2009-08-01
setting in Duc & Siegmund [28]: Definition A.10 (Dynamic partition of IR2). Consider the extended phase space, IR2 × I, associated with the flow...Fluid Dynamics, Cambridge University Press, Cam- bridge, 1967. [8] A. Berger, D. T. Son, and S. Siegmund , Nonautonomous finite-time dynamics, Discrete...28] L. H. Duc and S. Siegmund , Hyperbolicity and invariant manifolds for planar nonau- tonomous systems on finite time intervals, Int. J. Bif. Chaos
Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows.
Guo, Hanqi; He, Wenbin; Peterka, Tom; Shen, Han-Wei; Collis, Scott; Helmus, Jonathan
2016-02-29
The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.
Lagrangian Sediment Transport Model
NASA Astrophysics Data System (ADS)
Maderych, V.; Brovchenko, I.; Fenical, S.; Shepsis, V.
2004-12-01
A new two-dimensional Lagrangian sediment transport model was developed to simulate a wide-range of sediment transport processes, including sediment mobility under combined current and wave action, sediment transport and bed change under wave and currents effects, sediment transport patterns at nearshore coastal and offshore structures, and turbidity and sediment motion during dredging and dredged material placement. The Lagrangian technique was used to simulate transport of sediments, deposition, and re-suspension. The model can be applied to cohesive, non-cohesive, or mixed sediments. The sediment transport is simulated using bathymetry data, bed resistance characteristics, wave height and period, depth-averaged current velocity and bed material type, size and gradation, which vary throughout the model domain.The non-cohesive sediment transport model is based on a solution of two-dimensional mass conservation equations for the bed layer material and 2D equations for movement of sediment fractions either bed load or suspended load. The water column and bottom are divided into a set of layers: water layer, active layer, several active bed layers, and the bed layer. The model also takes into account the effects of armoring and changes in the bed composition. Cohesive sediments move entirely as suspended load in the water layer and sediment transport computations are based on a solution of the two-dimensional mass conservation equations for the bed layer material and two-dimensional equations for movement of sediment as suspended load. The water column and bed, as for non-cohesive sediments, was divided into a set of layers. Following the approach of Van Ledden (2002), the erosion of sediments made up of mud and sand mixtures is non-cohesive if the mud content is below a critical level. Above a critical mud content, the bed behaves cohesively. Deposition fluxes of mud and sand are independent. The sediment concentration in the water and active layer is represented by
Identifying finite-time coherent sets from limited quantities of Lagrangian data
Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.
2015-08-15
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
NASA Astrophysics Data System (ADS)
Droste, Stephanie; Governale, Michele
2016-04-01
We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.
Lagrangian statistical model for transport in highly heterogeneous velocity fields.
Le Borgne, Tanguy; Dentz, Marco; Carrera, Jesus
2008-08-29
We define an effective Lagrangian statistical model in phase space (x, t, v) for describing transport in highly heterogeneous velocity fields with complex spatial organizations. The spatial Markovian nature (and temporal non-Markovian nature) of Lagrangian velocities leads to an effective transport description that turns out to be a correlated continuous time random walk. This model correctly captures the Lagrangian velocity correlation properties and is demonstrated to represent a forward model for predicting transport in highly heterogeneous porous media for different types of velocity organizations.
On tide-induced lagrangian residual current and residual transport: 1. Lagrangian residual current
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.
Lagrangian Transport Signatures in Models and Observations
2011-09-30
in the context of oil spill forecast and mitigation. For this purpose, we computed the Finite Time Lyapunov Exponents (FTLEs) from the model...currently being undertaken and will be reported on in FY12. Here we present results from the surface layer. Two key characteristics of eddies are
2011-09-05
Lagrangian analysis during PREDICT 5 which satisfies the variational equation ξ̇=∇u(x(t),t)ξ. (4) Finite time Lyapunov exponents Finite time Lyapunov exponents ...than measuring the magnitude of deformations (Haller and Yuan , 2000). These Lagrangian time-scale methods include finite-size Lyapunov exponents (FSLEs...Lagrangian transport anal- ysis: stable and unstable manifolds of hyperbolic trajectories and finite time Lyapunov exponents . Nonlinear Processes in
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-04-20
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their naturalmore » dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. Lastly, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.« less
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-01-01
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. We also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport. PMID:27094206
Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Gruss, Daniel; Velizhanin, Kirill A.; Zwolak, Michael
2016-04-20
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. Lastly, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.
