Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

PubMed Central

2011-01-01

Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance. PMID:21324153

Using a new discretization approach to design a delayed LQG controller

NASA Astrophysics Data System (ADS)

Haraguchi, M.; Hu, H. Y.

2008-07-01

In general, discrete-time controls have become more and more preferable in engineering because of their easy implementation and simple computations. However, the available discretization approaches for the systems having time delays increase the system dimensions and have a high computational cost. This paper presents an effective discretization approach for the continuous-time systems with an input delay. The approach enables one to transform the input-delay system into a delay-free system, but retain the system dimensions unchanged in the state transformation. To demonstrate an application of the approach, this paper presents the design of an LQ regulator for continuous-time systems with an input delay and gives a state observer with a Kalman filter for estimating the full-state vector from some measurements of the system as well. The case studies in the paper well support the efficacy and efficiency of the proposed approach applied to the vibration control of a three-story structure model with the actuator delay taken into account.

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

NASA Technical Reports Server (NTRS)

Nixon, Douglas D.

2009-01-01

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

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.

A survival tree method for the analysis of discrete event times in clinical and epidemiological studies.

PubMed

Schmid, Matthias; Küchenhoff, Helmut; Hoerauf, Achim; Tutz, Gerhard

2016-02-28

Survival trees are a popular alternative to parametric survival modeling when there are interactions between the predictor variables or when the aim is to stratify patients into prognostic subgroups. A limitation of classical survival tree methodology is that most algorithms for tree construction are designed for continuous outcome variables. Hence, classical methods might not be appropriate if failure time data are measured on a discrete time scale (as is often the case in longitudinal studies where data are collected, e.g., quarterly or yearly). To address this issue, we develop a method for discrete survival tree construction. The proposed technique is based on the result that the likelihood of a discrete survival model is equivalent to the likelihood of a regression model for binary outcome data. Hence, we modify tree construction methods for binary outcomes such that they result in optimized partitions for the estimation of discrete hazard functions. By applying the proposed method to data from a randomized trial in patients with filarial lymphedema, we demonstrate how discrete survival trees can be used to identify clinically relevant patient groups with similar survival behavior. Copyright © 2015 John Wiley & Sons, Ltd.

Reply to "Comment on `Route from discreteness to the continuum for the Tsallis q -entropy' "

NASA Astrophysics Data System (ADS)

Oikonomou, Thomas; Bagci, G. Baris

2018-06-01

It has been known for some time that the usual q -entropy Sq(n ) cannot be shown to converge to the continuous case. In Phys. Rev. E 97, 012104 (2018), 10.1103/PhysRevE.97.012104, we have shown that the discrete q -entropy S˜q(n ) converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [previous Comment, Phys. Rev. E 97, 066101 (2018), 10.1103/PhysRevE.97.066101] noted that this form of the discrete q -entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability property by the discrete q -entropy strongly depends on the origin of the convergence factor, presenting an example in which S˜q(n ) is expandable.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

NASA Astrophysics Data System (ADS)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses

NASA Astrophysics Data System (ADS)

Mohamad, Sannay; Gopalsamy, K.

2009-01-01

This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.

On controllability of homogeneous and inhomogeneous discrete-time multi-input bilinear systems in dimension two

NASA Astrophysics Data System (ADS)

Tie, Lin

2017-08-01

In this paper, the controllability problem of two-dimensional discrete-time multi-input bilinear systems is completely solved. The homogeneous and the inhomogeneous cases are studied separately and necessary and sufficient conditions for controllability are established by using a linear algebraic method, which are easy to apply. Moreover, for the uncontrollable systems, near-controllability is considered and similar necessary and sufficient conditions are also obtained. Finally, examples are provided to demonstrate the results of this paper.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

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.

General optical discrete z transform: design and application.

PubMed

Ngo, Nam Quoc

2016-12-20

This paper presents a generalization of the discrete z transform algorithm. It is shown that the GOD-ZT algorithm is a generalization of several important conventional discrete transforms. Based on the GOD-ZT algorithm, a tunable general optical discrete z transform (GOD-ZT) processor is synthesized using the silica-based finite impulse response transversal filter. To demonstrate the effectiveness of the method, the design and simulation of a tunable optical discrete Fourier transform (ODFT) processor as a special case of the synthesized GOD-ZT processor is presented. It is also shown that the ODFT processor can function as a real-time optical spectrum analyzer. The tunable ODFT has an important potential application as a tunable optical demultiplexer at the receiver end of an optical orthogonal frequency-division multiplexing transmission system.

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

NASA Astrophysics Data System (ADS)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Discrete restricted four-body problem: Existence of proof of equilibria and reproducibility of periodic orbits

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

Minesaki, Yukitaka

2015-01-01

We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog thatmore » preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.« less

Alternative-Specific and Case-Specific Factors Involved in the Decisions of Islamic School Teachers Affecting Teacher Retention: A Discrete Choice Experiment

ERIC Educational Resources Information Center

Abd-El-Hafez, Alaa Karem

2015-01-01

Teacher retention is a concern in all educational sectors in America. It is of special importance to Islamic schools, which tend to lack the resources necessary in recruiting and training new teachers. This dissertation addressed this problem in full-time Islamic schools in New York State by conducting a discrete choice experiment, which reflects…

Persistence of non-Markovian Gaussian stationary processes in discrete time

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Lizana, Ludvig

2018-04-01

The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n . Few results are known for the persistence P0(n ) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n ) ˜θn . Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n ) analytically in z -transform space in terms of the autocorrelation function A (n ) . If A (n )→0 as n →∞ , we extract θ numerically, while if A (n )=0 , for finite n >N , we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A (n )=0 for n >1 , the double exponential-correlated "second order autoregressive process", where A (n ) =c1λ1n+c2λ2n , and power-law-correlated variables, where A (n ) ˜n-μ . Apart from the power-law case when μ <5 , we find excellent agreement with simulations.

Moving solitons in the discrete nonlinear Schrödinger equation.

PubMed

Oxtoby, O F; Barashenkov, I V

2007-09-01

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When the nonlinearity is of the cubic type, this amplitude is shown to be nonzero for all velocities and therefore small-amplitude solitons moving without emitting radiation do not exist. In the case of a saturable nonlinearity, on the other hand, the radiation is found to be completely suppressed when the soliton moves at one of certain isolated "sliding velocities." We show that a discrete soliton moving at a general speed will experience radiative deceleration until it either stops and remains pinned to the lattice or--in the saturable case--locks, metastably, onto one of the sliding velocities. When the soliton's amplitude is small, however, this deceleration is extremely slow; hence, despite losing energy to radiation, the discrete soliton may spend an exponentially long time traveling with virtually unchanged amplitude and speed.

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

NASA Technical Reports Server (NTRS)

Jones, Robert L.; Goode, Plesent W. (Technical Monitor)

2000-01-01

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

H2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

NASA Astrophysics Data System (ADS)

Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle

2017-10-01

This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space ?. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space ? considering the infinite time horizon case.

Discrete Deterministic and Stochastic Petri Nets

NASA Technical Reports Server (NTRS)

Zijal, Robert; Ciardo, Gianfranco

1996-01-01

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model

NASA Astrophysics Data System (ADS)

Webb, Christian

2011-12-01

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation—thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.

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.

Output synchronization of discrete-time dynamical networks based on geometrically incremental dissipativity.

PubMed

Li, Chensong; Zhao, Jun

2017-01-01

In this work, we investigate the output synchronization problem for discrete-time dynamical networks with identical nodes. Firstly, if each node of a network is geometrically incrementally dissipative, the entire network can be viewed as a geometrically dissipative nonlinear system by choosing a particular input-output pair. Then, based on the geometrical dissipativity property, we consider two cases: output synchronization under arbitrary topology and switching topology, respectively. For the first case, we establish several criteria of output synchronization under arbitrary switching between a set of connection topologies by employing a common Lyapunov function. For the other case, we give the design method of a switching signal to achieve output synchronization even if all subnetworks are not synchronous. Finally, an example is provided to illustrate the effectiveness of the main results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Discrete prepotential as an indicator of successful ablation in patients with coronary cusp ventricular arrhythmia.

PubMed

Hachiya, Hitoshi; Yamauchi, Yasuteru; Iesaka, Yoshito; Yagishita, Atsuhiko; Sasaki, Takeshi; Higuchi, Koji; Kawabata, Mihoko; Sugiyama, Koji; Tanaka, Yasuaki; Kusa, Shigeki; Nakamura, Hiroaki; Miyazaki, Shinsuke; Taniguchi, Hiroshi; Isobe, Mitsuaki; Hirao, Kenzo

2013-10-01

Although coronary cusp (CC) ventricular arrhythmia (VA) can be treated by catheter ablation, reliable indicators of successful ablation sites have not been fully identified. This study comprised 392 patients undergoing radiofrequency catheter ablation for outflow tract-VA at 3 institutions from January 2007 to August 2012. The successful ablation site was on the left CC or right CC in 35 (8.9%) of the 392 patients. In 9 (26%) of these 35 patients, a discrete prepotential was recognized, 5 of whom had left CC-VAs and 4 of whom had right CC-VAs. Radiofrequency catheter ablation was successful at the site of the prepotential in all 9 of these patients. The duration of the isoelectric line between the end of the discrete prepotential and the onset of the ventricular electrogram was 27±13 ms. The time from onset of the discrete prepotential at the successful ablation site on the CC to the QRS onset (activation time) was 69±20 ms (range, 50-98 ms). Pace mapping was graded as excellent at the successful ablation site in only 1 patient. No discrete prepotential was recorded in any successful right outflow tract-VA ablation case in this study. A discrete prepotential was seen in 9 (26%) of 35 patients with CC-VA. In left and right CC-VA, the site of a discrete prepotential with ≥50 ms activation time may indicate a successful ablation site.

Controlling the Shannon Entropy of Quantum Systems

PubMed Central

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the shannon entropy of quantum systems.

PubMed

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

Fate of a discrete time crystal in an open system

NASA Astrophysics Data System (ADS)

Lazarides, Achilleas; Moessner, Roderich

2017-05-01

Following the recent realization that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this phenomenon. Motivated by its conceptual importance as well as its experimental relevance, we consider the effect of coupling to an external environment. We use this to argue, both analytically and numerically, that the DTC in disordered one-dimensional systems is destroyed at long times by any such natural coupling. This holds true even in the case where the coupling is such that the system is prevented from heating up by an external thermal bath.

A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

NASA Astrophysics Data System (ADS)

Ho, Choon-Lin; Ide, Yusuke; Konno, Norio; Segawa, Etsuo; Takumi, Kentaro

2018-04-01

In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy's walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Online frequency estimation with applications to engine and generator sets

NASA Astrophysics Data System (ADS)

Manngård, Mikael; Böling, Jari M.

2017-07-01

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Casing pipe damage detection with optical fiber sensors: a case study in oil well constructions

NASA Astrophysics Data System (ADS)

Zhou, Zhi; He, Jianping; Huang, Minghua; He, Jun; Ou, Jinping; Chen, Genda

2010-04-01

Casing pipes in oil well constructions may suddenly buckle inward as their inside and outside hydrostatic pressure difference increases. For the safety of construction workers and the steady development of oil industries, it is critically important to measure the stress state of a casing pipe. This study develops a rugged, real-time monitoring, and warning system that combines the distributed Brillouin Scattering Time Domain Reflectometry (BOTDR) and the discrete fiber Bragg grating (FBG) measurement. The BOTDR optical fiber sensors were embedded with no optical fiber splice joints in a fiber reinforced polymer (FRP) rebar and the FBG sensors were wrapped in epoxy resins and glass clothes, both installed during the segmental construction of casing pipes. In-situ tests indicate that the proposed sensing system and installation technique can survive the downhole driving process of casing pipes, withstand a harsh service environment, and remain in tact with the casing pipes for compatible strain measurements. The relative error of the measured strains between the distributed and discrete sensors is less than 12%. The FBG sensors successfully measured the maximum horizontal principal stress with a relative error of 6.7% in comparison with a cross multi-pole array acoustic instrument.

Linear system theory

NASA Technical Reports Server (NTRS)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

IMEX HDG-DG: A coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for Euler systems on cubed sphere.

NASA Astrophysics Data System (ADS)

Kang, S.; Muralikrishnan, S.; Bui-Thanh, T.

2017-12-01

We propose IMEX HDG-DG schemes for Euler systems on cubed sphere. Of interest is subsonic flow, where the speed of the acoustic wave is faster than that of the nonlinear advection. In order to simulate these flows efficiently, we split the governing system into stiff part describing the fast waves and non-stiff part associated with nonlinear advection. The former is discretized implicitly with HDG method while explicit Runge-Kutta DG discretization is employed for the latter. The proposed IMEX HDG-DG framework: 1) facilitates high-order solution both in time and space; 2) avoids overly small time stepsizes; 3) requires only one linear system solve per time step; and 4) relatively to DG generates smaller and sparser linear system while promoting further parallelism owing to HDG discretization. Numerical results for various test cases demonstrate that our methods are comparable to explicit Runge-Kutta DG schemes in terms of accuracy, while allowing for much larger time stepsizes.

Non-integrability vs. integrability in pentagram maps

NASA Astrophysics Data System (ADS)

Khesin, Boris; Soloviev, Fedor

2015-01-01

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.

Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; Otoguro, Yuto

2018-04-01

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

Parent-Child Communication and Marijuana Initiation: Evidence Using Discrete-Time Survival Analysis

PubMed Central

Nonnemaker, James M.; Silber-Ashley, Olivia; Farrelly, Matthew C.; Dench, Daniel

2012-01-01

This study supplements existing literature on the relationship between parent-child communication and adolescent drug use by exploring whether parental and/or adolescent recall of specific drug-related conversations differentially impact youth's likelihood of initiating marijuana use. Using discrete-time survival analysis, we estimated the hazard of marijuana initiation using a logit model to obtain an estimate of the relative risk of initiation. Our results suggest that parent-child communication about drug use is either not protective (no effect) or—in the case of youth reports of communication—potentially harmful (leading to increased likelihood of marijuana initiation). PMID:22958867

An algebraic structure of discrete-time biaffine systems

NASA Technical Reports Server (NTRS)

Tarn, T.-J.; Nonoyama, S.

1979-01-01

New results on the realization of finite-dimensional, discrete-time, internally biaffine systems are presented in this paper. The external behavior of such systems is described by multiaffine functions and the state space is constructed via Nerode equivalence relations. We prove that the state space is an affine space. An algorithm which amounts to choosing a frame for the affine space is presented. Our algorithm reduces in the linear and bilinear case to a generalization of algorithms existing in the literature. Explicit existence criteria for span-canonical realizations as well as an affine isomorphism theorem are given.

Discrete harmony search algorithm for scheduling and rescheduling the reprocessing problems in remanufacturing: a case study

NASA Astrophysics Data System (ADS)

Gao, Kaizhou; Wang, Ling; Luo, Jianping; Jiang, Hua; Sadollah, Ali; Pan, Quanke

2018-06-01

In this article, scheduling and rescheduling problems with increasing processing time and new job insertion are studied for reprocessing problems in the remanufacturing process. To handle the unpredictability of reprocessing time, an experience-based strategy is used. Rescheduling strategies are applied for considering the effect of increasing reprocessing time and the new subassembly insertion. To optimize the scheduling and rescheduling objective, a discrete harmony search (DHS) algorithm is proposed. To speed up the convergence rate, a local search method is designed. The DHS is applied to two real-life cases for minimizing the maximum completion time and the mean of earliness and tardiness (E/T). These two objectives are also considered together as a bi-objective problem. Computational optimization results and comparisons show that the proposed DHS is able to solve the scheduling and rescheduling problems effectively and productively. Using the proposed approach, satisfactory optimization results can be achieved for scheduling and rescheduling on a real-life shop floor.

34 CFR Appendix D to Part 682 - Policy for Waiving the Secretary's Right To Recover or Refuse To Pay Interest Benefits, Special...

Code of Federal Regulations, 2014 CFR

2014-07-01

... following approaches to its enforcement of its own due diligence and timely filing rules for violations... engaged in, and documented, a case-by-case exercise of reasonable discretion allowing for guarantee... payments in accordance with the original repayment schedule or agreement.) In the case of a payment made by...

34 CFR Appendix D to Part 682 - Policy for Waiving the Secretary's Right To Recover or Refuse To Pay Interest Benefits, Special...

Code of Federal Regulations, 2013 CFR

2013-07-01

... following approaches to its enforcement of its own due diligence and timely filing rules for violations... engaged in, and documented, a case-by-case exercise of reasonable discretion allowing for guarantee... payments in accordance with the original repayment schedule or agreement.) In the case of a payment made by...

34 CFR Appendix D to Part 682 - Policy for Waiving the Secretary's Right To Recover or Refuse To Pay Interest Benefits, Special...

Code of Federal Regulations, 2011 CFR

2011-07-01

... following approaches to its enforcement of its own due diligence and timely filing rules for violations... engaged in, and documented, a case-by-case exercise of reasonable discretion allowing for guarantee... payments in accordance with the original repayment schedule or agreement.) In the case of a payment made by...

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Multiple Microcomputer Control Algorithm.

DTIC Science & Technology

1979-09-01

discrete and semaphore supervisor calls can be used with tasks in separate processors, in which case they are maintained in shared memory. Operations on ...the source or destination operand specifier of each mode in most cases . However, four of the 16 general register addressing modes and one of the 8 pro...instruction time is based on the specified usage factors and the best cast, and worst case execution times for the instruc- 1I 5 1NAVTRAEQZJ1PCrN M’.V7~j

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

PubMed

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

NASA Astrophysics Data System (ADS)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.

PubMed

Aftab, Muhammad Saleheen; Shafiq, Muhammad

2015-11-01

This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems

NASA Astrophysics Data System (ADS)

Kit Luk, Chuen; Chesi, Graziano

2015-11-01

This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. First, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Second, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimisation problem. Some numerical examples illustrate the proposed approach.

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

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

NASA Astrophysics Data System (ADS)

Carichino, Lucia; Guidoboni, Giovanna; Szopos, Marcela

2018-07-01

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.

Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.

PubMed

Dallaston, Michael C; Fontelos, Marco A; Tseluiko, Dmitri; Kalliadasis, Serafim

2018-01-19

The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.

Parent-child communication and marijuana initiation: evidence using discrete-time survival analysis.

PubMed

Nonnemaker, James M; Silber-Ashley, Olivia; Farrelly, Matthew C; Dench, Daniel

2012-12-01

This study supplements existing literature on the relationship between parent-child communication and adolescent drug use by exploring whether parental and/or adolescent recall of specific drug-related conversations differentially impact youth's likelihood of initiating marijuana use. Using discrete-time survival analysis, we estimated the hazard of marijuana initiation using a logit model to obtain an estimate of the relative risk of initiation. Our results suggest that parent-child communication about drug use is either not protective (no effect) or - in the case of youth reports of communication - potentially harmful (leading to increased likelihood of marijuana initiation). Copyright © 2012 Elsevier Ltd. All rights reserved.

On the Importance of the Dynamics of Discretizations

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)

1995-01-01

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

NASA Technical Reports Server (NTRS)

Spear, Ashley D.; Priest, Amanda R.; Veilleux, Michael G.; Ingraffea, Anthony R.; Hochhalter, Jacob D.

2011-01-01

A surrogate model methodology is described for predicting in real time the residual strength of flight structures with discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. A residual strength test of a metallic, integrally-stiffened panel is simulated to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data would, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high-fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Discrete-time modelling of musical instruments

NASA Astrophysics Data System (ADS)

Välimäki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti

2006-01-01

This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

USGS Publications Warehouse

Haney, M.M.

2007-01-01

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model - that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable. ?? 2007 Society of Exploration Geophysicists.

Adaptive control of periodic systems

NASA Astrophysics Data System (ADS)

Tian, Zhiling

2009-12-01

Adaptive control is needed to cope with parametric uncertainty in dynamical systems. The adaptive control of LTI systems in both discrete and continuous time has been studied for four decades and the results are currently used widely in many different fields. In recent years, interest has shifted to the adaptive control of time-varying systems. It is known that the adaptive control of arbitrarily rapidly time-varying systems is in general intractable, but systems with periodically time-varying parameters (LTP systems) which have much more structure, are amenable to mathematical analysis. Further, there is also a need for such control in practical problems which have arisen in industry during the past twenty years. This thesis is the first attempt to deal with the adaptive control of LTP systems. Adaptive Control involves estimation of unknown parameters, adjusting the control parameters based on the estimates, and demonstrating that the overall system is stable. System theoretic properties such as stability, controllability, and observability play an important role both in formulating of the problems, as well as in generating solutions for them. For LTI systems, these properties have been studied since 1960s, and algebraic conditions that have to be satisfied to assure these properties are now well established. In the case of LTP systems, these properties can be expressed only in terms of transition matrices that are much more involved than those for LTI systems. Since adaptive control problems can be formulated only when these properties are well understood, it is not surprising that systematic efforts have not been made thus far for formulating and solving adaptive control problems that arise in LTP systems. Even in the case of LTI systems, it is well recognized that problems related to adaptive discrete-time system are not as difficult as those that arise in the continuous-time systems. This is amply evident in the solutions that were derived in the 1980s and 1990s for all the important problems. These differences are even more amplified in the LTP case; some problems in continuous time cannot even be formulated precisely. This thesis consequently focuses primarily on the adaptive identification and control of discrete-time systems, and derives most of the results that currently exist in the literature for LTI systems. Based on these investigations of discrete-time adaptive systems, attempts are made in the thesis to examine their continuous-time counterparts, and discuss the principal difficulties encountered. The dissertation examines critically the system theoretic properties of LTP systems in Chapter 2, and the mathematical framework provided for their analysis by Floquet theory in Chapter 3. Assuming that adaptive identification and control problems can be formulated precisely, a unified method of developing stable adaptive laws using error models is treated in Chapter 4. Chapter 5 presents a detailed study of the adaptation in SISO discrete-time LTP systems, and represents the core of the thesis. The important problems of identification, stabilization, regulation, and tracking of arbitrary signals are investigated, and practically implementable stable adaptive laws are derived. The dissertation concludes with a discussion of continuous-time adaptive control in Chapter 6 and discrete multivariable systems in Chapter 7. Directions for future research are indicated towards the end of the dissertation.

Algorithms for optimization of branching gravity-driven water networks

NASA Astrophysics Data System (ADS)

Dardani, Ian; Jones, Gerard F.

2018-05-01

The design of a water network involves the selection of pipe diameters that satisfy pressure and flow requirements while considering cost. A variety of design approaches can be used to optimize for hydraulic performance or reduce costs. To help designers select an appropriate approach in the context of gravity-driven water networks (GDWNs), this work assesses three cost-minimization algorithms on six moderate-scale GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution which is mapped onto a discrete-diameter set. The backtracking algorithm finds the global optimum for all but the largest of cases tested, for which its long runtime makes it an infeasible option. The calculus-based algorithm's discrete-diameter solution produced slightly higher-cost results but was more scalable to larger network cases. Furthermore, the new calculus-based algorithm's continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. The genetic algorithm produced solutions even closer to the global optimum with consistently short run times, although slightly higher solution costs were seen for the larger network cases tested. The results of this study highlight the advantages and weaknesses of each GDWN design method including closeness to the global optimum, the ability to prune the solution space of infeasible and suboptimal candidates without missing the global optimum, and algorithm run time. We also extend an existing closed-form model of Jones (2011) to include minor losses and a more comprehensive two-part cost model, which realistically applies to pipe sizes that span a broad range typical of GDWNs of interest in this work, and for smooth and commercial steel roughness values.

The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation

NASA Astrophysics Data System (ADS)

Zhang, Liangyin; Chen, Michael Z. Q.; Li, Chanying

2017-07-01

In this paper, two new pairs of dual continuous-time algebraic Riccati equations (CAREs) and dual discrete-time algebraic Riccati equations (DAREs) are proposed. The dual DAREs are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix. Then, in the case of singular matrices, a generalised inverse is introduced to deal with the dual DARE problem. These dual AREs can easily lead us to an iterative procedure for finding the anti-stabilising solutions, especially to DARE, by means of that for the stabilising solutions. Furthermore, we provide the counterpart results on the set of all solutions to DARE inspired by the results for CARE. Two examples are presented to illustrate the theoretical results.

