exploration. The CONFIG hybrid discrete event simulation environment provides flexible and dynamically reconfigurable models of the behavior of components and fluids in the life support systems. Both discrete event and continuous (discrete time) simulation are supported, and flows and pressures are computed globally. This provides fast dynamic simulations of interacting hardware systems in closed loops that can be reconfigured during operations scenarios, producing complex cascading effects of operations and failures. Current object-oriented model libraries support modeling of fluid systems, and models have been developed of physico-chemical and biological subsystems for processing advanced life support gases. In FY01, water recovery system models will be developed.

Modeling of light dynamic cone penetration test - Panda 3 ® in granular material by using 3D Discrete element method

NASA Astrophysics Data System (ADS)

Tran, Quoc Anh; Chevalier, Bastien; Benz, Miguel; Breul, Pierre; Gourvès, Roland

2017-06-01

The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load-penetration curve σp - sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load-penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip's load-penetration curve. The load-penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.

Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences

NASA Astrophysics Data System (ADS)

Naimzada, A. K.; Pireddu, M.

2018-05-01

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are characterized by different preference structures. The reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is initially increasing with its visibility level, but it becomes decreasing when its visibility exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. More precisely, we investigate the existence of equilibria and their stability, and we perform a qualitative bifurcation analysis on varying the parameter describing the group's heterogeneity degree. From a global viewpoint, we detect, among others, multistability phenomena in which the group coexistence is dynamic, either regular or irregular, and the fashion cycle occurs. The existence of complex dynamics is proven via the method of the turbulent maps, working with homoclinic orbits. Finally, we provide a social and economic interpretation of the main scenarios.

Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences.

PubMed

Naimzada, A K; Pireddu, M

2018-05-01

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are characterized by different preference structures. The reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is initially increasing with its visibility level, but it becomes decreasing when its visibility exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. More precisely, we investigate the existence of equilibria and their stability, and we perform a qualitative bifurcation analysis on varying the parameter describing the group's heterogeneity degree. From a global viewpoint, we detect, among others, multistability phenomena in which the group coexistence is dynamic, either regular or irregular, and the fashion cycle occurs. The existence of complex dynamics is proven via the method of the turbulent maps, working with homoclinic orbits. Finally, we provide a social and economic interpretation of the main scenarios.

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

NASA Astrophysics Data System (ADS)

Khaninezhad, Mohammad-Reza; Golmohammadi, Azarang; Jafarpour, Behnam

2018-04-01

Subsurface flow model calibration involves many more unknowns than measurements, leading to ill-posed problems with nonunique solutions. To alleviate nonuniqueness, the problem is regularized by constraining the solution space using prior knowledge. In certain sedimentary environments, such as fluvial systems, the contrast in hydraulic properties of different facies types tends to dominate the flow and transport behavior, making the effect of within facies heterogeneity less significant. Hence, flow model calibration in those formations reduces to delineating the spatial structure and connectivity of different lithofacies types and their boundaries. A major difficulty in calibrating such models is honoring the discrete, or piecewise constant, nature of facies distribution. The problem becomes more challenging when complex spatial connectivity patterns with higher-order statistics are involved. This paper introduces a novel formulation for calibration of complex geologic facies by imposing appropriate constraints to recover plausible solutions that honor the spatial connectivity and discreteness of facies models. To incorporate prior connectivity patterns, plausible geologic features are learned from available training models. This is achieved by learning spatial patterns from training data, e.g., k-SVD sparse learning or the traditional Principal Component Analysis. Discrete regularization is introduced as a penalty functions to impose solution discreteness while minimizing the mismatch between observed and predicted data. An efficient gradient-based alternating directions algorithm is combined with variable splitting to minimize the resulting regularized nonlinear least squares objective function. Numerical results show that imposing learned facies connectivity and discreteness as regularization functions leads to geologically consistent solutions that improve facies calibration quality.

Time-domain damping models in structural acoustics using digital filtering

NASA Astrophysics Data System (ADS)

Parret-Fréaud, Augustin; Cotté, Benjamin; Chaigne, Antoine

2016-02-01

This paper describes a new approach in order to formulate well-posed time-domain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam, etc.), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Parametric instability of spinning elastic rings excited by fluctuating space-fixed stiffnesses

NASA Astrophysics Data System (ADS)

Liu, Chunguang; Cooley, Christopher G.; Parker, Robert G.

2017-07-01

This study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space-fixed discrete stiffnesses with periodically fluctuating stiffnesses. The rotating, elastic ring is modeled using thin-ring theory with radial and tangential deformations. Primary and combination instability regions are determined in closed-form using the method of multiple scales. The ratio of peak-to-peak fluctuation to average discrete stiffness is used as the perturbation parameter, so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses. The natural frequencies and vibration modes are determined by discretizing the governing equations using Galerkin's method. Results are demonstrated for compliant gear applications. The perturbation results are validated by direct numerical integration of the equations of motion and Floquet theory. The bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses. For rings with multiple discrete stiffnesses, the phase differences between them can eliminate large amplitude response under certain conditions.

Rigidity, Criticality and Prethermalization of Discrete Time Crystals

NASA Astrophysics Data System (ADS)

Yao, Norman

2017-04-01

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal (DTC) is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. In this talk, I will describe a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. I will analyze the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Effects of long-range interactions and pre-thermalization will be considered in the context of recent DTC realizations in trapped ions and solid-state spins.

Quantifying the effect of hydrogen on dislocation dynamics: A three-dimensional discrete dislocation dynamics framework

NASA Astrophysics Data System (ADS)

Gu, Yejun; El-Awady, Jaafar A.

2018-03-01

We present a new framework to quantify the effect of hydrogen on dislocations using large scale three-dimensional (3D) discrete dislocation dynamics (DDD) simulations. In this model, the first order elastic interaction energy associated with the hydrogen-induced volume change is accounted for. The three-dimensional stress tensor induced by hydrogen concentration, which is in equilibrium with respect to the dislocation stress field, is derived using the Eshelby inclusion model, while the hydrogen bulk diffusion is treated as a continuum process. This newly developed framework is utilized to quantify the effect of different hydrogen concentrations on the dynamics of a glide dislocation in the absence of an applied stress field as well as on the spacing between dislocations in an array of parallel edge dislocations. A shielding effect is observed for materials having a large hydrogen diffusion coefficient, with the shield effect leading to the homogenization of the shrinkage process leading to the glide loop maintaining its circular shape, as well as resulting in a decrease in dislocation separation distances in the array of parallel edge dislocations. On the other hand, for materials having a small hydrogen diffusion coefficient, the high hydrogen concentrations around the edge characters of the dislocations act to pin them. Higher stresses are required to be able to unpin the dislocations from the hydrogen clouds surrounding them. Finally, this new framework can open the door for further large scale studies on the effect of hydrogen on the different aspects of dislocation-mediated plasticity in metals. With minor modifications of the current formulations, the framework can also be extended to account for general inclusion-induced stress field in discrete dislocation dynamics simulations.

Dynamical Localization for Unitary Anderson Models

NASA Astrophysics Data System (ADS)

Hamza, Eman; Joye, Alain; Stolz, Günter

2009-11-01

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

Extensions to the Dynamic Aerospace Vehicle Exchange Markup Language

NASA Technical Reports Server (NTRS)

Brian, Geoffrey J.; Jackson, E. Bruce

2011-01-01

The Dynamic Aerospace Vehicle Exchange Markup Language (DAVE-ML) is a syntactical language for exchanging flight vehicle dynamic model data. It provides a framework for encoding entire flight vehicle dynamic model data packages for exchange and/or long-term archiving. Version 2.0.1 of DAVE-ML provides much of the functionality envisioned for exchanging aerospace vehicle data; however, it is limited in only supporting scalar time-independent data. Additional functionality is required to support vector and matrix data, abstracting sub-system models, detailing dynamics system models (both discrete and continuous), and defining a dynamic data format (such as time sequenced data) for validation of dynamics system models and vehicle simulation packages. Extensions to DAVE-ML have been proposed to manage data as vectors and n-dimensional matrices, and record dynamic data in a compatible form. These capabilities will improve the clarity of data being exchanged, simplify the naming of parameters, and permit static and dynamic data to be stored using a common syntax within a single file; thereby enhancing the framework provided by DAVE-ML for exchanging entire flight vehicle dynamic simulation models.

Dynamic cone penetration tests in granular media: Determination of the tip's dynamic load-penetration curve

NASA Astrophysics Data System (ADS)

Escobar, E.; Benz, M.; Gourvès, R.; Breul, P.

2013-06-01

In this article a two-dimensional discrete numerical model, realized in PFC2D, is presented. This model is used in the dynamic penetration tests in a granular medium. Its objective being the validation of the measurement technique offered by Panda 3® (Benz et al. 2011) which is designed to calculate the tip's load-penetration curve for each impact in the soil where different parameters are used. To do so, we have compared the results obtained by calculation during the impacts to those measured directly in the model of a penetrometer through the installation of the gauges at the cone.

Representing and reasoning about program in situation calculus

NASA Astrophysics Data System (ADS)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

Discrete-element simulation of sea-ice mechanics: Contact mechanics and granular jamming

NASA Astrophysics Data System (ADS)

Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.

2017-12-01

Lagrangian models of sea-ice dynamics offer several advantages to Eulerian continuum methods. Spatial discretization on the ice-floe scale is natural for Lagrangian models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in Eulerian models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum formulations, jamming occurs naturally in dense granular systems simulated in a Lagrangian framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-element framework for simulating Lagrangian sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.

Comments on "Drill-string horizontal dynamics with uncertainty on the frictional force" by T.G. Ritto, M.R. Escalante, Rubens Sampaio, M.B. Rosales [J. Sound Vib. 332 (2013) 145-153

NASA Astrophysics Data System (ADS)

Li, Zifeng

2016-12-01

This paper analyzes the mechanical and mathematical models in "Ritto et al. (2013) [1]". The results are that: (1) the mechanical model is obviously incorrect; (2) the mathematical model is not complete; (3) the differential equation is obviously incorrect; (4) the finite element equation is obviously not discretized from the corresponding mathematical model above, and is obviously incorrect. A mathematical model of dynamics should include the differential equations, the boundary conditions and the initial conditions.

Asymmetric statistics of order books: The role of discreteness and evidence for strategic order placement

NASA Astrophysics Data System (ADS)

Zaccaria, A.; Cristelli, M.; Alfi, V.; Ciulla, F.; Pietronero, L.

2010-06-01

We show that the statistics of spreads in real order books is characterized by an intrinsic asymmetry due to discreteness effects for even or odd values of the spread. An analysis of data from the New York Stock Exchange (NYSE) order book points out that traders’ strategies contribute to this asymmetry. We also investigate this phenomenon in the framework of a microscopic model and, by introducing a nonuniform deposition mechanism for limit orders, we are able to quantitatively reproduce the asymmetry found in the experimental data. Simulations of our model also show a realistic dynamics with a sort of intermittent behavior characterized by long periods in which the order book is compact and liquid interrupted by volatile configurations. The order placement strategies produce a nontrivial behavior of the spread relaxation dynamics which is similar to the one observed in real markets.

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

PubMed

Beard, D A; Schlick, T

2001-01-01

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels. Copyright 2000 John Wiley & Sons, Inc.

Ab initio folding of proteins using all-atom discrete molecular dynamics

PubMed Central

Ding, Feng; Tsao, Douglas; Nie, Huifen; Dokholyan, Nikolay V.

2008-01-01

Summary Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. Using the replica exchange method, we perform folding simulations of six small proteins (20–60 residues) with distinct native structures. In all cases, native or near-native states are reached in simulations. For three small proteins, multiple folding transitions are observed and the computationally-characterized thermodynamics are in quantitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes, and applied to protein engineering and design of protein-protein interactions. PMID:18611374

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Optimal post-experiment estimation of poorly modeled dynamic systems

NASA Technical Reports Server (NTRS)

Mook, D. Joseph

1988-01-01

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates.

Formal modeling and analysis of ER-α associated Biological Regulatory Network in breast cancer.

PubMed

Khalid, Samra; Hanif, Rumeza; Tareen, Samar H K; Siddiqa, Amnah; Bibi, Zurah; Ahmad, Jamil

2016-01-01

Breast cancer (BC) is one of the leading cause of death among females worldwide. The increasing incidence of BC is due to various genetic and environmental changes which lead to the disruption of cellular signaling network(s). It is a complex disease in which several interlinking signaling cascades play a crucial role in establishing a complex regulatory network. The logical modeling approach of René Thomas has been applied to analyze the behavior of estrogen receptor-alpha (ER- α ) associated Biological Regulatory Network (BRN) for a small part of complex events that leads to BC metastasis. A discrete model was constructed using the kinetic logic formalism and its set of logical parameters were obtained using the model checking technique implemented in the SMBioNet software which is consistent with biological observations. The discrete model was further enriched with continuous dynamics by converting it into an equivalent Petri Net (PN) to analyze the logical parameters of the involved entities. In-silico based discrete and continuous modeling of ER- α associated signaling network involved in BC provides information about behaviors and gene-gene interaction in detail. The dynamics of discrete model revealed, imperative behaviors represented as cyclic paths and trajectories leading to pathogenic states such as metastasis. Results suggest that the increased expressions of receptors ER- α , IGF-1R and EGFR slow down the activity of tumor suppressor genes (TSGs) such as BRCA1, p53 and Mdm2 which can lead to metastasis. Therefore, IGF-1R and EGFR are considered as important inhibitory targets to control the metastasis in BC. The in-silico approaches allow us to increase our understanding of the functional properties of living organisms. It opens new avenues of investigations of multiple inhibitory targets (ER- α , IGF-1R and EGFR) for wet lab experiments as well as provided valuable insights in the treatment of cancers such as BC.

A potential method for lift evaluation from velocity field data

NASA Astrophysics Data System (ADS)

de Guyon-Crozier, Guillaume; Mulleners, Karen

2017-11-01

Computing forces from velocity field measurements is one of the challenges in experimental aerodynamics. This work focuses on low Reynolds flows, where the dynamics of the leading and trailing edge vortices play a major role in lift production. Recent developments in 2D potential flow theory, using discrete vortex models, have shown good results for unsteady wing motions. A method is presented to calculate lift from experimental velocity field data using a discrete vortex potential flow model. The model continuously adds new point vortices at leading and trailing edges whose circulations are set directly from vorticity measurements. Forces are computed using the unsteady Blasius equation and compared with measured loads.

Sampling Versus Filtering in Large-Eddy Simulations

NASA Technical Reports Server (NTRS)

Debliquy, O.; Knaepen, B.; Carati, D.; Wray, A. A.

2004-01-01

A LES formalism in which the filter operator is replaced by a sampling operator is proposed. The unknown quantities that appear in the LES equations originate only from inadequate resolution (Discretization errors). The resulting viewpoint seems to make a link between finite difference approaches and finite element methods. Sampling operators are shown to commute with nonlinearities and to be purely projective. Moreover, their use allows an unambiguous definition of the LES numerical grid. The price to pay is that sampling never commutes with spatial derivatives and the commutation errors must be modeled. It is shown that models for the discretization errors may be treated using the dynamic procedure. Preliminary results, using the Smagorinsky model, are very encouraging.

Dark Energy from Discrete Spacetime

PubMed Central

Trout, Aaron D.

2013-01-01

Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502

Applying differential dynamic logic to reconfigurable biological networks.