Users manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)
Lagrangian Transport in a coupled Chemistry Climate Model
NASA Astrophysics Data System (ADS)
Hoppe, C.; Müller, R.; Günther, G.; Hoffmann, L.
2012-04-01
We describe the implementation of a Lagrangian transport core in a chemistry climate model (CCM). This is motivated by the problem that in many cases trace gas distributions in the stratosphere can not be represented properly in a classical Eulerian framework with a fixed model grid, especially in regions where strong trace gas gradients occur. Here, we focus on stratospheric water vapor, which is an important driver of surface climate change on decadal scales. In this case, the transport representation is particularly important in the tropical tropopause layer (TTL), where tropospheric air enters into the stratosphere, i.e. , where the entry level of stratospheric water vapor is determined. For this purpose, the Chemical Lagrangian Model of the Stratosphere (CLaMS) is coupled with the ECHAM/MESSy Atmospheric Chemistry Model (EMAC). The latter includes the ECHAM5 climate model, and a coupling interface, which allows for flexible coupling and switching between different submodels. The chemistry transport model CLaMS provides a full Lagrangian transport representation to calculate constituent transport on a set of air parcels that move along trajectories. In the Lagrangian frame of reference, different vertical velocity representations can be used to drive the trajectories: - kinematic transport in isobaric coordinates with omega as vertical velocity, - diabatic transport in isentropic coordinates, where thetadot calculated from diabatic heatingrates is used as vertical velocity. Since vertical winds in the statosphere derived with the kinematic method from the continuity equation often suffer from excessive numerical noise and errors, we expect that constituent transport using the diabatic method will improve the simulations of stratospheric water vapor. We will present preliminary results illustrating how the different transport representations influence simulated tracer distributions.
Lagrangian transport induced by peristaltic pumping in a closed channel
NASA Astrophysics Data System (ADS)
Ng, Chiu-On; Ma, Ye
2009-11-01
Lagrangian transport induced by peristaltic waves traveling on the boundaries of a two-dimensional rectangular closed channel is studied analytically. Based on the Lagrangian description, an asymptotic analysis is performed to generate explicit expressions for the leading-order oscillatory as well as the higher-order time-mean mass transport (or steady streaming) velocities as functions of the wave properties. Two cases are considered. The first case, which is for slow wave frequency or very small wave amplitude such that the steady-streaming Reynolds number (Res) is very small, recovers the one studied previously in the literature, but with all the results fully presented in the Lagrangian sense. The second case, corresponding to high-frequency pumping such as Res is order unity, is where it has been handled analytically. It is found that the overall mixing resulting from the mass transport can depend on the phase shift of the two waves, the wave number, the frequency, as well as the amplitude of the waves.
Enhancements to the Branched Lagrangian Transport Modeling System
Jobson, Harvey E.
1997-01-01
The Branched Lagrangian Transport Model (BLTM) has received wide use within the U.S. Geological Survey over the past 10 years. This report documents the enhancements and modifications that have been made to this modeling system since it was first introduced. The programs in the modeling system are arranged into five levels?programs to generate time-series of meteorological data (EQULTMP, SOLAR), programs to process time-series data (INTRP, MRG), programs to build input files for transport model (BBLTM, BQUAL2E), the model with defined reaction kinetics (BLTM, QUAL2E), and post processor plotting programs (CTPLT, CXPLT). An example application is presented to illustrate how the modeling system can be used to simulate 10 water-quality constituents in the Chattahoochee River below Atlanta, Georgia.
Chaotic Lagrangian transport and mixing in the ocean
NASA Astrophysics Data System (ADS)
Prants, S. V.
2014-12-01
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.
Lagrangian coherent structures in the thermosphere: Predictive transport barriers
NASA Astrophysics Data System (ADS)
Wang, N.; Ramirez, U.; Flores, F.; Datta-Barua, S.
2017-05-01
Lagrangian coherent structures (LCSs) in the time-varying flow of the upper atmosphere are found. The Horizontal Wind Model 2014 (HWM14) is used to simulate the neutral winds of the thermosphere at 150, 250, and 350 km altitude, for quiet and active geomagnetic conditions. Then LCS analysis of HWM14 winds at 100 km altitude is used to investigate space shuttle water vapor plume transport. LCSs are found to exist in the lower thermosphere but are more prominent at 250 km and 350 km, at 40°-80° latitudes on the dayside. Ionosphere-thermosphere coupling manifests in the response of thermospheric LCSs to geomagnetic activity. The LCSs shift equatorward and eastward, developing a more complex topology in the apparent form of two cells in the Northern Hemisphere high-latitude zone. We also show for the first time that the LCS demarcates the high-latitude boundary of shuttle plume observations after 48 h of transport.