Joint sparsity based heterogeneous data-level fusion for target detection and estimation

NASA Astrophysics Data System (ADS)

Niu, Ruixin; Zulch, Peter; Distasio, Marcello; Blasch, Erik; Shen, Dan; Chen, Genshe

2017-05-01

Typical surveillance systems employ decision- or feature-level fusion approaches to integrate heterogeneous sensor data, which are sub-optimal and incur information loss. In this paper, we investigate data-level heterogeneous sensor fusion. Since the sensors monitor the common targets of interest, whose states can be determined by only a few parameters, it is reasonable to assume that the measurement domain has a low intrinsic dimensionality. For heterogeneous sensor data, we develop a joint-sparse data-level fusion (JSDLF) approach based on the emerging joint sparse signal recovery techniques by discretizing the target state space. This approach is applied to fuse signals from multiple distributed radio frequency (RF) signal sensors and a video camera for joint target detection and state estimation. The JSDLF approach is data-driven and requires minimum prior information, since there is no need to know the time-varying RF signal amplitudes, or the image intensity of the targets. It can handle non-linearity in the sensor data due to state space discretization and the use of frequency/pixel selection matrices. Furthermore, for a multi-target case with J targets, the JSDLF approach only requires discretization in a single-target state space, instead of discretization in a J-target state space, as in the case of the generalized likelihood ratio test (GLRT) or the maximum likelihood estimator (MLE). Numerical examples are provided to demonstrate that the proposed JSDLF approach achieves excellent performance with near real-time accurate target position and velocity estimates.

4 CFR 22.6 - Motions, Briefs, and Other Statements [Rule 6].

Code of Federal Regulations, 2010 CFR

2010-01-01

..., in its discretion, may shorten or lengthen the time for the response and reply based on the nature of the motion, the nature and timing of the case, and the scheduling needs of the Board. The Board may... motion, for summary judgment, the Board will consider the pleadings, depositions, answers to...

Variance-reduced simulation of lattice discrete-time Markov chains with applications in reaction networks

NASA Astrophysics Data System (ADS)

Maginnis, P. A.; West, M.; Dullerud, G. E.

2016-10-01

We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a ;black-box;, i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.

Adaptive hybrid simulations for multiscale stochastic reaction networks

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

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

Multiresolution analysis of Bursa Malaysia KLCI time series

NASA Astrophysics Data System (ADS)

Ismail, Mohd Tahir; Dghais, Amel Abdoullah Ahmed

2017-05-01

In general, a time series is simply a sequence of numbers collected at regular intervals over a period. Financial time series data processing is concerned with the theory and practice of processing asset price over time, such as currency, commodity data, and stock market data. The primary aim of this study is to understand the fundamental characteristics of selected financial time series by using the time as well as the frequency domain analysis. After that prediction can be executed for the desired system for in sample forecasting. In this study, multiresolution analysis which the assist of discrete wavelet transforms (DWT) and maximal overlap discrete wavelet transform (MODWT) will be used to pinpoint special characteristics of Bursa Malaysia KLCI (Kuala Lumpur Composite Index) daily closing prices and return values. In addition, further case study discussions include the modeling of Bursa Malaysia KLCI using linear ARIMA with wavelets to address how multiresolution approach improves fitting and forecasting results.

Networked event-triggered control: an introduction and research trends

NASA Astrophysics Data System (ADS)

Mahmoud, Magdi S.; Sabih, Muhammad

2014-11-01

A physical system can be studied as either continuous time or discrete-time system depending upon the control objectives. Discrete-time control systems can be further classified into two categories based on the sampling: (1) time-triggered control systems and (2) event-triggered control systems. Time-triggered systems sample states and calculate controls at every sampling instant in a periodic fashion, even in cases when states and calculated control do not change much. This indicates unnecessary and useless data transmission and computation efforts of a time-triggered system, thus inefficiency. For networked systems, the transmission of measurement and control signals, thus, cause unnecessary network traffic. Event-triggered systems, on the other hand, have potential to reduce the communication burden in addition to reducing the computation of control signals. This paper provides an up-to-date survey on the event-triggered methods for control systems and highlights the potential research directions.

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.

High-Order Space-Time Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2013-01-01

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

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.

A generalization of Fatou's lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time.

PubMed

Kamihigashi, Takashi

2017-01-01

Given a sequence [Formula: see text] of measurable functions on a σ -finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text], we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.

Discrete element method for emergency flow of pedestrian in S-type corridor.

PubMed

Song, Gyeongwon; Park, Junyoung

2014-10-01

Pedestrian flow in curved corridor should be modeled before design because this type of corridor can be most dangerous part during emergency evacuation. In this study, this flow is analyzed by Discrete Element Method with psychological effects. As the turning slope of corridor increases, the evacuation time is linearly increases. However, in the view of crashed death accident, the case with 90 degree turning slope can be dangerous because there are 3 dangerous points. To solve this matter, the pedestrian gathering together in curved part should be dispersed.

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

Vanderbei, Robert J., E-mail: rvdb@princeton.edu; P Latin-Small-Letter-Dotless-I nar, Mustafa C., E-mail: mustafap@bilkent.edu.tr; Bozkaya, Efe B.

An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problemmore » as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.« less

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.

The Effects of Time Advance Mechanism on Simple Agent Behaviors in Combat Simulations

DTIC Science & Technology

2011-12-01

modeling packages that illustrate the differences between discrete-time simulation (DTS) and discrete-event simulation ( DES ) methodologies. Many combat... DES ) models , often referred to as “next-event” (Law and Kelton 2000) or discrete time simulation (DTS), commonly referred to as “time-step.” DTS...discrete-time simulation (DTS) and discrete-event simulation ( DES ) methodologies. Many combat models use DTS as their simulation time advance mechanism

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

Numerical simulation of the nonlinear dynamics of harmonically driven Riesz-fractional extensions of the Fermi-Pasta-Ulam chains

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-02-01

In this work, we introduce a spatially discrete model that is a modification of the well-known α-Fermi-Pasta-Ulam chain with damping. The system is perturbed at one end by a harmonic disturbance irradiating at a frequency in the forbidden band-gap of the classical regime, and a nonlocal coupling between the oscillators is considered using discrete Riesz fractional derivatives. We propose fully discrete expressions to approximate an energy functional of the system, and we use them to calculate the total energy of fractional chains over a relatively long period of time [Fract. Diff. Appl. 4 (2004) 153-162]. The approach is thoroughly tested in the case of local couplings against known qualitative results, including simulations of the process of nonlinear recurrence in the traditional chains of anharmonic oscillators. As an application, we provide evidence that the process of supratransmission is present in spatially discrete Fermi-Pasta-Ulam lattices with Riesz fractional derivatives in space. Moreover, we perform numerical experiments for small and large amplitudes of the harmonic disturbance. In either case, we establish the dependency of the critical amplitude at which supratransmission begins as a function of the driving frequency. Our results are in good agreement with the analytic predictions for the classical Fermi-Pasta-Ulam chain.

On Some Parabolic Type Problems from Thin Film Theory and Chemical Reaction-Diffusion Networks

NASA Astrophysics Data System (ADS)

Mohamed, Fatma Naser Ali

This dissertation considers some parabolic type problems from thin film theory and chemical reaction-diffusion networks. The dissertation consists of two parts: In the first part, we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove an existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that, in this case, the surface-tension energy dissipation is the mechanism responsible for the H1-norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type, are also successfully treated by the same means. [special characters omitted]. In the second part, we are concerned with the convergence of a certain space-discretization scheme -the so-called method of lines- for mass-action reaction-diffusion systems. First, we start with a toy model, namely. [special characters omitted]. and prove convergence of method of lines for this linear case. Here weak convergence in L2(0,1) is enough to prove convergence of the method of lines. Then we adopt the framework for convergence analysis introduced in [23] and concentrate on the proof-of-concept reaction. within 1D space, while at the same time noting that our techniques are readily generalizable to other reaction-diffusion networks and to more than one space dimension. Indeed, it will be obvious how to extend our proofs to the multi-dimensional case; we only note that the proof of the comparison principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream numerical tool and the specialized literature is rather scarce. The method amounts to discretizing evolutionary PDE's in space only, so it produces a semi-discrete numerical scheme which consists of a system of ODE's (in the time variable). To prove convergence of the semi-discrete MOL scheme to the original PDE one needs to perform some more or less traditional analysis: it is necessary to show that the scheme is consistent with the continuous problem and that the discretized version of the spatial differential operator retains sufficient dissipative properties in order to allow an application of Gronwall's Lemma to the error term. As shown in [23], a uniform (in time) consistency estimate is sufficient to obtain convergence; however, the consistency estimate we proved is not uniform for a small time, so we cannot directly employ the results in [23] to prove convergence in our case. Instead, we prove all the required estimates "from the scratch", then we use their exact quantitative form in order to conclude convergence.

Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-11-01

In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz’s original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N→∞) of a single-particle discrete time system, even in the case of very small system sizes (N⩽22) . This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP.

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

NASA Technical Reports Server (NTRS)

Batina, John T.

1991-01-01

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Positivity-preserving dual time stepping schemes for gas dynamics

NASA Astrophysics Data System (ADS)

Parent, Bernard

2018-05-01

A new approach at discretizing the temporal derivative of the Euler equations is here presented which can be used with dual time stepping. The temporal discretization stencil is derived along the lines of the Cauchy-Kowalevski procedure resulting in cross differences in spacetime but with some novel modifications which ensure the positivity of the discretization coefficients. It is then shown that the so-obtained spacetime cross differences result in changes to the wave speeds and can thus be incorporated within Roe or Steger-Warming schemes (with and without reconstruction-evolution) simply by altering the eigenvalues. The proposed approach is advantaged over alternatives in that it is positivity-preserving for the Euler equations. Further, it yields monotone solutions near discontinuities while exhibiting a truncation error in smooth regions less than the one of the second- or third-order accurate backward-difference-formula (BDF) for either small or large time steps. The high resolution and positivity preservation of the proposed discretization stencils are independent of the convergence acceleration technique which can be set to multigrid, preconditioning, Jacobian-free Newton-Krylov, block-implicit, etc. Thus, the current paper also offers the first implicit integration of the time-accurate Euler equations that is positivity-preserving in the strict sense (that is, the density and temperature are guaranteed to remain positive). This is in contrast to all previous positivity-preserving implicit methods which only guaranteed the positivity of the density, not of the temperature or pressure. Several stringent reacting and inert test cases confirm the positivity-preserving property of the proposed method as well as its higher resolution and higher computational efficiency over other second-order and third-order implicit temporal discretization strategies.

Efficient genetic algorithms using discretization scheduling.

PubMed

McLay, Laura A; Goldberg, David E

2005-01-01

In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling.

Using Simulation to Interpret a Discrete Time Survival Model in a Complex Biological System: Fertility and Lameness in Dairy Cows

PubMed Central

Hudson, Christopher D.; Huxley, Jonathan N.; Green, Martin J.

2014-01-01

The ever-growing volume of data routinely collected and stored in everyday life presents researchers with a number of opportunities to gain insight and make predictions. This study aimed to demonstrate the usefulness in a specific clinical context of a simulation-based technique called probabilistic sensitivity analysis (PSA) in interpreting the results of a discrete time survival model based on a large dataset of routinely collected dairy herd management data. Data from 12,515 dairy cows (from 39 herds) were used to construct a multilevel discrete time survival model in which the outcome was the probability of a cow becoming pregnant during a given two day period of risk, and presence or absence of a recorded lameness event during various time frames relative to the risk period amongst the potential explanatory variables. A separate simulation model was then constructed to evaluate the wider clinical implications of the model results (i.e. the potential for a herd’s incidence rate of lameness to influence its overall reproductive performance) using PSA. Although the discrete time survival analysis revealed some relatively large associations between lameness events and risk of pregnancy (for example, occurrence of a lameness case within 14 days of a risk period was associated with a 25% reduction in the risk of the cow becoming pregnant during that risk period), PSA revealed that, when viewed in the context of a realistic clinical situation, a herd’s lameness incidence rate is highly unlikely to influence its overall reproductive performance to a meaningful extent in the vast majority of situations. Construction of a simulation model within a PSA framework proved to be a very useful additional step to aid contextualisation of the results from a discrete time survival model, especially where the research is designed to guide on-farm management decisions at population (i.e. herd) rather than individual level. PMID:25101997

Using simulation to interpret a discrete time survival model in a complex biological system: fertility and lameness in dairy cows.

PubMed

Hudson, Christopher D; Huxley, Jonathan N; Green, Martin J

2014-01-01

The ever-growing volume of data routinely collected and stored in everyday life presents researchers with a number of opportunities to gain insight and make predictions. This study aimed to demonstrate the usefulness in a specific clinical context of a simulation-based technique called probabilistic sensitivity analysis (PSA) in interpreting the results of a discrete time survival model based on a large dataset of routinely collected dairy herd management data. Data from 12,515 dairy cows (from 39 herds) were used to construct a multilevel discrete time survival model in which the outcome was the probability of a cow becoming pregnant during a given two day period of risk, and presence or absence of a recorded lameness event during various time frames relative to the risk period amongst the potential explanatory variables. A separate simulation model was then constructed to evaluate the wider clinical implications of the model results (i.e. the potential for a herd's incidence rate of lameness to influence its overall reproductive performance) using PSA. Although the discrete time survival analysis revealed some relatively large associations between lameness events and risk of pregnancy (for example, occurrence of a lameness case within 14 days of a risk period was associated with a 25% reduction in the risk of the cow becoming pregnant during that risk period), PSA revealed that, when viewed in the context of a realistic clinical situation, a herd's lameness incidence rate is highly unlikely to influence its overall reproductive performance to a meaningful extent in the vast majority of situations. Construction of a simulation model within a PSA framework proved to be a very useful additional step to aid contextualisation of the results from a discrete time survival model, especially where the research is designed to guide on-farm management decisions at population (i.e. herd) rather than individual level.

Modelling approaches: the case of schizophrenia.

PubMed

Heeg, Bart M S; Damen, Joep; Buskens, Erik; Caleo, Sue; de Charro, Frank; van Hout, Ben A

2008-01-01

Schizophrenia is a chronic disease characterized by periods of relative stability interrupted by acute episodes (or relapses). The course of the disease may vary considerably between patients. Patient histories show considerable inter- and even intra-individual variability. We provide a critical assessment of the advantages and disadvantages of three modelling techniques that have been used in schizophrenia: decision trees, (cohort and micro-simulation) Markov models and discrete event simulation models. These modelling techniques are compared in terms of building time, data requirements, medico-scientific experience, simulation time, clinical representation, and their ability to deal with patient heterogeneity, the timing of events, prior events, patient interaction, interaction between co-variates and variability (first-order uncertainty). We note that, depending on the research question, the optimal modelling approach should be selected based on the expected differences between the comparators, the number of co-variates, the number of patient subgroups, the interactions between co-variates, and simulation time. Finally, it is argued that in case micro-simulation is required for the cost-effectiveness analysis of schizophrenia treatments, a discrete event simulation model is best suited to accurately capture all of the relevant interdependencies in this chronic, highly heterogeneous disease with limited long-term follow-up data.

Detecting dynamical changes in time series by using the Jensen Shannon divergence

NASA Astrophysics Data System (ADS)

Mateos, D. M.; Riveaud, L. E.; Lamberti, P. W.

2017-08-01

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult because they have a common wide band power spectrum, a delta like autocorrelation function, and share other features as well. In general, signals are presented as continuous records and require to be discretized for being analyzed. In this work, we introduce different schemes for discretizing and for detecting dynamical changes in time series. One of the main motivations is to detect transitions between the chaotic and random regime. The tools here used here originate from the Information Theory. The schemes proposed are applied to simulated and real life signals, showing in all cases a high proficiency for detecting changes in the dynamics of the associated time series.

Detection and Modeling of High-Dimensional Thresholds for Fault Detection and Diagnosis

NASA Technical Reports Server (NTRS)

He, Yuning

2015-01-01

Many Fault Detection and Diagnosis (FDD) systems use discrete models for detection and reasoning. To obtain categorical values like oil pressure too high, analog sensor values need to be discretized using a suitablethreshold. Time series of analog and discrete sensor readings are processed and discretized as they come in. This task isusually performed by the wrapper code'' of the FDD system, together with signal preprocessing and filtering. In practice,selecting the right threshold is very difficult, because it heavily influences the quality of diagnosis. If a threshold causesthe alarm trigger even in nominal situations, false alarms will be the consequence. On the other hand, if threshold settingdoes not trigger in case of an off-nominal condition, important alarms might be missed, potentially causing hazardoussituations. In this paper, we will in detail describe the underlying statistical modeling techniques and algorithm as well as the Bayesian method for selecting the most likely shape and its parameters. Our approach will be illustrated by several examples from the Aerospace domain.

Synthesis and operation of an FFT-decoupled fixed-order reversed-field pinch plasma control system based on identification data

NASA Astrophysics Data System (ADS)

Olofsson, K. Erik J.; Brunsell, Per R.; Witrant, Emmanuel; Drake, James R.

2010-10-01

Recent developments and applications of system identification methods for the reversed-field pinch (RFP) machine EXTRAP T2R have yielded plasma response parameters for decoupled dynamics. These data sets are fundamental for a real-time implementable fast Fourier transform (FFT) decoupled discrete-time fixed-order strongly stabilizing synthesis as described in this work. Robustness is assessed over the data set by bootstrap calculation of the sensitivity transfer function worst-case H_{\\infty} -gain distribution. Output tracking and magnetohydrodynamic mode m = 1 tracking are considered in the same framework simply as two distinct weighted traces of a performance channel output-covariance matrix as derived from the closed-loop discrete-time Lyapunov equation. The behaviour of the resulting multivariable controller is investigated with dedicated T2R experiments.

Mapping of uncertainty relations between continuous and discrete time

NASA Astrophysics Data System (ADS)

Chiuchiú, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Mapping of uncertainty relations between continuous and discrete time.

PubMed

Chiuchiù, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\\infty }$ Performances.

PubMed

Choi, Hyun Duck; Ahn, Choon Ki; Karimi, Hamid Reza; Lim, Myo Taeg

2017-10-01

This paper studies delay-dependent exponential dissipative and l 2 - l ∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l 2 - l ∞ senses. The design of the desired exponential dissipative and l 2 - l ∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

PubMed Central

Zucker, David M.; Spiegelman, Donna

2013-01-01

SUMMARY We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain ‘localized error’ condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer. PMID:18219700

On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination

NASA Astrophysics Data System (ADS)

Alonso-Quesada, S.; De la Sen, M.; Ibeas, A.

2017-01-01

This paper deals with the discretization and control of an SEIR epidemic model. Such a model describes the transmission of an infectious disease among a time-varying host population. The model assumes mortality from causes related to the disease. Our study proposes a discretization method including a free-design parameter to be adjusted for guaranteeing the positivity of the resulting discrete-time model. Such a method provides a discrete-time model close to the continuous-time one without the need for the sampling period to be as small as other commonly used discretization methods require. This fact makes possible the design of impulsive vaccination control strategies with less burden of measurements and related computations if one uses the proposed instead of other discretization methods. The proposed discretization method and the impulsive vaccination strategy designed on the resulting discretized model are the main novelties of the paper. The paper includes (i) the analysis of the positivity of the obtained discrete-time SEIR model, (ii) the study of stability of the disease-free equilibrium point of a normalized version of such a discrete-time model and (iii) the existence and the attractivity of a globally asymptotically stable disease-free periodic solution under a periodic impulsive vaccination. Concretely, the exposed and infectious subpopulations asymptotically converge to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization individuals oscillate in the context of such a solution. Finally, a numerical example illustrates the theoretic results.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

The "Polar Light Sign" is a useful tool to detect discrete membranous supravalvular mitral stenosis.

PubMed

Hertwig, Christine; Haas, Nikolaus A; Habash, Sheeraz; Hanslik, Andreas; Kececioglu, Deniz; Sandica, Eugen; Laser, Kai-Thorsten

2015-02-01

Mitral valve stenosis caused by a discrete supravalvular membrane is a rare congenital malformation haemodynamically leading to significant mitral valve stenosis. When the supravalvular mitral stenosis consists of a discrete supravalvular membrane adherent to the mitral valve, it is usually not clearly detectable by routine echocardiography. We report about the typical echocardiographic finding in three young patients with this rare form of a discrete membranous supravalvular stenosis caused by a membrane adherent to the mitral valve. These cases present a typical echocardiographic feature in colour Doppler generated by the pathognomonic supramitral flow acceleration. Whereas typical supravalvular mitral stenosis caused by cor triatriatum or a clearly visible supravalvular ring is easily detectable by echocardiography, a discrete supravalvular membrane adjacent to the mitral valve leaflets resembling valvular mitral stenosis is difficult to differentiate by routine echocardiography. In our opinion, this colour phenomenon does resemble the visual impression of polar lights in the northern hemisphere; owing to its typical appearance, it may therefore be named as "Polar Light Sign". This phenomenon may help to detect this anatomical entity by echocardiography in time and therefore improve the prognosis for repair.

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.

Progress in unstructured-grid methods development for unsteady aerodynamic applications

NASA Technical Reports Server (NTRS)

Batina, John T.

1992-01-01

The development of unstructured-grid methods for the solution of the equations of fluid flow and what was learned over the course of the research are summarized. The focus of the discussion is on the solution of the time-dependent Euler equations including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an implicit upwind method using a CFL number of infinity is presented for the Boeing 747 aircraft. The results were obtained in less than one hour CPU time on a Cray-2 computer, thus, demonstrating the speed and robustness of the capability. Additional calculations for the ONERA M6 wing demonstrate the accuracy of the method through the good agreement between calculated results and experimental data for a standard transonic flow case.

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.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Cone penetrometer testing and discrete-depth ground water sampling techniques: A cost-effective method of site characterization in a multiple-aquifer setting

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

Zemo, D.A.; Pierce, Y.G.; Gallinatti, J.D.

Cone penetrometer testing (CPT), combined with discrete-depth ground water sampling methods, can significantly reduce the time and expense required to characterize large sites that have multiple aquifers. Results from the screening site characterization can then be used to design and install a cost-effective monitoring well network. At a site in northern California, it was necessary to characterize the stratigraphy and the distribution of volatile organic compounds (VOCs). To expedite characterization, a five-week field screening program was implemented that consisted of a shallow ground water survey, CPT soundings and pore-pressure measurements, and discrete-depth ground water sampling. Based on continuous lithologic informationmore » provided by the CPT soundings, four predominantly coarse-grained, water yielding stratigraphic packages were identified. Seventy-nine discrete-depth ground water samples were collected using either shallow ground water survey techniques, the BAT Enviroprobe, or the QED HydroPunch I, depending on subsurface conditions. Using results from these efforts, a 20-well monitoring network was designed and installed to monitor critical points within each stratigraphic package. Good correlation was found for hydraulic head and chemical results between discrete-depth screening data and monitoring well data. Understanding the vertical VOC distribution and concentrations produced substantial time and cost savings by minimizing the number of permanent monitoring wells and reducing the number of costly conductor casings that had to be installed. Additionally, significant long-term cost savings will result from reduced sampling costs, because fewer wells comprise the monitoring network. The authors estimate these savings to be 50% for site characterization costs, 65% for site characterization time, and 60% for long-term monitoring costs.« less

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

NASA Technical Reports Server (NTRS)

Roe, P. L.

1984-01-01

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.

Entropy production of doubly stochastic quantum channels

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

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less

SSAW: A new sequence similarity analysis method based on the stationary discrete wavelet transform.

PubMed

Lin, Jie; Wei, Jing; Adjeroh, Donald; Jiang, Bing-Hua; Jiang, Yue

2018-05-02

Alignment-free sequence similarity analysis methods often lead to significant savings in computational time over alignment-based counterparts. A new alignment-free sequence similarity analysis method, called SSAW is proposed. SSAW stands for Sequence Similarity Analysis using the Stationary Discrete Wavelet Transform (SDWT). It extracts k-mers from a sequence, then maps each k-mer to a complex number field. Then, the series of complex numbers formed are transformed into feature vectors using the stationary discrete wavelet transform. After these steps, the original sequence is turned into a feature vector with numeric values, which can then be used for clustering and/or classification. Using two different types of applications, namely, clustering and classification, we compared SSAW against the the-state-of-the-art alignment free sequence analysis methods. SSAW demonstrates competitive or superior performance in terms of standard indicators, such as accuracy, F-score, precision, and recall. The running time was significantly better in most cases. These make SSAW a suitable method for sequence analysis, especially, given the rapidly increasing volumes of sequence data required by most modern applications.

A genetic algorithm for dynamic inbound ordering and outbound dispatching problem with delivery time windows

NASA Astrophysics Data System (ADS)

Kim, Byung Soo; Lee, Woon-Seek; Koh, Shiegheun

2012-07-01

This article considers an inbound ordering and outbound dispatching problem for a single product in a third-party warehouse, where the demands are dynamic over a discrete and finite time horizon, and moreover, each demand has a time window in which it must be satisfied. Replenishing orders are shipped in containers and the freight cost is proportional to the number of containers used. The problem is classified into two cases, i.e. non-split demand case and split demand case, and a mathematical model for each case is presented. An in-depth analysis of the models shows that they are very complicated and difficult to find optimal solutions as the problem size becomes large. Therefore, genetic algorithm (GA) based heuristic approaches are designed to solve the problems in a reasonable time. To validate and evaluate the algorithms, finally, some computational experiments are conducted.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Interpreting Significant Discrete-Time Periods in Survival Analysis.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Denson, Kathleen B.