PubMed

Figueiredo, Daniel; Martins, Manuel A; Chaves, Madalena

2017-09-01

Qualitative and quantitative modeling frameworks are widely used for analysis of biological regulatory networks, the former giving a preliminary overview of the system's global dynamics and the latter providing more detailed solutions. Another approach is to model biological regulatory networks as hybrid systems, i.e., systems which can display both continuous and discrete dynamic behaviors. Actually, the development of synthetic biology has shown that this is a suitable way to think about biological systems, which can often be constructed as networks with discrete controllers, and present hybrid behaviors. In this paper we discuss this approach as a special case of the reconfigurability paradigm, well studied in Computer Science (CS). In CS there are well developed computational tools to reason about hybrid systems. We argue that it is worth applying such tools in a biological context. One interesting tool is differential dynamic logic (dL), which has recently been developed by Platzer and applied to many case-studies. In this paper we discuss some simple examples of biological regulatory networks to illustrate how dL can be used as an alternative, or also as a complement to methods already used. Copyright © 2017 Elsevier Inc. All rights reserved.

Flexible histone tails in a new mesoscopic oligonucleosome model.

PubMed

Arya, Gaurav; Zhang, Qing; Schlick, Tamar

2006-07-01

We describe a new mesoscopic model of oligonucleosomes that incorporates flexible histone tails. The nucleosome cores are modeled using the discrete surface-charge optimization model, which treats the nucleosome as an electrostatic surface represented by hundreds of point charges; the linker DNAs are treated using a discrete elastic chain model; and the histone tails are modeled using a bead/chain hydrodynamic approach as chains of connected beads where each bead represents five protein residues. Appropriate charges and force fields are assigned to each histone chain so as to reproduce the electrostatic potential, structure, and dynamics of the corresponding atomistic histone tails at different salt conditions. The dynamics of resulting oligonucleosomes at different sizes and varying salt concentrations are simulated by Brownian dynamics with complete hydrodynamic interactions. The analyses demonstrate that the new mesoscopic model reproduces experimental results better than its predecessors, which modeled histone tails as rigid entities. In particular, our model with flexible histone tails: correctly accounts for salt-dependent conformational changes in the histone tails; yields the experimentally obtained values of histone-tail mediated core/core attraction energies; and considers the partial shielding of electrostatic repulsion between DNA linkers as a result of the spatial distribution of histone tails. These effects are crucial for regulating chromatin structure but are absent or improperly treated in models with rigid histone tails. The development of this model of oligonucleosomes thus opens new avenues for studying the role of histone tails and their variants in mediating gene expression through modulation of chromatin structure.

Multiscale Modeling of Cell Interaction in Angiogenesis: From the Micro- to Macro-scale

NASA Astrophysics Data System (ADS)

Pillay, Samara; Maini, Philip; Byrne, Helen

Solid tumors require a supply of nutrients to grow in size. To this end, tumors induce the growth of new blood vessels from existing vasculature through the process of angiogenesis. In this work, we use a discrete agent-based approach to model the behavior of individual endothelial cells during angiogenesis. We incorporate crowding effects through volume exclusion, motility of cells through biased random walks, and include birth and death processes. We use the transition probabilities associated with the discrete models to determine collective cell behavior, in terms of partial differential equations, using a Markov chain and master equation framework. We find that the cell-level dynamics gives rise to a migrating cell front in the form of a traveling wave on the macro-scale. The behavior of this front depends on the cell interactions that are included and the extent to which volume exclusion is taken into account in the discrete micro-scale model. We also find that well-established continuum models of angiogenesis cannot distinguish between certain types of cell behavior on the micro-scale. This may impact drug development strategies based on these models.

Scale-free avalanche dynamics in crystal plasticity

NASA Astrophysics Data System (ADS)

Ispanovity, Pater Dusan; Laurson, Lasse; Zaiser, Michael; Zapperi, Stefano; Groma, Istvan; Alava, Mikko

2015-03-01

We investigate the properties of strain bursts (dislocation avalanches) occurring during plastic deformation of crystalline matter using two dimensional discrete dislocation dynamics (DDD). We perform quasistatic stress-controlled simulations with three DDD models differing in the spatiotemporal discretization and the mobility law assumed for individual dislocations. We find that each model exhibits identical avalanche dynamics with the following properties: (i) strain burst sizes follow a power law distribution characterized by an exponent τ ~ 1 . 0 and (ii) the distribution in truncated at a cutoff that diverges with increasing system size at any applied stress level. It has been proposed earlier that plastic yielding can be described in terms of a continuous phase transition of depinning type and its critical point is at the yield stress. We will demonstrate, however, that our results are inconsistent with cutoff scaling in depinning systems (like magnetic domain walls or earthquakes) and that the system behaves as critical at every stress level. We, therefore, conclude that in the models studied plastic yielding cannot be associated with a continuous phase transition. Financial supports of the Hungarian Scientific Research Fund (OTKA) under Contract Numbers PD-105256 and K-105335 and of the European Commission under Grant Agreement No. CIG-321842 are acknowledged.

Distinct Functional Modules for Discrete and Rhythmic Forelimb Movements in the Mouse Motor Cortex.

PubMed

Hira, Riichiro; Terada, Shin-Ichiro; Kondo, Masashi; Matsuzaki, Masanori

2015-09-30

Movements of animals are composed of two fundamental dynamics: discrete and rhythmic movements. Although the movements with distinct dynamics are thought to be differently processed in the CNS, it is unclear how they are represented in the cerebral cortex. Here, we investigated the cortical representation of movement dynamics by developing prolonged transcranial optogenetic stimulation (pTOS) using awake, channelrhodopsin-2 transgenic mice. We found two domains that induced discrete forelimb movements in the forward and backward directions, and these sandwiched a domain that generated rhythmic forelimb movements. The forward discrete movement had an intrinsic velocity profile and the rhythmic movement had an intrinsic oscillation frequency. Each of the forward discrete and rhythmic domains possessed intracortical synaptic connections within its own domain, independently projected to the spinal cord, and weakened the neuronal activity and movement induction of the other domain. pTOS-induced movements were also classified as ethologically relevant movements. Forepaw-to-mouth movement was mapped in a part of the forward discrete domain, while locomotion-like movement was in a part of the rhythmic domain. Interestingly, photostimulation of the rhythmic domain resulted in a nonrhythmic, continuous lever-pull movement when a lever was present. The motor cortex possesses functional modules for distinct movement dynamics, and these can adapt to environmental constraints for purposeful movements. Significance statement: Animal behavior has discrete and rhythmic components, such as reaching and locomotion. It is unclear how these movements with distinct dynamics are represented in the cerebral cortex. We investigated the dynamics of movements induced by long-duration transcranial photostimulation on the dorsal cortex of awake channelrhodopsin-2 transgenic mice. We found two domains causing forward and backward discrete forelimb movements and a domain for rhythmic forelimb movements. A domain for forward discrete movement and a domain for rhythmic movement mutually weakened neuronal activity and movement size. The photostimulation of the rhythmic domain also induced nonrhythmic, lever-pull movement, when the lever was present. Thus, the motor cortex has functional modules with distinct dynamics, and each module retains flexibility for adaptation to different environments. Copyright © 2015 the authors 0270-6474/15/3513311-12$15.00/0.

SmaggIce User Guide. 1.0

NASA Technical Reports Server (NTRS)

Baez, Marivell; Vickerman, Mary; Choo, Yung

2000-01-01

SmaggIce (Surface Modeling And Grid Generation for Iced Airfoils) is one of NASNs aircraft icing research codes developed at the Glenn Research Center. It is a software toolkit used in the process of aerodynamic performance prediction of iced airfoils. It includes tools which complement the 2D grid-based Computational Fluid Dynamics (CFD) process: geometry probing; surface preparation for gridding: smoothing and re-discretization of geometry. Future releases will also include support for all aspects of gridding: domain decomposition; perimeter discretization; grid generation and modification.

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

NASA Astrophysics Data System (ADS)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

Numerical modeling of the transmission dynamics of drug-sensitive and drug-resistant HSV-2

NASA Astrophysics Data System (ADS)

Gumel, A. B.

2001-03-01

A competitive finite-difference method will be constructed and used to solve a modified deterministic model for the spread of herpes simplex virus type-2 (HSV-2) within a given population. The model monitors the transmission dynamics and control of drug-sensitive and drug-resistant HSV-2. Unlike the fourth-order Runge-Kutta method (RK4), which fails when the discretization parameters exceed certain values, the novel numerical method to be developed in this paper gives convergent results for all parameter values.

Modeling of Stick-Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite-Discrete Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Ke; Euser, Bryan J.; Rougier, Esteban

Sheared granular layers undergoing stick-slip behavior are broadly employed to study the physics and dynamics of earthquakes. In this paper, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation whilemore » particle-particle and particle-plate interactions are modeled using DEM-derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases; (ii) the gouge layer thickness shows a decreasing trend; and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. Finally, the simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge, but also demonstrate the capabilities of FDEM for studying stick-slip dynamic behavior of granular fault systems.« less

Modeling of Stick-Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite-Discrete Element Method

DOE PAGES

Gao, Ke; Euser, Bryan J.; Rougier, Esteban; ...

2018-06-20

Sheared granular layers undergoing stick-slip behavior are broadly employed to study the physics and dynamics of earthquakes. In this paper, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation whilemore » particle-particle and particle-plate interactions are modeled using DEM-derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases; (ii) the gouge layer thickness shows a decreasing trend; and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. Finally, the simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge, but also demonstrate the capabilities of FDEM for studying stick-slip dynamic behavior of granular fault systems.« less

A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems

NASA Astrophysics Data System (ADS)

Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay

2017-01-01

In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.

Dynamics and Control of Flexible Space Vehicles

NASA Technical Reports Server (NTRS)

Likins, P. W.

1970-01-01

The purpose of this report is twofold: (1) to survey the established analytic procedures for the simulation of controlled flexible space vehicles, and (2) to develop in detail methods that employ a combination of discrete and distributed ("modal") coordinates, i.e., the hybrid-coordinate methods. Analytic procedures are described in three categories: (1) discrete-coordinate methods, (2) hybrid-coordinate methods, and (3) vehicle normal-coordinate methods. Each of these approaches is described and analyzed for its advantages and disadvantages, and each is found to have an area of applicability. The hybrid-coordinate method combines the efficiency of the vehicle normal-coordinate method with the versatility of the discrete-coordinate method, and appears to have the widest range of practical application. The results in this report have practical utility in two areas: (1) complex digital computer simulation of flexible space vehicles of arbitrary configuration subject to realistic control laws, and (2) preliminary control system design based on transfer functions for linearized models of dynamics and control laws.

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train-track interaction and inelastic deformations

NASA Astrophysics Data System (ADS)

Andersson, Robin; Torstensson, Peter T.; Kabo, Elena; Larsson, Fredrik

2015-11-01

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle-track interaction accounting for transient non-Hertzian wheel-rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang-Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

Fractal attractors in economic growth models with random pollution externalities

NASA Astrophysics Data System (ADS)

La Torre, Davide; Marsiglio, Simone; Privileggi, Fabio

2018-05-01

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.

A study of a diffusive model of asset returns and an empirical analysis of financial markets

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

A diffusive model for market dynamics is studied and the predictions of the model are compared to real financial markets. The model has a non-constant diffusion coefficient which depends both on the asset value and the time. A general solution for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases, piecewise linear and quadratic diffusion. The effects of discreteness in the market dynamics on the model are also studied. For the quadratic diffusion case, a type of phase transition leading to fat tails is observed as the discrete distribution approaches the continuum limit. It is also found that the model captures some of the empirical stylized facts observed in real markets, including fat-tails and scaling behavior in the distribution of returns. An analysis of empirical data for the EUR/USD currency exchange rate and the S&P 500 index is performed. Both markets show time scaling behavior consistent with a value of 1/2 for the Hurst exponent. Finally, the results show that the distribution of returns for the two markets is well fitted by the model, and the corresponding empirical diffusion coefficients are determined.

Software Surface Modeling and Grid Generation Steering Committee

NASA Technical Reports Server (NTRS)

Smith, Robert E. (Editor)

1992-01-01

It is a NASA objective to promote improvements in the capability and efficiency of computational fluid dynamics. Grid generation, the creation of a discrete representation of the solution domain, is an essential part of computational fluid dynamics. However, grid generation about complex boundaries requires sophisticated surface-model descriptions of the boundaries. The surface modeling and the associated computation of surface grids consume an extremely large percentage of the total time required for volume grid generation. Efficient and user friendly software systems for surface modeling and grid generation are critical for computational fluid dynamics to reach its potential. The papers presented here represent the state-of-the-art in software systems for surface modeling and grid generation. Several papers describe improved techniques for grid generation.

Encoding dependence in Bayesian causal networks

USDA-ARS?s Scientific Manuscript database

Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

Event-driven management algorithm of an Engineering documents circulation system

NASA Astrophysics Data System (ADS)

Kuzenkov, V.; Zebzeev, A.; Gromakov, E.

2015-04-01

Development methodology of an engineering documents circulation system in the design company is reviewed. Discrete event-driven automatic models using description algorithms of project management is offered. Petri net use for dynamic design of projects is offered.

Discrete Event-based Performance Prediction for Temperature Accelerated Dynamics

NASA Astrophysics Data System (ADS)

Junghans, Christoph; Mniszewski, Susan; Voter, Arthur; Perez, Danny; Eidenbenz, Stephan

2014-03-01

We present an example of a new class of tools that we call application simulators, parameterized fast-running proxies of large-scale scientific applications using parallel discrete event simulation (PDES). We demonstrate our approach with a TADSim application simulator that models the Temperature Accelerated Dynamics (TAD) method, which is an algorithmically complex member of the Accelerated Molecular Dynamics (AMD) family. The essence of the TAD application is captured without the computational expense and resource usage of the full code. We use TADSim to quickly characterize the runtime performance and algorithmic behavior for the otherwise long-running simulation code. We further extend TADSim to model algorithm extensions to standard TAD, such as speculative spawning of the compute-bound stages of the algorithm, and predict performance improvements without having to implement such a method. Focused parameter scans have allowed us to study algorithm parameter choices over far more scenarios than would be possible with the actual simulation. This has led to interesting performance-related insights into the TAD algorithm behavior and suggested extensions to the TAD method.

Study of a Simulation Tool to Determine Achievable Control Dynamics and Control Power Requirements with Perfect Tracking

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.

1998-01-01

This paper contains a study of two methods for use in a generic nonlinear simulation tool that could be used to determine achievable control dynamics and control power requirements while performing perfect tracking maneuvers over the entire flight envelope. The two methods are NDI (nonlinear dynamic inversion) and the SOFFT(Stochastic Optimal Feedforward and Feedback Technology) feedforward control structure. Equivalent discrete and continuous SOFFT feedforward controllers have been developed. These equivalent forms clearly show that the closed-loop plant model loop is a plant inversion and is the same as the NDI formulation. The main difference is that the NDI formulation has a closed-loop controller structure whereas SOFFT uses an open-loop command model. Continuous, discrete, and hybrid controller structures have been developed and integrated into the formulation. Linear simulation results show that seven different configurations all give essentially the same response, with the NDI hybrid being slightly different. The SOFFT controller gave better tracking performance compared to the NDI controller when a nonlinear saturation element was added. Future plans include evaluation using a nonlinear simulation.

Discretization chaos - Feedback control and transition to chaos

NASA Technical Reports Server (NTRS)

Grantham, Walter J.; Athalye, Amit M.

1990-01-01

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

NASA Astrophysics Data System (ADS)

Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.