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
NASA Astrophysics Data System (ADS)
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Lagrangian transported MDF methods for compressible high speed flows
NASA Astrophysics Data System (ADS)
Gerlinger, Peter
2017-06-01
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).
Stochastic Simulation of Lagrangian Particle Transport in Turbulent Flows
NASA Astrophysics Data System (ADS)
Sun, Guangyuan
This dissertation presents the development and validation of the One Dimensional Turbulence (ODT) multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent-particle mixing and transport at low computational cost. The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes. The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle-eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively. The Type-IC model combines the features of the Type-I and -C models. The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet. Particle dispersion, dispersion coefficients, and velocity statistics are predicted and compared with experimental data. The models accurately reproduces the experimental data sets and capture particle inertial effects and trajectory crossing effect. A new adjustable particle parameter is introduced into the ODT model, and sensitivity analysis is performed to facilitate parameter estimation and selection. A novel algorithm of the two-way momentum coupling between the particle and carrier phases is developed in the ODT multiphase model. Momentum exchange between the phases is accounted for through particle source terms in the viscous diffusion. The source term is implemented in eddy events through a new kernel transformation and an iterative procedure is required for eddy selection. This model is applied to a particle-laden turbulent jet flow, and simulation results are compared with experimental measurements. The effect of particle addition on the velocities of the gas phase is investigated. The development of
Comparison between Eulerian and Lagrangian Atmospheric Transport Models
NASA Astrophysics Data System (ADS)
Heinrich, P.; Grillon, Y.
2001-05-01
Two numerical atmospheric models are tested and compared both in backward and forward modes to study the transport and dispersion of radioactive gases in the framework of the Comprehensive Test Ban Treaty. The first one (LMDZ) has been developed at the Laboratoire de Meteorologie Dynamique in Paris,it calculates eulerian large-scale advection based upon finite-volume methods and parametrization of turbulent mixing and convection. The second one (HYSPLIT), developed by the Air Resources Laboratory of NOAA, is lagrangian and calculated 3D trajectories of particules, taking also into account dispersion due to wind shear. Concentrations of particules are compared at stations of the CTBT network for a fictitious source in the Pacific Ocean, that is assumed to be punctual in time and space. In the backward mode, concentrations are calculated and compared over 15 days from a point source at Tahiti to determine the field of regard for this station. Sensitivity tests are carried out by varying the spatial resolution of models.
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
NASA Technical Reports Server (NTRS)
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
NASA Technical Reports Server (NTRS)
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
Lagrangian Turbulence and Transport in Semi-enclosed Basins and Coastal Regions
2011-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Lagrangian Turbulence and Transport in Semi-enclosed...LONG-TERM GOALS The long-term goal of this project is the development and application of new methods of investigation for the use of Lagrangian ...data and other emerging in-situ and remote instruments (drifters, HF radar, gliders and satellite ) that provide information on upper ocean advection
Monitoring the Amazon plume northwestward transport along Lagrangian pathways
NASA Astrophysics Data System (ADS)
Fournier, Severine; Gaultier, Lucile; Vandemark, Douglas; Lee, Tong; Gierach, Michelle
2016-04-01
area. The objective of this study is to investigate the interannual variability in Amazon-Orinoco freshwater transport from the rivers' mouth northwestward over 2010-2014. We use a Lagrangian advection method to track the particles and follow their biophysical properties along their trajectory using measurements from Aquarius, SMOS, and Aqua MODIS. The pathways of the Amazon-Orinoco plume waters can therefore be analyzed and quantified, enabling an investigation of the biophysical processes associated with the Amazon River and Orinoco River freshwaters as they are advected from the river mouth to the open ocean. From one year to another, the amount of Amazon-Orinoco particles reaching the northwestern part of the plume is variable causing different physical and biogeochemical influences in the area. In 2011, a larger amount of particles reaches that area, the mechanisms responsible for this unusual northwestward transport of the shallow plume waters are under investigation, such as river discharge, advection, NBC rings. On the contrary, in 2014, fewer particles reach this northwestern area taking a more coastal pathway. This suggests a higher influence of the Orinoco River that year.
Parallel algorithms for semi-Lagrangian transport in global atmospheric circulation models
Drake, J.B.; Worley, P.H.; Michalakes, J.; Foster, I.T.