Discrete-time survival analysis is a new method for educational researchers to employ when looking at the timing of certain educational events. Previous continuous-time methods do not allow for the flexibility inherent in a discrete-time method. Because both time-invariant and time-varying predictor variables can now be used, the interaction of…

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

Space-Time Discrete KPZ Equation

NASA Astrophysics Data System (ADS)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Comprehensive Benchmark Suite for Simulation of Particle Laden Flows Using the Discrete Element Method with Performance Profiles from the Multiphase Flow with Interface eXchanges (MFiX) Code

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

Liu, Peiyuan; Brown, Timothy; Fullmer, William D.

Five benchmark problems are developed and simulated with the computational fluid dynamics and discrete element model code MFiX. The benchmark problems span dilute and dense regimes, consider statistically homogeneous and inhomogeneous (both clusters and bubbles) particle concentrations and a range of particle and fluid dynamic computational loads. Several variations of the benchmark problems are also discussed to extend the computational phase space to cover granular (particles only), bidisperse and heat transfer cases. A weak scaling analysis is performed for each benchmark problem and, in most cases, the scalability of the code appears reasonable up to approx. 103 cores. Profiling ofmore » the benchmark problems indicate that the most substantial computational time is being spent on particle-particle force calculations, drag force calculations and interpolating between discrete particle and continuum fields. Hardware performance analysis was also carried out showing significant Level 2 cache miss ratios and a rather low degree of vectorization. These results are intended to serve as a baseline for future developments to the code as well as a preliminary indicator of where to best focus performance optimizations.« less

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

Fermion systems in discrete space-time

NASA Astrophysics Data System (ADS)

Finster, Felix

2007-05-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Input-output identification of controlled discrete manufacturing systems

NASA Astrophysics Data System (ADS)

Estrada-Vargas, Ana Paula; López-Mellado, Ernesto; Lesage, Jean-Jacques

2014-03-01

The automated construction of discrete event models from observations of external system's behaviour is addressed. This problem, often referred to as system identification, allows obtaining models of ill-known (or even unknown) systems. In this article, an identification method for discrete event systems (DESs) controlled by a programmable logic controller is presented. The method allows processing a large quantity of observed long sequences of input/output signals generated by the controller and yields an interpreted Petri net model describing the closed-loop behaviour of the automated DESs. The proposed technique allows the identification of actual complex systems because it is sufficiently efficient and well adapted to cope with both the technological characteristics of industrial controllers and data collection requirements. Based on polynomial-time algorithms, the method is implemented as an efficient software tool which constructs and draws the model automatically; an overview of this tool is given through a case study dealing with an automated manufacturing system.

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

NASA Technical Reports Server (NTRS)

Spear, Ashley D.; Priest, Amanda R.; Veilleux, Michael G.; Ingraffea, Anthony R.; Hochhalter, Jacob D.

2011-01-01

A surrogate model methodology is described for predicting, during flight, the residual strength of aircraft structures that sustain discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. Two ductile fracture simulations are presented to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data does, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Working the System

ERIC Educational Resources Information Center

Berks, Darla R.; Vlasnik, Amber N.

2014-01-01

Unfortunately, many students learn about the concept of systems of linear equations in a procedural way. The lessons are taught as three discrete methods. Connections between the methods, in many cases, are not made. As a result, the students' overall understanding of the concept is very limited. By the time the teacher reaches the end of the…

75 FR 29877 - Affordable Housing Program Amendments: Federal Home Loan Bank Mortgage Refinancing Authority

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-28

... Banks with greater flexibility to manage the timing of the counseling required for households, and gives the Banks discretion to permit members to determine, prior to counseling, whether a household could... AHP refinancing set-aside program prior to counseling. In all cases, the household must obtain the...

29 CFR 1987.108 - Role of Federal agencies.

Code of Federal Regulations, 2014 CFR

2014-07-01

... (CONTINUED) PROCEDURES FOR HANDLING RETALIATION COMPLAINTS UNDER SECTION 402 OF THE FDA FOOD SAFETY...) The FDA, if interested in a proceeding, may participate as amicus curiae at any time in the proceeding, at the FDA's discretion. At the request of the FDA, copies of all documents in a case must be sent to...

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

PubMed

Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong

2018-07-01

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Discrete-Time Deterministic $Q$ -Learning: A Novel Convergence Analysis.

PubMed

Wei, Qinglai; Lewis, Frank L; Sun, Qiuye; Yan, Pengfei; Song, Ruizhuo

2017-05-01

In this paper, a novel discrete-time deterministic Q -learning algorithm is developed. In each iteration of the developed Q -learning algorithm, the iterative Q function is updated for all the state and control spaces, instead of updating for a single state and a single control in traditional Q -learning algorithm. A new convergence criterion is established to guarantee that the iterative Q function converges to the optimum, where the convergence criterion of the learning rates for traditional Q -learning algorithms is simplified. During the convergence analysis, the upper and lower bounds of the iterative Q function are analyzed to obtain the convergence criterion, instead of analyzing the iterative Q function itself. For convenience of analysis, the convergence properties for undiscounted case of the deterministic Q -learning algorithm are first developed. Then, considering the discounted factor, the convergence criterion for the discounted case is established. Neural networks are used to approximate the iterative Q function and compute the iterative control law, respectively, for facilitating the implementation of the deterministic Q -learning algorithm. Finally, simulation results and comparisons are given to illustrate the performance of the developed algorithm.

Lectures on algebraic system theory: Linear systems over rings

NASA Technical Reports Server (NTRS)

Kamen, E. W.

1978-01-01

The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.

29 CFR 4903.21 - Application of Federal Claims Collection Standards.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Section 4903.21 Labor Regulations Relating to Labor (Continued) PENSION BENEFIT GUARANTY CORPORATION... is feasible on a case-by-case basis in the exercise of sound discretion. In making such... against which offset is contemplated. (b) Repayment agreements. The PBGC will exercise its discretion in...

Galerkin v. discrete-optimal projection in nonlinear model reduction

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

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors.

PubMed

Yu, Jinpeng; Shi, Peng; Yu, Haisheng; Chen, Bing; Lin, Chong

2015-07-01

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

Process for producing dispersed particulate composite materials

DOEpatents

Henager, Jr., Charles H.; Hirth, John P.

1995-01-01

This invention is directed to a process for forming noninterwoven dispersed particulate composite products. In one case a composite multi-layer film product comprises a substantially noninterwoven multi-layer film having a plurality of discrete layers. This noninterwoven film comprises at least one discrete layer of a first material and at least one discrete layer of a second material. In another case the first and second materials are blended together with each other. In either case, the first material comprises a metalloid and the second material a metal compound. At least one component of a first material in one discrete layer undergoes a solid state displacement reaction with at least one component of a second material thereby producing the requisite noninterwoven composite film product. Preferably, the first material comprises silicon, the second material comprises Mo.sub.2 C, the third material comprises SiC and the fourth material comprises MoSi.sub.2.

Concealed Accessory Pathways with a Single Ventricular and Two Discrete Atrial Insertion Sites.

PubMed

Kipp, Ryan T; Abu Sham'a, Raed; Hiroyuki, Ito; Han, Frederick T; Refaat, Marwan; Hsu, Jonathan C; Field, Michael E; Kopp, Douglas E; Marcus, Gregory M; Scheinman, Melvin M; Hoffmayer, Kurt S

2017-03-01

Atrioventricular reciprocating tachycardia (AVRT) utilizing a concealed accessory pathway is common. It is well appreciated that some patients may have multiple accessory pathways with separate atrial and ventricular insertion sites. We present three cases of AVRT utilizing concealed pathways with evidence that each utilizing a single ventricular insertion and two discrete atrial insertion sites. In case one, two discrete atrial insertion sites were mapped in two separate procedures, and only during the second ablation was the Kent potential identified. Ablation of the Kent potential at this site remote from the two atrial insertion sites resulted in the termination of the retrograde conduction in both pathways. Case two presented with supraventricular tachycardia (SVT) with alternating eccentric atrial activation patterns without alteration in the tachycardia cycle length. The two distinct atrial insertion sites during orthodromic AVRT and ventricular pacing were targeted and each of the two atrial insertion sites were successfully mapped and ablated. In case three, retrograde decremental conduction utilizing both atrial insertion sites was identified prior to ablation. After mapping and ablation of the first discrete atrial insertion site, tachycardia persisted utilizing the second atrial insertion site. Only after ablation of the second atrial insertion site was SVT noninducible, and VA conduction was no longer present. Concealed retrograde accessory pathways with discrete atrial insertion sites may have a common ventricular insertion site. Identification and ablation of the ventricular insertion site or the separate discrete atrial insertion sites result in successful treatment. © 2017 Wiley Periodicals, Inc.

Assessing Columbine's Impact on Students' Fourth Amendment Case Outcomes: Implications for Administrative Discretion and Decision Making

ERIC Educational Resources Information Center

Torres, Mario S., Jr.; Chen, Yihsuan

2006-01-01

This study examined Columbine's impact on case outcomes related to student searches and its implications for civil liberties and school leader discretion. Using data from 236 court cases since the U.S. Supreme Court ruling of New Jersey v. T.L.O. in 1985, critical search dimensions and outcomes (e.g., level of suspicion) were examined using…

Quantum cellular automata and free quantum field theory

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro; Perinotti, Paolo

2017-02-01

In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

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

Control of Uncertain Systems under Constraints: Switching Horizon Predictive Control of Persistently Disturbed Input-Saturated Plants

DTIC Science & Technology

2006-12-01

on at any time from a family of candidate feedback-gains so as to control a discrete- time input-saturated LTI system possibly subject to persistent... times robustness Mosca, E. (2006) Control of Uncertain Systems under Constraints: Switching Horizon Predictive Control of Persistently Disturbed...feedback controls u = f(x̂) (3) so as to ensure, under suitable conditions, stability in the noiseless case as well as finite l∞-induced gain of the

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.

Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra

NASA Astrophysics Data System (ADS)

Rezakhah, Saeid; Maleki, Yasaman

2016-07-01

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

PubMed Central

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-01-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID:24829517

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

PubMed

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Group velocity of discrete-time quantum walks

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

Kempf, A.; Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; Portugal, R.

2009-05-15

We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate causally, we propose the use of these wave velocities in our definition for the hitting time of quantum walks. Our definition of hitting time has the advantage that it requires neither the specification of a walker's initial condition nor of an arrival probability threshold. We give full details for the case of quantum walks on the Cayley graphs of Abelianmore » groups. This includes the special cases of quantum walks on the line and on hypercubes.« less

A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics

PubMed Central

Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo

2013-01-01

We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085

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.

Discretization and control of an SEIR epidemic model under equilibrium Wiener noise disturbances

NASA Astrophysics Data System (ADS)

Alonso, Santiago; De la Sen, Manuel; Nistal, Raul; Ibeas, Asier

2017-11-01

A discretized SEIR epidemic model, subject to Wiener noise disturbances of the equilibrium points, is studied. The discrete-time model is got from a general discretization technique applied to its continuous-time counterpart so that its behaviour be close to its continuous-time counterpart irrespective of the size of the discretization period. The positivity and stability of a normalized version of such a discrete-time model are emphasized. The paper also proposes the design of a periodic impulsive vaccination which is periodically injected to the susceptible subpopulation in order to eradicate the propagation of the disease or, at least, to reduce its unsuitable infective effects within the potentially susceptible subpopulation. The existence and asymptotic stability of a disease-free periodic solution are proved. In particular, both the exposed and infectious subpopulations converge asymptotically to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization oscillate.

Generating chaos for discrete time-delayed systems via impulsive control.

PubMed

Guan, Zhi-Hong; Liu, Na

2010-03-01

Generating chaos for a class of discrete time-delayed systems via impulsive control is investigated in this paper. With the augmented matrix method, the time-delay impulsive systems can be transformed into a new class of linear discrete impulsive systems. Based on the largest Lyapunov exponent and the boundedness of the systems, some theoretical results about the chaotification for the discrete impulsive systems with time delay are derived and an example is given to visualize the satisfactory control performance.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Upscaling from particle models to entropic gradient flows

NASA Astrophysics Data System (ADS)

Dirr, Nicolas; Laschos, Vaios; Zimmer, Johannes

2012-06-01

We prove that, for the case of Gaussians on the real line, the functional derived by a time discretization of the diffusion equation as entropic gradient flow is asymptotically equivalent to the rate functional derived from the underlying microscopic process. This result strengthens a conjecture that the same statement is actually true for all measures with second finite moment.

Periodic measure for the stochastic equation of the barotropic viscous gas in a discretized one-dimensional domain

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

Benseghir, Rym, E-mail: benseghirrym@ymail.com, E-mail: benseghirrym@ymail.com; Benchettah, Azzedine, E-mail: abenchettah@hotmail.com; Raynaud de Fitte, Paul, E-mail: prf@univ-rouen.fr

2015-11-30

A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas’minskii’s theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.

Reinforcement-learning-based dual-control methodology for complex nonlinear discrete-time systems with application to spark engine EGR operation.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A

2008-08-01

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.

SToRM: A numerical model for environmental surface flows

USGS Publications Warehouse

Simoes, Francisco J.

2009-01-01

SToRM (System for Transport and River Modeling) is a numerical model developed to simulate free surface flows in complex environmental domains. It is based on the depth-averaged St. Venant equations, which are discretized using unstructured upwind finite volume methods, and contains both steady and unsteady solution techniques. This article provides a brief description of the numerical approach selected to discretize the governing equations in space and time, including important aspects of solving natural environmental flows, such as the wetting and drying algorithm. The presentation is illustrated with several application examples, covering both laboratory and natural river flow cases, which show the model’s ability to solve complex flow phenomena.

Stabilization and robustness of non-linear unity-feedback system - Factorization approach

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Kabuli, M. G.

1988-01-01

The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.

On pseudo-spectral time discretizations in summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Nordström, Jan

2018-05-01

Fully-implicit discrete formulations in summation-by-parts form for initial-boundary value problems must be invertible in order to provide well functioning procedures. We prove that, under mild assumptions, pseudo-spectral collocation methods for the time derivative lead to invertible discrete systems when energy-stable spatial discretizations are used.

Demands, skill discretion, decision authority and social climate at work as determinants of major depression in a 3-year follow-up study.

PubMed

Fandiño-Losada, Andrés; Forsell, Yvonne; Lundberg, Ingvar

2013-07-01

The psychosocial work environment may be a determinant of the development and course of depressive disorders, but the literature shows inconsistent findings. Thus, the aim of this study is to determine longitudinal effects of the job demands-control-support model (JDCSM) variables on the occurrence of major depression among working men and women from the general population. The sample comprised 4,710 working women and men living in Stockholm, who answered the same questionnaire twice, 3 years apart, who were not depressed during the first wave and had the same job in both waves. The questionnaire included JDCSM variables (demands, skill discretion, decision authority and social climate) and other co-variables (income, education, occupational group, social support, help and small children at home, living with an adult and depressive symptoms at time 1; and negative life events at time 2). Multiple logistic regressions were run to calculate odds ratios of having major depression at time 2, after adjustment for other JDCSM variables and co-variables. Among women, inadequate work social climate was the only significant risk indicator for major depression. Surprisingly, among men, high job demands and low skill discretion appeared as protective factors against major depression. The results showed a strong relationship between inadequate social climate and major depression among women, while there were no certain effects for the remaining exposure variables. Among men, few cases of major depression hampered well-founded conclusions regarding our findings of low job demands and high skill discretion as related to major depression.

Direct Numerical Simulation of Turbulent Flow Over Complex Bathymetry

NASA Astrophysics Data System (ADS)

Yue, L.; Hsu, T. J.

2017-12-01

Direct numerical simulation (DNS) is regarded as a powerful tool in the investigation of turbulent flow featured with a wide range of time and spatial scales. With the application of coordinate transformation in a pseudo-spectral scheme, a parallelized numerical modeling system was created aiming at simulating flow over complex bathymetry with high numerical accuracy and efficiency. The transformed governing equations were integrated in time using a third-order low-storage Runge-Kutta method. For spatial discretization, the discrete Fourier expansion was adopted in the streamwise and spanwise direction, enforcing the periodic boundary condition in both directions. The Chebyshev expansion on Chebyshev-Gauss-Lobatto points was used in the wall-normal direction, assuming there is no-slip on top and bottom walls. The diffusion terms were discretized with a Crank-Nicolson scheme, while the advection terms dealiased with the 2/3 rule were discretized with an Adams-Bashforth scheme. In the prediction step, the velocity was calculated in physical domain by solving the resulting linear equation directly. However, the extra terms introduced by coordinate transformation impose a strict limitation to time step and an iteration method was applied to overcome this restriction in the correction step for pressure by solving the Helmholtz equation. The numerical solver is written in object-oriented C++ programing language utilizing Armadillo linear algebra library for matrix computation. Several benchmarking cases in laminar and turbulent flow were carried out to verify/validate the numerical model and very good agreements are achieved. Ongoing work focuses on implementing sediment transport capability for multiple sediment classes and parameterizations for flocculation processes.

Uncertainty relation for the discrete Fourier transform.

PubMed

Massar, Serge; Spindel, Philippe

2008-05-16

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation.

Controllability of discrete bilinear systems with bounded control.

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Elliott, D. L.; Goka, T.

1973-01-01

The subject of this paper is the controllability of time-invariant discrete-time bilinear systems. Bilinear systems are classified into two categories; homogeneous and inhomogeneous. Sufficient conditions which ensure the global controllability of discrete-time bilinear systems are obtained by localized analysis in control variables.

The Spectrum of Mathematical Models.

ERIC Educational Resources Information Center

Karplus, Walter J.

1983-01-01

Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…

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.

From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

NASA Astrophysics Data System (ADS)

Finster, Felix

This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

Robust inference in discrete hazard models for randomized clinical trials.

PubMed

Nguyen, Vinh Q; Gillen, Daniel L

2012-10-01

Time-to-event data in which failures are only assessed at discrete time points are common in many clinical trials. Examples include oncology studies where events are observed through periodic screenings such as radiographic scans. When the survival endpoint is acknowledged to be discrete, common methods for the analysis of observed failure times include the discrete hazard models (e.g., the discrete-time proportional hazards and the continuation ratio model) and the proportional odds model. In this manuscript, we consider estimation of a marginal treatment effect in discrete hazard models where the constant treatment effect assumption is violated. We demonstrate that the estimator resulting from these discrete hazard models is consistent for a parameter that depends on the underlying censoring distribution. An estimator that removes the dependence on the censoring mechanism is proposed and its asymptotic distribution is derived. Basing inference on the proposed estimator allows for statistical inference that is scientifically meaningful and reproducible. Simulation is used to assess the performance of the presented methodology in finite samples.

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

NASA Astrophysics Data System (ADS)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Wavelet transforms with discrete-time continuous-dilation wavelets

NASA Astrophysics Data System (ADS)

Zhao, Wei; Rao, Raghuveer M.

1999-03-01

Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.

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.

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

PubMed Central

Chen, Rui; Hyrien, Ollivier

2011-01-01

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356

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

Naughton, M.J.; Bourke, W.; Browning, G.L.

The convergence of spectral model numerical solutions of the global shallow-water equations is examined as a function of the time step and the spectral truncation. The contributions to the errors due to the spatial and temporal discretizations are separately identified and compared. Numerical convergence experiments are performed with the inviscid equations from smooth (Rossby-Haurwitz wave) and observed (R45 atmospheric analysis) initial conditions, and also with the diffusive shallow-water equations. Results are compared with the forced inviscid shallow-water equations case studied by Browning et al. Reduction of the time discretization error by the removal of fast waves from the solution usingmore » initialization is shown. The effects of forcing and diffusion on the convergence are discussed. Time truncation errors are found to dominate when a feature is large scale and well resolved; spatial truncation errors dominate for small-scale features and also for large scale after the small scales have affected them. Possible implications of these results for global atmospheric modeling are discussed. 31 refs., 14 figs., 4 tabs.« less

(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation

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

Behbahani, Siavosh R.; /SLAC /Stanford U., Phys. Dept. /Boston U.; Dymarsky, Anatoly

2012-06-06

We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson {pi} is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber.more » We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n > 2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.« less

The discrimination of discrete and continuous amounts in African grey parrots (Psittacus erithacus).

PubMed

Aïn, Syrina Al; Giret, Nicolas; Grand, Marion; Kreutzer, Michel; Bovet, Dalila

2009-01-01

A wealth of research in infants and animals demonstrates discrimination of quantities, in some cases nonverbal numerical perception, and even elementary calculation capacities. We investigated the ability of three African grey parrots (Psittacus erithacus) to select the largest amount of food between two sets, either discrete food items (experiment 1) or as volume of a food substance (experiment 2). The two amounts were presented simultaneously and were visible at the time of choice. Parrots were tested several times for all possible combinations between 1 and 5 seeds or 0.2 and 1 ml of food substance. In both conditions, subjects performed above chance for almost all combinations. Accuracy was negatively correlated with the ratio, that is performance improved with greater differences between amounts. Therefore, these results with both individual items and volume discrimination suggest that parrots use an analogue of magnitude, rather than object-file mechanisms to quantify items and substances.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

Vaca, M. V.; Tretter, S. A.

1977-01-01

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

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.

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

NASA Astrophysics Data System (ADS)

Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.

2017-07-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.

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.

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

NASA Astrophysics Data System (ADS)

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels.

PubMed

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a Courant number of nine thousand, even complete multigrid breakdown is observed. Local Fourier analysis indicates that the degradation of the convergence rate is associated with the coarse-grid correction algorithm. An implicit scheme for the Euler equations that makes use of the present method was, nevertheless, able to outperform a standard explicit scheme on a time-dependent problem with a Courant number of order 1000. Conclusions: For steady-state problems, the described approach enables the construction of parallelizable, efficient, and robust implicit hydrodynamics solvers. The applicability of the method to time-dependent problems is presently restricted to cases with moderately high Courant numbers. This is due to an insufficient coarse-grid correction of the employed multigrid algorithm for large time steps. Further research will be required to help us to understand and overcome the observed multigrid convergence difficulties for time-dependent problems.

Joint modeling of longitudinal data and discrete-time survival outcome.

PubMed

Qiu, Feiyou; Stein, Catherine M; Elston, Robert C

2016-08-01

A predictive joint shared parameter model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and a generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on predicting discrete time-to-event outcome, taking advantage of repeated measurements. We show that the probability of an event in a time window can be more precisely predicted by incorporating the longitudinal measurements. The model was investigated by comparison with a two-step model and a discrete-time survival model. Results from both a study on the occurrence of tuberculosis and simulated data show that the joint model is superior to the other models in discrimination ability, especially as the latent variables related to both survival times and the longitudinal measurements depart from 0. © The Author(s) 2013.

a Structure of Experienced Time

NASA Astrophysics Data System (ADS)

Havel, Ivan M.

2005-10-01

The subjective experience of time will be taken as a primary motivation for an alternative, essentially discontinuous conception of time. Two types of such experience will be discussed, one based on personal episodic memory, the other on the theoretical fine texture of experienced time below the threshold of phenomenal awareness. The former case implies a discrete structure of temporal episodes on a large scale, while the latter case suggests endowing psychological time with a granular structure on a small scale, i.e. interpreting it as a semi-ordered flow of smeared (not point-like) subliminal time grains. Only on an intermediate temporal scale would the subjectively felt continuity and fluency of time emerge. Consequently, there is no locally smooth mapping of phenomenal time onto the real number continuum. Such a model has certain advantages; for instance, it avoids counterintuitive interpretations of some neuropsychological experiments (e.g. Libet's measurement) in which the temporal order of events is crucial.

The Pauli Objection

NASA Astrophysics Data System (ADS)

Leon, Juan; Maccone, Lorenzo

2017-12-01

Schrödinger's equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli concluded that constructing a general a time operator is impossible (although clearly it can be done in specific cases). Here we show how the Pauli argument fails when one uses an external system (a "clock") to track time, so that time arises as correlations between the system and the clock (conditional probability amplitudes framework). In this case, the time operator is conjugate to the clock Hamiltonian and not to the system Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians.

Siegert-state expansion for nonstationary systems. IV. Three-dimensional case

NASA Astrophysics Data System (ADS)

Tolstikhin, Oleg I.

2008-03-01

The Siegert-state expansion approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)] is extended to the three-dimensional case. Coupled equations defining the time evolution of coefficients in the expansion of the solution to the time-dependent Schrödinger equation in terms of partial-wave Siegert states are derived, and physical observables (probabilities of transitions to discrete states and the momentum distribution of ejected particles) are expressed in terms of these coefficients. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations of the photodetachment of H- by strong high-frequency laser pulses. The present calculations demonstrate that the interference effect in the laser-atom interaction dynamics found recently in the one-dimensional case [K. Toyota , Phys. Rev. A 76, 043418 (2007)] reveals itself in the three-dimensional case as well.

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

Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions.