2006-05-01

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

A model of economic growth with physical and human capital: The role of time delays.

PubMed

Gori, Luca; Guerrini, Luca; Sodini, Mauro

2016-09-01

This article aims at analysing a two-sector economic growth model with discrete delays. The focus is on the dynamic properties of the emerging system. In particular, this study concentrates on the stability properties of the stationary solution, characterised by analytical results and geometrical techniques (stability crossing curves), and the conditions under which oscillatory dynamics emerge (through Hopf bifurcations). In addition, this article proposes some numerical simulations to illustrate the behaviour of the system when the stationary equilibrium is unstable.

Structured population dynamics: continuous size and discontinuous stage structures.

PubMed

Buffoni, Giuseppe; Pasquali, Sara

2007-04-01

A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.

Application of Petri Nets in Bone Remodeling

PubMed Central

Li, Lingxi; Yokota, Hiroki

2009-01-01

Understanding a mechanism of bone remodeling is a challenging task for both life scientists and model builders, since this highly interactive and nonlinear process can seldom be grasped by simple intuition. A set of ordinary differential equations (ODEs) have been built for simulating bone formation as well as bone resorption. Although solving ODEs numerically can provide useful predictions for dynamical behaviors in a continuous time frame, an actual bone remodeling process in living tissues is driven by discrete events of molecular and cellular interactions. Thus, an event-driven tool such as Petri nets (PNs), which may dynamically and graphically mimic individual molecular collisions or cellular interactions, seems to augment the existing ODE-based systems analysis. Here, we applied PNs to expand the ODE-based approach and examined discrete, dynamical behaviors of key regulatory molecules and bone cells. PNs have been used in many engineering areas, but their application to biological systems needs to be explored. Our PN model was based on 8 ODEs that described an osteoprotegerin linked molecular pathway consisting of 4 types of bone cells. The models allowed us to conduct both qualitative and quantitative evaluations and evaluate homeostatic equilibrium states. The results support that application of PN models assists understanding of an event-driven bone remodeling mechanism using PN-specific procedures such as places, transitions, and firings. PMID:19838338

Complex dynamics of a delayed discrete neural network of two nonidentical neurons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yuanlong; Huang, Tingwen; Huang, Yu, E-mail: stshyu@mail.sysu.edu.cn

2014-03-15

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zoumore » [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.« less

Complex dynamics of a delayed discrete neural network of two nonidentical neurons.

PubMed

Chen, Yuanlong; Huang, Tingwen; Huang, Yu

2014-03-01

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.

Divergence compensation for hardware-in-the-loop simulation of stiffness-varying discrete contact in space

NASA Astrophysics Data System (ADS)

Qi, Chenkun; Zhao, Xianchao; Gao, Feng; Ren, Anye; Hu, Yan

2016-11-01

The hardware-in-the-loop (HIL) contact simulation for flying objects in space is challenging due to the divergence caused by the time delay. In this study, a divergence compensation approach is proposed for the stiffness-varying discrete contact. The dynamic response delay of the motion simulator and the force measurement delay are considered. For the force measurement delay, a phase lead based force compensation approach is used. For the dynamic response delay of the motion simulator, a response error based force compensation approach is used, where the compensation force is obtained from the real-time identified contact stiffness and real-time measured position response error. The dynamic response model of the motion simulator is not required. The simulations and experiments show that the simulation divergence can be compensated effectively and satisfactorily by using the proposed approach.

Principles of dynamical modularity in biological regulatory networks

PubMed Central

Deritei, Dávid; Aird, William C.; Ercsey-Ravasz, Mária; Regan, Erzsébet Ravasz

2016-01-01

Intractable diseases such as cancer are associated with breakdown in multiple individual functions, which conspire to create unhealthy phenotype-combinations. An important challenge is to decipher how these functions are coordinated in health and disease. We approach this by drawing on dynamical systems theory. We posit that distinct phenotype-combinations are generated by interactions among robust regulatory switches, each in control of a discrete set of phenotypic outcomes. First, we demonstrate the advantage of characterizing multi-switch regulatory systems in terms of their constituent switches by building a multiswitch cell cycle model which points to novel, testable interactions critical for early G2/M commitment to division. Second, we define quantitative measures of dynamical modularity, namely that global cell states are discrete combinations of switch-level phenotypes. Finally, we formulate three general principles that govern the way coupled switches coordinate their function. PMID:26979940

Simple deterministic models and applications. Comment on "Coupled disease-behavior dynamics on complex networks: A review" by Z. Wang et al.

NASA Astrophysics Data System (ADS)

Yang, Hyun Mo

2015-12-01

Currently, discrete modellings are largely accepted due to the access to computers with huge storage capacity and high performance processors and easy implementation of algorithms, allowing to develop and simulate increasingly sophisticated models. Wang et al. [7] present a review of dynamics in complex networks, focusing on the interaction between disease dynamics and human behavioral and social dynamics. By doing an extensive review regarding to the human behavior responding to disease dynamics, the authors briefly describe the complex dynamics found in the literature: well-mixed populations networks, where spatial structure can be neglected, and other networks considering heterogeneity on spatially distributed populations. As controlling mechanisms are implemented, such as social distancing due 'social contagion', quarantine, non-pharmaceutical interventions and vaccination, adaptive behavior can occur in human population, which can be easily taken into account in the dynamics formulated by networked populations.

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Effect of antibodies on pathogen dynamics with delays and two routes of infection

NASA Astrophysics Data System (ADS)

Elaiw, A. M.; Almatrafi, A. A.; Hobiny, A. D.

2018-06-01

We study the global stability of pathogen dynamics models with saturated pathogen-susceptible and infected-susceptible incidence. The models incorporate antibody immune response and three types of discrete or distributed time delays. We first show that the solutions of the model are nonnegative and ultimately bounded. We determine two threshold parameters, the basic reproduction number and antibody response activation number. We establish the existence and stability of the steady states. We study the global stability analysis of models using Lyapunov method. The numerical simulations have shown that antibodies can reduce the pathogen progression.

Adaptive feedback synchronisation of complex dynamical network with discrete-time communications and delayed nodes

NASA Astrophysics Data System (ADS)

Wang, Tong; Ding, Yongsheng; Zhang, Lei; Hao, Kuangrong

2016-08-01

This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov-Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.

Discrete-time pilot model. [human dynamics and digital simulation

NASA Technical Reports Server (NTRS)

Cavalli, D.

1978-01-01

Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.

Using CONFIG for Simulation of Operation of Water Recovery Subsystems for Advanced Control Software Evaluation

NASA Technical Reports Server (NTRS)

Malin, Jane T.; Flores, Luis; Fleming, Land; Throop, Daiv

2002-01-01

A hybrid discrete/continuous simulation tool, CONFIG, has been developed to support evaluation of the operability life support systems. CON FIG simulates operations scenarios in which flows and pressures change continuously while system reconfigurations occur as discrete events. In simulations, intelligent control software can interact dynamically with hardware system models. CONFIG simulations have been used to evaluate control software and intelligent agents for automating life support systems operations. A CON FIG model of an advanced biological water recovery system has been developed to interact with intelligent control software that is being used in a water system test at NASA Johnson Space Center

Simulation of Population Processes with a Programmable Pocket Calculator.

ERIC Educational Resources Information Center

Kidd, N. A. C.

1979-01-01

Presents a set of simulation models for use in teaching population dynamics. These models are designed specifically for use with a programmable pocket calculator, and can be used to demonstrate growth of populations with discrete or overlapping generations and also to explore effects of density-dependent and -independent mortality. (Author/CS)

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

A robust computational technique for model order reduction of two-time-scale discrete systems via genetic algorithms.

PubMed

Alsmadi, Othman M K; Abo-Hammour, Zaer S

2015-01-01

A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.

A model of the human in a cognitive prediction task.

NASA Technical Reports Server (NTRS)

Rouse, W. B.

1973-01-01

The human decision maker's behavior when predicting future states of discrete linear dynamic systems driven by zero-mean Gaussian processes is modeled. The task is on a slow enough time scale that physiological constraints are insignificant compared with cognitive limitations. The model is basically a linear regression system identifier with a limited memory and noisy observations. Experimental data are presented and compared to the model.

Digital controller design: Continuous and discrete describing function analysis of the IPS system

NASA Technical Reports Server (NTRS)

1977-01-01

The dynamic equations and the mathematical model of the continuous-data IPS control system are developed. The IPS model considered included one flexible body mode and was hardmounted to the Orbiter/Pallet. The model contains equations describing a torque feed-forward loop (using accelerometers as inputs) which will aid in reducing the pointing errors caused by Orbiter disturbances.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Youngsoo; Carlberg, Kevin Thomas

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over allmore » space and time in a weighted ℓ 2-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.« less

A BASIC Program for Use in Teaching Population Dynamics.

ERIC Educational Resources Information Center

Kidd, N. A. C.

1984-01-01

Describes an interactive simulation model which can be used to demonstrate population growth with discrete or overlapping populations and the effects of random, constant, or density-dependent mortality. The program listing (for Commodore PET 4032 microcomputer) is included. (Author/DH)

A juvenile-adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects.

PubMed

Veprauskas, Amy; Cushing, J M

2017-03-01

We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial-nesting gulls, specifically the glaucous-winged gull (Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile-adult structure model. Mathematically, the model is unusual in that it involves a high co-dimension bifurcation at [Formula: see text] which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non-cannibalistic population cannot.

Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities.

PubMed

Tchinang Tchameu, J D; Togueu Motcheyo, A B; Tchawoua, C

2014-10-01

We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov model to take into account the competition between local compression and local dilatation of the lattice, thus leading to the interplay between self-focusing and defocusing saturable nonlinearities. Site-centered (sc) mode and/or bond-centered mode like discrete multihump soliton (DMHS) solutions are found numerically and their stability is analyzed. As a result, we obtained the existence and stability diagrams for all observed types of sc DMHS solutions. We also note that the stability of sc DMHS solutions depends not only on the value of the interpeak separation but also on the number of peaks, while their counterpart having at least one intersite soliton is instable. A study of mobility is achieved and it appears that, depending on the higher-order saturable nonlinearity, DMHS-like mechanism for vibrational energy transport along the protein chain is possible.

From microscopic rules to macroscopic dynamics with active colloidal snakes

NASA Astrophysics Data System (ADS)

Zhang, Jie; Yan, Jing; Granick, Steve

Seeking to learn about self-assembly far from equilibrium, these imaging experiments inspect self-propelled colloidal particles whose heads and tails attract other particles reversibly as they swim. We observe processes akin to polymerization (short times) and chain scission and recombination (long times). The steady-state of dilute systems consists of discrete rings rotating in place with largely quenched dynamics, but when concentration is high, the system dynamics share features with turbulence. The dynamical rules of this model system appear to be scale-independent and hence potentially relevant more generally.

Small-signal model for the series resonant converter

NASA Technical Reports Server (NTRS)

King, R. J.; Stuart, T. A.

1985-01-01

The results of a previous discrete-time model of the series resonant dc-dc converter are reviewed and from these a small signal dynamic model is derived. This model is valid for low frequencies and is based on the modulation of the diode conduction angle for control. The basic converter is modeled separately from its output filter to facilitate the use of these results for design purposes. Experimental results are presented.

Individual-based modelling of population growth and diffusion in discrete time.

PubMed

Tkachenko, Natalie; Weissmann, John D; Petersen, Wesley P; Lake, George; Zollikofer, Christoph P E; Callegari, Simone

2017-01-01

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

Air-structure coupling features analysis of mining contra-rotating axial flow fan cascade

NASA Astrophysics Data System (ADS)

Chen, Q. G.; Sun, W.; Li, F.; Zhang, Y. J.

2013-12-01

The interaction between contra-rotating axial flow fan blade and working gas has been studied by means of establishing air-structure coupling control equation and combining Computational Fluid Dynamics (CFD) and Computational solid mechanics (CSM). Based on the single flow channel model, the Finite Volume Method was used to make the field discrete. Additionally, the SIMPLE algorithm, the Standard k-ε model and the Arbitrary Lagrangian-Eulerian dynamic grids technology were utilized to get the airflow motion by solving the discrete governing equations. At the same time, the Finite Element Method was used to make the field discrete to solve dynamic response characteristics of blade. Based on weak coupling method, data exchange from the fluid solver and the solid solver was processed on the coupling interface. Then interpolation was used to obtain the coupling characteristics. The results showed that the blade's maximum amplitude was on the tip of the last-stage blade and aerodynamic force signal could reflect the blade working conditions to some extent. By analyzing the flow regime in contra-rotating axial flow fan, it could be found that the vortex core region was mainly in the blade surface, the hub and the blade clearance. In those regions, the turbulence intensity was very high. The last-stage blade's operating life is shorter than that of the pre-stage blade due to the fatigue fracture occurs much more easily on the last-stage blade which bears more stress.

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach

NASA Astrophysics Data System (ADS)

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.; Marone, Chris; Carmeliet, Jan

2017-05-01

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this paper, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that the (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.

Dark energy from discrete spacetime.

PubMed

Trout, Aaron D

2013-01-01

Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.

Stochastic modeling for dynamics of HIV-1 infection using cellular automata: A review.

PubMed

Precharattana, Monamorn

2016-02-01

Recently, the description of immune response by discrete models has emerged to play an important role to study the problems in the area of human immunodeficiency virus type 1 (HIV-1) infection, leading to AIDS. As infection of target immune cells by HIV-1 mainly takes place in the lymphoid tissue, cellular automata (CA) models thus represent a significant step in understanding when the infected population is dispersed. Motivated by these, the studies of the dynamics of HIV-1 infection using CA in memory have been presented to recognize how CA have been developed for HIV-1 dynamics, which issues have been studied already and which issues still are objectives in future studies.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Effects of Gas Rarefaction on Dynamic Characteristics of Micro Spiral-Grooved Thrust Bearing.

PubMed

Liu, Ren; Wang, Xiao-Li; Zhang, Xiao-Qing

2012-04-01

The effects of gas-rarefaction on dynamic characteristics of micro spiral-grooved-thrust-bearing are studied. The Reynolds equation is modified by the first order slip model, and the corresponding perturbation equations are then obtained on the basis of the linear small perturbation method. In the converted spiral-curve-coordinates system, the finite-volume-method (FVM) is employed to discrete the surface domain of micro bearing. The results show, compared with the continuum-flow model, that under the slip-flow regime, the decrease in the pressure and stiffness become obvious with the increasing of the compressibility number. Moreover, with the decrease of the relative gas-film-thickness, the deviations of dynamic coefficients between slip-flow-model and continuum-flow-model are increasing.

Scalar and vector Keldysh models in the time domain

NASA Astrophysics Data System (ADS)

Kiselev, M. N.; Kikoin, K. A.

2009-04-01

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z 2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the vector Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.

Large-scale hydropower system optimization using dynamic programming and object-oriented programming: the case of the Northeast China Power Grid.

PubMed

Li, Ji-Qing; Zhang, Yu-Shan; Ji, Chang-Ming; Wang, Ai-Jing; Lund, Jay R

2013-01-01

This paper examines long-term optimal operation using dynamic programming for a large hydropower system of 10 reservoirs in Northeast China. Besides considering flow and hydraulic head, the optimization explicitly includes time-varying electricity market prices to maximize benefit. Two techniques are used to reduce the 'curse of dimensionality' of dynamic programming with many reservoirs. Discrete differential dynamic programming (DDDP) reduces the search space and computer memory needed. Object-oriented programming (OOP) and the ability to dynamically allocate and release memory with the C++ language greatly reduces the cumulative effect of computer memory for solving multi-dimensional dynamic programming models. The case study shows that the model can reduce the 'curse of dimensionality' and achieve satisfactory results.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

PubMed

Ma, Li-Yuan; Zhu, Zuo-Nong

2014-09-01

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

NASA Astrophysics Data System (ADS)

Li, Ling; Xiao, Xin-Biao; Jin, Xue-Song

2011-04-01

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen-Hedrick-Elkins' model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.