1995-02-01
Global atmospheric circulation models (GCM) typically have three primary algorithmic components: columnar physics, spectral transform, and semi-Lagrangian transport. In developing parallel implementations, these three components are equally important and can be examined somewhat independently. A two-dimensional horizontal data decomposition of the three-dimensional computational grid leaves all physics computations on processor, and the only efficiency issues arise in load balancing. A recently completed study by the authors of different approaches to parallelizing the spectral transform showed several viable algorithms. Preliminary results of an analogous study of algorithmic alternatives for parallel semi-Lagrangian transport are described here.
Lagrangian transport for two-dimensional deep-water surface gravity wave groups
NASA Astrophysics Data System (ADS)
van den Bremer, T. S.; Taylor, P. H.
2016-08-01
The Lagrangian trajectories of neutrally buoyant particles underneath surface gravity wave groups are dictated by two physical phenomena: the Stokes drift results in a net displacement of particles in the direction of propagation of the group, whereas the Eulerian return flow, as described by the multi-chromatic wave theory of Longuet-Higgins & Stewart (1962 J. Fluid Mech. 13, 481-504. (doi:10.1017/S0022112062000877)), transports such particles in the opposite direction. By pursuing a separation of scales expansion, we develop simple closed-form expressions for the net Lagrangian displacement of particles. By comparing the results from the separation of scales expansion at different orders in bandwidth, we study the effect of frequency dispersion on the local Lagrangian transport, which we show can be ignored for realistic sea states.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling.
Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F
2014-02-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations - such as missing the Lagrangian parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified Lagrangian" sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data
Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater
Ewing, R.E.; Wang, Hong
1996-12-31
In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling
Antweiler, Ronald C.; Writer, Jeffrey H.; Murphy, Sheila F.
2014-01-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations – such as missing the Lagrangian parcel by less than 1 h – can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed “verified Lagrangian” sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2–4 h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we
A Lagrangian stochastic model for aerial spray transport above an oak forest
Wang, Yansen; Miller, David R.; Anderson, Dean E.; McManus, Michael L.
1995-01-01
An aerial spray droplets' transport model has been developed by applying recent advances in Lagrangian stochastic simulation of heavy particles. A two-dimensional Lagrangian stochastic model was adopted to simulate the spray droplet dispersion in atmospheric turbulence by adjusting the Lagrangian integral time scale along the drop trajectory. The other major physical processes affecting the transport of spray droplets above a forest canopy, the aircraft wingtip vortices and the droplet evaporation, were also included in each time step of the droplets' transport.The model was evaluated using data from an aerial spray field experiment. In generally neutral stability conditions, the accuracy of the model predictions varied from run-to-run as expected. The average root-mean-square error was 24.61 IU cm−2, and the average relative error was 15%. The model prediction was adequate in two-dimensional steady wind conditions, but was less accurate in variable wind condition. The results indicated that the model can simulate successfully the ensemble; average transport of aerial spray droplets under neutral, steady atmospheric wind conditions.
NASA Astrophysics Data System (ADS)
Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory
2012-10-01
Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a Lagrangian Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat Eulerian and Lagrangian components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the Lagrangian approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.
Applying Dispersive Changes to Lagrangian Particles in Groundwater Transport Models
Konikow, L.F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative. ?? US Government 2010.
Applying dispersive changes to Lagrangian particles in groundwater transport models
Konikow, Leonard F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.
A modified Lagrangian-volumes method to simulate chemical transport in heterogeneous porous media
NASA Astrophysics Data System (ADS)
de Dreuzy, J.; Davy, P.
2008-12-01
Transport in subsurface environments is conditioned by physical and chemical processes in interaction, the most common being advection and dispersion for the physical processes and sorption for chemical reactions. Several numerical approaches have been developed to solve the complex set of equations governing this type of solute transport. These methods become time consuming in highly heterogeneous porous media having a broad-range velocity distribution. In this paper; we discuss a new efficient Lagrangian method. This method, modified from the Lagrangian-volumes approach, consists in dividing the aqueous phase in elementary volumes moved with the flow and interacting with the solid phase. Like in continuous time random walk algorithms, rather than keeping a constant time step, the time is adapted to the mesh velocity and computed so that an elementary volume crosses a mesh in a single numerical step. The modified Lagrangian-volume approach remains thus efficient whatever the velocity field. This approach is also highly flexible as it achieves a decoupling of the physical and chemical processes at the elementary volume scale, i.e. at the lowest considered scale, giving way to model virtually all possible chemical reactions. The modified Lagrangian volume approach can model both reactions between species in solution and sorption reactions. Reactions in solution are modeled by exchanges of solutes between Lagrangian volumes. For sorption reactions, the surface-to-volume ratio variability, a key parameter of sorption reactions, is accounted for by deforming the shape of the elementary volume. We implement and validate the algorithm on the specific case of the nonlinear Freundlich kinetic sorption in highly heterogeneous lognormal and multifractal permeability fields.