PubMed

Acosta-Mesa, Héctor-Gabriel; Rechy-Ramírez, Fernando; Mezura-Montes, Efrén; Cruz-Ramírez, Nicandro; Hernández Jiménez, Rodolfo

2014-06-01

In this work, we present a novel application of time series discretization using evolutionary programming for the classification of precancerous cervical lesions. The approach optimizes the number of intervals in which the length and amplitude of the time series should be compressed, preserving the important information for classification purposes. Using evolutionary programming, the search for a good discretization scheme is guided by a cost function which considers three criteria: the entropy regarding the classification, the complexity measured as the number of different strings needed to represent the complete data set, and the compression rate assessed as the length of the discrete representation. This discretization approach is evaluated using a time series data based on temporal patterns observed during a classical test used in cervical cancer detection; the classification accuracy reached by our method is compared with the well-known times series discretization algorithm SAX and the dimensionality reduction method PCA. Statistical analysis of the classification accuracy shows that the discrete representation is as efficient as the complete raw representation for the present application, reducing the dimensionality of the time series length by 97%. This representation is also very competitive in terms of classification accuracy when compared with similar approaches. Copyright © 2014 Elsevier Inc. All rights reserved.

An alternative to traditional goodness-of-fit tests for discretely measured continuous data

Treesearch

KaDonna C. Randolph; Bill Seaver

2007-01-01

Traditional goodness-of-fit tests such as the Kolmogorov-Smirnov and x2 tests are easily applied to data of the continuous or discrete type, respectively. Occasionally, however, the case arises when continuous data are recorded into discrete categories due to an imprecise measurement system. In this instance, the traditional goodness-of-fit...

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

NASA Astrophysics Data System (ADS)

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform

NASA Astrophysics Data System (ADS)

Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.

2001-12-01

Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an n-th order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer polynomial transforms.

On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay.

PubMed

Feng, Zhiguang; Zheng, Wei Xing

2015-12-01

In this brief, the problem of extended dissipativity analysis for discrete-time neural networks with time-varying delay is investigated. The definition of extended dissipativity of discrete-time neural networks is proposed, which unifies several performance measures, such as the H∞ performance, passivity, l2 - l∞ performance, and dissipativity. By introducing a triple-summable term in Lyapunov function, the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term and then the extended dissipativity criterion for discrete-time neural networks with time-varying delay is established. The derived condition guarantees not only the extended dissipativity but also the stability of the neural networks. Two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results.

Accurate green water loads calculation using naval hydro pack

NASA Astrophysics Data System (ADS)

Jasak, H.; Gatin, I.; Vukčević, V.

2017-12-01

An extensive verification and validation of Finite Volume based CFD software Naval Hydro based on foam-extend is presented in this paper for green water loads. Two-phase numerical model with advanced methods for treating the free surface is employed. Pressure loads on horizontal deck of Floating Production Storage and Offloading vessel (FPSO) model are compared to experimental results from [1] for three incident regular waves. Pressure peaks and integrals of pressure in time are measured on ten different locations on deck for each case. Pressure peaks and integrals are evaluated as average values among the measured incident wave periods, where periodic uncertainty is assessed for both numerical and experimental results. Spatial and temporal discretization refinement study is performed providing numerical discretization uncertainties.

Optical chirp z-transform processor with a simplified architecture.

PubMed

Ngo, Nam Quoc

2014-12-29

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

Adaptive temporal refinement in injection molding

NASA Astrophysics Data System (ADS)

Karyofylli, Violeta; Schmitz, Mauritius; Hopmann, Christian; Behr, Marek

2018-05-01

Mold filling is an injection molding stage of great significance, because many defects of the plastic components (e.g. weld lines, burrs or insufficient filling) can occur during this process step. Therefore, it plays an important role in determining the quality of the produced parts. Our goal is the temporal refinement in the vicinity of the evolving melt front, in the context of 4D simplex-type space-time grids [1, 2]. This novel discretization method has an inherent flexibility to employ completely unstructured meshes with varying levels of resolution both in spatial dimensions and in the time dimension, thus allowing the use of local time-stepping during the simulations. This can lead to a higher simulation precision, while preserving calculation efficiency. A 3D benchmark case, which concerns the filling of a plate-shaped geometry, is used for verifying our numerical approach [3]. The simulation results obtained with the fully unstructured space-time discretization are compared to those obtained with the standard space-time method and to Moldflow simulation results. This example also serves for providing reliable timing measurements and the efficiency aspects of the filling simulation of complex 3D molds while applying adaptive temporal refinement.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

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

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Time Span of Discretion and Administrative Work in School Systems: Results of a Pilot Study.

ERIC Educational Resources Information Center

Allison, Derek J.; Morfitt, Grace

This paper presents findings of a study that utilized Elliott Jaques' theories of organizational depth structure and time span of discretion in administrative work to examine administrators' responsibilities in two Ontario (Canada) school systems. The theory predicts that the time-span of discretion associated with the administrative tasks will…

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

NASA Astrophysics Data System (ADS)

Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-12-01

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

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.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

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 discrete model of a modified Burgers' partial differential equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Convergence of Spectral Discretizations of the Vlasov--Poisson System

DOE PAGES

Manzini, G.; Funaro, D.; Delzanno, G. L.

2017-09-26

Here we prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1Vmore » case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.« less

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

PubMed

Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

2011-08-01

We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds.

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

NASA Astrophysics Data System (ADS)

Aurzada, Frank; Buck, Micha

2018-02-01

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97-111, 1999) and Molchan (J Stat Phys 167(6):1546-1554, 2017) to a wide class of discrete-time processes.

Discrete-time Markovian stochastic Petri nets

NASA Technical Reports Server (NTRS)

Ciardo, Gianfranco

1995-01-01

We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.

Improved robustness and performance of discrete time sliding mode control systems.

PubMed

Chakrabarty, Sohom; Bartoszewicz, Andrzej

2016-11-01

This paper presents a theoretical analysis along with simulations to show that increased robustness can be achieved for discrete time sliding mode control systems by choosing the sliding variable, or the output, to be of relative degree two instead of relative degree one. In other words it successfully reduces the ultimate bound of the sliding variable compared to the ultimate bound for standard discrete time sliding mode control systems. It is also found out that for such a selection of relative degree two output of the discrete time system, the reduced order system during sliding becomes finite time stable in absence of disturbance. With disturbance, it becomes finite time ultimately bounded. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Finsler Geometry of Nonlinear Elastic Solids with Internal Structure

DTIC Science & Technology

2017-01-01

should enable regularized numerical solutions with discretization -size independence for representation of materials demonstrating softening, e.g...additional possibility of a discrete larger void/cavity forming at the core of the sphere. In the second case, comparison with the classical...core of the domain. This hollow sphere physically represents a discrete cavity, while the constant field ξH physically represents a continuous

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

Fractional discrete-time consensus models for single- and double-summator dynamics

NASA Astrophysics Data System (ADS)

Wyrwas, Małgorzata; Mozyrska, Dorota; Girejko, Ewa

2018-04-01

The leader-following consensus problem of fractional-order multi-agent discrete-time systems is considered. In the systems, interactions between opinions are defined like in Krause and Cucker-Smale models but the memory is included by taking the fractional-order discrete-time operator on the left-hand side of the nonlinear systems. In this paper, we investigate fractional-order models of opinions for the single- and double-summator dynamics of discrete-time by analytical methods as well as by computer simulations. The necessary and sufficient conditions for the leader-following consensus are formulated by proposing a consensus control law for tracking the virtual leader.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

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.

Time crystals: a review

NASA Astrophysics Data System (ADS)

Sacha, Krzysztof; Zakrzewski, Jakub

2018-01-01

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals—the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek’s idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

PubMed

Mishchenko, Michael I; Dlugach, Janna M; Yurkin, Maxim A; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R Lee; Travis, Larry D; Yang, Ping; Zakharova, Nadezhda T

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ , or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

PubMed Central

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies. PMID:29657355

Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

PubMed

Seiffertt, John; Sanyal, Suman; Wunsch, Donald C

2008-08-01

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

A SAS-based solution to evaluate study design efficiency of phase I pediatric oncology trials via discrete event simulation.

PubMed

Barrett, Jeffrey S; Jayaraman, Bhuvana; Patel, Dimple; Skolnik, Jeffrey M

2008-06-01

Previous exploration of oncology study design efficiency has focused on Markov processes alone (probability-based events) without consideration for time dependencies. Barriers to study completion include time delays associated with patient accrual, inevaluability (IE), time to dose limiting toxicities (DLT) and administrative and review time. Discrete event simulation (DES) can incorporate probability-based assignment of DLT and IE frequency, correlated with cohort in the case of DLT, with time-based events defined by stochastic relationships. A SAS-based solution to examine study efficiency metrics and evaluate design modifications that would improve study efficiency is presented. Virtual patients are simulated with attributes defined from prior distributions of relevant patient characteristics. Study population datasets are read into SAS macros which select patients and enroll them into a study based on the specific design criteria if the study is open to enrollment. Waiting times, arrival times and time to study events are also sampled from prior distributions; post-processing of study simulations is provided within the decision macros and compared across designs in a separate post-processing algorithm. This solution is examined via comparison of the standard 3+3 decision rule relative to the "rolling 6" design, a newly proposed enrollment strategy for the phase I pediatric oncology setting.

Illustrating chaos: a schematic discretization of the general three-body problem in Newtonian gravity

NASA Astrophysics Data System (ADS)

Leigh, Nathan W. C.; Wegsman, Shalma

2018-05-01

We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction into a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.

On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Godoy, William F.; DesJardin, Paul E.

2010-05-01

The application of flux limiters to the discrete ordinates method (DOM), SN, for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to "exact" solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.

On the lagrangian 1-form structure of the hyperbolic calogero-moser system

NASA Astrophysics Data System (ADS)

Jairuk, Umpon; Tanasittikosol, Monsit; Yoo-Kong, Sikarin

2017-06-01

In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero-Moser system in both discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. Furthermore, it is shown that the hyperbolic Calogero-Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level.

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.

Discrete spacetime, quantum walks, and relativistic wave equations

NASA Astrophysics Data System (ADS)

Mlodinow, Leonard; Brun, Todd A.

2018-04-01

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper, we define the three-dimensional discrete-time walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space; each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis—that is, that the walk be symmetric under parity transformations and steps along different axes of the cubic lattice be uncorrelated—leads, in the case of the simplest solution, to the requirement that the continuum limit of the walk is fully Lorentz-invariant. We show further that, in the case of a massive particle, this symmetry requirement necessitates the use of a four-dimensional internal space (as in the Dirac equation). The "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated with each dimension must all anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

PubMed

Oettinger, D; Mendoza, M; Herrmann, H J

2013-07-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

Using discrete event computer simulation to improve patient flow in a Ghanaian acute care hospital.

PubMed

Best, Allyson M; Dixon, Cinnamon A; Kelton, W David; Lindsell, Christopher J; Ward, Michael J

2014-08-01

Crowding and limited resources have increased the strain on acute care facilities and emergency departments worldwide. These problems are particularly prevalent in developing countries. Discrete event simulation is a computer-based tool that can be used to estimate how changes to complex health care delivery systems such as emergency departments will affect operational performance. Using this modality, our objective was to identify operational interventions that could potentially improve patient throughput of one acute care setting in a developing country. We developed a simulation model of acute care at a district level hospital in Ghana to test the effects of resource-neutral (eg, modified staff start times and roles) and resource-additional (eg, increased staff) operational interventions on patient throughput. Previously captured deidentified time-and-motion data from 487 acute care patients were used to develop and test the model. The primary outcome was the modeled effect of interventions on patient length of stay (LOS). The base-case (no change) scenario had a mean LOS of 292 minutes (95% confidence interval [CI], 291-293). In isolation, adding staffing, changing staff roles, and varying shift times did not affect overall patient LOS. Specifically, adding 2 registration workers, history takers, and physicians resulted in a 23.8-minute (95% CI, 22.3-25.3) LOS decrease. However, when shift start times were coordinated with patient arrival patterns, potential mean LOS was decreased by 96 minutes (95% CI, 94-98), and with the simultaneous combination of staff roles (registration and history taking), there was an overall mean LOS reduction of 152 minutes (95% CI, 150-154). Resource-neutral interventions identified through discrete event simulation modeling have the potential to improve acute care throughput in this Ghanaian municipal hospital. Discrete event simulation offers another approach to identifying potentially effective interventions to improve patient flow in emergency and acute care in resource-limited settings. Copyright © 2014 Elsevier Inc. All rights reserved.

Perfect discretization of path integrals

NASA Astrophysics Data System (ADS)

Steinhaus, Sebastian

2012-05-01

In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

A Scale-Invariant ``Discrete-Time'' Balitsky--Kovchegov Equation

NASA Astrophysics Data System (ADS)

Bialas, A.; Peschanski, R.

2005-06-01

We consider a version of QCD dipole cascading corresponding to a finite number n of discrete Δ Y steps of branching in rapidity. Using the discretization scheme preserving the holomorphic factorizability and scale-invariance in position space of the dipole splitting function, we derive an exact recurrence formula from step to step which plays the rôle of a ``discrete-time'' Balitsky--Kovchegov equation. The BK solutions are recovered in the limit n=∞ and Δ Y=0.

Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure

NASA Astrophysics Data System (ADS)

Diethert, A.; Finster, F.; Schiefeneder, D.

As toy models for space-time at the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

NASA Astrophysics Data System (ADS)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 122 907 No. of bytes in distributed program, including test data, etc.: 609 662 Distribution format: tar.gz Programming language: FORTRAN 77 and Fortran 90/95 Computer: PC Operating system: Linux, Unix RAM: 1 GByte (i, iv, v), 2 GByte (ii, vi, vii, x, xi), 4 GByte (iii, viii, xii), 8 GByte (ix) Classification: 2.9, 4.3, 4.12 Nature of problem: These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Solution method: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems. Additional comments: This package consists of 12 programs, see "Program title", above. FORTRAN77 versions are provided for each of the 12 and, in addition, Fortran 90/95 versions are included for ii, iii, vi, viii, ix, xii. For the particular purpose of each program please see the below. Running time: Minutes on a medium PC (i, iv, v, vii, x, xi), a few hours on a medium PC (ii, vi, viii, xii), days on a medium PC (iii, ix). Program summary (1)Title of program: imagtime1d.F Title of electronic file: imagtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (2)Title of program: imagtimecir.F Title of electronic file: imagtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (3)Title of program: imagtimesph.F Title of electronic file: imagtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (4)Title of program: realtime1d.F Title of electronic file: realtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (5)Title of program: realtimecir.F Title of electronic file: realtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (6)Title of program: realtimesph.F Title of electronic file: realtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (7)Title of programs: imagtimeaxial.F and imagtimeaxial.f90 Title of electronic file: imagtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (8)Title of program: imagtime2d.F and imagtime2d.f90 Title of electronic file: imagtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (9)Title of program: realtimeaxial.F and realtimeaxial.f90 Title of electronic file: realtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (10)Title of program: realtime2d.F and realtime2d.f90 Title of electronic file: realtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (11)Title of program: imagtime3d.F and imagtime3d.f90 Title of electronic file: imagtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (12)Title of program: realtime3d.F and realtime3d.f90 Title of electronic file: realtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum Ram Memory: 8 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems.

Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao

In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

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.

A case study on Discrete Wavelet Transform based Hurst exponent for epilepsy detection.

PubMed

Madan, Saiby; Srivastava, Kajri; Sharmila, A; Mahalakshmi, P

2018-01-01

Epileptic seizures are manifestations of epilepsy. Careful analysis of EEG records can provide valuable insight and improved understanding of the mechanism causing epileptic disorders. The detection of epileptic form discharges in EEG is an important component in the diagnosis of epilepsy. As EEG signals are non-stationary, the conventional frequency and time domain analysis does not provide better accuracy. So, in this work an attempt has been made to provide an overview of the determination of epilepsy by implementation of Hurst exponent (HE)-based discrete wavelet transform techniques for feature extraction from EEG data sets obtained during ictal and pre ictal stages of affected person and finally classifying EEG signals using SVM and KNN Classifiers. The The highest accuracy of 99% is obtained using SVM.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Hybrid modeling in biochemical systems theory by means of functional petri nets.

PubMed

Wu, Jialiang; Voit, Eberhard

2009-02-01

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1991-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1990-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Detection of coupling delay: A problem not yet solved

NASA Astrophysics Data System (ADS)

Coufal, David; Jakubík, Jozef; Jajcay, Nikola; Hlinka, Jaroslav; Krakovská, Anna; Paluš, Milan

2017-08-01

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed—the method based on conditional mutual information—the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping—the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.

Variability of a "force signature" during windmill softball pitching and relationship between discrete force variables and pitch velocity.

PubMed

Nimphius, Sophia; McGuigan, Michael R; Suchomel, Timothy J; Newton, Robert U

2016-06-01

This study assessed reliability of discrete ground reaction force (GRF) variables over multiple pitching trials, investigated the relationships between discrete GRF variables and pitch velocity (PV) and assessed the variability of the "force signature" or continuous force-time curve during the pitching motion of windmill softball pitchers. Intraclass correlation coefficient (ICC) for all discrete variables was high (0.86-0.99) while the coefficient of variance (CV) was low (1.4-5.2%). Two discrete variables were significantly correlated to PV; second vertical peak force (r(5)=0.81, p=0.03) and time between peak forces (r(5)=-0.79; p=0.03). High ICCs and low CVs support the reliability of discrete GRF and PV variables over multiple trials and significant correlations indicate there is a relationship between the ability to produce force and the timing of this force production with PV. The mean of all pitchers' curve-average standard deviation of their continuous force-time curves demonstrated low variability (CV=4.4%) indicating a repeatable and identifiable "force signature" pattern during this motion. As such, the continuous force-time curve in addition to discrete GRF variables should be examined in future research as a potential method to monitor or explain changes in pitching performance. Copyright © 2016 Elsevier B.V. All rights reserved.

The Law of Federal Labor-Management Relations

DTIC Science & Technology

2001-12-04

definitive interpretations and rulings on the provisions of the Order; to decide major policy issues; to entertain, at its discretion, appeals from...transcribed unless they are appealed ; are not published; and are final and binding only with respect to the parties to the case. With limited ...regulation was not essential to these agency objectives. In so deciding the FLRA noted that the agency regulation provided that the appeal time limit

Hyper-resolution hydrological modeling: Completeness of Formulation, Appropriateness of Descritization, and Physical LImits of Predictability

NASA Astrophysics Data System (ADS)

Ogden, F. L.

2017-12-01

HIgh performance computing and the widespread availabilities of geospatial physiographic and forcing datasets have enabled consideration of flood impact predictions with longer lead times and more detailed spatial descriptions. We are now considering multi-hour flash flood forecast lead times at the subdivision level in so-called hydroblind regions away from the National Hydrography network. However, the computational demands of such models are high, necessitating a nested simulation approach. Research on hyper-resolution hydrologic modeling over the past three decades have illustrated some fundamental limits on predictability that are simultaneously related to runoff generation mechanism(s), antecedent conditions, rates and total amounts of precipitation, discretization of the model domain, and complexity or completeness of the model formulation. This latter point is an acknowledgement that in some ways hydrologic understanding in key areas related to land use, land cover, tillage practices, seasonality, and biological effects has some glaring deficiencies. This presentation represents a review of what is known related to the interacting effects of precipitation amount, model spatial discretization, antecedent conditions, physiographic characteristics and model formulation completeness for runoff predictions. These interactions define a region in multidimensional forcing, parameter and process space where there are in some cases clear limits on predictability, and in other cases diminished uncertainty.

Test Score Equating Using Discrete Anchor Items versus Passage-Based Anchor Items: A Case Study Using "SAT"® Data. Research Report. ETS RR-14-14

ERIC Educational Resources Information Center

Liu, Jinghua; Zu, Jiyun; Curley, Edward; Carey, Jill

2014-01-01

The purpose of this study is to investigate the impact of discrete anchor items versus passage-based anchor items on observed score equating using empirical data.This study compares an "SAT"® critical reading anchor that contains more discrete items proportionally, compared to the total tests to be equated, to another anchor that…

Pinning impulsive control algorithms for complex network

NASA Astrophysics Data System (ADS)

Sun, Wen; Lü, Jinhu; Chen, Shihua; Yu, Xinghuo

2014-03-01

In this paper, we further investigate the synchronization of complex dynamical network via pinning control in which a selection of nodes are controlled at discrete times. Different from most existing work, the pinning control algorithms utilize only the impulsive signals at discrete time instants, which may greatly improve the communication channel efficiency and reduce control cost. Two classes of algorithms are designed, one for strongly connected complex network and another for non-strongly connected complex network. It is suggested that in the strongly connected network with suitable coupling strength, a single controller at any one of the network's nodes can always pin the network to its homogeneous solution. In the non-strongly connected case, the location and minimum number of nodes needed to pin the network are determined by the Frobenius normal form of the coupling matrix. In addition, the coupling matrix is not necessarily symmetric or irreducible. Illustrative examples are then given to validate the proposed pinning impulsive control algorithms.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Fault-tolerant optimised tracking control for unknown discrete-time linear systems using a combined reinforcement learning and residual compensation methodology

NASA Astrophysics Data System (ADS)

Han, Ke-Zhen; Feng, Jian; Cui, Xiaohong

2017-10-01

This paper considers the fault-tolerant optimised tracking control (FTOTC) problem for unknown discrete-time linear system. A research scheme is proposed on the basis of data-based parity space identification, reinforcement learning and residual compensation techniques. The main characteristic of this research scheme lies in the parity-space-identification-based simultaneous tracking control and residual compensation. The specific technical line consists of four main contents: apply subspace aided method to design observer-based residual generator; use reinforcement Q-learning approach to solve optimised tracking control policy; rely on robust H∞ theory to achieve noise attenuation; adopt fault estimation triggered by residual generator to perform fault compensation. To clarify the design and implementation procedures, an integrated algorithm is further constructed to link up these four functional units. The detailed analysis and proof are subsequently given to explain the guaranteed FTOTC performance of the proposed conclusions. Finally, a case simulation is provided to verify its effectiveness.

Sliding Mode Control for Discrete-Time Systems With Markovian Packet Dropouts.

PubMed

Song, Heran; Chen, Shih-Chi; Yam, Yeung

2017-11-01

This paper presents the design of a sliding mode controller for networked control systems subject to successive Markovian packet dropouts. This paper adopts the Gilbert-Elliott channel model to describe the temporal correlation among packet losses, and proposes an update scheme to select the assumed available states for use in a sliding mode control law. A technique used in the theory of discrete-time Markov jump linear systems is applied to tackle the effect of the packet losses. This involves introducing a couple of Lyapunov functions dependent on the indicator functions of the instantaneous packet loss, and proving that the sliding mode controller is able to drive the system state trajectories into the neighborhood of the designed integral sliding surface in mean-square sense given that the corresponding Lyapunov inequalities are satisfied. The system is guaranteed thereafter to remain inside the neighborhood of the sliding surface. Simulated case studies are presented to illustrate the effectiveness of the control law.

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

Donders revisited: Discrete or continuous temporal processing underlying reaction time distributions?

PubMed

Bao, Yan; Yang, Taoxi; Lin, Xiaoxiong; Pöppel, Ernst

2016-09-01

Differences of reaction times to specific stimulus configurations are used as indicators of cognitive processing stages. In this classical experimental paradigm, continuous temporal processing is implicitly assumed. Multimodal response distributions indicate, however, discrete time sampling, which is often masked by experimental conditions. Differences in reaction times reflect discrete temporal mechanisms that are pre-semantically implemented and suggested to be based on entrained neural oscillations. © 2016 The Institute of Psychology, Chinese Academy of Sciences and John Wiley & Sons Australia, Ltd.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

NASA Astrophysics Data System (ADS)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

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.

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.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

NASA Astrophysics Data System (ADS)

Raz, Oren; Subasi, Yigit; Jarzynski, Christopher

Under static conditions, a system satisfying detailed balance generically relaxes to an equilibrium state in which there are no currents: to generate persistent currents, either detailed balance must be broken or the system must be driven in a time-dependent manner. A stationary system that violates detailed balance evolves to a nonequilibrium steady state (NESS) characterized by fixed currents. Conversely, a system that satisfies instantaneous detailed balance but is driven by the time-periodic variation of external parameters - also known as a stochastic pump (SP) - reaches a periodic state with non-vanishing currents. In both cases, these currents are maintained at the cost of entropy production. Are these two paradigmatic scenarios effectively equivalent? For discrete-state systems we establish a mapping between NESS and SP. Given a NESS characterized by a particular set of stationary probabilities, currents and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish a proof of principle: they show that SP are able to mimic the behavior of NESS, and vice-versa, within the theoretical framework of discrete-state stochastic thermodynamics.

Examining Passenger Flow Choke Points at Airports Using Discrete Event Simulation

NASA Technical Reports Server (NTRS)

Brown, Jeremy R.; Madhavan, Poomima

2011-01-01

The movement of passengers through an airport quickly, safely, and efficiently is the main function of the various checkpoints (check-in, security. etc) found in airports. Human error combined with other breakdowns in the complex system of the airport can disrupt passenger flow through the airport leading to lengthy waiting times, missing luggage and missed flights. In this paper we present a model of passenger flow through an airport using discrete event simulation that will provide a closer look into the possible reasons for breakdowns and their implications for passenger flow. The simulation is based on data collected at Norfolk International Airport (ORF). The primary goal of this simulation is to present ways to optimize the work force to keep passenger flow smooth even during peak travel times and for emergency preparedness at ORF in case of adverse events. In this simulation we ran three different scenarios: real world, increased check-in stations, and multiple waiting lines. Increased check-in stations increased waiting time and instantaneous utilization. while the multiple waiting lines decreased both the waiting time and instantaneous utilization. This simulation was able to show how different changes affected the passenger flow through the airport.