Discrete event simulation for exploring strategies: an urban water management case.

PubMed

Huang, Dong-Bin; Scholz, Roland W; Gujer, Willi; Chitwood, Derek E; Loukopoulos, Peter; Schertenleib, Roland; Siegrist, Hansruedi

2007-02-01

This paper presents a model structure aimed at offering an overview of the various elements of a strategy and exploring their multidimensional effects through time in an efficient way. It treats a strategy as a set of discrete events planned to achieve a certain strategic goal and develops a new form of causal networks as an interfacing component between decision makers and environment models, e.g., life cycle inventory and material flow models. The causal network receives a strategic plan as input in a discrete manner and then outputs the updated parameter sets to the subsequent environmental models. Accordingly, the potential dynamic evolution of environmental systems caused by various strategies can be stepwise simulated. It enables a way to incorporate discontinuous change in models for environmental strategy analysis, and enhances the interpretability and extendibility of a complex model by its cellular constructs. It is exemplified using an urban water management case in Kunming, a major city in Southwest China. By utilizing the presented method, the case study modeled the cross-scale interdependencies of the urban drainage system and regional water balance systems, and evaluated the effectiveness of various strategies for improving the situation of Dianchi Lake.

Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Marinelli, Dimitri; Marzuoli, Annalisa

2013-05-01

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second-order difference equation which, by a complex phase change, we turn into a discrete Schrödinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantum mechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary ‘quantum of space’, and a transparent asymptotic picture of the semiclassical and classical regimes emerges. The definition of coordinates adapted to the Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.

Attractors for discrete periodic dynamical systems

Treesearch

John E. Franke; James F. Selgrade

2003-01-01

A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...

Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.

ERIC Educational Resources Information Center

Gannon, Gerald E.; Martelli, Mario U.

2001-01-01

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows.

PubMed

Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Luo, Kai Hong; Li, Yingjun

2017-11-01

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific-heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

The Estimation Theory Framework of Data Assimilation

NASA Technical Reports Server (NTRS)

Cohn, S.; Atlas, Robert (Technical Monitor)

2002-01-01

Lecture 1. The Estimation Theory Framework of Data Assimilation: 1. The basic framework: dynamical and observation models; 2. Assumptions and approximations; 3. The filtering, smoothing, and prediction problems; 4. Discrete Kalman filter and smoother algorithms; and 5. Example: A retrospective data assimilation system

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. V.; Yerazunis, S. W.

1973-01-01

Problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars are reported. Problem areas include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis, terrain modeling and path selection; and chemical analysis of specimens. These tasks are summarized: vehicle model design, mathematical model of vehicle dynamics, experimental vehicle dynamics, obstacle negotiation, electrochemical controls, remote control, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, and chromatograph model evaluation and improvement.

Orbital maneuvering engine feed system coupled stability investigation

NASA Technical Reports Server (NTRS)

Kahn, D. R.; Schuman, M. D.; Hunting, J. K.; Fertig, K. W.

1975-01-01

A digital computer model used to analyze and predict engine feed system coupled instabilities over a frequency range of 10 to 1000 Hz was developed and verified. The analytical approach to modeling the feed system hydrodynamics, combustion dynamics, chamber dynamics, and overall engineering model structure is described and the governing equations in each of the technical areas are presented. This is followed by a description of the generalized computer model, including formulation of the discrete subprograms and their integration into an overall engineering model structure. The operation and capabilities of the engineering model were verified by comparing the model's theoretical predictions with experimental data from an OMS-type engine with a known feed system/engine chugging history.

A Role for M-Matrices in Modelling Population Growth

ERIC Educational Resources Information Center

James, Glyn; Rumchev, Ventsi

2006-01-01

Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results,…

Dynamical behaviour of a discrete selection-migration model with arbitrary dominance

Treesearch

James F. Selgrade; Jordan West Bostic; James H. Roberds

2009-01-01

To study the effects of immigration of genes (possibly transgenic) into a natural population, a one-island selection-migration model with density-dependent regulation is used to track allele frequency and population size. The existence and uniqueness of a polymorphic genetic equilibrium is proved under a general assumption about dominance in fitnesses. Also, conditions...

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

NASA Astrophysics Data System (ADS)

Xia, Xilin; Liang, Qiuhua; Ming, Xiaodong; Hou, Jingming

2017-05-01

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces.

PubMed

Fedele, Marco; Faggiano, Elena; Dedè, Luca; Quarteroni, Alfio

2017-10-01

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier-Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier-Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.

Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties.

PubMed

Stamatakos, Georgios S; Dionysiou, Dimitra D

2009-10-21

The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the "summarize and jump" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed.

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

NASA Astrophysics Data System (ADS)

Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan

2018-05-01

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.

Computational modeling of brain tumors: discrete, continuum or hybrid?

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Deisboeck, Thomas S.

In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silico brain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.

Computational modeling of brain tumors: discrete, continuum or hybrid?

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Deisboeck, Thomas S.

2008-04-01

In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silicobrain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Continuous distribution of emission states from single CdSe/ZnS quantum dots.

PubMed

Zhang, Kai; Chang, Hauyee; Fu, Aihua; Alivisatos, A Paul; Yang, Haw

2006-04-01

The photoluminescence dynamics of colloidal CdSe/ZnS/streptavidin quantum dots were studied using time-resolved single-molecule spectroscopy. Statistical tests of the photon-counting data suggested that the simple "on/off" discrete state model is inconsistent with experimental results. Instead, a continuous emission state distribution model was found to be more appropriate. Autocorrelation analysis of lifetime and intensity fluctuations showed a nonlinear correlation between them. These results were consistent with the model that charged quantum dots were also emissive, and that time-dependent charge migration gave rise to the observed photoluminescence dynamics.

A non-orthogonal decomposition of flows into discrete events

NASA Astrophysics Data System (ADS)

Boxx, Isaac; Lewalle, Jacques

1998-11-01

This work is based on the formula for the inverse Hermitian wavelet transform. A signal can be interpreted as a (non-unique) superposition of near-singular, partially overlapping events arising from Dirac functions and/or its derivatives combined with diffusion.( No dynamics implied: dimensionless diffusion is related to the definition of the analyzing wavelets.) These events correspond to local maxima of spectral energy density. We successfully fitted model events of various orders on a succession of fields, ranging from elementary signals to one-dimensional hot-wire traces. We document edge effects, event overlap and its implications on the algorithm. The interpretation of the discrete singularities as flow events (such as coherent structures) and the fundamental non-uniqueness of the decomposition are discussed. The dynamics of these events will be examined in the companion paper.

Dynamic generation of light states with discrete symmetries

NASA Astrophysics Data System (ADS)

Cordero, S.; Nahmad-Achar, E.; Castaños, O.; López-Peña, R.

2018-01-01

A dynamic procedure is established within the generalized Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group Cn. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, |ψ〉 M1,and |ψ〉 M 2, is considered. It can be generated by the proper selection of the time of flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order n =| M1-M2| .

Sampling rare fluctuations of discrete-time Markov chains

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Sampling rare fluctuations of discrete-time Markov chains.

PubMed

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Modeling of abnormal mechanical properties of nickel-based single crystal superalloy by three-dimensional discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Yang, Hui; Li, Zhenhuan; Huang, Minsheng

2014-12-01

Unlike common single crystals, the nickel-based single crystal superalloy shows surprisingly anomalous flow strength (i.e. with the increase of temperature, the yield strength first increases to a peak value and then decreases) and tension-compression (TC) asymmetry. A comprehensive three-dimensional discrete dislocation dynamics (3D-DDD) procedure was developed to model these abnormal mechanical properties. For this purpose, a series of complicated dynamic evolution details of Kear-Wilsdorf (KW) locks, which are closely related to the flow strength anomaly and TC asymmetry, were incorporated into this 3D-DDD framework. Moreover, the activation of the cubic slip system, which is the origin of the decrease in yield strength with increasing temperature at relatively high temperatures, was especially taken into account by introducing a competition criterion between the unlocking of the KW locks and the activation of the cubic slip system. To test our framework, a series of 3D-DDD simulations were performed on a representative volume cell model with a cuboidal Ni3Al precipitate phase embedded in a nickel matrix. Results show that the present 3D-DDD procedure can successfully capture the dynamic evolution of KW locks, the flow strength anomaly and TC asymmetry. Then, the underlying dislocation mechanisms leading to these abnormal mechanical responses were investigated and discussed in detail. Finally, a cyclic deformation of the nickel-based single crystal superalloy was modeled by using the present DDD model, with a special focus on the influence of KW locks on the Bauschinger effect and cyclic softening.

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining

PubMed Central

Truccolo, Wilson

2017-01-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics (“order parameters”) inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. PMID:28336305

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining.

PubMed

Truccolo, Wilson

2016-11-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.

On the dynamical basis of the classification of normal galaxies

PubMed Central

Haass, J.; Bertin, G.; Lin, C. C.

1982-01-01

Some realistic galaxy models have been found to support discrete unstable spiral modes. Here, through the study of the relevant physical mechanisms and an extensive numerical investigation of the properties of the dominant modes in a wide class of galactic equilibria, we show how spiral structures are excited with different morphological features, depending on the properties of the equilibrium model. We identify the basic dynamical parameters and mechanisms and compare the resulting morphology of spiral modes with the actual classification of galaxies. The present study suggests a dynamical basis for the transition among various types and subclasses of normal and barred spiral galaxies. Images PMID:16593200

A Two-Timescale Discretization Scheme for Collocation

NASA Technical Reports Server (NTRS)

Desai, Prasun; Conway, Bruce A.

2004-01-01

The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.

Sub-Scale Analysis of New Large Aircraft Pool Fire-Suppression

DTIC Science & Technology

2016-01-01

discrete ordinates radiation and single step Khan and Greeves soot model provided radiation and soot interaction. Agent spray dynamics were...Notable differences observed showed a modeled increase in the mockup surface heat-up rate as well as a modeled decreased rate of soot production...488 K SUPPRESSION STARTED  Large deviation between sensors due to sensor alignment challenges and asymmetric fuel surface ignition  Unremarkable

Nonlinear dynamic failure process of tunnel-fault system in response to strong seismic event

NASA Astrophysics Data System (ADS)

Yang, Zhihua; Lan, Hengxing; Zhang, Yongshuang; Gao, Xing; Li, Langping

2013-03-01

Strong earthquakes and faults have significant effect on the stability capability of underground tunnel structures. This study used a 3-Dimensional Discrete Element model and the real records of ground motion in the Wenchuan earthquake to investigate the dynamic response of tunnel-fault system. The typical tunnel-fault system was composed of one planned railway tunnel and one seismically active fault. The discrete numerical model was prudentially calibrated by means of the comparison between the field survey and numerical results of ground motion. It was then used to examine the detailed quantitative information on the dynamic response characteristics of tunnel-fault system, including stress distribution, strain, vibration velocity and tunnel failure process. The intensive tunnel-fault interaction during seismic loading induces the dramatic stress redistribution and stress concentration in the intersection of tunnel and fault. The tunnel-fault system behavior is characterized by the complicated nonlinear dynamic failure process in response to a real strong seismic event. It can be qualitatively divided into 5 main stages in terms of its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. This study provides the insight into the further stability estimation of underground tunnel structures under the combined effect of strong earthquakes and faults.

Simultaneous Observation of Hybrid States for Cyber-Physical Systems: A Case Study of Electric Vehicle Powertrain.

PubMed

Lv, Chen; Liu, Yahui; Hu, Xiaosong; Guo, Hongyan; Cao, Dongpu; Wang, Fei-Yue

2017-08-22

As a typical cyber-physical system (CPS), electrified vehicle becomes a hot research topic due to its high efficiency and low emissions. In order to develop advanced electric powertrains, accurate estimations of the unmeasurable hybrid states, including discrete backlash nonlinearity and continuous half-shaft torque, are of great importance. In this paper, a novel estimation algorithm for simultaneously identifying the backlash position and half-shaft torque of an electric powertrain is proposed using a hybrid system approach. System models, including the electric powertrain and vehicle dynamics models, are established considering the drivetrain backlash and flexibility, and also calibrated and validated using vehicle road testing data. Based on the developed system models, the powertrain behavior is represented using hybrid automata according to the piecewise affine property of the backlash dynamics. A hybrid-state observer, which is comprised of a discrete-state observer and a continuous-state observer, is designed for the simultaneous estimation of the backlash position and half-shaft torque. In order to guarantee the stability and reachability, the convergence property of the proposed observer is investigated. The proposed observer are validated under highly dynamical transitions of vehicle states. The validation results demonstrates the feasibility and effectiveness of the proposed hybrid-state observer.

A single predator multiple prey model with prey mutation

NASA Astrophysics Data System (ADS)

Mullan, Rory; Abernethy, Gavin M.; Glass, David H.; McCartney, Mark

2016-11-01

A multiple species predator-prey model is expanded with the introduction of a coupled map lattice for the prey, allowing the prey to mutate discretely into other prey species. The model is examined in its single predator, multiple mutating prey form. Two unimodal maps are used for the underlying dynamics of the prey species, with different predation strategies being used. Conclusions are drawn on how varying the control parameters of the model governs the overall behaviour and survival of the species. It is observed that in such a complex system, with multiple mutating prey, a large range of non-linear dynamics is possible.

The Thick Level-Set model for dynamic fragmentation

DOE PAGES

Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas

2017-01-04

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

Breaking of rod-shaped model material during compression

NASA Astrophysics Data System (ADS)

Lukas, Kulaviak; Vera, Penkavova; Marek, Ruzicka; Miroslav, Puncochar; Petr, Zamostny; Zdenek, Grof; Frantisek, Stepanek; Marek, Schongut; Jaromir, Havlica

2017-06-01

The breakage of a model anisometric dry granular material caused by uniaxial compression was studied. The bed of uniform rod-like pasta particles (8 mm long, aspect ratio 1:8) was compressed (Gamlen Tablet Press) and their size distribution was measured after each run (Dynamic Image Analysing). The compression dynamics was recorded and the effect of several parameters was tested (rate of compression, volume of granular bed, pressure magnitude and mode of application). Besides the experiments, numerical modelling of the compressed breakable material was performed as well, employing the DEM approach (Discrete Element Method). The comparison between the data and the model looks promising.

BioNSi: A Discrete Biological Network Simulator Tool.