? and ? nonquadratic stabilisation of discrete-time Takagi-Sugeno systems based on multi-instant fuzzy Lyapunov functions

NASA Astrophysics Data System (ADS)

Tognetti, Eduardo S.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

2015-01-01

The problem of state feedback control design for discrete-time Takagi-Sugeno (TS) (T-S) fuzzy systems is investigated in this paper. A Lyapunov function, which is quadratic in the state and presents a multi-polynomial dependence on the fuzzy weighting functions at the current and past instants of time, is proposed.This function contains, as particular cases, other previous Lyapunov functions already used in the literature, being able to provide less conservative conditions of control design for TS fuzzy systems. The structure of the proposed Lyapunov function also motivates the design of a new stabilising compensator for Takagi-Sugeno fuzzy systems. The main novelty of the proposed state feedback control law is that the gain is composed of matrices with multi-polynomial dependence on the fuzzy weighting functions at a set of past instants of time, including the current one. The conditions for the existence of a stabilising state feedback control law that minimises an upper bound to the ? or ? norms are given in terms of linear matrix inequalities. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature.

Discrete rational and breather solution in the spatial discrete complex modified Korteweg-de Vries equation and continuous counterparts.

PubMed

Zhao, Hai-Qiong; Yu, Guo-Fu

2017-04-01

In this paper, a spatial discrete complex modified Korteweg-de Vries equation is investigated. The Lax pair, conservation laws, Darboux transformations, and breather and rational wave solutions to the semi-discrete system are presented. The distinguished feature of the model is that the discrete rational solution can possess new W-shape rational periodic-solitary waves that were not reported before. In addition, the first-order rogue waves reach peak amplitudes which are at least three times of the background amplitude, whereas their continuous counterparts are exactly three times the constant background. Finally, the integrability of the discrete system, including Lax pair, conservation laws, Darboux transformations, and explicit solutions, yields the counterparts of the continuous system in the continuum limit.

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

2013-07-01

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

Boundaries, kinetic properties, and final domain structure of plane discrete uniform Poisson-Voronoi tessellations with von Neumann neighborhoods.

PubMed

Korobov, A

2009-03-01

Discrete random tessellations appear not infrequently in describing nucleation and growth transformations. Generally, several non-Euclidean metrics are possible in this case. Previously [A. Korobov, Phys. Rev. B 76, 085430 (2007)] continual analogs of such tessellations have been studied. Here one of the simplest discrete varieties of the Kolmogorov-Johnson-Mehl-Avrami model, namely, the model with von Neumann neighborhoods, has been examined per se, i.e., without continualization. The tessellation is uniform in the sense that domain boundaries consist of tiles. Similarities and distinctions between discrete and continual models are discussed.

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

Blood Based Biomarkers of Early Onset Breast Cancer

DTIC Science & Technology

2016-12-01

discretizes the data, and also using logistic elastic net – a form of linear regression - we were unable to build a classifier that could accurately...classifier for differentiating cases from controls off discretized data. The first pass analysis demonstrated a 35 gene signature that differentiated...to the discretized data for mRNA gene signature, the samples used to “train” were also included in the final samples used to “test” the algorithm

Design of a blade stiffened composite panel by a genetic algorithm

NASA Technical Reports Server (NTRS)

Nagendra, S.; Haftka, R. T.; Gurdal, Z.

1993-01-01

Genetic algorithms (GAs) readily handle discrete problems, and can be made to generate many optima, as is presently illustrated for the case of design for minimum-weight stiffened panels with buckling constraints. The GA discrete design procedure proved superior to extant alternatives for both stiffened panels with cutouts and without cutouts. High computational costs are, however, associated with this discrete design approach at the current level of its development.

Comparison of cell centered and cell vertex scheme in the calculation of high speed compressible flows

NASA Astrophysics Data System (ADS)

Rahman, Syazila; Yusoff, Mohd. Zamri; Hasini, Hasril

2012-06-01

This paper describes the comparison between the cell centered scheme and cell vertex scheme in the calculation of high speed compressible flow properties. The calculation is carried out using Computational Fluid Dynamic (CFD) in which the mass, momentum and energy equations are solved simultaneously over the flow domain. The geometry under investigation consists of a Binnie and Green convergent-divergent nozzle and structured mesh scheme is implemented throughout the flow domain. The finite volume CFD solver employs second-order accurate central differencing scheme for spatial discretization. In addition, the second-order accurate cell-vertex finite volume spatial discretization is also introduced in this case for comparison. The multi-stage Runge-Kutta time integration is implemented for solving a set of non-linear governing equations with variables stored at the vertices. Artificial dissipations used second and fourth order terms with pressure switch to detect changes in pressure gradient. This is important to control the solution stability and capture shock discontinuity. The result is compared with experimental measurement and good agreement is obtained for both cases.

Discrete decoding based ultrafast multidimensional nuclear magnetic resonance spectroscopy

NASA Astrophysics Data System (ADS)

Wei, Zhiliang; Lin, Liangjie; Ye, Qimiao; Li, Jing; Cai, Shuhui; Chen, Zhong

2015-07-01

The three-dimensional (3D) nuclear magnetic resonance (NMR) spectroscopy constitutes an important and powerful tool in analyzing chemical and biological systems. However, the abundant 3D information arrives at the expense of long acquisition times lasting hours or even days. Therefore, there has been a continuous interest in developing techniques to accelerate recordings of 3D NMR spectra, among which the ultrafast spatiotemporal encoding technique supplies impressive acquisition speed by compressing a multidimensional spectrum in a single scan. However, it tends to suffer from tradeoffs among spectral widths in different dimensions, which deteriorates in cases of NMR spectroscopy with more dimensions. In this study, the discrete decoding is proposed to liberate the ultrafast technique from tradeoffs among spectral widths in different dimensions by focusing decoding on signal-bearing sites. For verifying its feasibility and effectiveness, we utilized the method to generate two different types of 3D spectra. The proposed method is also applicable to cases with more than three dimensions, which, based on the experimental results, may widen applications of the ultrafast technique.

Effect of Vertical Concentration Gradient on Globally Planar Detonation with Detailed Reaction Mechanism

NASA Astrophysics Data System (ADS)

Song, Qingguana; Wang, Cheng; Han, Yong; Gao, Dayuan; Duan, Yingliang

2017-06-01

Since detonation often initiates and propagates in the non-homogeneous mixtures, investigating its behavior in non-uniform mixtures is significant not only for the industrial explosion in the leakage combustible gas, but also for the experimental investigations with a vertical concentration gradient caused by the difference in the molecular weight of gas mixture. Objective of this work is to show the detonation behavior in the mixture with different concentration gradients with detailed chemical reaction mechanism. A globally planar detonation in H2-O2 system is simulated by a high-resolution code based on the fifth-order weighted essentially non-oscillatory (WENO) scheme in spatial discretization and the third-order Additive Runge-Kutta schemes in time discretization. The different shocked combustion modes appear in the rich-fuel and poor-fuel layers due to the concentration gradient effect. Globally, for the cases with the lower gradient detonation can be sustained in a way of the alternation of the multi-heads mode and single-head mode, whereas for the cases with the higher gradient detonation propagates with a single-head mode. Institute of Chemical Materials, CAEP.

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Single product lot-sizing on unrelated parallel machines with non-decreasing processing times

NASA Astrophysics Data System (ADS)

Eremeev, A.; Kovalyov, M.; Kuznetsov, P.

2018-01-01

We consider a problem in which at least a given quantity of a single product has to be partitioned into lots, and lots have to be assigned to unrelated parallel machines for processing. In one version of the problem, the maximum machine completion time should be minimized, in another version of the problem, the sum of machine completion times is to be minimized. Machine-dependent lower and upper bounds on the lot size are given. The product is either assumed to be continuously divisible or discrete. The processing time of each machine is defined by an increasing function of the lot volume, given as an oracle. Setup times and costs are assumed to be negligibly small, and therefore, they are not considered. We derive optimal polynomial time algorithms for several special cases of the problem. An NP-hard case is shown to admit a fully polynomial time approximation scheme. An application of the problem in energy efficient processors scheduling is considered.

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%.

Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

PubMed

Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L

2016-09-01

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

The discrete hungry Lotka Volterra system and a new algorithm for computing matrix eigenvalues

NASA Astrophysics Data System (ADS)

Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa

2009-01-01

The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.

The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy

NASA Astrophysics Data System (ADS)

Li, Maohua; He, Jingsong

2016-05-01

From the constrained discrete Kadomtsev-Petviashvili (cdKP) hierarchy, the discrete nonlinear Schrödinger (DNLS) equations have been derived. By means of the gauge transformation, the Wronskian solution of DNLS equations have been given. The u1 of the cdKP hierarchy is a Y-type soliton solution for odd times of the gauge transformation, but it becomes a dark-bright soliton solution for even times of the gauge transformation. The role of the discrete variable n in the profile of the u1 is discussed.

Discrete Space-Time: History and Recent Developments

NASA Astrophysics Data System (ADS)

Crouse, David

2017-01-01

Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.

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.

Homoclinic snaking in the discrete Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Kusdiantara, R.; Susanto, H.

2017-12-01

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

Effect of the surface charge discretization on electric double layers: a Monte Carlo simulation study.

PubMed

Madurga, Sergio; Martín-Molina, Alberto; Vilaseca, Eudald; Mas, Francesc; Quesada-Pérez, Manuel

2007-06-21

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

A New Time-Space Accurate Scheme for Hyperbolic Problems. 1; Quasi-Explicit Case

NASA Technical Reports Server (NTRS)

Sidilkover, David

1998-01-01

This paper presents a new discretization scheme for hyperbolic systems of conservations laws. It satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently. This work can be regarded as a first step towards extending the genuinely multidimensional approach to unsteady problems. Discontinuity capturing capabilities and accuracy of the scheme are verified by a set of numerical tests.

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.

A Calculus of Macro-Events: Progress Report

DTIC Science & Technology

2000-01-01

1410, USA iliano@itd.nrl.navy.mil Angelo Montanari Dipartimento di Matematica e Informatica Universita di Udine Via delle Scienze, 206 { 33100 Udine...and process iteration. This proposal builds on work by Chittaro and Montanari [10] on mod- eling discrete processes. The set of constructors of the...situations, in many cases the occurrence of an event happens over a period of time [24]. Capturing this possibility enables ner mod- els , as we can now

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.

Discrete-time nonlinear damping backstepping control with observers for rejection of low and high frequency disturbances

NASA Astrophysics Data System (ADS)

Kim, Wonhee; Chen, Xu; Lee, Youngwoo; Chung, Chung Choo; Tomizuka, Masayoshi

2018-05-01

A discrete-time backstepping control algorithm is proposed for reference tracking of systems affected by both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. A discrete time DOB, which is constructed based on infinite impulse response filters is applied to compensate for narrow band disturbances at high frequencies. A discrete-time nonlinear damping backstepping controller with an augmented observer is proposed to track the desired output and to compensate for low frequency broadband disturbances along with a disturbance observer, for rejecting narrow band high frequency disturbances. This combination has the merit of simultaneously compensating both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. The performance of the proposed method is validated via experiments.

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.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

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.

Robustness of quantum key distribution with discrete and continuous variables to channel noise

NASA Astrophysics Data System (ADS)

Lasota, Mikołaj; Filip, Radim; Usenko, Vladyslav C.

2017-06-01

We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for continuous-variable quantum key distribution, to the discrete-variable case. Then we perform a comparison of the bounds on the tolerable channel noise between these two kinds of protocols using the same noise parametrization, in the case of implementation which is perfect otherwise. Obtained results show that continuous-variable protocols can exhibit similar robustness to the channel noise when the transmittance of the channel is relatively high. However, for strong loss discrete-variable protocols are superior and can overcome even the infinite-squeezing continuous-variable protocol while using limited nonclassical resources. The requirement on the probability of a single-photon production which would have to be fulfilled by a practical source of photons in order to demonstrate such superiority is feasible thanks to the recent rapid development in this field.

Discrete fractional solutions of a Legendre equation

NASA Astrophysics Data System (ADS)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities: The case of a single fermion-antifermion pair

NASA Astrophysics Data System (ADS)

Duret, Q.; Machet, B.

2010-10-01

Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.

High performance computation of radiative transfer equation using the finite element method

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Favennec, Y.

2018-05-01

This article deals with an efficient strategy for numerically simulating radiative transfer phenomena using distributed computing. The finite element method alongside the discrete ordinate method is used for spatio-angular discretization of the monochromatic steady-state radiative transfer equation in an anisotropically scattering media. Two very different methods of parallelization, angular and spatial decomposition methods, are presented. To do so, the finite element method is used in a vectorial way. A detailed comparison of scalability, performance, and efficiency on thousands of processors is established for two- and three-dimensional heterogeneous test cases. Timings show that both algorithms scale well when using proper preconditioners. It is also observed that our angular decomposition scheme outperforms our domain decomposition method. Overall, we perform numerical simulations at scales that were previously unattainable by standard radiative transfer equation solvers.

Theory of a microfluidic serial dilution bioreactor for growth of planktonic and biofilm populations.

PubMed

Hsu, Sze-Bi; Yang, Ya-Tang

2016-04-01

We present the theory of a microfluidic bioreactor with a two-compartment growth chamber and periodic serial dilution. In the model, coexisting planktonic and biofilm populations exchange by adsorption and detachment. The criteria for coexistence and global extinction are determined by stability analysis of the global extinction state. Stability analysis yields the operating diagram in terms of the dilution and removal ratios, constrained by the plumbing action of the bioreactor. The special case of equal uptake function and logistic growth is analytically solved and explicit growth curves are plotted. The presented theory is applicable to generic microfluidic bioreactors with discrete growth chambers and periodic dilution at discrete time points. Therefore, the theory is expected to assist the design of microfluidic devices for investigating microbial competition and microbial biofilm growth under serial dilution conditions.

Effects of measurement resolution on the analysis of temperature time series for stream-aquifer flux estimation

NASA Astrophysics Data System (ADS)

Soto-López, Carlos D.; Meixner, Thomas; Ferré, Ty P. A.

2011-12-01

From its inception in the mid-1960s, the use of temperature time series (thermographs) to estimate vertical fluxes has found increasing use in the hydrologic community. Beginning in 2000, researchers have examined the impacts of measurement and parameter uncertainty on the estimates of vertical fluxes. To date, the effects of temperature measurement discretization (resolution), a characteristic of all digital temperature loggers, on the determination of vertical fluxes has not been considered. In this technical note we expand the analysis of recently published work to include the effects of temperature measurement resolution on estimates of vertical fluxes using temperature amplitude and phase shift information. We show that errors in thermal front velocity estimation introduced by discretizing thermographs differ when amplitude or phase shift data are used to estimate vertical fluxes. We also show that under similar circumstances sensor resolution limits the range over which vertical velocities are accurately reproduced more than uncertainty in temperature measurements, uncertainty in sensor separation distance, and uncertainty in the thermal diffusivity combined. These effects represent the baseline error present and thus the best-case scenario when discrete temperature measurements are used to infer vertical fluxes. The errors associated with measurement resolution can be minimized by using the highest-resolution sensors available. But thoughtful experimental design could allow users to select the most cost-effective temperature sensors to fit their measurement needs.

A Short-Term Population Model of the Suicide Risk: The Case of Spain.

PubMed

De la Poza, Elena; Jódar, Lucas

2018-06-14

A relevant proportion of deaths by suicide have been attributed to other causes that produce the number of suicides remains hidden. The existence of a hidden number of cases is explained by the nature of the problem. Problems like this involve violence, and produce fear and social shame in victims' families. The existence of violence, fear and social shame experienced by victims favours a considerable number of suicides, identified as accidents or natural deaths. This paper proposes a short time discrete compartmental mathematical model to measure the suicidal risk for the case of Spain. The compartment model classifies and quantifies the amount of the Spanish population within the age intervals (16, 78) by their degree of suicide risk and their changes over time. Intercompartmental transits are due to the combination of quantitative and qualitative factors. Results are computed and simulations are performed to analyze the sensitivity of the model under uncertain coefficients.

Index Theory of One Dimensional Quantum Walks and Cellular Automata

NASA Astrophysics Data System (ADS)

Gross, D.; Nesme, V.; Vogts, H.; Werner, R. F.

2012-03-01

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems — namely quantum walks and cellular automata — we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S 1, S 2 can be "pieced together", in the sense that there is a system S which acts like S 1 in one region and like S 2 in some other region, if and only if S 1 and S 2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S 1 into S 2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map {S mapsto ind S} is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

PubMed Central

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Simulation of Non-Abelian Braiding in Majorana Time Crystals

NASA Astrophysics Data System (ADS)

Bomantara, Raditya Weda; Gong, Jiangbin

2018-06-01

Discrete time crystals have attracted considerable theoretical and experimental studies but their potential applications have remained unexplored. A particular type of discrete time crystals, termed "Majorana time crystals," is found to emerge in a periodically driven superconducting wire accommodating two different species of topological edge modes. It is further shown that one can manipulate different Majorana edge modes separated in the time lattice, giving rise to an unforeseen scenario for topologically protected gate operations mimicking braiding. The proposed protocol can also generate a magic state that is important for universal quantum computation. This study thus advances the quantum control in discrete time crystals and reveals their great potential arising from their time-domain properties.

Distinct timing mechanisms produce discrete and continuous movements.

PubMed

Huys, Raoul; Studenka, Breanna E; Rheaume, Nicole L; Zelaznik, Howard N; Jirsa, Viktor K

2008-04-25

The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems) to accomplish varying behavioral functions such as speed constraints.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Hybrid Automated Diagnosis of Discrete/Continuous Systems

NASA Technical Reports Server (NTRS)

Park, Han; James, Mark; MacKey, Ryan; Cannon, Howard; Bajwa, Anapa; Maul, William

2007-01-01

A recently conceived method of automated diagnosis of a complex electromechanical system affords a complete set of capabilities for hybrid diagnosis in the case in which the state of the electromechanical system is characterized by both continuous and discrete values (as represented by analog and digital signals, respectively). The method is an integration of two complementary diagnostic systems: (1) beacon-based exception analysis for multi-missions (BEAM), which is primarily useful in the continuous domain and easily performs diagnoses in the presence of transients; and (2) Livingstone, which is primarily useful in the discrete domain and is typically restricted to quasi-steady conditions. BEAM has been described in several prior NASA Tech Briefs articles: "Software for Autonomous Diagnosis of Complex Systems" (NPO-20803), Vol. 26, No. 3 (March 2002), page 33; "Beacon-Based Exception Analysis for Multimissions" (NPO-20827), Vol. 26, No. 9 (September 2002), page 32; "Wavelet-Based Real-Time Diagnosis of Complex Systems" (NPO-20830), Vol. 27, No. 1 (January 2003), page 67; and "Integrated Formulation of Beacon-Based Exception Analysis for Multimissions" (NPO-21126), Vol. 27, No. 3 (March 2003), page 74. Briefly, BEAM is a complete data-analysis method, implemented in software, for real-time or off-line detection and characterization of faults. The basic premise of BEAM is to characterize a system from all available observations and train the characterization with respect to normal phases of operation. The observations are primarily continuous in nature. BEAM isolates anomalies by analyzing the deviations from nominal for each phase of operation. Livingstone is a model-based reasoner that uses a model of a system, controller commands, and sensor observations to track the system s state, and detect and diagnose faults. Livingstone models a system within the discrete domain. Therefore, continuous sensor readings, as well as time, must be discretized. To reason about continuous systems, Livingstone uses monitors that discretize the sensor readings using trending and thresholding techniques. In development of the a hybrid method, BEAM results were sent to Livingstone to serve as an independent source of evidence that is in addition to the evidence gathered by Livingstone standard monitors. The figure depicts the flow of data in an early version of a hybrid system dedicated to diagnosing a simulated electromechanical system. In effect, BEAM served as a "smart" monitor for Livingstone. BEAM read the simulation data, processed the data to form observations, and stored the observations in a file. A monitor stub synchronized the events recorded by BEAM with the output of the Livingstone standard monitors according to time tags. This information was fed to a real-time interface, which buffered and fed the information to Livingstone, and requested diagnoses at the appropriate times. In a test, the hybrid system was found to correctly identify a failed component in an electromechanical system for which neither BEAM nor Livingstone alone yielded the correct diagnosis.

On an LAS-integrated soft PLC system based on WorldFIP fieldbus.

PubMed

Liang, Geng; Li, Zhijun; Li, Wen; Bai, Yan

2012-01-01

Communication efficiency is lowered and real-time performance is not good enough in discrete control based on traditional WorldFIP field intelligent nodes in case that the scale of control in field is large. A soft PLC system based on WorldFIP fieldbus was designed and implemented. Link Activity Scheduler (LAS) was integrated into the system and field intelligent I/O modules acted as networked basic nodes. Discrete control logic was implemented with the LAS-integrated soft PLC system. The proposed system was composed of configuration and supervisory sub-systems and running sub-systems. The configuration and supervisory sub-system was implemented with a personal computer or an industrial personal computer; running subsystems were designed and implemented based on embedded hardware and software systems. Communication and schedule in the running subsystem was implemented with an embedded sub-module; discrete control and system self-diagnosis were implemented with another embedded sub-module. Structure of the proposed system was presented. Methodology for the design of the sub-systems was expounded. Experiments were carried out to evaluate the performance of the proposed system both in discrete and process control by investigating the effect of network data transmission delay induced by the soft PLC in WorldFIP network and CPU workload on resulting control performances. The experimental observations indicated that the proposed system is practically applicable. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Teaching Discrete Mathematics Entirely from Primary Historical Sources

ERIC Educational Resources Information Center

Barnett, Janet Heine; Bezhanishvili, Guram; Lodder, Jerry; Pengelley, David

2016-01-01

We describe teaching an introductory discrete mathematics course entirely from student projects based on primary historical sources. We present case studies of four projects that cover the content of a one-semester course, and mention various other courses that we have taught with primary source projects.

Continuum approach to the BF vacuum: The U(1) case

NASA Astrophysics Data System (ADS)

Drobiński, Patryk; Lewandowski, Jerzy

2017-12-01

A quantum representation of holonomies and exponentiated fluxes of a U(1) gauge theory that contains the Pullin-Dittrich-Geiller (DG) vacuum is presented and discussed. Our quantization is performed manifestly in a continuum theory, without any discretization. The discreteness emerges on the quantum level as a property of the spectrum of the quantum holonomy operators. The new type of a cylindrical consistency present in the DG approach now follows easily and naturally. A generalization to the non-Abelian case seems possible.

Genetic-evolution-based optimization methods for engineering design

NASA Technical Reports Server (NTRS)

Rao, S. S.; Pan, T. S.; Dhingra, A. K.; Venkayya, V. B.; Kumar, V.

1990-01-01

This paper presents the applicability of a biological model, based on genetic evolution, for engineering design optimization. Algorithms embodying the ideas of reproduction, crossover, and mutation are developed and applied to solve different types of structural optimization problems. Both continuous and discrete variable optimization problems are solved. A two-bay truss for maximum fundamental frequency is considered to demonstrate the continuous variable case. The selection of locations of actuators in an actively controlled structure, for minimum energy dissipation, is considered to illustrate the discrete variable case.

The inverse problem of the calculus of variations for discrete systems

NASA Astrophysics Data System (ADS)

Barbero-Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián; Martín de Diego, David

2018-05-01

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.

Algebraic perturbation theory for dense liquids with discrete potentials

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2007-06-01

A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

Trajectory Planning by Preserving Flexibility: Metrics and Analysis

NASA Technical Reports Server (NTRS)

Idris, Husni R.; El-Wakil, Tarek; Wing, David J.

2008-01-01

In order to support traffic management functions, such as mitigating traffic complexity, ground and airborne systems may benefit from preserving or optimizing trajectory flexibility. To help support this hypothesis trajectory flexibility metrics have been defined in previous work to represent the trajectory robustness and adaptability to the risk of violating safety and traffic management constraints. In this paper these metrics are instantiated in the case of planning a trajectory with the heading degree of freedom. A metric estimation method is presented based on simplifying assumptions, namely discrete time and heading maneuvers. A case is analyzed to demonstrate the estimation method and its use in trajectory planning in a situation involving meeting a time constraint and avoiding loss of separation with nearby traffic. The case involves comparing path-stretch trajectories, in terms of adaptability and robustness along each, deduced from a map of estimated flexibility metrics over the solution space. The case demonstrated anecdotally that preserving flexibility may result in enhancing certain factors that contribute to traffic complexity, namely reducing proximity and confrontation.

Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

NASA Astrophysics Data System (ADS)

Bonaventura, Luca; Fernández-Nieto, Enrique D.; Garres-Díaz, José; Narbona-Reina, Gladys

2018-07-01

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in which the number of vertical layers and their distribution are allowed to change in different regions of the computational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a significant efficiency improvement for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justified, the resulting discretization does not introduce any major spurious feature and allows again to reduce substantially the computational cost in areas with complex bathymetry. As an example of the potential of the proposed technique, an application to a sediment transport problem is presented, showing a remarkable improvement with respect to standard discretization approaches.

Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

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

Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

2016-02-15

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

Simultaneous optical flow and source estimation: Space–time discretization and preconditioning

PubMed Central

Andreev, R.; Scherzer, O.; Zulehner, W.

2015-01-01

We consider the simultaneous estimation of an optical flow field and an illumination source term in a movie sequence. The particular optical flow equation is obtained by assuming that the image intensity is a conserved quantity up to possible sources and sinks which represent varying illumination. We formulate this problem as an energy minimization problem and propose a space–time simultaneous discretization for the optimality system in saddle-point form. We investigate a preconditioning strategy that renders the discrete system well-conditioned uniformly in the discretization resolution. Numerical experiments complement the theory. PMID:26435561

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.

Improving Our Ability to Evaluate Underlying Mechanisms of Behavioral Onset and Other Event Occurrence Outcomes: A Discrete-Time Survival Mediation Model

PubMed Central

Fairchild, Amanda J.; Abara, Winston E.; Gottschall, Amanda C.; Tein, Jenn-Yun; Prinz, Ronald J.

2015-01-01

The purpose of this article is to introduce and describe a statistical model that researchers can use to evaluate underlying mechanisms of behavioral onset and other event occurrence outcomes. Specifically, the article develops a framework for estimating mediation effects with outcomes measured in discrete-time epochs by integrating the statistical mediation model with discrete-time survival analysis. The methodology has the potential to help strengthen health research by targeting prevention and intervention work more effectively as well as by improving our understanding of discretized periods of risk. The model is applied to an existing longitudinal data set to demonstrate its use, and programming code is provided to facilitate its implementation. PMID:24296470

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

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

Alexeyev, C. N.; Volyar, A. V.; Yavorsky, M. A.

We study energy transfer and orbital angular momentum of supermodes in a double-ring array of evanescently coupled monomode optical fibers. The structure of supermodes and the spectra of their propagation constants are obtained. The geometrical parameters of the array, at which the energy is mostly confined within the layers, are determined. The developed method for finding the supermodes of concentric arrays is generalized for the case of multiring arrays. The orbital angular momentum carried by a supermode of a double-ring array is calculated. The discrete lattice current is introduced. It is shown that the sum of discrete currents over themore » array is a conserved quantity. The connection of the total discrete current with orbital angular momentum of discrete optical vortices is made.« less

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

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

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

The Selection of Computed Tomography Scanning Schemes for Lengthy Symmetric Objects

NASA Astrophysics Data System (ADS)

Trinh, V. B.; Zhong, Y.; Osipov, S. P.

2017-04-01

. The article describes the basic computed tomography scan schemes for lengthy symmetric objects: continuous (discrete) rotation with a discrete linear movement; continuous (discrete) rotation with discrete linear movement to acquire 2D projection; continuous (discrete) linear movement with discrete rotation to acquire one-dimensional projection and continuous (discrete) rotation to acquire of 2D projection. The general method to calculate the scanning time is discussed in detail. It should be extracted the comparison principle to select a scanning scheme. This is because data are the same for all scanning schemes: the maximum energy of the X-ray radiation; the power of X-ray radiation source; the angle of the X-ray cone beam; the transverse dimension of a single detector; specified resolution and the maximum time, which is need to form one point of the original image and complies the number of registered photons). It demonstrates the possibilities of the above proposed method to compare the scanning schemes. Scanning object was a cylindrical object with the mass thickness is 4 g/cm2, the effective atomic number is 15 and length is 1300 mm. It analyzes data of scanning time and concludes about the efficiency of scanning schemes. It examines the productivity of all schemes and selects the effective one.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

A Brownian Bridge Movement Model to Track Mobile Targets

DTIC Science & Technology

2016-09-01

breakout of Chinese forces in the South China Sea. Probability heat maps, depicting the probability of a target location at discrete times, are...achieve a higher probability of detection, it is more effective to have sensors cover a wider area at fewer discrete points in time than to have a...greater number of discrete looks using sensors covering smaller areas. 14. SUBJECT TERMS Brownian bridge movement models, unmanned sensors

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Reinforcement-learning-based output-feedback control of nonstrict nonlinear discrete-time systems with application to engine emission control.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, Sarangapani; Drallmeier, James A

2009-10-01

A novel reinforcement-learning-based output adaptive neural network (NN) controller, which is also referred to as the adaptive-critic NN controller, is developed to deliver the desired tracking performance for a class of nonlinear discrete-time systems expressed in nonstrict feedback form in the presence of bounded and unknown disturbances. The adaptive-critic NN controller consists of an observer, a critic, and two action NNs. The observer estimates the states and output, and the two action NNs provide virtual and actual control inputs to the nonlinear discrete-time system. The critic approximates a certain strategic utility function, and the action NNs minimize the strategic utility function and control inputs. All NN weights adapt online toward minimization of a performance index, utilizing the gradient-descent-based rule, in contrast with iteration-based adaptive-critic schemes. Lyapunov functions are used to show the stability of the closed-loop tracking error, weights, and observer estimates. Separation and certainty equivalence principles, persistency of excitation condition, and linearity in the unknown parameter assumption are not needed. Experimental results on a spark ignition (SI) engine operating lean at an equivalence ratio of 0.75 show a significant (25%) reduction in cyclic dispersion in heat release with control, while the average fuel input changes by less than 1% compared with the uncontrolled case. Consequently, oxides of nitrogen (NO(x)) drop by 30%, and unburned hydrocarbons drop by 16% with control. Overall, NO(x)'s are reduced by over 80% compared with stoichiometric levels.

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.

ODP Site 1063 (Bermuda Rise) revisited: Oxygen isotopes, excursions and paleointensity in the Brunhes Chron

NASA Astrophysics Data System (ADS)

Channell, J. E. T.; Hodell, D. A.; Curtis, J. H.

2012-02-01

An age model for the Brunhes Chron of Ocean Drilling Program (ODP) Site 1063 (Bermuda Rise) is constructed by tandem correlation of oxygen isotope and relative paleointensity data to calibrated reference templates. Four intervals in the Brunhes Chron where paleomagnetic inclinations are negative for both u-channel samples and discrete samples are correlated to the following magnetic excursions with Site 1063 ages in brackets: Laschamp (41 ka), Blake (116 ka), Iceland Basin (190 ka), Pringle Falls (239 ka). These ages are consistent with current age estimates for three of these excursions, but not for "Pringle Falls" which has an apparent age older than a recently published estimate by ˜28 kyr. For each of these excursions (termed Category 1 excursions), virtual geomagnetic poles (VGPs) reach high southerly latitudes implying paired polarity reversals of the Earth's main dipole field, that apparently occurred in a brief time span (<2 kyr in each case), several times shorter than the apparent duration of regular polarity transitions. In addition, several intervals of low paleomagnetic inclination (low and negative in one case) are observed both in u-channel and discrete samples at ˜318 ka (MIS 9), ˜412 ka (MIS 11) and in the 500-600 ka interval (MIS 14-15). These "Category 2" excursions may constitute inadequately recorded (Category 1) excursions, or high amplitude secular variation.

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1986-01-01

A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid points are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed.

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

NASA Technical Reports Server (NTRS)

Tal-Ezer, H.

1984-01-01

A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information.

PubMed

Yang, Xinsong; Feng, Zhiguo; Feng, Jianwen; Cao, Jinde

2017-01-01

In this paper, synchronization in an array of discrete-time neural networks (DTNNs) with time-varying delays coupled by Markov jump topologies is considered. It is assumed that the switching information can be collected by a tracker with a certain probability and transmitted from the tracker to controller precisely. Then the controller selects suitable control gains based on the received switching information to synchronize the network. This new control scheme makes full use of received information and overcomes the shortcomings of mode-dependent and mode-independent control schemes. Moreover, the proposed control method includes both the mode-dependent and mode-independent control techniques as special cases. By using linear matrix inequality (LMI) method and designing new Lyapunov functionals, delay-dependent conditions are derived to guarantee that the DTNNs with Markov jump topologies to be asymptotically synchronized. Compared with existing results on Markov systems which are obtained by separately using mode-dependent and mode-independent methods, our result has great flexibility in practical applications. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

A discrete-time localization method for capsule endoscopy based on on-board magnetic sensing

NASA Astrophysics Data System (ADS)

Salerno, Marco; Ciuti, Gastone; Lucarini, Gioia; Rizzo, Rocco; Valdastri, Pietro; Menciassi, Arianna; Landi, Alberto; Dario, Paolo

2012-01-01

Recent achievements in active capsule endoscopy have allowed controlled inspection of the bowel by magnetic guidance. Capsule localization represents an important enabling technology for such kinds of platforms. In this paper, the authors present a localization method, applied as first step in time-discrete capsule position detection, that is useful for establishing a magnetic link at the beginning of an endoscopic procedure or for re-linking the capsule in the case of loss due to locomotion. The novelty of this approach consists in using magnetic sensors on board the capsule whose output is combined with pre-calculated magnetic field analytical model solutions. A magnetic field triangulation algorithm is used for obtaining the position of the capsule inside the gastrointestinal tract. Experimental validation has demonstrated that the proposed procedure is stable, accurate and has a wide localization range in a volume of about 18 × 103 cm3. Position errors of 14 mm along the X direction, 11 mm along the Y direction and 19 mm along the Z direction were obtained in less than 27 s of elaboration time. The proposed approach, being compatible with magnetic fields used for locomotion, can be easily extended to other platforms for active capsule endoscopy.

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.

A discrete time-varying internal model-based approach for high precision tracking of a multi-axis servo gantry.

PubMed

Zhang, Zhen; Yan, Peng; Jiang, Huan; Ye, Peiqing

2014-09-01

In this paper, we consider the discrete time-varying internal model-based control design for high precision tracking of complicated reference trajectories generated by time-varying systems. Based on a novel parallel time-varying internal model structure, asymptotic tracking conditions for the design of internal model units are developed, and a low order robust time-varying stabilizer is further synthesized. In a discrete time setting, the high precision tracking control architecture is deployed on a Voice Coil Motor (VCM) actuated servo gantry system, where numerical simulations and real time experimental results are provided, achieving the tracking errors around 3.5‰ for frequency-varying signals. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

Time-discretized steady compressible Navier-Stokes equations with inflow and outflow boundaries

NASA Astrophysics Data System (ADS)

Yoon, Gangjoon; Yang, Sung-Dae; Song, Minsu; Gunzburger, Max

2013-12-01

The time-discretized steady compressible Navier-Stokes equations in n-dimensional bounded domains with the velocity specified only at the inflow boundary are considered. The existence and uniqueness of L p solutions are proved for p > n. For time-discretized steady flows, results of Kweon and Kellogg and of Kweon and Song are extended in a manner that allows for more general domains and for density-dependent viscosity coefficients. Moreover, we only require p > n which is a critical barrier in the previous works.

Complexity and chaos control in a discrete-time prey-predator model

NASA Astrophysics Data System (ADS)

Din, Qamar

2017-08-01

We investigate the complex behavior and chaos control in a discrete-time prey-predator model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete-time prey-predator system with predator partially dependent on prey and investigate the boundedness, existence and uniqueness of positive equilibrium and bifurcation analysis of the system by using center manifold theorem and bifurcation theory. Various feedback control strategies are implemented for controlling the bifurcation and chaos in the system. Numerical simulations are provided to illustrate theoretical discussion.

Longitudinal Evaluation of Muscle Composition Using Magnetic Resonance in 4 Boys With Duchenne Muscular Dystrophy: Case Series.

PubMed

Senesac, Claudia R; Lott, Donovan J; Forbes, Sean C; Mathur, Sunita; Arpan, Ishu; Senesac, Emily S; Walter, Glenn A; Vandenborne, Krista

2015-07-01

Duchenne muscular dystrophy (DMD), an inherited recessive X chromosome-linked disease, is the most severe childhood form of muscular dystrophy. Boys with DMD experience muscle loss, with infiltration of intramuscular fat into muscles. This case series describes the progression of DMD in boys using magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS). Magnetic resonance results are then compared with an established functional timed test. Four boys with DMD and 4 healthy age-matched controls were chosen from a larger cohort. Boys with DMD were assessed at 4 time points over 2 years, with controls assessed at baseline only. Progression of the disease was documented by assessing the plantar flexors using MRI and MRS techniques and by assessing ambulation using the 30-Foot Fast Walk Test. Transverse relaxation time (T2) values were elevated in all boys with DMD at baseline. The lipid ratio increased rapidly as the disease progressed in 2 boys. Discrete changes in T2 in the other 2 boys with DMD indicated a slower disease progression. Magnetic resonance imaging and MRS allowed monitoring of the disease over all time periods regardless of ambulation status. The magnetic resonance data were collected with 2 different magnets at 2 different field strengths (1.5 and 3.0 T). Although we corrected for this difference, care must be taken in interpreting data when different image collection systems are used. This was a case series of 4 boys with DMD taken from a larger cohort study. Magnetic resonance imaging and MRS are objective, noninvasive techniques for measuring muscle pathology and can be used to detect discrete changes in both people who are ambulatory and those who are nonambulatory. These techniques should be considered when monitoring DMD progression and assessing efficacy of therapeutic interventions. © 2015 American Physical Therapy Association.

Longitudinal Evaluation of Muscle Composition Using Magnetic Resonance in 4 Boys With Duchenne Muscular Dystrophy: Case Series

PubMed Central

Lott, Donovan J.; Forbes, Sean C.; Mathur, Sunita; Arpan, Ishu; Senesac, Emily S.; Walter, Glenn A.; Vandenborne, Krista

2015-01-01

Background Duchenne muscular dystrophy (DMD), an inherited recessive X chromosome-linked disease, is the most severe childhood form of muscular dystrophy. Boys with DMD experience muscle loss, with infiltration of intramuscular fat into muscles. Objectives This case series describes the progression of DMD in boys using magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS). Magnetic resonance results are then compared with an established functional timed test. Methods Four boys with DMD and 4 healthy age-matched controls were chosen from a larger cohort. Boys with DMD were assessed at 4 time points over 2 years, with controls assessed at baseline only. Progression of the disease was documented by assessing the plantar flexors using MRI and MRS techniques and by assessing ambulation using the 30-Foot Fast Walk Test. Results Transverse relaxation time (T2) values were elevated in all boys with DMD at baseline. The lipid ratio increased rapidly as the disease progressed in 2 boys. Discrete changes in T2 in the other 2 boys with DMD indicated a slower disease progression. Magnetic resonance imaging and MRS allowed monitoring of the disease over all time periods regardless of ambulation status. Limitations The magnetic resonance data were collected with 2 different magnets at 2 different field strengths (1.5 and 3.0 T). Although we corrected for this difference, care must be taken in interpreting data when different image collection systems are used. This was a case series of 4 boys with DMD taken from a larger cohort study. Conclusions Magnetic resonance imaging and MRS are objective, noninvasive techniques for measuring muscle pathology and can be used to detect discrete changes in both people who are ambulatory and those who are nonambulatory. These techniques should be considered when monitoring DMD progression and assessing efficacy of therapeutic interventions. PMID:25592189

a Study of Multiplexing Schemes for Voice and Data.

NASA Astrophysics Data System (ADS)

Sriram, Kotikalapudi

Voice traffic variations are characterized by on/off transitions of voice calls, and talkspurt/silence transitions of speakers in conversations. A speaker is known to be in silence for more than half the time during a telephone conversation. In this dissertation, we study some schemes which exploit speaker silences for an efficient utilization of the transmission capacity in integrated voice/data multiplexing and in digital speech interpolation. We study two voice/data multiplexing schemes. In each scheme, any time slots momentarily unutilized by the voice traffic are made available to data. In the first scheme, the multiplexer does not use speech activity detectors (SAD), and hence the voice traffic variations are due to call on/off only. In the second scheme, the multiplexer detects speaker silences using SAD and transmits voice only during talkspurts. The multiplexer with SAD performs digital speech interpolation (DSI) as well as dynamic channel allocation to voice and data. The performance of the two schemes is evaluated using discrete-time modeling and analysis. The data delay performance for the case of English speech is compared with that for the case of Japanese speech. A closed form expression for the mean data message delay is derived for the single-channel single-talker case. In a DSI system, occasional speech losses occur whenever the number of speakers in simultaneous talkspurt exceeds the number of TDM voice channels. In a buffered DSI system, speech loss is further reduced at the cost of delay. We propose a novel fixed-delay buffered DSI scheme. In this scheme, speech fill-in/hangover is not required because there are no variable delays. Hence, all silences that naturally occur in speech are fully utilized. Consequently, a substantial improvement in the DSI performance is made possible. The scheme is modeled and analyzed in discrete -time. Its performance is evaluated in terms of the probability of speech clipping, packet rejection ratio, DSI advantage, and the delay.

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Role of conviction in nonequilibrium models of opinion formation

NASA Astrophysics Data System (ADS)

Crokidakis, Nuno; Anteneodo, Celia

2012-12-01

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value (±1 or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability p (1-p), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point pc that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

Copula-based prediction of economic movements

NASA Astrophysics Data System (ADS)

García, J. E.; González-López, V. A.; Hirsh, I. D.

2016-06-01

In this paper we model the discretized returns of two paired time series BM&FBOVESPA Dividend Index and BM&FBOVESPA Public Utilities Index using multivariate Markov models. The discretization corresponds to three categories, high losses, high profits and the complementary periods of the series. In technical terms, the maximal memory that can be considered for a Markov model, can be derived from the size of the alphabet and dataset. The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain. In this case the size of the database is not large enough for a consistent estimation of the model. We apply a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consist on obtaining a partition of the state space which is constructed from a combination, of the partitions corresponding to the two marginal processes and the partition corresponding to the multivariate Markov chain. In order to estimate the transition probabilities, all the partitions are linked using a copula. In our application this strategy provides a significant improvement in the movement predictions.

Probe-Independent EEG Assessment of Mental Workload in Pilots

DTIC Science & Technology

2015-05-18

Teager Energy Operator - Frequency Modulated Component - z- score 10.94 17.46 10 Hurst Exponent - Discrete Second Order Derivative 7.02 17.06 D. Best...Teager Energy Operator– Frequency Modulated Component – Z-score 45. Line Length – Time Series 46. Line Length – Time Series – Z-score 47. Hurst Exponent ...Discrete Second Order Derivative 48. Hurst Exponent – Wavelet Based Adaptation 49. Hurst Exponent – Rescaled Range 50. Hurst Exponent – Discrete

Optimal generalized multistep integration formulae for real-time digital simulation

NASA Technical Reports Server (NTRS)

Moerder, D. D.; Halyo, N.

1985-01-01

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Scalar discrete nonlinear multipoint boundary value problems

NASA Astrophysics Data System (ADS)

Rodriguez, Jesus; Taylor, Padraic

2007-06-01

In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].

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.

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.

Boolean dynamics of genetic regulatory networks inferred from microarray time series data

DOE PAGES

Martin, Shawn; Zhang, Zhaoduo; Martino, Anthony; ...

2007-01-31

Methods available for the inference of genetic regulatory networks strive to produce a single network, usually by optimizing some quantity to fit the experimental observations. In this paper we investigate the possibility that multiple networks can be inferred, all resulting in similar dynamics. This idea is motivated by theoretical work which suggests that biological networks are robust and adaptable to change, and that the overall behavior of a genetic regulatory network might be captured in terms of dynamical basins of attraction. We have developed and implemented a method for inferring genetic regulatory networks for time series microarray data. Our methodmore » first clusters and discretizes the gene expression data using k-means and support vector regression. We then enumerate Boolean activation–inhibition networks to match the discretized data. In conclusion, the dynamics of the Boolean networks are examined. We have tested our method on two immunology microarray datasets: an IL-2-stimulated T cell response dataset and a LPS-stimulated macrophage response dataset. In both cases, we discovered that many networks matched the data, and that most of these networks had similar dynamics.« less

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Discrete-time systems with random switches: From systems stability to networks synchronization.

PubMed

Guo, Yao; Lin, Wei; Ho, Daniel W C

2016-03-01

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.

Discrete-time systems with random switches: From systems stability to networks synchronization

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

Guo, Yao; Lin, Wei, E-mail: wlin@fudan.edu.cn; Shanghai Key Laboratory of Contemporary Applied Mathematics, LMNS, and Shanghai Center for Mathematical Sciences, Shanghai 200433

2016-03-15

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developedmore » approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.« less

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Flux-Based Finite Volume representations for general thermal problems

NASA Technical Reports Server (NTRS)

Mohan, Ram V.; Tamma, Kumar K.

1993-01-01

Flux-Based Finite Volume (FV) element representations for general thermal problems are given in conjunction with a generalized trapezoidal gamma-T family of algorithms, formulated following the spirit of what we term as the Lax-Wendroff based FV formulations. The new flux-based representations introduced offer an improved physical interpretation of the problem along with computationally convenient and attractive features. The space and time discretization emanate from a conservation form of the governing equation for thermal problems, and in conjunction with the flux-based element representations give rise to a physically improved and locally conservative numerical formulations. The present representations seek to involve improved locally conservative properties, improved physical representations and computational features; these are based on a 2D, bilinear FV element and can be extended for other cases. Time discretization based on a gamma-T family of algorithms in the spirit of a Lax-Wendroff based FV formulations are employed. Numerical examples involving linear/nonlinear steady and transient situations are shown to demonstrate the applicability of the present representations for thermal analysis situations.

Predicting fruit fly's sensing rate with insect flight simulations.

PubMed

Chang, Song; Wang, Z Jane

2014-08-05

Without sensory feedback, flies cannot fly. Exactly how various feedback controls work in insects is a complex puzzle to solve. What do insects measure to stabilize their flight? How often and how fast must insects adjust their wings to remain stable? To gain insights into algorithms used by insects to control their dynamic instability, we develop a simulation tool to study free flight. To stabilize flight, we construct a control algorithm that modulates wing motion based on discrete measurements of the body-pitch orientation. Our simulations give theoretical bounds on both the sensing rate and the delay time between sensing and actuation. Interpreting our findings together with experimental results on fruit flies' reaction time and sensory motor reflexes, we conjecture that fruit flies sense their kinematic states every wing beat to stabilize their flight. We further propose a candidate for such a control involving the fly's haltere and first basalar motor neuron. Although we focus on fruit flies as a case study, the framework for our simulation and discrete control algorithms is applicable to studies of both natural and man-made fliers.

Development and application of the modal space self-tuning regulator

NASA Astrophysics Data System (ADS)

Schultze, John Francis

The control and reduction of vibration of flexible structures is currently an area of much research and concern in the aerospace and automotive industries. Often these systems are idealized as discrete systems with a finite number of degrees of freedom. Traditional active control approaches have attempted either to identify the complete system and design an appropriate controller or; use an ad-hoc set of single degree of freedom controllers. Both methods have limitations. The former requires great computational and control design effort. This approach also attempts to reduce the vibration across the complete spectrum as opposed to applying control effort only to the problematic mode(s). The latter method is often limited by its inability to address the structural coupling inherent in these systems. The Modal Space Self Tuning Regulator (MSSTR) method proposed in this research addresses both of these problems as well as changes in the structural properties of a system. The control problem is approached in a two stage effort, decoupling and adaptive control. The structure's motion is decoupled through the Modified Reciprocal Modal Vector method. The control is then implemented in modal space as a new acceleration feedback based, single degree of freedom, form of the Self Tuning Regulator. The range of application of this controller in terms of maximum additive damping, actuator location sensitivity, and discrete and continuous system mass changes are investigated. Also, the behavior of the internal controller parameters are studied for the extension of this method to system monitoring and damage detection. Proof of the numeric stability of the controller in the ideal case is presented as well as its practical implementation issues. This control approach was shown to be effective for the cases of specified damping increases up to 10 dB, several actuator locations, three discrete mass perturbations and several continuous mass change cases. There appears to be little dependence on the actuator position until the additive damping limit is reached. The discrete mass change tests investigate both increases and reductions in the effective moving mass of the system. The controller performed well in all cases investigated achieving a minimum of 7 dB and up to 15 dB of attenuation. The continuous mass change cases, modeling tool-wear, fuel consumption, or other time varying phenomena, show good convergence behavior of the system model and the accompanying regulator law parameters. This validates the controller for its implementation in a rapidly changing system. The MSSTR performed well in several varied test cases, showing both insensitivity to actuator location and resilience to changing system parameters. Extensions to multi-input, multi-mode control appears within ready grasp.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

NASA Astrophysics Data System (ADS)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes.