PubMed

Rubinstein, Amir; Bracha, Noga; Rudner, Liat; Zucker, Noga; Sloin, Hadas E; Chor, Benny

2016-08-05

Modeling and simulation of biological networks is an effective and widely used research methodology. The Biological Network Simulator (BioNSi) is a tool for modeling biological networks and simulating their discrete-time dynamics, implemented as a Cytoscape App. BioNSi includes a visual representation of the network that enables researchers to construct, set the parameters, and observe network behavior under various conditions. To construct a network instance in BioNSi, only partial, qualitative biological data suffices. The tool is aimed for use by experimental biologists and requires no prior computational or mathematical expertise. BioNSi is freely available at http://bionsi.wix.com/bionsi , where a complete user guide and a step-by-step manual can also be found.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

NASA Technical Reports Server (NTRS)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Ubiquity of Beutler-Fano profiles: From scattering to dissipative processes

NASA Astrophysics Data System (ADS)

Finkelstein-Shapiro, Daniel; Keller, Arne

2018-02-01

Fano models—consisting of a Hamiltonian with a discrete-continuous spectrum—are one of the basic toy models in spectroscopy. They have been successful in explaining the line shape of experiments in atomic physics and condensed matter. These models, however, have largely been beyond the scope of dissipative dynamics, with only a handful of works considering the effect of a thermal bath. Yet in nanostructures and condensed-matter systems, dissipation strongly modulates the dynamics. We present an overview of the theory of Fano interferences coupled to a thermal bath and compare them to the scattering formalism. We provide the solution to any discrete-continuous Hamiltonian structure within the wideband approximation coupled to a Markovian bath. In doing so, we update the toy models that have been available for unitary evolution since the 1960s. We find that the Fano line shape is preserved as long as we allow a rescaling of the parameters, and an additional Lorentzian contribution that reflects the destruction of the interference by dephasings. The universality of the line shape can be traced back to specific properties of the effective Liouvillian.

A discrete mechanics approach to dislocation dynamics in BCC crystals

NASA Astrophysics Data System (ADS)

Ramasubramaniam, A.; Ariza, M. P.; Ortiz, M.

2007-03-01

A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers' vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.

A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves

NASA Astrophysics Data System (ADS)

Pecora, Nicolò; Sodini, Mauro

2018-05-01

This article considers a Cournot duopoly model in a continuous-time framework and analyze its dynamic behavior when the competitors are heterogeneous in determining their output decision. Specifically the model is expressed in the form of differential equations with discrete delays. The stability conditions of the unique Nash equilibrium of the system are determined and the emergence of Hopf bifurcations is shown. Applying some recent mathematical techniques (stability switching curves) and performing numerical simulations, the paper confirms how different time delays affect the stability of the economy.

Loop-quantum-gravity vertex amplitude.

PubMed

Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo

2007-10-19

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.

Inertia-Controlled Twinning in Ni-Mn-Ga Actuators: A Discrete Twin-Boundary Dynamics Study

NASA Astrophysics Data System (ADS)

Faran, Eilon; Riccardi, Leonardo; Shilo, Doron

2017-09-01

A discrete twin-boundary modeling approach is applied for simulating the dynamic magnetomechanical response of a Ni-Mn-Ga actuator over a wide frequency range. The model is based on experimentally measured kinetic relation of individual twin boundaries and takes into account inertial forces due to acceleration of the actuator's mass. The calculated results show good agreement with experimental measurements performed on a specially designed Ni-Mn-Ga linear spring-mass actuator. In addition, the simulation reveals several new effects that have not been considered before and can be applied to the design of improved actuators. It is identified that the demagnetization effect plays a role of an "effective spring" and results in a resonance-type response. The effects of the actuator's mass and the twin-boundary density on the resonance response and the actuator performance are explored numerically. In particular, it is shown that mass-inertia poses an inherent upper limit over the actuator's bandwidth, which is approximately constant and equals to about 200 Hz.

Modeling and Simulation of Metallurgical Process Based on Hybrid Petri Net

NASA Astrophysics Data System (ADS)

Ren, Yujuan; Bao, Hong

2016-11-01

In order to achieve the goals of energy saving and emission reduction of iron and steel enterprises, an increasing number of modeling and simulation technologies are used to research and analyse metallurgical production process. In this paper, the basic principle of Hybrid Petri net is used to model and analyse the Metallurgical Process. Firstly, the definition of Hybrid Petri Net System of Metallurgical Process (MPHPNS) and its modeling theory are proposed. Secondly, the model of MPHPNS based on material flow is constructed. The dynamic flow of materials and the real-time change of each technological state in metallurgical process are simulated vividly by using this model. The simulation process can implement interaction between the continuous event dynamic system and the discrete event dynamic system at the same level, and play a positive role in the production decision.

Modelling machine ensembles with discrete event dynamical system theory

NASA Technical Reports Server (NTRS)

Hunter, Dan

1990-01-01

Discrete Event Dynamical System (DEDS) theory can be utilized as a control strategy for future complex machine ensembles that will be required for in-space construction. The control strategy involves orchestrating a set of interactive submachines to perform a set of tasks for a given set of constraints such as minimum time, minimum energy, or maximum machine utilization. Machine ensembles can be hierarchically modeled as a global model that combines the operations of the individual submachines. These submachines are represented in the global model as local models. Local models, from the perspective of DEDS theory , are described by the following: a set of system and transition states, an event alphabet that portrays actions that takes a submachine from one state to another, an initial system state, a partial function that maps the current state and event alphabet to the next state, and the time required for the event to occur. Each submachine in the machine ensemble is presented by a unique local model. The global model combines the local models such that the local models can operate in parallel under the additional logistic and physical constraints due to submachine interactions. The global model is constructed from the states, events, event functions, and timing requirements of the local models. Supervisory control can be implemented in the global model by various methods such as task scheduling (open-loop control) or implementing a feedback DEDS controller (closed-loop control).

Tracking vortices in superconductors: Extracting singularities from a discretized complex scalar field evolving in time

DOE PAGES

Phillips, Carolyn L.; Guo, Hanqi; Peterka, Tom; ...

2016-02-19

In type-II superconductors, the dynamics of magnetic flux vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter field. Earlier, we introduced a method for extracting vortices from the discretized complex order parameter field generated by a large-scale simulation of vortex matter. With this method, at a fixed time step, each vortex [simplistically, a one-dimensional (1D) curve in 3D space] can be represented as a connected graph extracted from the discretized field. Here we extend this method as a function of time as well. A vortex now corresponds to a 2Dmore » space-time sheet embedded in 4D space time that can be represented as a connected graph extracted from the discretized field over both space and time. Vortices that interact by merging or splitting correspond to disappearance and appearance of holes in the connected graph in the time direction. This method of tracking vortices, which makes no assumptions about the scale or behavior of the vortices, can track the vortices with a resolution as good as the discretization of the temporally evolving complex scalar field. In addition, even details of the trajectory between time steps can be reconstructed from the connected graph. With this form of vortex tracking, the details of vortex dynamics in a model of a superconducting materials can be understood in greater detail than previously possible.« less

Fast Fourier transform discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Graham, J. T.; Rollett, A. D.; LeSar, R.

2016-12-01

Discrete dislocation dynamics simulations have been generally limited to modeling systems described by isotropic elasticity. Effects of anisotropy on dislocation interactions, which can be quite large, have generally been ignored because of the computational expense involved when including anisotropic elasticity. We present a different formalism of dislocation dynamics in which the dislocations are represented by the deformation tensor, which is a direct measure of the slip in the lattice caused by the dislocations and can be considered as an eigenstrain. The stresses arising from the dislocations are calculated with a fast Fourier transform (FFT) method, from which the forces are determined and the equations of motion are solved. Use of the FFTs means that the stress field is only available at the grid points, which requires some adjustments/regularizations to be made to the representation of the dislocations and the calculation of the force on individual segments, as is discussed hereinafter. A notable advantage of this approach is that there is no computational penalty for including anisotropic elasticity. We review the method and apply it in a simple dislocation dynamics calculation.

Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model

PubMed Central

Rehkopf, David; Tuljapurkar, Shripad; Horvitz, Carol C.

2018-01-01

Recent studies have examined the risk of poverty throughout the life course, but few have considered how transitioning in and out of poverty shape the dynamic heterogeneity and mortality disparities of a cohort at each age. Here we use state-by-age modeling to capture individual heterogeneity in crossing one of three different poverty thresholds (defined as 1×, 2× or 3× the “official” poverty threshold) at each age. We examine age-specific state structure, the remaining life expectancy, its variance, and cohort simulations for those above and below each threshold. Survival and transitioning probabilities are statistically estimated by regression analyses of data from the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth. Using the results of these regression analyses, we parameterize discrete state, discrete age matrix models. We found that individuals above all three thresholds have higher annual survival than those in poverty, especially for mid-ages to about age 80. The advantage is greatest when we classify individuals based on 1× the “official” poverty threshold. The greatest discrepancy in average remaining life expectancy and its variance between those above and in poverty occurs at mid-ages for all three thresholds. And fewer individuals are in poverty between ages 40-60 for all three thresholds. Our findings are consistent with results based on other data sets, but also suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of those above poverty, more disparities). This paper applies the approach of age-by-stage matrix models to human demography and individual poverty dynamics. In so doing we extend the literature on individual poverty dynamics across the life course. PMID:29768416

Modelling of high-frequency structure-borne sound transmission on FEM grids using the Discrete Flow Mapping technique

NASA Astrophysics Data System (ADS)

Hartmann, Timo; Tanner, Gregor; Xie, Gang; Chappell, David; Bajars, Janis

2016-09-01

Dynamical Energy Analysis (DEA) combined with the Discrete Flow Mapping technique (DFM) has recently been introduced as a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly re-modelling strategies. In addition, DFM provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. We will present here progress in the development of the DEA method towards handling complex FEM-meshes including Rigid Body Elements. In addition, structure borne transmission paths due to spot welds are considered. We will present applications for a car floor structure.

Nonlinear Socio-Ecological Dynamics and First Principles ofCollective Choice Behavior of ``Homo Socialis"

NASA Astrophysics Data System (ADS)

Sonis, M.

Socio-ecological dynamics emerged from the field of Mathematical SocialSciences and opened up avenues for re-examination of classical problems of collective behavior in Social and Spatial sciences. The ``engine" of this collective behavior is the subjective mental evaluation of level of utilities in the future, presenting sets of composite socio-economic-temporal-locational advantages. These dynamics present new laws of collective multi-population behavior which are the meso-level counterparts of the utility optimization individual behavior. The central core of the socio-ecological choice dynamics includes the following first principle of the collective choice behavior of ``Homo Socialis" based on the existence of ``collective consciousness": the choice behavior of ``Homo Socialis" is a collective meso-level choice behavior such that the relative changes in choice frequencies depend on the distribution of innovation alternatives between adopters of innovations. The mathematical basis of the Socio-Ecological Dynamics includes two complementary analytical approaches both based on the use of computer modeling as a theoretical and simulation tool. First approach is the ``continuous approach" --- the systems of ordinary and partial differential equations reflecting the continuous time Volterra ecological formalism in a form of antagonistic and/or cooperative collective hyper-games between different sub-sets of choice alternatives. Second approach is the ``discrete approach" --- systems of difference equations presenting a new branch of the non-linear discrete dynamics --- the Discrete Relative m-population/n-innovations Socio-Spatial Dynamics (Dendrinos and Sonis, 1990). The generalization of the Volterra formalism leads further to the meso-level variational principle of collective choice behavior determining the balance between the resulting cumulative social spatio-temporal interactions among the population of adopters susceptible to the choice alternatives and the cumulative equalization of the power of elites supporting different choice alternatives. This balance governs the dynamic innovation choice process and constitutes the dynamic meso-level counterpart of the micro-economic individual utility maximization principle.

Reduced-order model for dynamic optimization of pressure swing adsorption processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agarwal, A.; Biegler, L.; Zitney, S.

2007-01-01

Over the past decades, pressure swing adsorption (PSA) processes have been widely used as energy-efficient gas and liquid separation techniques, especially for high purity hydrogen purification from refinery gases. The separation processes are based on solid-gas equilibrium and operate under periodic transient conditions. Models for PSA processes are therefore multiple instances of partial differential equations (PDEs) in time and space with periodic boundary conditions that link the processing steps together. The solution of this coupled stiff PDE system is governed by steep concentrations and temperature fronts moving with time. As a result, the optimization of such systems for either designmore » or operation represents a significant computational challenge to current differential algebraic equation (DAE) optimization techniques and nonlinear programming algorithms. Model reduction is one approach to generate cost-efficient low-order models which can be used as surrogate models in the optimization problems. The study develops a reduced-order model (ROM) based on proper orthogonal decomposition (POD), which is a low-dimensional approximation to a dynamic PDE-based model. Initially, a representative ensemble of solutions of the dynamic PDE system is constructed by solving a higher-order discretization of the model using the method of lines, a two-stage approach that discretizes the PDEs in space and then integrates the resulting DAEs over time. Next, the ROM method applies the Karhunen-Loeve expansion to derive a small set of empirical eigenfunctions (POD modes) which are used as basis functions within a Galerkin's projection framework to derive a low-order DAE system that accurately describes the dominant dynamics of the PDE system. The proposed method leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization before and making optimization problem computationally-efficient. The method has been applied to the dynamic coupled PDE-based model of a two-bed four-step PSA process for separation of hydrogen from methane. Separate ROMs have been developed for each operating step with different POD modes for each of them. A significant reduction in the order of the number of states has been achieved. The gas-phase mole fraction, solid-state loading and temperature profiles from the low-order ROM and from the high-order simulations have been compared. Moreover, the profiles for a different set of inputs and parameter values fed to the same ROM were compared with the accurate profiles from the high-order simulations. Current results indicate the proposed ROM methodology as a promising surrogate modeling technique for cost-effective optimization purposes. Moreover, deviations from the ROM for different set of inputs and parameters suggest that a recalibration of the model is required for the optimization studies. Results for these will also be presented with the aforementioned results.« less

Optimization of Shipboard Manning Levels Using Imprint Pro Forces Module

DTIC Science & Technology

2015-09-01

NPS-OR-15-008 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA OPTIMIZATION OF SHIPBOARD MANNING LEVELS USING IMPRINT PRO...Optimization of Shipboard Manning Levels Using IMPRINT Pro Forces Module 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...ABSTRACT The Improved Performance Research Integration Tool ( IMPRINT ) is a dynamic, stochastic, discrete-event modeling tool used to develop a model

Dynamical Analysis of Density-dependent Selection in a Discrete one-island Migration Model

Treesearch

James H. Roberds; James F. Selgrade

2000-01-01

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in...

Dynamics of an advertising competition model with sales promotion

NASA Astrophysics Data System (ADS)

Jiang, Hui; Feng, Zhaosheng; Jiang, Guirong

2017-01-01

In this paper, an advertising competition model with sales promotion is constructed and investigated. Conditions of the existence and stability of period-T solutions are obtained by means of the discrete map. Flip bifurcation is analyzed by using the center manifold theory and three sales promotion strategies are discussed. Example and numerical simulations are illustrated which agree well with our theoretical analysis.

Molecular dynamics simulation of propagating cracks

NASA Technical Reports Server (NTRS)

Mullins, M.

1982-01-01

Steady state crack propagation is investigated numerically using a model consisting of 236 free atoms in two (010) planes of bcc alpha iron. The continuum region is modeled using the finite element method with 175 nodes and 288 elements. The model shows clear (010) plane fracture to the edge of the discrete region at moderate loads. Analysis of the results obtained indicates that models of this type can provide realistic simulation of steady state crack propagation.

A cellular automaton model for ship traffic flow in waterways

NASA Astrophysics Data System (ADS)

Qi, Le; Zheng, Zhongyi; Gang, Longhui

2017-04-01

With the development of marine traffic, waterways become congested and more complicated traffic phenomena in ship traffic flow are observed. It is important and necessary to build a ship traffic flow model based on cellular automata (CAs) to study the phenomena and improve marine transportation efficiency and safety. Spatial discretization rules for waterways and update rules for ship movement are two important issues that are very different from vehicle traffic. To solve these issues, a CA model for ship traffic flow, called a spatial-logical mapping (SLM) model, is presented. In this model, the spatial discretization rules are improved by adding a mapping rule. And the dynamic ship domain model is considered in the update rules to describe ships' interaction more exactly. Take the ship traffic flow in the Singapore Strait for example, some simulations were carried out and compared. The simulations show that the SLM model could avoid ship pseudo lane-change efficiently, which is caused by traditional spatial discretization rules. The ship velocity change in the SLM model is consistent with the measured data. At finally, from the fundamental diagram, the relationship between traffic ability and the lengths of ships is explored. The number of ships in the waterway declines when the proportion of large ships increases.