PubMed

Ming, Yi; Ling, Dong-Bo; Li, Hui-Min; Ding, Ze-Jun

2017-06-01

So far, only the energy thresholds of single discrete breathers in nonlinear Hamiltonian systems have been analytically obtained. In this work, the energy thresholds of discrete breathers in thermal equilibrium and the energy thresholds of long-lived discrete breathers which can remain after a long time relaxation are analytically estimated for nonlinear chains. These energy thresholds are size dependent. The energy thresholds of discrete breathers in thermal equilibrium are the same as the previous analytical results for single discrete breathers. The energy thresholds of long-lived discrete breathers in relaxation processes are different from the previous results for single discrete breathers but agree well with the published numerical results known to us. Because real systems are either in thermal equilibrium or in relaxation processes, the obtained results could be important for experimental detection of discrete breathers.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

Signal processing method and system for noise removal and signal extraction

DOEpatents

Fu, Chi Yung; Petrich, Loren

2009-04-14

A signal processing method and system combining smooth level wavelet pre-processing together with artificial neural networks all in the wavelet domain for signal denoising and extraction. Upon receiving a signal corrupted with noise, an n-level decomposition of the signal is performed using a discrete wavelet transform to produce a smooth component and a rough component for each decomposition level. The n.sup.th level smooth component is then inputted into a corresponding neural network pre-trained to filter out noise in that component by pattern recognition in the wavelet domain. Additional rough components, beginning at the highest level, may also be retained and inputted into corresponding neural networks pre-trained to filter out noise in those components also by pattern recognition in the wavelet domain. In any case, an inverse discrete wavelet transform is performed on the combined output from all the neural networks to recover a clean signal back in the time domain.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian

NASA Astrophysics Data System (ADS)

Zabrodin, A.; Zotov, A.

2018-02-01

We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) glN Ruijsenaars-Schneider model. It is based on the first order equations in N + M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars-Schneider model. In the elliptic case it holds M = N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero-Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars-Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero-Moser models arise from ordinary intermediate long wave and Benjamin-Ono equations.

Some Classes of Imperfect Information Finite State-Space Stochastic Games with Finite-Dimensional Solutions

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

McEneaney, William M.

2004-08-15

Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity ofmore » an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.« less

Surface oscillation of levitated liquid droplets under microgravity

NASA Astrophysics Data System (ADS)

Watanabe, Masahito; Hibiya, Taketoshi; Ozawa, Shumpei; Mizuno, Akitoshi

2012-07-01

Microgravity conditions have advantages of measurement of surface tension and viscosity of metallic liquids by the oscillating drop method with an electromagnetic levitation (EML) device. Thus, we are now planning the thermophysical properties, the surface tension, viscosity, density and etc., measurements of liquid alloys using the electromagnetic levitator named MSL-EML (Materials Science Laboratory Electromagnetic Levitator), which ahs been developed by the European Space Agency (ESA), installed in the International Space Station (ISS). The surface tension and the viscosity of liquid samples by the oscillating drop method are obtained from the surface oscillation frequency and damping time of surface oscillation respectively. However, analysis of oscillating drop method in EML must be improved even in the microgravity conditions, because on the EML conditions the electromagnetic force (EMF) cannot generate the surface oscillation with discretely oscillation mode. Since under microgravity the levitated droplet shape is completely spherical, the surface oscillation frequency with different oscillation modes degenerates into the single frequency. Therefore, surface tension will be not affected the EML condition under microgravity, but viscosity will be affected on the different oscillation mode of surface oscillations. Because dumping time of surface oscillation of liquid droplets depends on the oscillation modes, the case of surface oscillation including multi oscillation modes the viscosity values obtained from dumping time will be modified from the correct viscosity. Therefore, we investigate the dumping time of surface oscillation of levitated droplets with different oscillation modes and also with including multi oscillation modes using the electrostatic levitation (ESL) on ground and EML under microgravity conditions by the parabolic flight of airplane. The ESL can discretely generate the surface oscillation with different oscillation modes by the change of generation frequency of surface oscillation, so we can obtain dumping time of surface oscillation with discrete oscillation mode. We repot the results of the damping time of the surface oscillation of levitated liquid droplet by ESL and EML experiment with numerical simulation of the damped oscillation model.

Discrete-time model reduction in limited frequency ranges

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Tail shortening by discrete hydrodynamics

NASA Astrophysics Data System (ADS)

Kiefer, J.; Visscher, P. B.

1982-02-01

A discrete formulation of hydrodynamics was recently introduced, whose most important feature is that it is exactly renormalizable. Previous numerical work has found that it provides a more efficient and rapidly convergent method for calculating transport coefficients than the usual Green-Kubo method. The latter's convergence difficulties are due to the well-known "long-time tail" of the time correlation function which must be integrated over time. The purpose of the present paper is to present additional evidence that these difficulties are really absent in the discrete equation of motion approach. The "memory" terms in the equation of motion are calculated accurately, and shown to decay much more rapidly with time than the equilibrium time correlations do.

Autonomous learning by simple dynamical systems with a discrete-time formulation

NASA Astrophysics Data System (ADS)

Bilen, Agustín M.; Kaluza, Pablo

2017-05-01

We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Adaptive Discrete Hypergraph Matching.

PubMed

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

FLOCK cluster analysis of plasma cell flow cytometry data predicts bone marrow involvement by plasma cell neoplasia.

PubMed

Dorfman, David M; LaPlante, Charlotte D; Li, Betty

2016-09-01

We analyzed plasma cell populations in bone marrow samples from 353 patients with possible bone marrow involvement by a plasma cell neoplasm, using FLOCK (FLOw Clustering without K), an unbiased, automated, computational approach to identify cell subsets in multidimensional flow cytometry data. FLOCK identified discrete plasma cell populations in the majority of bone marrow specimens found by standard histologic and immunophenotypic criteria to be involved by a plasma cell neoplasm (202/208 cases; 97%), including 34 cases that were negative by standard flow cytometric analysis that included clonality assessment. FLOCK identified discrete plasma cell populations in only a minority of cases negative for involvement by a plasma cell neoplasm by standard histologic and immunophenotypic criteria (38/145 cases; 26%). Interestingly, 55% of the cases negative by standard analysis, but containing a FLOCK-identified discrete plasma cell population, were positive for monoclonal gammopathy by serum protein electrophoresis and immunofixation. FLOCK-identified and quantitated plasma cell populations accounted for 3.05% of total cells on average in cases positive for involvement by a plasma cell neoplasm by standard histologic and immunophenotypic criteria, and 0.27% of total cells on average in cases negative for involvement by a plasma cell neoplasm by standard histologic and immunophenotypic criteria (p<0.0001; area under the curve by ROC analysis=0.96). The presence of a FLOCK-identified discrete plasma cell population was predictive of the presence of plasma cell neoplasia with a sensitivity of 97%, compared with only 81% for standard flow cytometric analysis, and had specificity of 74%, PPV of 84% and NPV of 95%. FLOCK analysis, which has been shown to provide useful diagnostic information for evaluating patients with suspected systemic mastocytosis, is able to identify neoplastic plasma cell populations analyzed by flow cytometry, and may be helpful in the diagnostic evaluation of bone marrow samples for involvement by plasma cell neoplasia. Copyright © 2016 Elsevier Ltd. All rights reserved.

Time-changed geometric fractional Brownian motion and option pricing with transaction costs

NASA Astrophysics Data System (ADS)

Gu, Hui; Liang, Jin-Rong; Zhang, Yun-Xiu

2012-08-01

This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black-Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.

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.

Discrete differential geometry: The nonplanar quadrilateral mesh

NASA Astrophysics Data System (ADS)

Twining, Carole J.; Marsland, Stephen

2012-06-01

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

An analysis of numerical convergence in discrete velocity gas dynamics for internal flows

NASA Astrophysics Data System (ADS)

Sekaran, Aarthi; Varghese, Philip; Goldstein, David

2018-07-01

The Discrete Velocity Method (DVM) for solving the Boltzmann equation has significant advantages in the modeling of non-equilibrium and near equilibrium flows as compared to other methods in terms of reduced statistical noise, faster solutions and the ability to handle transient flows. Yet the DVM performance for rarefied flow in complex, small-scale geometries, in microelectromechanical (MEMS) devices for instance, is yet to be studied in detail. The present study focuses on the performance of the DVM for locally large Knudsen number flows of argon around sharp corners and other sources for discontinuities in the distribution function. Our analysis details the nature of the solution for some benchmark cases and introduces the concept of solution convergence for the transport terms in the discrete velocity Boltzmann equation. The limiting effects of the velocity space discretization are also investigated and the constraints on obtaining a robust, consistent solution are derived. We propose techniques to maintain solution convergence and demonstrate the implementation of a specific strategy and its effect on the fidelity of the solution for some benchmark cases.

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

DOE PAGES

Seleson, Pablo; Du, Qiang; Parks, Michael L.

2016-08-16

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Furthermore, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.« less

Lattice Wigner equation.

PubMed

Solórzano, S; Mendoza, M; Succi, S; Herrmann, H J

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Lattice Wigner equation

NASA Astrophysics Data System (ADS)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

78 FR 23817 - Limitation on Claims Against Proposed Public Transportation Projects

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-22

... the discrete actions taken by FTA at this time, as described below. Nothing in this notice affects FTA... street level. This notice only applies to the discrete actions taken by FTA at this time, as described...

Hydra effects in discrete-time models of stable communities.

PubMed

Cortez, Michael H

2016-12-21

A species exhibits a hydra effect when, counter-intuitively, increased mortality of the species causes an increase in its abundance. Hydra effects have been studied in many continuous time (differential equation) multispecies models, but only rarely have hydra effects been observed in or studied with discrete time (difference equation) multispecies models. In addition most discrete time theory focuses on single-species models. Thus, it is unclear what unifying characteristics determine when hydra effects arise in discrete time models. Here, using discrete time multispecies models (where total abundance is the single variable describing each population), I show that a species exhibits a hydra effect in a stable system only when fixing that species' density at its equilibrium density destabilizes the system. This general characteristic is referred to as subsystem instability. I apply this result to two-species models and identify specific mechanisms that cause hydra effects in stable communities, e.g., in host--parasitoid models, host Allee effects and saturating parasitoid functional responses can cause parasitoid hydra effects. I discuss how the general characteristic can be used to identify mechanisms causing hydra effects in communities with three or more species. I also show that the condition for hydra effects at stable equilibria implies the system is reactive (i.e., density perturbations can grow before ultimately declining). This study extends previous work on conditions for hydra effects in single-species models by identifying necessary conditions for stable systems and sufficient conditions for cyclic systems. In total, these results show that hydra effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models. Copyright © 2016 Elsevier Ltd. All rights reserved.

High-resolution space-time characterization of convective rain cells: implications on spatial aggregation and temporal sampling operated by coarser resolution instruments

NASA Astrophysics Data System (ADS)

Marra, Francesco; Morin, Efrat

2017-04-01

Forecasting the occurrence of flash floods and debris flows is fundamental to save lives and protect infrastructures and properties. These natural hazards are generated by high-intensity convective storms, on space-time scales that cannot be properly monitored by conventional instrumentation. Consequently, a number of early-warning systems are nowadays based on remote sensing precipitation observations, e.g. from weather radars or satellites, that proved effective in a wide range of situations. However, the uncertainty affecting rainfall estimates represents an important issue undermining the operational use of early-warning systems. The uncertainty related to remote sensing estimates results from (a) an instrumental component, intrinsic of the measurement operation, and (b) a discretization component, caused by the discretization of the continuous rainfall process. Improved understanding on these sources of uncertainty will provide crucial information to modelers and decision makers. This study aims at advancing knowledge on the (b) discretization component. To do so, we take advantage of an extremely-high resolution X-Band weather radar (60 m, 1 min) recently installed in the Eastern Mediterranean. The instrument monitors a semiarid to arid transition area also covered by an accurate C-Band weather radar and by a relatively sparse rain gauge network ( 1 gauge/ 450 km2). Radar quantitative precipitation estimation includes corrections reducing the errors due to ground echoes, orographic beam blockage and attenuation of the signal in heavy rain. Intense, convection-rich, flooding events recently occurred in the area serve as study cases. We (i) describe with very high detail the spatiotemporal characteristics of the convective cores, and (ii) quantify the uncertainty due to spatial aggregation (spatial discretization) and temporal sampling (temporal discretization) operated by coarser resolution remote sensing instruments. We show that instantaneous rain intensity decreases very steeply with the distance from the core of convection with intensity observed at 1 km (2 km) being 10-40% (1-20%) of the core value. The use of coarser temporal resolutions leads to gaps in the observed rainfall and even relatively high resolutions (5 min) can be affected by the problem. We conclude providing to the final user indications about the effects of the discretization component of estimation uncertainty and suggesting viable ways to decrease them.

An Application of the Difference Potentials Method to Solving External Problems in CFD

NASA Technical Reports Server (NTRS)

Ryaben 'Kii, Victor S.; Tsynkov, Semyon V.

1997-01-01

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Discrete retardance second harmonic generation ellipsometry.

PubMed

Dehen, Christopher J; Everly, R Michael; Plocinik, Ryan M; Hedderich, Hartmut G; Simpson, Garth J

2007-01-01

A new instrument was constructed to perform discrete retardance nonlinear optical ellipsometry (DR-NOE). The focus of the design was to perform second harmonic generation NOE while maximizing sample and application flexibility and minimizing data acquisition time. The discrete retardance configuration results in relatively simple computational algorithms for performing nonlinear optical ellipsometric analysis. NOE analysis of a disperse red 19 monolayer yielded results that were consistent with previously reported values for the same surface system, but with significantly reduced acquisition times.

Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes

NASA Astrophysics Data System (ADS)

Pascoli, Silvia; Zhou, Ye-Ling

2016-10-01

In leptonic flavour models with discrete flavour symmetries, couplings between flavons and leptons can result in special flavour structures after they gain vacuum expectation values. At the same time, they can also contribute to the other lepton-flavour-violating processes. We study the flavon-induced LFV 3-body charged lepton decays and radiative decays and we take as example the A 4 discrete symmetry. In A 4 models, a Z 3 residual symmetry roughly holds in the charged lepton sector for the realisation of tri-bimaximal mixing at leading order. The only processes allowed by this symmetry are τ - → μ + e - e - , e + μ - μ -, and the other 3-body and all radiative decays are suppressed by small Z 3-breaking effects. These processes also depend on the representation the flavon is in, whether pseudo-real (case i) or complex (case ii). We calculate the decay rates for all processes for each case and derive their strong connection with lepton flavour mixing. In case i, sum rules for the branching ratios of these processes are obtained, with typical examples Br( τ - → μ + e - e -) ≈ Br( τ - → e + μ - μ -) and Br( τ - → e -γ) ≈ Br( τ - → μ -γ). In case ii, we observe that the mixing between two Z 3-covariant flavons plays an important role. All processes are suppressed by charged lepton masses and current experimental con- straints allow the electroweak scale and the flavon masses to be around hundreds of GeV. Our discussion can be generalised in other flavour models with different flavour symmetries.

Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional Elastica

NASA Astrophysics Data System (ADS)

Turco, Emilio

2018-04-01

Complex problems such as those concerning the mechanics of materials can be confronted only by considering numerical simulations. Analytical methods are useful to build guidelines or reference solutions but, for general cases of technical interest, they have to be solved numerically, especially in the case of large displacements and deformations. Probably continuous models arose for producing inspiring examples and stemmed from homogenization techniques. These techniques allowed for the solution of some paradigmatic examples but, in general, always require a discretization method for solving problems dictated by the applications. Therefore, and also by taking into account that computing powers are nowadays more largely available and cheap, the question arises: why not using directly a discrete model for 3D beams? In other words, it could be interesting to formulate a discrete model without using an intermediate continuum one, as this last, at the end, has to be discretized in any case. These simple considerations immediately evoke some very basic models developed many years ago when the computing powers were practically inexistent but the problem of finding simple solutions to beam deformation problem was already an emerging one. Actually, in recent years, the keynotes of Hencky and Piola attracted a renewed attention [see, one for all, the work (Turco et al. in Zeitschrift für Angewandte Mathematik und Physik 67(4):1-28, 2016)]: generalizing their results, in the present paper, a novel directly discrete three-dimensional beam model is presented and discussed, in the framework of geometrically nonlinear analysis. Using a stepwise algorithm based essentially on Newton's method to compute the extrapolations and on the Riks' arc-length method to perform the corrections, we could obtain some numerical simulations showing the computational effectiveness of presented model: Indeed, it presents a convenient balance between accuracy and computational cost.

Circuit-based versus full-wave modelling of active microwave circuits

NASA Astrophysics Data System (ADS)

Bukvić, Branko; Ilić, Andjelija Ž.; Ilić, Milan M.

2018-03-01

Modern full-wave computational tools enable rigorous simulations of linear parts of complex microwave circuits within minutes, taking into account all physical electromagnetic (EM) phenomena. Non-linear components and other discrete elements of the hybrid microwave circuit are then easily added within the circuit simulator. This combined full-wave and circuit-based analysis is a must in the final stages of the circuit design, although initial designs and optimisations are still faster and more comfortably done completely in the circuit-based environment, which offers real-time solutions at the expense of accuracy. However, due to insufficient information and general lack of specific case studies, practitioners still struggle when choosing an appropriate analysis method, or a component model, because different choices lead to different solutions, often with uncertain accuracy and unexplained discrepancies arising between the simulations and measurements. We here design a reconfigurable power amplifier, as a case study, using both circuit-based solver and a full-wave EM solver. We compare numerical simulations with measurements on the manufactured prototypes, discussing the obtained differences, pointing out the importance of measured parameters de-embedding, appropriate modelling of discrete components and giving specific recipes for good modelling practices.

Variational formulation of macroparticle models for electromagnetic plasma simulations

DOE PAGES

Stamm, Alexander B.; Shadwick, Bradley A.; Evstatiev, Evstati G.

2014-06-01

A variational method is used to derive a self-consistent macroparticle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work, discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macroparticles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with lab frame coordinates or moving window coordinates; the latter can greatly improve computational efficiency for studying some types of laser-plasma interactions. The primary advantage of the variational approach is the preservation of Lagrangian symmetries, which in our case leads tomore » energy conservation and thus avoids difficulties with grid heating. In addition, this approach decouples particle size from grid spacing and relaxes restrictions on particle shape, leading to low numerical noise. The variational approach also guarantees consistent approximations in the equations of motion and is amenable to higher order methods in both space and time. We restrict our attention to the 1.5-D case (one coordinate and two momenta). Lastly, simulations are performed with the new models and demonstrate energy conservation and low noise.« less

Time Operator in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Khorasani, Sina

2017-07-01

It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

Control of the maneuvering SCOLE structure

NASA Technical Reports Server (NTRS)

Lim, S.; Meirovitch, L.

1992-01-01

This paper is concerned with the vibration control of the SCOLE structure while it undergoes a slewing maneuver. The control law is designed according to the linear quadratic regulator theory. In view of saturation limits on the actuators, the actual implementation is modified so as to observe these limits, resulting in suboptimal control. State estimation is carried out by means of a Kalman filter. The control and state estimation are carried out in discrete time. Numerical simulations for several cases of interest are presented.

Digital Systems Validation Handbook. Volume 2

DTIC Science & Technology

1989-02-01

power. 2. A grid of wires, solid sheet, or foil. 3. A wire from circuit to grounding block or case. 4. A wire from circuit to structure. 5. Shield...RETURN. (11) 1. Structure, for power, fault, and "discrete" circuits. 2. A grid of wires, solid sheet, or foil. 3. A wire from circuit load back to...TV (14) Television TWTD (13) Thin Wire Time Domain TX (5) Transmit U.K. (13,141 United Kingdom U.S. (14) United States UART (15) Universal Asynchronous

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Continuous- and discrete-time stimulus sequences for high stimulus rate paradigm in evoked potential studies.

PubMed

Wang, Tao; Huang, Jiang-hua; Lin, Lin; Zhan, Chang'an A

2013-01-01

To obtain reliable transient auditory evoked potentials (AEPs) from EEGs recorded using high stimulus rate (HSR) paradigm, it is critical to design the stimulus sequences of appropriate frequency properties. Traditionally, the individual stimulus events in a stimulus sequence occur only at discrete time points dependent on the sampling frequency of the recording system and the duration of stimulus sequence. This dependency likely causes the implementation of suboptimal stimulus sequences, sacrificing the reliability of resulting AEPs. In this paper, we explicate the use of continuous-time stimulus sequence for HSR paradigm, which is independent of the discrete electroencephalogram (EEG) recording system. We employ simulation studies to examine the applicability of the continuous-time stimulus sequences and the impacts of sampling frequency on AEPs in traditional studies using discrete-time design. Results from these studies show that the continuous-time sequences can offer better frequency properties and improve the reliability of recovered AEPs. Furthermore, we find that the errors in the recovered AEPs depend critically on the sampling frequencies of experimental systems, and their relationship can be fitted using a reciprocal function. As such, our study contributes to the literature by demonstrating the applicability and advantages of continuous-time stimulus sequences for HSR paradigm and by revealing the relationship between the reliability of AEPs and sampling frequencies of the experimental systems when discrete-time stimulus sequences are used in traditional manner for the HSR paradigm.

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

Numerical stability analysis of two-dimensional solute transport along a discrete fracture in a porous rock matrix

NASA Astrophysics Data System (ADS)

Watanabe, Norihiro; Kolditz, Olaf

2015-07-01

This work reports numerical stability conditions in two-dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective-dispersive problem described in Tang et al. (1981) and examine the stability of the Crank-Nicolson Galerkin finite element method (CN-GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method-flux corrected transport (FEM-FCT) method by Kuzmin () to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov-Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM-FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM-FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue.

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

NASA Astrophysics Data System (ADS)

Hulko, Artem

2018-03-01

In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

Evaluation of Characteristic Energy Scales of Pressure Stabilized Oxygen Chain States in YBa2Cu3Ox Films

DTIC Science & Technology

2017-03-14

2], and [4]. In the case of YBa2Cu3O∇x, the application of sufficient uniaxial pressure results in the film having discrete regions of uniform...that discrete regions of uniform oxygen content are stabilized where x ≈ [6, 6.5, 6.72, 6.81, 7]. The latter four oxygen content levels correspond to...associated energy levels of the stabilized lattice states ᝺>, �>, >, and ə>, and find evidence for discrete energy levels of the pressure

Evaluation of the CPU time for solving the radiative transfer equation with high-order resolution schemes applying the normalized weighting-factor method

NASA Astrophysics Data System (ADS)

Xamán, J.; Zavala-Guillén, I.; Hernández-López, I.; Uriarte-Flores, J.; Hernández-Pérez, I.; Macías-Melo, E. V.; Aguilar-Castro, K. M.

2018-03-01

In this paper, we evaluated the convergence rate (CPU time) of a new mathematical formulation for the numerical solution of the radiative transfer equation (RTE) with several High-Order (HO) and High-Resolution (HR) schemes. In computational fluid dynamics, this procedure is known as the Normalized Weighting-Factor (NWF) method and it is adopted here. The NWF method is used to incorporate the high-order resolution schemes in the discretized RTE. The NWF method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) technique for the calculations of a two-dimensional cavity with emitting-absorbing-scattering gray media using the discrete ordinates method. Six parameters, viz. the grid size, the order of quadrature, the absorption coefficient, the emissivity of the boundary surface, the under-relaxation factor, and the scattering albedo are considered to evaluate ten schemes. The results showed that using the DC method, in general, the scheme that had the lowest CPU time is the SOU. In contrast, with the results of theDC procedure the CPU time for DIAMOND and QUICK schemes using the NWF method is shown to be, between the 3.8 and 23.1% faster and 12.6 and 56.1% faster, respectively. However, the other schemes are more time consuming when theNWFis used instead of the DC method. Additionally, a second test case was presented and the results showed that depending on the problem under consideration, the NWF procedure may be computationally faster or slower that the DC method. As an example, the CPU time for QUICK and SMART schemes are 61.8 and 203.7%, respectively, slower when the NWF formulation is used for the second test case. Finally, future researches to explore the computational cost of the NWF method in more complex problems are required.

On the Motion of Agents across Terrain with Obstacles

NASA Astrophysics Data System (ADS)

Kuznetsov, A. V.

2018-01-01

The paper is devoted to finding the time optimal route of an agent travelling across a region from a given source point to a given target point. At each point of this region, a maximum allowed speed is specified. This speed limit may vary in time. The continuous statement of this problem and the case when the agent travels on a grid with square cells are considered. In the latter case, the time is also discrete, and the number of admissible directions of motion at each point in time is eight. The existence of an optimal solution of this problem is proved, and estimates of the approximate solution obtained on the grid are obtained. It is found that decreasing the size of cells below a certain limit does not further improve the approximation. These results can be used to estimate the quasi-optimal trajectory of the agent motion across the rugged terrain produced by an algorithm based on a cellular automaton that was earlier developed by the author.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Improved Results for Route Planning in Stochastic Transportation Networks

NASA Technical Reports Server (NTRS)

Boyan, Justin; Mitzenmacher, Michael

2000-01-01

In the bus network problem, the goal is to generate a plan for getting from point X to point Y within a city using buses in the smallest expected time. Because bus arrival times are not determined by a fixed schedule but instead may be random. the problem requires more than standard shortest path techniques. In recent work, Datar and Ranade provide algorithms in the case where bus arrivals are assumed to be independent and exponentially distributed. We offer solutions to two important generalizations of the problem, answering open questions posed by Datar and Ranade. First, we provide a polynomial time algorithm for a much wider class of arrival distributions, namely those with increasing failure rate. This class includes not only exponential distributions but also uniform, normal, and gamma distributions. Second, in the case where bus arrival times are independent and geometric discrete random variable,. we provide an algorithm for transportation networks of buses and trains, where trains run according to a fixed schedule.

Synchronization Of Parallel Discrete Event Simulations

NASA Technical Reports Server (NTRS)

Steinman, Jeffrey S.

1992-01-01

Adaptive, parallel, discrete-event-simulation-synchronization algorithm, Breathing Time Buckets, developed in Synchronous Parallel Environment for Emulation and Discrete Event Simulation (SPEEDES) operating system. Algorithm allows parallel simulations to process events optimistically in fluctuating time cycles that naturally adapt while simulation in progress. Combines best of optimistic and conservative synchronization strategies while avoiding major disadvantages. Algorithm processes events optimistically in time cycles adapting while simulation in progress. Well suited for modeling communication networks, for large-scale war games, for simulated flights of aircraft, for simulations of computer equipment, for mathematical modeling, for interactive engineering simulations, and for depictions of flows of information.

Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System

NASA Astrophysics Data System (ADS)

Rovny, Jared; Blum, Robert L.; Barrett, Sean E.

2018-05-01

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.

Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System.

PubMed

Rovny, Jared; Blum, Robert L; Barrett, Sean E

2018-05-04

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems.

PubMed

Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip

2015-05-01

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Submovement control processes in discrete aiming as a function of space-time constraints.

PubMed

Hsieh, Tsung-Yu; Liu, Yeou-Teh; Newell, Karl M

2017-01-01

There is preliminary evidence that there are several types of submovements in movement aiming that reflect different processes of control and can result from particular task constraints. The purpose of the study was to investigate the effect of movement space and time task criteria on the prevalence of different submovement control characteristics in discrete aiming. Twelve participants completed 3 distance x 5 time conditions each with 100 trials in a target-aiming movement task. The kinematic structure of the trajectory determined the prevalence of 5 submovement types (none; pre-peak, post-peak movement velocity; undershoot, overshoot). The findings showed that the overall number of submovements increased in the slower space-time conditions and was predominantly characterized by post-peak trajectory submovements rather than discrete overshoot submovements. Overshoot submovements were more frequent in the high average movement velocity and short time duration conditions. We concluded that there are qualitatively different distributional patterns of submovement types in discrete aiming tasks that are organized by the quantitative scaling of the average movement velocity arising from multiple control processes to meet the specific space-time task constraints.

Novel non-parametric models to estimate evolutionary rates and divergence times from heterochronous sequence data.

PubMed

Fourment, Mathieu; Holmes, Edward C

2014-07-24

Early methods for estimating divergence times from gene sequence data relied on the assumption of a molecular clock. More sophisticated methods were created to model rate variation and used auto-correlation of rates, local clocks, or the so called "uncorrelated relaxed clock" where substitution rates are assumed to be drawn from a parametric distribution. In the case of Bayesian inference methods the impact of the prior on branching times is not clearly understood, and if the amount of data is limited the posterior could be strongly influenced by the prior. We develop a maximum likelihood method--Physher--that uses local or discrete clocks to estimate evolutionary rates and divergence times from heterochronous sequence data. Using two empirical data sets we show that our discrete clock estimates are similar to those obtained by other methods, and that Physher outperformed some methods in the estimation of the root age of an influenza virus data set. A simulation analysis suggests that Physher can outperform a Bayesian method when the real topology contains two long branches below the root node, even when evolution is strongly clock-like. These results suggest it is advisable to use a variety of methods to estimate evolutionary rates and divergence times from heterochronous sequence data. Physher and the associated data sets used here are available online at http://code.google.com/p/physher/.

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals.

PubMed

Soto-Quiros, Pablo

2015-01-01

This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Discrete and morphometric traits reveal contrasting patterns and processes in the macroevolutionary history of a clade of scorpions.

PubMed

Mongiardino Koch, N; Ceccarelli, F S; Ojanguren-Affilastro, A A; Ramírez, M J

2017-04-01

Many palaeontological studies have investigated the evolution of entire body plans, generally relying on discrete character-taxon matrices. In contrast, macroevolutionary studies performed by neontologists have mostly focused on morphometric traits. Although these data types are very different, some studies have suggested that they capture common patterns. Nonetheless, the tests employed to support this claim have not explicitly incorporated a phylogenetic framework and may therefore be susceptible to confounding effects due to the presence of common phylogenetic structure. We address this question using the scorpion genus Brachistosternus Pocock 1893 as case study. We make use of a time-calibrated multilocus molecular phylogeny, and compile discrete and traditional morphometric data sets, both capturing the overall morphology of the organisms. We find that morphospaces derived from these matrices are significantly different, and that the degree of discordance cannot be replicated by simulations of random character evolution. Moreover, we find strong support for contrasting modes of evolution, with discrete characters being congruent with an 'early burst' scenario whereas morphometric traits suggest species-specific adaptations to have driven morphological evolution. The inferred macroevolutionary dynamics are therefore contingent on the choice of character type. Finally, we confirm that metrics of correlation fail to detect these profound differences given common phylogenetic structure in both data sets, and that methods incorporating a phylogenetic framework and accounting for expected covariance should be favoured. © 2017 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2017 European Society For Evolutionary Biology.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

EnvironmentalWaveletTool: Continuous and discrete wavelet analysis and filtering for environmental time series

NASA Astrophysics Data System (ADS)

Galiana-Merino, J. J.; Pla, C.; Fernandez-Cortes, A.; Cuezva, S.; Ortiz, J.; Benavente, D.

2014-10-01

A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of several environmental time series, particularly focused on the analyses of cave monitoring data. The continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform have been implemented to provide a fast and precise time-period examination of the time series at different period bands. Moreover, statistic methods to examine the relation between two signals have been included. Finally, the entropy of curves and splines based methods have also been developed for segmenting and modeling the analyzed time series. All these methods together provide a user-friendly and fast program for the environmental signal analysis, with useful, practical and understandable results.

Electrostatic coupling of ion pumps.

PubMed

Nieto-Frausto, J; Lüger, P; Apell, H J

1992-01-01

In this paper the electrostatic interactions between membrane-embedded ion-pumps and their consequences for the kinetics of pump-mediated transport processes have been examined. We show that the time course of an intrinsically monomolecular transport reaction can become distinctly nonexponential, if the reaction is associated with charge translocation and takes place in an aggregate of pump molecules. First we consider the electrostatic coupling of a single dimer of ion-pumps embedded in the membrane. Then we apply the treatment to the kinetic analysis of light-driven proton transport by bacteriorhodopsin which forms two-dimensional hexagonal lattices. Finally, for the case of nonordered molecules, we also consider a model in which the pumps are randomly distributed over the nodes of a lattice. Here the average distance is equal to that deduced experimentally and the elemental size of the lattice is the effective diameter of one single pump. This latter model is applied to an aggregate of membrane-embedded Na, K- and Ca-pumps. In all these cases the electrostatic potential considered is the exact solution calculated from the method of electrical images for a plane membrane of finite thickness immersed in an infinite aqueous solution environment. The distributions of charges (ions or charged binding sites) are considered homogeneous or discrete in the membrane and/or in the external solution. In the case of discrete distributions we compare the results from a mean field approximation and a stochastic simulation.

Mixed Integer PDE Constrained Optimization for the Control of a Wildfire Hazard

DTIC Science & Technology

2017-01-01

are nodes suitable for extinguishing the fire. We introduce a discretization of the time horizon [0, T] by the set of time T := {0, At,..., ntZ\\t = T...of the constraints and objective with a discrete counterpart. The PDE is replaced by a linear system obtained from a convergent finite difference...method [5] and the integral is replaced by a quadrature formula. The domain is discretized by replacing 17 with an equidistant grid of length Ax

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Discrete subvalvular aortic stenosis in the Beckwith-Wiedemann syndrome.

PubMed

Shirani, J; Natarajan, K; Varga, P; Vitullo, D A

1993-07-01

Various congenital cardiac malformations have been described in patients with Beckwith-Wiedemann (BW) syndrome, including reversible obstructive subaortic stenosis in one patient. We herein present a case of a 2.5-year-old black boy with BW syndrome and discrete subvalvular aortic stenosis of the membraneous type. Such association of these two entities has previously not been documented.

A discrete-time adaptive control scheme for robot manipulators

NASA Technical Reports Server (NTRS)

Tarokh, M.

1990-01-01

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.

Universal scaling function in discrete time asymmetric exclusion processes

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-03-01

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz' original publication this universality has been verified for a variety of continuous time systems in the KPZ universality class. We study the Derrida-Lebowitz scaling function for multi-particle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the Derrida-Lebowitz scaling function not only properly characterizes the large system size limit, but even accurately describes surprisingly small systems. These results have immediate applications in searching biological sequence databases.

On Faraday's law in the presence of extended conductors

NASA Astrophysics Data System (ADS)

Bilbao, Luis

2018-06-01

The use of Faraday's Law of induction for calculating the induced currents in an extended conducting body is discussed. In a general case with arbitrary geometry, the solution to the problem of a moving metal object in the presence of a magnetic field is difficult and implies solving Maxwell's equations in a time-dependent situation. In many cases, including cases with good conductors (but not superconductors) Ampère's Law can be neglected and a simpler solution based solely in Faraday's law can be obtained. The integral form of Faraday's Law along any loop in the conducting body is equivalent to a Kirkhhoff's voltage law of a circuit. Therefore, a numerical solution can be obtained by solving a linear system of equations corresponding to a discrete number of loops in the body.

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.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

PubMed

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

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

Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which verticesmore » (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.« less

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

PubMed Central

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

Fast Mix Table Construction for Material Discretization

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

Johnson, Seth R

2013-01-01

An effective hybrid Monte Carlo--deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a ``mix table,'' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table inmore » $$O(\\text{number of voxels}\\times \\log \\text{number of mixtures})$$ time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation.« less

A Surrogate Technique for Investigating Deterministic Dynamics in Discrete Human Movement.

PubMed

Taylor, Paul G; Small, Michael; Lee, Kwee-Yum; Landeo, Raul; O'Meara, Damien M; Millett, Emma L

2016-10-01

Entropy is an effective tool for investigation of human movement variability. However, before applying entropy, it can be beneficial to employ analyses to confirm that observed data are not solely the result of stochastic processes. This can be achieved by contrasting observed data with that produced using surrogate methods. Unlike continuous movement, no appropriate method has been applied to discrete human movement. This article proposes a novel surrogate method for discrete movement data, outlining the processes for determining its critical values. The proposed technique reliably generated surrogates for discrete joint angle time series, destroying fine-scale dynamics of the observed signal, while maintaining macro structural characteristics. Comparison of entropy estimates indicated observed signals had greater regularity than surrogates and were not only the result of stochastic but also deterministic processes. The proposed surrogate method is both a valid and reliable technique to investigate determinism in other discrete human movement time series.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Open shop scheduling problem to minimize total weighted completion time

NASA Astrophysics Data System (ADS)

Bai, Danyu; Zhang, Zhihai; Zhang, Qiang; Tang, Mengqian

2017-01-01

A given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.

Gross-Pitaevski map as a chaotic dynamical system.

PubMed

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

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

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

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.

Examining the Influence of Campus Climate on Students' Time to Degree: A Multilevel Discrete-Time Survival Analysis

ERIC Educational Resources Information Center

Zhou, Ji; Castellanos, Michelle

2013-01-01

Utilizing longitudinal data of 3477 students from 28 institutions, we examine the effects of structural diversity and quality of interracial relation on students' persistence towards graduation within six years. We utilize multilevel discrete-time survival analysis to account for the longitudinal persistence patterns as well as the nested…

Computations of Flow over a Hump Model Using Higher Order Method with Turbulence Modeling

NASA Technical Reports Server (NTRS)

Balakumar, P.

2005-01-01

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k - omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially. nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as those observed in the experiments. The computed separation regions are much longer than those observed experimentally. However, the percentage reduction in the separation region in the steady suction case is closer to what was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than the measured values pointing towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Quantifying the uncertainty introduced by discretization and time-averaging in two-fluid model predictions

DOE PAGES

Syamlal, Madhava; Celik, Ismail B.; Benyahia, Sofiane

2017-07-12

The two-fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time-averaging. First, we show that successive grid refinement may not yield grid-independent transient quantities, including cross-section–averaged quantities. Successive grid refinement would yield grid-independent time-averaged quantities on sufficiently fine grids. A Richardson extrapolation can then be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not workmore » for industrial-scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time-averaging TFM data.« less

Does Age of Entrance Affect Community College Completion Probabilities? Evidence from a Discrete-Time Hazard Model

ERIC Educational Resources Information Center

Calcagno, Juan Carlos; Crosta, Peter; Bailey, Thomas; Jenkins, Davis

2007-01-01

Research has consistently shown that older students--those who enter college for the first time at age 25 or older--are less likely to complete a degree or certificate. The authors estimate a single-risk discrete-time hazard model using transcript data on a cohort of first-time community college students in Florida to compare the educational…

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

NASA Astrophysics Data System (ADS)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition.

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.

Proportional exponentiated link transformed hazards (ELTH) models for discrete time survival data with application

PubMed Central

Joeng, Hee-Koung; Chen, Ming-Hui; Kang, Sangwook

2015-01-01

Discrete survival data are routinely encountered in many fields of study including behavior science, economics, epidemiology, medicine, and social science. In this paper, we develop a class of proportional exponentiated link transformed hazards (ELTH) models. We carry out a detailed examination of the role of links in fitting discrete survival data and estimating regression coefficients. Several interesting results are established regarding the choice of links and baseline hazards. We also characterize the conditions for improper survival functions and the conditions for existence of the maximum likelihood estimates under the proposed ELTH models. An extensive simulation study is conducted to examine the empirical performance of the parameter estimates under the Cox proportional hazards model by treating discrete survival times as continuous survival times, and the model comparison criteria, AIC and BIC, in determining links and baseline hazards. A SEER breast cancer dataset is analyzed in details to further demonstrate the proposed methodology. PMID:25772374

Discrete-Time Demodulator Architectures for Free-Space Broadband Optical Pulse-Position Modulation

NASA Technical Reports Server (NTRS)

Gray, A. A.; Lee, C.

2004-01-01

The objective of this work is to develop discrete-time demodulator architectures for broadband optical pulse-position modulation (PPM) that are capable of processing Nyquist or near-Nyquist data rates. These architectures are motivated by the numerous advantages of realizing communications demodulators in digital very large scale integrated (VLSI) circuits. The architectures are developed within a framework that encompasses a large body of work in optical communications, synchronization, and multirate discrete-time signal processing and are constrained by the limitations of the state of the art in digital hardware. This work attempts to create a bridge between theoretical communication algorithms and analysis for deep-space optical PPM and modern digital VLSI. The primary focus of this work is on the synthesis of discrete-time processing architectures for accomplishing the most fundamental functions required in PPM demodulators, post-detection filtering, synchronization, and decision processing. The architectures derived are capable of closely approximating the theoretical performance of the continuous-time algorithms from which they are derived. The work concludes with an outline of the development path that leads to hardware.

Dimers in Piecewise Temperleyan Domains

NASA Astrophysics Data System (ADS)

Russkikh, Marianna

2018-03-01

We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the scaling limit (as the mesh size tends to zero) to the Gaussian Free Field with Dirichlet boundary conditions. We extend Kenyon's result to a more general class of discretizations. Moreover, we introduce a new factorization of the coupling function of the double-dimer model into two discrete holomorphic functions, which are similar to discrete fermions defined in Smirnov (Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, 2006; Ann Math (2) 172:1435-1467, 2010). For Temperleyan discretizations with appropriate boundary modifications, the results of Kenyon imply that the expectation of the double-dimer height function converges to a harmonic function in the scaling limit. We use the above factorization to extend this result to the class of all polygonal discretizations, that are not necessarily Temperleyan. Furthermore, we show that, quite surprisingly, the expectation of the double-dimer height function in the Temperleyan case is exactly discrete harmonic (for an appropriate choice of Laplacian) even before taking the scaling limit.

Different-Level Simultaneous Minimization Scheme for Fault Tolerance of Redundant Manipulator Aided with Discrete-Time Recurrent Neural Network

PubMed Central

Jin, Long; Liao, Bolin; Liu, Mei; Xiao, Lin; Guo, Dongsheng; Yan, Xiaogang

2017-01-01

By incorporating the physical constraints in joint space, a different-level simultaneous minimization scheme, which takes both the robot kinematics and robot dynamics into account, is presented and investigated for fault-tolerant motion planning of redundant manipulator in this paper. The scheme is reformulated as a quadratic program (QP) with equality and bound constraints, which is then solved by a discrete-time recurrent neural network. Simulative verifications based on a six-link planar redundant robot manipulator substantiate the efficacy and accuracy of the presented acceleration fault-tolerant scheme, the resultant QP and the corresponding discrete-time recurrent neural network. PMID:28955217

Fast parallel approach for 2-D DHT-based real-valued discrete Gabor transform.

PubMed

Tao, Liang; Kwan, Hon Keung

2009-12-01

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.

Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems.

PubMed

Liang, Hongjing; Zhang, Huaguang; Wang, Zhanshan

2015-11-01

This paper considers output synchronization of discrete-time multi-agent systems with directed communication topologies. The directed communication graph contains a spanning tree and the exosystem as its root. Distributed observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct the observer-based protocols. In light of the discrete-time algebraic Riccati equation and internal model principle, synchronization problem is completed. At last, numerical simulation is provided to verify the effectiveness of the theoretical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

It's Deja Vu All over Again: Using Multiple-Spell Discrete-Time Survival Analysis.

ERIC Educational Resources Information Center

Willett, John B.; Singer, Judith D.

1995-01-01

The multiple-spell discrete-time survival analysis method is introduced and illustrated using longitudinal data on exit from and reentry into the teaching profession. The method is applicable to many educational problems involving the sequential occurrence of disparate events or episodes. (SLD)

A latent class multiple constraint multiple discrete-continuous extreme value model of time use and goods consumption.

DOT National Transportation Integrated Search

2016-06-01

This paper develops a microeconomic theory-based multiple discrete continuous choice model that considers: (a) that both goods consumption and time allocations (to work and non-work activities) enter separately as decision variables in the utility fu...

Pricing European option with transaction costs under the fractional long memory stochastic volatility model

NASA Astrophysics Data System (ADS)

Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu

2012-02-01

This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.

Adaptive critic designs for discrete-time zero-sum games with application to H(infinity) control.

PubMed

Al-Tamimi, Asma; Abu-Khalaf, Murad; Lewis, Frank L

2007-02-01

In this correspondence, adaptive critic approximate dynamic programming designs are derived to solve the discrete-time zero-sum game in which the state and action spaces are continuous. This results in a forward-in-time reinforcement learning algorithm that converges to the Nash equilibrium of the corresponding zero-sum game. The results in this correspondence can be thought of as a way to solve the Riccati equation of the well-known discrete-time H(infinity) optimal control problem forward in time. Two schemes are presented, namely: 1) a heuristic dynamic programming and 2) a dual-heuristic dynamic programming, to solve for the value function and the costate of the game, respectively. An H(infinity) autopilot design for an F-16 aircraft is presented to illustrate the results.

Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations

DTIC Science & Technology

2015-06-01

using larger time steps versus lower-order time integration with smaller time steps.4 In the present work, an attempt is made to gener - alize these... generality and because of interest in multi-speed and high Reynolds number, wall-bounded flow regimes, a dual-time framework is adopted in the present work...errors of general combinations of high-order spatial and temporal discretizations. Different Runge-Kutta time integrators are applied to central

Algorithms for Brownian first-passage-time estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

On reinitializing level set functions

NASA Astrophysics Data System (ADS)

Min, Chohong

2010-04-01

In this paper, we consider reinitializing level functions through equation ϕt+sgn(ϕ0)(‖∇ϕ‖-1)=0[16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation. We compare the three temporal discretizations: the second order Runge-Kutta method, the forward Euler method, and a Gauss-Seidel iteration of the forward Euler method. The fact that the time in the equation is fictitious makes a hypothesis that all the temporal discretizations result in the same result in their stationary states. The fact that the absolute stability region of the forward Euler method is not wide enough to include all the eigenvalues of the linearized semi-discrete system of the second order ENO spatial discretization makes another hypothesis that the forward Euler temporal discretization should invoke numerical instability. Our results in this paper contradict both the hypotheses. The Runge-Kutta and Gauss-Seidel methods obtain the second order accuracy, and the forward Euler method converges with order between one and two. Examining all their properties, we conclude that the Gauss-Seidel method is the best among the three. Compared to the Runge-Kutta, it is twice faster and requires memory two times less with the same accuracy.

Hybrid discrete-time neural networks.

PubMed

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

Robust passivity analysis for discrete-time recurrent neural networks with mixed delays

NASA Astrophysics Data System (ADS)

Huang, Chuan-Kuei; Shu, Yu-Jeng; Chang, Koan-Yuh; Shou, Ho-Nien; Lu, Chien-Yu

2015-02-01

This article considers the robust passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with mixed time-delays and uncertain parameters. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays in a given range are presented, and the uncertain parameters are norm-bounded. The activation functions are assumed to be globally Lipschitz continuous. Based on new bounding technique and appropriate type of Lyapunov functional, a sufficient condition is investigated to guarantee the existence of the desired robust passivity condition for the DRNNs, which can be derived in terms of a family of linear matrix inequality (LMI). Some free-weighting matrices are introduced to reduce the conservatism of the criterion by using the bounding technique. A numerical example is given to illustrate the effectiveness and applicability.

Reliable fusion of control and sensing in intelligent machines. Thesis

NASA Technical Reports Server (NTRS)

Mcinroy, John E.

1991-01-01

Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

NASA Astrophysics Data System (ADS)

Negri, Federico; Manzoni, Andrea; Amsallem, David

2015-12-01

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the empirical interpolation method (EIM) and its discrete variant DEIM. In this paper we show that MDEIM represents a very efficient approach to deal with complex physical and geometrical parametrizations in a non-intrusive, efficient and purely algebraic way. We propose different strategies to combine MDEIM with a state approximation resulting either from a reduced basis greedy approach or Proper Orthogonal Decomposition. A posteriori error estimates accounting for the MDEIM error are also developed in the case of parametrized elliptic and parabolic equations. Finally, the capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems.

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

Discrete time-crystalline order in black diamond

NASA Astrophysics Data System (ADS)

Zhou, Hengyun; Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman; Demler, Eugene; Lukin, Mikhail D.

2017-04-01

The interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic ``time-crystalline'' phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of 106 dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.

Discrete time Markov chains (DTMC) susceptible infected susceptible (SIS) epidemic model with two pathogens in two patches

NASA Astrophysics Data System (ADS)

Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami

2017-06-01

The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.

Analysis hierarchical model for discrete event systems

NASA Astrophysics Data System (ADS)

Ciortea, E. M.

2015-11-01

The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

Proposal of Classification Method of Time Series Data in International Emissions Trading Market Using Agent-based Simulation

NASA Astrophysics Data System (ADS)

Nakada, Tomohiro; Takadama, Keiki; Watanabe, Shigeyoshi

This paper proposes the classification method using Bayesian analytical method to classify the time series data in the international emissions trading market depend on the agent-based simulation and compares the case with Discrete Fourier transform analytical method. The purpose demonstrates the analytical methods mapping time series data such as market price. These analytical methods have revealed the following results: (1) the classification methods indicate the distance of mapping from the time series data, it is easier the understanding and inference than time series data; (2) these methods can analyze the uncertain time series data using the distance via agent-based simulation including stationary process and non-stationary process; and (3) Bayesian analytical method can show the 1% difference description of the emission reduction targets of agent.

Program For Parallel Discrete-Event Simulation

NASA Technical Reports Server (NTRS)

Beckman, Brian C.; Blume, Leo R.; Geiselman, John S.; Presley, Matthew T.; Wedel, John J., Jr.; Bellenot, Steven F.; Diloreto, Michael; Hontalas, Philip J.; Reiher, Peter L.; Weiland, Frederick P.

1991-01-01

User does not have to add any special logic to aid in synchronization. Time Warp Operating System (TWOS) computer program is special-purpose operating system designed to support parallel discrete-event simulation. Complete implementation of Time Warp mechanism. Supports only simulations and other computations designed for virtual time. Time Warp Simulator (TWSIM) subdirectory contains sequential simulation engine interface-compatible with TWOS. TWOS and TWSIM written in, and support simulations in, C programming language.

Discretization-dependent model for weakly connected excitable media

NASA Astrophysics Data System (ADS)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.