Simulation of dynamic vehicle-track interaction on small radius curves

NASA Astrophysics Data System (ADS)

Torstensson, Peter T.; Nielsen, Jens C. O.

2011-11-01

A time-domain method for the simulation of general three-dimensional dynamic interaction between a vehicle and a curved railway track, accounting for a prescribed relative wheel-rail displacement excitation in a wide frequency range (up to several hundred Hz), is presented. The simulation model is able to capture the low-frequency vehicle dynamics simultaneously due to curving and the high-frequency track dynamics due to the excitation by, for example, the short-pitch corrugation on the low rail. The adopted multibody dynamics formulation considers inertia forces, such as centrifugal and Coriolis forces, as well as the structural flexibility of vehicle and track components. To represent a wheel/rail surface irregularity, isoparametric two-dimensional elements able to describe generally curved surface shapes are used. The computational effort is reduced by including only one bogie in the vehicle model. The influence of the low-frequency vehicle dynamics of the remaining parts of the vehicle is considered by pre-calculated look-up tables of forces and moments acting in the secondary suspension. For a track model taken as rigid, good agreement is observed between the results calculated with the presented model and a commercial software. The features of the model are demonstrated by a number of numerical examples. The influence of the structural flexibility of the wheelset and track on wheel-rail contact forces is investigated. For a discrete rail irregularity excitation, it is shown that the longitudinal creep force is significantly influenced by the wheelset eigenmodes. The introduction of a velocity-dependent friction law is found to induce an oscillation in the tangential contact force on the low rail with a frequency corresponding to the first anti-symmetric torsional mode of the wheelset. Further, under the application of driving moments on the two wheelsets and excitation by a discrete irregularity on the high rail, the frequency content of the tangential contact forces on the low rail is significantly influenced by the P2 resonance as well as by several wheelset eigenmodes.

Dynamics of Phonological Cognition

ERIC Educational Resources Information Center

Gafos, Adamantios I.; Benus, Stefan

2006-01-01

A fundamental problem in spoken language is the duality between the continuous aspects of phonetic performance and the discrete aspects of phonological competence. We study 2 instances of this problem from the phenomenon of voicing neutralization and vowel harmony. In each case, we present a model where the experimentally observed continuous…

Potentials Unbounded Below

NASA Astrophysics Data System (ADS)

Curtright, Thomas

2011-04-01

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V. Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the particle. The Beverton-Holt and Skellam models of population dynamics, and particular cases of the logistic map are used to illustrate these features.

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach: STICK-SLIP IN SATURATED FAULT GOUGE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this study, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that themore » (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Finally, our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.« less

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach: STICK-SLIP IN SATURATED FAULT GOUGE

DOE PAGES

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.; ...

2017-05-01

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this study, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that themore » (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Finally, our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.« less

Programmed coherent coupling in a synthetic DNA-based excitonic circuit

NASA Astrophysics Data System (ADS)

Boulais, Étienne; Sawaya, Nicolas P. D.; Veneziano, Rémi; Andreoni, Alessio; Banal, James L.; Kondo, Toru; Mandal, Sarthak; Lin, Su; Schlau-Cohen, Gabriela S.; Woodbury, Neal W.; Yan, Hao; Aspuru-Guzik, Alán; Bathe, Mark

2018-02-01

Natural light-harvesting systems spatially organize densely packed chromophore aggregates using rigid protein scaffolds to achieve highly efficient, directed energy transfer. Here, we report a synthetic strategy using rigid DNA scaffolds to similarly program the spatial organization of densely packed, discrete clusters of cyanine dye aggregates with tunable absorption spectra and strongly coupled exciton dynamics present in natural light-harvesting systems. We first characterize the range of dye-aggregate sizes that can be templated spatially by A-tracts of B-form DNA while retaining coherent energy transfer. We then use structure-based modelling and quantum dynamics to guide the rational design of higher-order synthetic circuits consisting of multiple discrete dye aggregates within a DX-tile. These programmed circuits exhibit excitonic transport properties with prominent circular dichroism, superradiance, and fast delocalized exciton transfer, consistent with our quantum dynamics predictions. This bottom-up strategy offers a versatile approach to the rational design of strongly coupled excitonic circuits using spatially organized dye aggregates for use in coherent nanoscale energy transport, artificial light-harvesting, and nanophotonics.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exporation

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

The problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars were investigated. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; navigation, terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks were studied: vehicle model design, mathematical modeling of dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement and transport parameter evaluation.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

Investigation of problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars has been undertaken. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks have been under study: vehicle model design, mathematical modeling of a dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer sybsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement.

The stochastic system approach for estimating dynamic treatments effect.

PubMed

Commenges, Daniel; Gégout-Petit, Anne

2015-10-01

The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.

a Marker-Based Eulerian-Lagrangian Method for Multiphase Flow with Supersonic Combustion Applications

NASA Astrophysics Data System (ADS)

Fan, Xiaofeng; Wang, Jiangfeng

2016-06-01

The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Opinion Dynamics with Disagreement and Modulated Information

NASA Astrophysics Data System (ADS)

Sîrbu, Alina; Loreto, Vittorio; Servedio, Vito D. P.; Tria, Francesca

2013-04-01

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices.

Modeling and control of fuel cell based distributed generation systems

NASA Astrophysics Data System (ADS)

Jung, Jin Woo

This dissertation presents circuit models and control algorithms of fuel cell based distributed generation systems (DGS) for two DGS topologies. In the first topology, each DGS unit utilizes a battery in parallel to the fuel cell in a standalone AC power plant and a grid-interconnection. In the second topology, a Z-source converter, which employs both the L and C passive components and shoot-through zero vectors instead of the conventional DC/DC boost power converter in order to step up the DC-link voltage, is adopted for a standalone AC power supply. In Topology 1, two applications are studied: a standalone power generation (Single DGS Unit and Two DGS Units) and a grid-interconnection. First, dynamic model of the fuel cell is given based on electrochemical process. Second, two full-bridge DC to DC converters are adopted and their controllers are designed: an unidirectional full-bridge DC to DC boost converter for the fuel cell and a bidirectional full-bridge DC to DC buck/boost converter for the battery. Third, for a three-phase DC to AC inverter without or with a Delta/Y transformer, a discrete-time state space circuit model is given and two discrete-time feedback controllers are designed: voltage controller in the outer loop and current controller in the inner loop. And last, for load sharing of two DGS units and power flow control of two DGS units or the DGS connected to the grid, real and reactive power controllers are proposed. Particularly, for the grid-connected DGS application, a synchronization issue between an islanding mode and a paralleling mode to the grid is investigated, and two case studies are performed. To demonstrate the proposed circuit models and control strategies, simulation test-beds using Matlab/Simulink are constructed for each configuration of the fuel cell based DGS with a three-phase AC 120 V (L-N)/60 Hz/50 kVA and various simulation results are presented. In Topology 2, this dissertation presents system modeling, modified space vector PWM implementation (MSVPWM) and design of a closed-loop controller of the Z-source converter which utilizes L and C components and shoot-through zero vectors for the standalone AC power generation. The fuel cell system is modeled by an electrical R-C circuit in order to include slow dynamics of the fuel cells and a voltage-current characteristic of a cell is also considered. A discrete-time state space model is derived to implement digital control and a space vector pulse-width modulation (SVPWM) technique is modified to realize the shoot-through zero vectors that boost the DC-link voltage. Also, three discrete-time feedback controllers are designed: a discrete-time optimal voltage controller, a discrete-time sliding mode current controller, and a discrete-time PI DC-link voltage controller. Furthermore, an asymptotic observer is used to reduce the number of sensors and enhance the reliability of the system. To demonstrate the analyzed circuit model and proposed control strategy, various simulation results using Matlab/Simulink are presented under both light/heavy loads and linear/nonlinear loads for a three-phase AC 208 V (L-L)/60 Hz/10 kVA.

Haptics-based dynamic implicit solid modeling.

PubMed

Hua, Jing; Qin, Hong

2004-01-01

This paper systematically presents a novel, interactive solid modeling framework, Haptics-based Dynamic Implicit Solid Modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semi-algebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback.

Topics in Modeling of Cochlear Dynamics: Computation, Response and Stability Analysis

NASA Astrophysics Data System (ADS)

Filo, Maurice G.

This thesis touches upon several topics in cochlear modeling. Throughout the literature, mathematical models of the cochlea vary according to the degree of biological realism to be incorporated. This thesis casts the cochlear model as a continuous space-time dynamical system using operator language. This framework encompasses a wider class of cochlear models and makes the dynamics more transparent and easier to analyze before applying any numerical method to discretize space. In fact, several numerical methods are investigated to study the computational efficiency of the finite dimensional realizations in space. Furthermore, we study the effects of the active gain perturbations on the stability of the linearized dynamics. The stability analysis is used to explain possible mechanisms underlying spontaneous otoacoustic emissions and tinnitus. Dynamic Mode Decomposition (DMD) is introduced as a useful tool to analyze the response of nonlinear cochlear models. Cochlear response features are illustrated using DMD which has the advantage of explicitly revealing the spatial modes of vibrations occurring in the Basilar Membrane (BM). Finally, we address the dynamic estimation problem of BM vibrations using Extended Kalman Filters (EKF). Due to the limitations of noninvasive sensing schemes, such algorithms are inevitable to estimate the dynamic behavior of a living cochlea.

Efficient numerical method for investigating diatomic molecules with single active electron subjected to intense and ultrashort laser fields

NASA Astrophysics Data System (ADS)

Kiss, Gellért Zsolt; Borbély, Sándor; Nagy, Ladislau

2017-12-01

We have presented here an efficient numerical approach for the ab initio numerical solution of the time-dependent Schrödinger Equation describing diatomic molecules, which interact with ultrafast laser pulses. During the construction of the model we have assumed a frozen nuclear configuration and a single active electron. In order to increase efficiency our system was described using prolate spheroidal coordinates, where the wave function was discretized using the finite-element discrete variable representation (FE-DVR) method. The discretized wave functions were efficiently propagated in time using the short-iterative Lanczos algorithm. As a first test we have studied here how the laser induced bound state dynamics in H2+ is influenced by the strength of the driving laser field.

Empirical evidence that metabolic theory describes the temperature dependency of within-host parasite dynamics.

PubMed

Kirk, Devin; Jones, Natalie; Peacock, Stephanie; Phillips, Jessica; Molnár, Péter K; Krkošek, Martin; Luijckx, Pepijn

2018-02-01

The complexity of host-parasite interactions makes it difficult to predict how host-parasite systems will respond to climate change. In particular, host and parasite traits such as survival and virulence may have distinct temperature dependencies that must be integrated into models of disease dynamics. Using experimental data from Daphnia magna and a microsporidian parasite, we fitted a mechanistic model of the within-host parasite population dynamics. Model parameters comprising host aging and mortality, as well as parasite growth, virulence, and equilibrium abundance, were specified by relationships arising from the metabolic theory of ecology. The model effectively predicts host survival, parasite growth, and the cost of infection across temperature while using less than half the parameters compared to modeling temperatures discretely. Our results serve as a proof of concept that linking simple metabolic models with a mechanistic host-parasite framework can be used to predict temperature responses of parasite population dynamics at the within-host level.

Empirical evidence that metabolic theory describes the temperature dependency of within-host parasite dynamics

PubMed Central

Jones, Natalie; Peacock, Stephanie; Phillips, Jessica; Molnár, Péter K.; Krkošek, Martin; Luijckx, Pepijn

2018-01-01

The complexity of host–parasite interactions makes it difficult to predict how host–parasite systems will respond to climate change. In particular, host and parasite traits such as survival and virulence may have distinct temperature dependencies that must be integrated into models of disease dynamics. Using experimental data from Daphnia magna and a microsporidian parasite, we fitted a mechanistic model of the within-host parasite population dynamics. Model parameters comprising host aging and mortality, as well as parasite growth, virulence, and equilibrium abundance, were specified by relationships arising from the metabolic theory of ecology. The model effectively predicts host survival, parasite growth, and the cost of infection across temperature while using less than half the parameters compared to modeling temperatures discretely. Our results serve as a proof of concept that linking simple metabolic models with a mechanistic host–parasite framework can be used to predict temperature responses of parasite population dynamics at the within-host level. PMID:29415043

Interfacial properties in a discrete model for tumor growth

NASA Astrophysics Data System (ADS)

Moglia, Belén; Guisoni, Nara; Albano, Ezequiel V.

2013-03-01

We propose and study, by means of Monte Carlo numerical simulations, a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent β=0.32(2) that governs the early time regime, (ii) the roughness exponent α=0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z=α/β≃1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g., ξ∝t1/z, where ξ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang universality class, in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture or tumor.

Discrete and continuum modelling of soil cutting

NASA Astrophysics Data System (ADS)

Coetzee, C. J.

2014-12-01

Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Human dynamic orientation model applied to motion simulation. M.S. Thesis

NASA Technical Reports Server (NTRS)

Borah, J. D.

1976-01-01

The Ormsby model of dynamic orientation, in the form of a discrete time computer program was used to predict non-visually induced sensations during an idealized coordinated aircraft turn. To predict simulation fidelity, the Ormsby model was used to assign penalties for incorrect attitude and angular rate perceptions. It was determined that a three rotational degree of freedom simulation should remain faithful to attitude perception even at the expense of incorrect angular rate sensations. Implementing this strategy, a simulation profile for the idealized turn was designed for a Link GAT-1 trainer. A simple optokinetic display was added to improve the fidelity of roll rate sensations.

Analytical solution for a class of network dynamics with mechanical and financial applications

NASA Astrophysics Data System (ADS)

Krejčí, P.; Lamba, H.; Melnik, S.; Rachinskii, D.

2014-09-01

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

Lessons Learned from using a Livingstone Model to Diagnose a Main Propulsion System

NASA Technical Reports Server (NTRS)

Sweet, Adam; Bajwa, Anupa

2003-01-01

NASA researchers have demonstrated that qualitative, model-based reasoning can be used for fault detection in a Main Propulsion System (MPS), a complex, continuous system. At the heart of this diagnostic system is Livingstone, a discrete, propositional logic-based inference engine. Livingstone comprises a language for specifying a discrete model of the system and a set of algorithms that use the model to track the system's state. Livingstone uses the model to test assumptions about the state of a component - observations from the system are compared with values predicted by the model. The intent of this paper is to summarize some advantages of Livingstone seen through our modeling experience: for instance, flexibility in modeling, speed and maturity. We also describe some shortcomings we perceived in the implementation of Livingstone, such as modeling continuous dynamics and handling of transients. We list some upcoming enhancements to the next version of Livingstone that may resolve some of the current limitations.

Paintbrush of Discovery: Using Java Applets to Enhance Mathematics Education

ERIC Educational Resources Information Center

Eason, Ray; Heath, Garrett

2004-01-01

This article addresses the enhancement of the learning environment by using Java applets in the mathematics classroom. Currently, the first year mathematics program at the United States Military Academy involves one semester of modeling with discrete dynamical systems (DDS). Several faculty members from the Academy have integrated Java applets…

A Computational Model of Event Segmentation from Perceptual Prediction

ERIC Educational Resources Information Center

Reynolds, Jeremy R.; Zacks, Jeffrey M.; Braver, Todd S.

2007-01-01

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used…

Welfare Reform when Recipients Are Forward-Looking

ERIC Educational Resources Information Center

Swann, Christopher A.

2005-01-01

By studying recipients of aid under the Temporary Assistance for Needy Families (TANF) welfare scheme, the effect of time limits of welfare schemes on forward looking recipients is assessed using a discrete-choice dynamic programming framework model. The policy simulations for the preferred specification of utility reveal that two year time limits…

TOWARDS A MULTI-SCALE AGENT-BASED PROGRAMMING LANGUAGE METHODOLOGY

PubMed Central

Somogyi, Endre; Hagar, Amit; Glazier, James A.

2017-01-01

Living tissues are dynamic, heterogeneous compositions of objects, including molecules, cells and extra-cellular materials, which interact via chemical, mechanical and electrical process and reorganize via transformation, birth, death and migration processes. Current programming language have difficulty describing the dynamics of tissues because: 1: Dynamic sets of objects participate simultaneously in multiple processes, 2: Processes may be either continuous or discrete, and their activity may be conditional, 3: Objects and processes form complex, heterogeneous relationships and structures, 4: Objects and processes may be hierarchically composed, 5: Processes may create, destroy and transform objects and processes. Some modeling languages support these concepts, but most cannot translate models into executable simulations. We present a new hybrid executable modeling language paradigm, the Continuous Concurrent Object Process Methodology (CCOPM) which naturally expresses tissue models, enabling users to visually create agent-based models of tissues, and also allows computer simulation of these models. PMID:29282379

TOWARDS A MULTI-SCALE AGENT-BASED PROGRAMMING LANGUAGE METHODOLOGY.

PubMed

Somogyi, Endre; Hagar, Amit; Glazier, James A

2016-12-01

Living tissues are dynamic, heterogeneous compositions of objects , including molecules, cells and extra-cellular materials, which interact via chemical, mechanical and electrical process and reorganize via transformation, birth, death and migration processes . Current programming language have difficulty describing the dynamics of tissues because: 1: Dynamic sets of objects participate simultaneously in multiple processes, 2: Processes may be either continuous or discrete, and their activity may be conditional, 3: Objects and processes form complex, heterogeneous relationships and structures, 4: Objects and processes may be hierarchically composed, 5: Processes may create, destroy and transform objects and processes. Some modeling languages support these concepts, but most cannot translate models into executable simulations. We present a new hybrid executable modeling language paradigm, the Continuous Concurrent Object Process Methodology ( CCOPM ) which naturally expresses tissue models, enabling users to visually create agent-based models of tissues, and also allows computer simulation of these models.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability.

PubMed

Shiroky, I B; Gendelman, O V

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions-discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability

NASA Astrophysics Data System (ADS)

Shiroky, I. B.; Gendelman, O. V.

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions—discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

Phenotypic models of evolution and development: geometry as destiny.

PubMed

François, Paul; Siggia, Eric D

2012-12-01

Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations). The expression-time to space map for Hox genes and the posterior dominance rule are phenotypes that naturally follow from computational evolution without considering the genetics of Hox regulation. Copyright © 2012 Elsevier Ltd. All rights reserved.

A new epidemic modeling approach: Multi-regions discrete-time model with travel-blocking vicinity optimal control strategy.

PubMed

Zakary, Omar; Rachik, Mostafa; Elmouki, Ilias

2017-08-01

First, we devise in this paper, a multi-regions discrete-time model which describes the spatial-temporal spread of an epidemic which starts from one region and enters to regions which are connected with their neighbors by any kind of anthropological movement. We suppose homogeneous Susceptible-Infected-Removed (SIR) populations, and we consider in our simulations, a grid of colored cells, which represents the whole domain affected by the epidemic while each cell can represent a sub-domain or region. Second, in order to minimize the number of infected individuals in one region, we propose an optimal control approach based on a travel-blocking vicinity strategy which aims to control only one cell by restricting movements of infected people coming from all neighboring cells. Thus, we show the influence of the optimal control approach on the controlled cell. We should also note that the cellular modeling approach we propose here, can also describes infection dynamics of regions which are not necessarily attached one to an other, even if no empty space can be viewed between cells. The theoretical method we follow for the characterization of the travel-locking optimal controls, is based on a discrete version of Pontryagin's maximum principle while the numerical approach applied to the multi-points boundary value problems we obtain here, is based on discrete progressive-regressive iterative schemes. We illustrate our modeling and control approaches by giving an example of 100 regions.

Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Boyle, Richard D.

2014-01-01

Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.

Trade-offs Between Command and Control Architectures and Force Capabilities Using Battlespace Awareness

DTIC Science & Technology

2014-06-01

information superiority in Network- centric warfare .34 A brief discussion of the implementation of battlespace awareness is given. The method 3 Figure 2...developing the model used for this study. Lanchester Equations,39 System Dynamics models,40–42 Discrete Event Simulation, and Agent-based models (ABMs) were...popularity in the military modeling community in recent years due to their ability to effectively capture complex interactions in warfare scenarios with many

SAINT: A combined simulation language for modeling man-machine systems

NASA Technical Reports Server (NTRS)

Seifert, D. J.

1979-01-01

SAINT (Systems Analysis of Integrated Networks of Tasks) is a network modeling and simulation technique for design and analysis of complex man machine systems. SAINT provides the conceptual framework for representing systems that consist of discrete task elements, continuous state variables, and interactions between them. It also provides a mechanism for combining human performance models and dynamic system behaviors in a single modeling structure. The SAINT technique is described and applications of the SAINT are discussed.

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

Acquisition Community Team Dynamics: The Tuckman Model vs. the DAU Model

DTIC Science & Technology

2007-04-30

courses . These student teams are used to enable the generation of more complex products and to prepare the students for the ...requirement for stage discreteness was met, I developed a stage-separation test that, when applied to the data representing the experience of a... test the reliability, and validate an improved questionnaire instrument that: – Redefines “Storming” with new storming questions Less focused

Modeling and analysis of pinhole occulter experiment

NASA Technical Reports Server (NTRS)

Ring, J. R.

1986-01-01

The objectives were to improve pointing control system implementation by converting the dynamic compensator from a continuous domain representation to a discrete one; to determine pointing stability sensitivites to sensor and actuator errors by adding sensor and actuator error models to treetops and by developing an error budget for meeting pointing stability requirements; and to determine pointing performance for alternate mounting bases (space station for example).

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

NASA Astrophysics Data System (ADS)

Wu, Hao; Nüske, Feliks; Paul, Fabian; Klus, Stefan; Koltai, Péter; Noé, Frank

2017-04-01

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.

Symmetric linear systems - An application of algebraic systems theory

NASA Technical Reports Server (NTRS)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Discrete Particle Method for Simulating Hypervelocity Impact Phenomena.

PubMed

Watson, Erkai; Steinhauser, Martin O

2017-04-02

In this paper, we introduce a computational model for the simulation of hypervelocity impact (HVI) phenomena which is based on the Discrete Element Method (DEM). Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms -1 . We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy-conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

Autonomous control of production networks using a pheromone approach

NASA Astrophysics Data System (ADS)

Armbruster, D.; de Beer, C.; Freitag, M.; Jagalski, T.; Ringhofer, C.

2006-04-01

The flow of parts through a production network is usually pre-planned by a central control system. Such central control fails in presence of highly fluctuating demand and/or unforeseen disturbances. To manage such dynamic networks according to low work-in-progress and short throughput times, an autonomous control approach is proposed. Autonomous control means a decentralized routing of the autonomous parts themselves. The parts’ decisions base on backward propagated information about the throughput times of finished parts for different routes. So, routes with shorter throughput times attract parts to use this route again. This process can be compared to ants leaving pheromones on their way to communicate with following ants. The paper focuses on a mathematical description of such autonomously controlled production networks. A fluid model with limited service rates in a general network topology is derived and compared to a discrete-event simulation model. Whereas the discrete-event simulation of production networks is straightforward, the formulation of the addressed scenario in terms of a fluid model is challenging. Here it is shown, how several problems in a fluid model formulation (e.g. discontinuities) can be handled mathematically. Finally, some simulation results for the pheromone-based control with both the discrete-event simulation model and the fluid model are presented for a time-dependent influx.

Discrete Particle Method for Simulating Hypervelocity Impact Phenomena

PubMed Central

Watson, Erkai; Steinhauser, Martin O.

2017-01-01

In this paper, we introduce a computational model for the simulation of hypervelocity impact (HVI) phenomena which is based on the Discrete Element Method (DEM). Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms−1. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength. PMID:28772739

Optimal control on hybrid ode systems with application to a tick disease model.

PubMed

Ding, Wandi

2007-10-01

We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.

Extinction dynamics of a discrete population in an oasis.

PubMed

Berti, Stefano; Cencini, Massimo; Vergni, Davide; Vulpiani, Angelo

2015-07-01

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.

A discrete Markov metapopulation model for persistence and extinction of species.

PubMed

Thompson, Colin J; Shtilerman, Elad; Stone, Lewi

2016-09-07

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. Copyright © 2016 Elsevier Ltd. All rights reserved.

A new 2D segmentation method based on dynamic programming applied to computer aided detection in mammography.

PubMed

Timp, Sheila; Karssemeijer, Nico

2004-05-01

Mass segmentation plays a crucial role in computer-aided diagnosis (CAD) systems for classification of suspicious regions as normal, benign, or malignant. In this article we present a robust and automated segmentation technique--based on dynamic programming--to segment mass lesions from surrounding tissue. In addition, we propose an efficient algorithm to guarantee resulting contours to be closed. The segmentation method based on dynamic programming was quantitatively compared with two other automated segmentation methods (region growing and the discrete contour model) on a dataset of 1210 masses. For each mass an overlap criterion was calculated to determine the similarity with manual segmentation. The mean overlap percentage for dynamic programming was 0.69, for the other two methods 0.60 and 0.59, respectively. The difference in overlap percentage was statistically significant. To study the influence of the segmentation method on the performance of a CAD system two additional experiments were carried out. The first experiment studied the detection performance of the CAD system for the different segmentation methods. Free-response receiver operating characteristics analysis showed that the detection performance was nearly identical for the three segmentation methods. In the second experiment the ability of the classifier to discriminate between malignant and benign lesions was studied. For region based evaluation the area Az under the receiver operating characteristics curve was 0.74 for dynamic programming, 0.72 for the discrete contour model, and 0.67 for region growing. The difference in Az values obtained by the dynamic programming method and region growing was statistically significant. The differences between other methods were not significant.

Comparison of dislocation density tensor fields derived from discrete dislocation dynamics and crystal plasticity simulations of torsion

DOE PAGES

Jones, Reese E.; Zimmerman, Jonathan A.; Po, Giacomo; ...

2016-02-01

Accurate simulation of the plastic deformation of ductile metals is important to the design of structures and components to performance and failure criteria. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused at the global material response that use DD-generated information to enhance the fidelity of CPmore » models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity ow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Furthermore, our results show that, for the case of torsion, that the two material models can produce comparable spatial dislocation density distributions.« less

Correction to the gas phase pressure term in the continuum model for partially saturated granular media presented by Pietruszczak and co-workers

NASA Astrophysics Data System (ADS)

Iveson, Simon M.

2003-06-01

Pietruszczak and coworkers (Internat. J. Numer. Anal. Methods Geomech. 1994; 18(2):93-105; Comput. Geotech. 1991; 12( ):55-71) have presented a continuum-based model for predicting the dynamic mechanical response of partially saturated granular media with viscous interstitial liquids. In their model they assume that the gas phase is distributed uniformly throughout the medium as discrete spherical air bubbles occupying the voids between the particles. However, their derivation of the air pressure inside these gas bubbles is inconsistent with their stated assumptions. In addition the resultant dependence of gas pressure on liquid saturation lies outside of the plausible range of possible values for discrete air bubbles. This results in an over-prediction of the average bulk modulus of the void phase. Corrected equations are presented.

Evaluation of dynamical models: dissipative synchronization and other techniques.

PubMed

Aguirre, Luis Antonio; Furtado, Edgar Campos; Tôrres, Leonardo A B

2006-12-01

Some recent developments for the validation of nonlinear models built from data are reviewed. Besides giving an overall view of the field, a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model, which is very useful in validating models that should reproduce dominant dynamical features, like bifurcations, of the original system. In order to assess the discriminating power of the procedure, four well-known benchmarks have been used: namely, Duffing-Ueda, Duffing-Holmes, and van der Pol oscillators, plus the Hénon map. The procedure, developed for discrete-time systems, is focused on the dynamical properties of the model, rather than on statistical issues. For all the systems investigated, it is shown that the discriminating power of the procedure is similar to that of bifurcation diagrams--which in turn is much greater than, say, that of correlation dimension--but at a much lower computational cost.

Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey

2015-12-01

The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.

A rationale for human operator pulsive control behavior

NASA Technical Reports Server (NTRS)

Hess, R. A.

1979-01-01

When performing tracking tasks which involve demanding controlled elements such as those with K/s-squared dynamics, the human operator often develops discrete or pulsive control outputs. A dual-loop model of the human operator is discussed, the dominant adaptive feature of which is the explicit appearance of an internal model of the manipulator-controlled element dynamics in an inner feedback loop. Using this model, a rationale for pulsive control behavior is offered which is based upon the assumption that the human attempts to reduce the computational burden associated with time integration of sensory inputs. It is shown that such time integration is a natural consequence of having an internal representation of the K/s-squared-controlled element dynamics in the dual-loop model. A digital simulation is discussed in which a modified form of the dual-loop model is shown to be capable of producing pulsive control behavior qualitively comparable to that obtained in experiment.

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

Chaos in a dynamic model of traffic flows in an origin-destination network.

PubMed

Zhang, Xiaoyan; Jarrett, David F.

1998-06-01

In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

NASA Astrophysics Data System (ADS)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

Secure Hashing of Dynamic Hand Signatures Using Wavelet-Fourier Compression with BioPhasor Mixing and [InlineEquation not available: see fulltext.] Discretization

NASA Astrophysics Data System (ADS)

Wai Kuan, Yip; Teoh, Andrew B. J.; Ngo, David C. L.

2006-12-01

We introduce a novel method for secure computation of biometric hash on dynamic hand signatures using BioPhasor mixing and[InlineEquation not available: see fulltext.] discretization. The use of BioPhasor as the mixing process provides a one-way transformation that precludes exact recovery of the biometric vector from compromised hashes and stolen tokens. In addition, our user-specific[InlineEquation not available: see fulltext.] discretization acts both as an error correction step as well as a real-to-binary space converter. We also propose a new method of extracting compressed representation of dynamic hand signatures using discrete wavelet transform (DWT) and discrete fourier transform (DFT). Without the conventional use of dynamic time warping, the proposed method avoids storage of user's hand signature template. This is an important consideration for protecting the privacy of the biometric owner. Our results show that the proposed method could produce stable and distinguishable bit strings with equal error rates (EERs) of[InlineEquation not available: see fulltext.] and[InlineEquation not available: see fulltext.] for random and skilled forgeries for stolen token (worst case) scenario, and[InlineEquation not available: see fulltext.] for both forgeries in the genuine token (optimal) scenario.

Geometric Nonlinear Computation of Thin Rods and Shells

NASA Astrophysics Data System (ADS)

Grinspun, Eitan

2011-03-01

We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.

Numerical uncertainty in computational engineering and physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hemez, Francois M

2009-01-01

Obtaining a solution that approximates ordinary or partial differential equations on a computational mesh or grid does not necessarily mean that the solution is accurate or even 'correct'. Unfortunately assessing the quality of discrete solutions by questioning the role played by spatial and temporal discretizations generally comes as a distant third to test-analysis comparison and model calibration. This publication is contributed to raise awareness of the fact that discrete solutions introduce numerical uncertainty. This uncertainty may, in some cases, overwhelm in complexity and magnitude other sources of uncertainty that include experimental variability, parametric uncertainty and modeling assumptions. The concepts ofmore » consistency, convergence and truncation error are overviewed to explain the articulation between the exact solution of continuous equations, the solution of modified equations and discrete solutions computed by a code. The current state-of-the-practice of code and solution verification activities is discussed. An example in the discipline of hydro-dynamics illustrates the significant effect that meshing can have on the quality of code predictions. A simple method is proposed to derive bounds of solution uncertainty in cases where the exact solution of the continuous equations, or its modified equations, is unknown. It is argued that numerical uncertainty originating from mesh discretization should always be quantified and accounted for in the overall uncertainty 'budget' that supports decision-making for applications in computational physics and engineering.« less

A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops

PubMed Central

Acharya, Biswa R.; Jeon, Byeong Wook; Zañudo, Jorge G. T.; Zhu, Mengmeng; Osman, Karim; Assmann, Sarah M.

2017-01-01

Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA). This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs) of the protein kinase OPEN STOMATA 1 (OST1) and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich) component as well as its in- and out-components. The network’s domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure) and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed several predictions of the model with regard to reactive oxygen species, cytosolic Ca2+ (Ca2+c), and heterotrimeric G-protein signaling. We analyzed dynamics-determining positive and negative feedback loops, thereby elucidating the attractor (dynamic behavior) repertoire of the system and the groups of nodes that determine each attractor. Based on this analysis, we predict the likely presence of a previously unrecognized feedback mechanism dependent on Ca2+c. This mechanism would provide model agreement with 10 additional experimental observations, for a validation rate of 85%. Our research underscores the importance of feedback regulation in generating robust and adaptable biological responses. The high validation rate of our model illustrates the advantages of discrete dynamic modeling for complex, nonlinear systems common in biology. PMID:28937978

Analysis of dynamics and fit of diving suits

NASA Astrophysics Data System (ADS)

Mahnic Naglic, M.; Petrak, S.; Gersak, J.; Rolich, T.

2017-10-01

Paper presents research on dynamical behaviour and fit analysis of customised diving suits. Diving suits models are developed using the 3D flattening method, which enables the construction of a garment model directly on the 3D computer body model and separation of discrete 3D surfaces as well as transformation into 2D cutting parts. 3D body scanning of male and female test subjects was performed with the purpose of body measurements analysis in static and dynamic postures and processed body models were used for construction and simulation of diving suits prototypes. All necessary parameters, for 3D simulation were applied on obtained cutting parts, as well as parameters values for mechanical properties of neoprene material. Developed computer diving suits prototypes were used for stretch analysis on areas relevant for body dimensional changes according to dynamic anthropometrics. Garment pressures against the body in static and dynamic conditions was also analysed. Garments patterns for which the computer prototype verification was conducted were used for real prototype production. Real prototypes were also used for stretch and pressure analysis in static and dynamic conditions. Based on the obtained results, correlation analysis between body changes in dynamic positions and dynamic stress, determined on computer and real prototypes, was performed.

Dynamical and statistical behavior of discrete combustion waves: a theoretical and numerical study.

PubMed

Bharath, Naine Tarun; Rashkovskiy, Sergey A; Tewari, Surya P; Gundawar, Manoj Kumar

2013-04-01

We present a detailed theoretical and numerical study of combustion waves in a discrete one-dimensional disordered system. The distances between neighboring reaction cells were modeled with a gamma distribution. The results show that the random structure of the microheterogeneous system plays a crucial role in the dynamical and statistical behavior of the system. This is a consequence of the nonlinear interaction of the random structure of the system with the thermal wave. An analysis of the experimental data on the combustion of a gasless system (Ti + xSi) and a wide range of thermite systems was performed in view of the developed model. We have shown that the burning rate of the powder system sensitively depends on its internal structure. The present model allows for reproducing theoretically the experimental data for a wide range of pyrotechnic mixtures. We show that Arrhenius' macrokinetics at combustion of disperse systems can take place even in the absence of Arrhenius' microkinetics; it can have a purely thermal nature and be related to their heterogeneity and to the existence of threshold temperature. It is also observed that the combustion of disperse systems always occurs in the microheterogeneous mode according to the relay-race mechanism.

Dynamical and statistical behavior of discrete combustion waves: A theoretical and numerical study

NASA Astrophysics Data System (ADS)

Bharath, Naine Tarun; Rashkovskiy, Sergey A.; Tewari, Surya P.; Gundawar, Manoj Kumar

2013-04-01

We present a detailed theoretical and numerical study of combustion waves in a discrete one-dimensional disordered system. The distances between neighboring reaction cells were modeled with a gamma distribution. The results show that the random structure of the microheterogeneous system plays a crucial role in the dynamical and statistical behavior of the system. This is a consequence of the nonlinear interaction of the random structure of the system with the thermal wave. An analysis of the experimental data on the combustion of a gasless system (Ti + xSi) and a wide range of thermite systems was performed in view of the developed model. We have shown that the burning rate of the powder system sensitively depends on its internal structure. The present model allows for reproducing theoretically the experimental data for a wide range of pyrotechnic mixtures. We show that Arrhenius’ macrokinetics at combustion of disperse systems can take place even in the absence of Arrhenius’ microkinetics; it can have a purely thermal nature and be related to their heterogeneity and to the existence of threshold temperature. It is also observed that the combustion of disperse systems always occurs in the microheterogeneous mode according to the relay-race mechanism.

Incorporating social impact on new product adoption in choice modeing: A case study in green vehicles

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Lin; Wang, Mingxian; Chen, Wei

While discrete choice analysis is prevalent in capturing consumer preferences and describing their choice behaviors in product design, the traditional choice modeling approach assumes that each individual makes independent decisions, without considering the social impact. However, empirical studies show that choice is social - influenced by many factors beyond engineering performance of a product and consumer attributes. To alleviate this limitation, we propose a new choice modeling framework to capture the dynamic influence from social networks on consumer adoption of new products. By introducing social influence attributes into a choice utility function, social network simulation is integrated with the traditionalmore » discrete choice analysis in a three-stage process. Our study shows the need for considering social impact in forecasting new product adoption. Using hybrid electric vehicles as an example, our work illustrates the procedure of social network construction, social influence evaluation, and choice model estimation based on data from the National Household Travel Survey. Our study also demonstrates several interesting findings on the dynamic nature of new technology adoption and how social networks may influence hybrid electric vehicle adoption. (C) 2014 Elsevier Ltd. All rights reserved« less

Fixed interval smoothing with discrete measurements.

NASA Technical Reports Server (NTRS)

Bierman, G. J.

1972-01-01

Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.

Consensus Emerging from the Bottom-up: the Role of Cognitive Variables in Opinion Dynamics

NASA Astrophysics Data System (ADS)

Giardini, Francesca; Vilone, Daniele; Conte, Rosaria

2015-09-01

The study of opinions - e.g., their formation and change, and their effects on our society - by means of theoretical and numerical models has been one of the main goals of sociophysics until now, but it is one of the defining topics addressed by social psychology and complexity science. Despite the flourishing of different models and theories, several key questions still remain unanswered. The aim of this paper is to provide a cognitively grounded computational model of opinions in which they are described as mental representations and defined in terms of distinctive mental features. We also define how these representations change dynamically through different processes, describing the interplay between mental and social dynamics of opinions. We present two versions of the model, one with discrete opinions (voter model-like), and one with continuous ones (Deffuant-like). By means of numerical simulations, we compare the behaviour of our cognitive model with the classical sociophysical models, and we identify interesting differences in the dynamics of consensus for each of the models considered.

Lithium-ion battery cell-level control using constrained model predictive control and equivalent circuit models

NASA Astrophysics Data System (ADS)

Xavier, Marcelo A.; Trimboli, M. Scott

2015-07-01

This paper introduces a novel application of model predictive control (MPC) to cell-level charging of a lithium-ion battery utilizing an equivalent circuit model of battery dynamics. The approach employs a modified form of the MPC algorithm that caters for direct feed-though signals in order to model near-instantaneous battery ohmic resistance. The implementation utilizes a 2nd-order equivalent circuit discrete-time state-space model based on actual cell parameters; the control methodology is used to compute a fast charging profile that respects input, output, and state constraints. Results show that MPC is well-suited to the dynamics of the battery control problem and further suggest significant performance improvements might be achieved by extending the result to electrochemical models.

Opening up closure. Semiotics across scales

PubMed

Lemke

2000-01-01

The dynamic emergence of new levels of organization in complex systems is related to the semiotic reorganization of discrete/continuous variety at the level below as continuous/discrete meaning for the level above. In this view both the semiotic and the dynamic closure of system levels is reopened to allow the development and evolution of greater complexity.

Dissipative open systems theory as a foundation for the thermodynamics of linear systems.

PubMed

Delvenne, Jean-Charles; Sandberg, Henrik

2017-03-06

In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

A DISCRETE-EVENT SIMULATION APPROACH TO IDENTIFY RULES THAT GOVERN ARBOR REMODELING FOR BRANCHING CUTANEOUS AFFERENTS IN HAIRY SKIN.

PubMed

Kang, Hyojung; Orlowsky, Rachel L; Gerling, Gregory J

2017-12-01

In mammals, touch is encoded by sensory receptors embedded in the skin. For one class of receptors in the mouse, the architecture of its Merkel cells, unmyelinated neurites, and heminodes follow particular renewal and remodeling trends over hair cycle stages from ages 4 to 10 weeks. As it is currently impossible to observe such trends across a single animal's hair cycle, this work employs discrete event simulation to identify and evaluate policies of Merkel cell and heminode dynamics. Well matching the observed data, the results show that the baseline model replicates dynamic remodeling behaviors between stages of the hair cycle - based on particular addition and removal polices and estimated probabilities tied to constituent parts of Merkel cells, terminal branch neurites and heminodes. The analysis shows further that certain policies hold greater influence than others. This use of computation is a novel approach to understanding neuronal development.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

Kink dynamics in a topological φ4 lattice

NASA Astrophysics Data System (ADS)

Adib, A. B.; Almeida, C. A. S.

2001-09-01

Recently proposed was a discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was then suggested that these ``topological discrete systems'' are a natural choice for the numerical study of continuum kink dynamics. Giving particular emphasis to the φ4 theory, we numerically investigate kink-antikink scattering and breather formation in these topological lattices. Our results indicate that, even though these systems are quite accurate for studying free kinks in coarse lattices, for legitimate dynamical kink problems the accuracy is rather restricted to fine lattices (h~0.1). We suggest that this fact is related to the breaking of the Bogomol'nyi bound during the kink-antikink interaction, where the field profile loses its static property as required by the Bogomol'nyi argument. We conclude, therefore, that these lattices are not suitable for the study of more general kink dynamics, since a standard discretization is simpler and has effectively the same accuracy for such resolutions.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Waiting time distribution for continuous stochastic systems

NASA Astrophysics Data System (ADS)

Gernert, Robert; Emary, Clive; Klapp, Sabine H. L.

2014-12-01

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012), 10.1103/PhysRevE.86.061135]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carlo estimation for multilevel models with applications to discrete time survival models.

PubMed

Browne, William J; Steele, Fiona; Golalizadeh, Mousa; Green, Martin J

2009-06-01

We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.

STITCHER: Dynamic assembly of likely amyloid and prion β-structures from secondary structure predictions

PubMed Central

Bryan, Allen W; O’Donnell, Charles W; Menke, Matthew; Cowen, Lenore J; Lindquist, Susan; Berger, Bonnie

2012-01-01

The supersecondary structure of amyloids and prions, proteins of intense clinical and biological interest, are difficult to determine by standard experimental or computational means. In addition, significant conformational heterogeneity is known or suspected to exist in many amyloid fibrils. Previous work has demonstrated that probability-based prediction of discrete β-strand pairs can offer insight into these structures. Here, we devise a system of energetic rules that can be used to dynamically assemble these discrete β-strand pairs into complete amyloid β-structures. The STITCHER algorithm progressively ‘stitches’ strand-pairs into full β-sheets based on a novel free-energy model, incorporating experimentally observed amino-acid side-chain stacking contributions, entropic estimates, and steric restrictions for amyloidal parallel β-sheet construction. A dynamic program computes the top 50 structures and returns both the highest scoring structure and a consensus structure taken by polling this list for common discrete elements. Putative structural heterogeneity can be inferred from sequence regions that compose poorly. Predictions show agreement with experimental models of Alzheimer’s amyloid beta peptide and the Podospora anserina Het-s prion. Predictions of the HET-s homolog HET-S also reflect experimental observations of poor amyloid formation. We put forward predicted structures for the yeast prion Sup35, suggesting N-terminal structural stability enabled by tyrosine ladders, and C-terminal heterogeneity. Predictions for the Rnq1 prion and alpha-synuclein are also given, identifying a similar mix of homogenous and heterogeneous secondary structure elements. STITCHER provides novel insight into the energetic basis of amyloid structure, provides accurate structure predictions, and can help guide future experimental studies. Proteins 2012. © 2011 Wiley Periodicals, Inc. PMID:22095906

STITCHER: Dynamic assembly of likely amyloid and prion β-structures from secondary structure predictions.

PubMed

Bryan, Allen W; O'Donnell, Charles W; Menke, Matthew; Cowen, Lenore J; Lindquist, Susan; Berger, Bonnie

2012-02-01

The supersecondary structure of amyloids and prions, proteins of intense clinical and biological interest, are difficult to determine by standard experimental or computational means. In addition, significant conformational heterogeneity is known or suspected to exist in many amyloid fibrils. Previous work has demonstrated that probability-based prediction of discrete β-strand pairs can offer insight into these structures. Here, we devise a system of energetic rules that can be used to dynamically assemble these discrete β-strand pairs into complete amyloid β-structures. The STITCHER algorithm progressively 'stitches' strand-pairs into full β-sheets based on a novel free-energy model, incorporating experimentally observed amino-acid side-chain stacking contributions, entropic estimates, and steric restrictions for amyloidal parallel β-sheet construction. A dynamic program computes the top 50 structures and returns both the highest scoring structure and a consensus structure taken by polling this list for common discrete elements. Putative structural heterogeneity can be inferred from sequence regions that compose poorly. Predictions show agreement with experimental models of Alzheimer's amyloid beta peptide and the Podospora anserina Het-s prion. Predictions of the HET-s homolog HET-S also reflect experimental observations of poor amyloid formation. We put forward predicted structures for the yeast prion Sup35, suggesting N-terminal structural stability enabled by tyrosine ladders, and C-terminal heterogeneity. Predictions for the Rnq1 prion and alpha-synuclein are also given, identifying a similar mix of homogenous and heterogeneous secondary structure elements. STITCHER provides novel insight into the energetic basis of amyloid structure, provides accurate structure predictions, and can help guide future experimental studies. Copyright © 2011 Wiley Periodicals, Inc.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.