Lagrangian transport of water vapor and CFCs in a coupled Chemistry Climate Model
NASA Astrophysics Data System (ADS)
Hoppe, Charlotte; Müller, Rolf; Hoffmann, Lars; Konopka, Paul; Plöger, Felix; Grooß, Jens-Uwe
2013-04-01
We describe the implementation of a Lagrangian transport core in a chemistry climate model (CCM). Thereby we address the common problem of properly representing trace gas distributions in a classical Eulerian framework with a fixed model grid, particularly in regions with strong trace gas gradients. A prominent example is stratospheric water vapor, which is an important driver of surface climate change on decadal scales. In this case, the transport representation is particularly important in the tropical tropopause layer (TTL), where tropospheric air enters into the stratosphere. We have coupled the Chemical Lagrangian Model of the Stratosphere (CLaMS) with the ECHAM-MESSy Atmospheric Chemistry Model (EMAC). The latter includes the ECHAM5 climate model, and the MESSy interface, which allows for flexible coupling and switching between different submodels. The chemistry transport model CLaMS provides a fully Lagrangian transport representation to calculate constituent transport for an ensemble of air parcels that move along trajectories. To facilitate the calculation of long time-series a simplified chemistry scheme was implemented. Various studies show that the CLaMS model is particularly suited to properly represent dynamics and chemistry in the UT/LS region. The analysis of mean age of stratospheric air gives insight into the different transport characteristics of the Eulerian and the Lagrangian transport schemes. Mean age of air, calculated in both frameworks, is compared regarding the representation of important processes, i.e. descent in the polar vortex, upwelling in the tropical pipe, and isentropic in-mixing in subtropical regions. We also compared the zonal mean distributions and photochemical lifetimes of CFC-11 and CFC-12 with climatologies from different satellite experiments (ACE-FTS, HIRDLS, and MIPAS). CLaMS stratospheric water vapor distributions show remarkable differences compared to the stratospheric water vapor simulated by ECHAM, especially in
Lagrangian Tracer Transport and Dispersion in Shallow Tidal Inlets & River Mouths
2011-01-01
Tidal Inlets & River Mouths R. T. Guza & Falk Feddersen Scripps Institution of Oceanography La Jolla, CA 92093-0209 phone: (858) 534-0585 fax...our existing field capability in preparation for participation in the tidal inlet/river mouth DRI APPROACH Wave breaking occurs most of the time...AND SUBTITLE Lagrangian Tracer Transport and Dispersion in Shallow Tidal Inlets & River Mouths 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM
Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.
2014-09-01
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X_{⊥} /X_{∥} becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L^{2}_{∥}/X1L^{2}_{⊥} → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.
NASA Astrophysics Data System (ADS)
Rypina, Irina I.
The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust three-gyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the
A Lagrangian particle method with remeshing for tracer transport on the sphere
NASA Astrophysics Data System (ADS)
Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane
2017-07-01
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin-Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...
2017-03-30
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less
PTV measurements of Lagrangian particle transport by surface gravity wave groups
NASA Astrophysics Data System (ADS)
van den Bremer, Ton; Whittaker, Colin; Raby, Alison; Taylor, Paul
2015-11-01
We present detailed PTV (particle tracking velocimetry) measurements of the Lagrangian transport and trajectories of neutrally buoyant particles underneath two-dimensional surface gravity wave groups in a laboratory flume. By focussing our attention on wave groups of moderate steepness, we confirm the predictions of standard second-order multi-chromatic wave theory, in which the body of fluid satisfies the potential flow equations. Particles near the surface are transported forwards and their motion is dominated by Stokes drift. Particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for surface wave groups ensuring the (irrotational) mass balance holds. Finally, we provide experimental validation of a simple scaling relationship, derived based under the assumption of separation of scales, for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current. We present results for a range of effective water depths.
Refining finite-time Lyapunov exponent ridges and the challenges of classifying them.
Allshouse, Michael R; Peacock, Thomas
2015-08-01
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.
NASA Astrophysics Data System (ADS)
Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.
2010-11-01
This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, for reproducibility of tracer gas variation affected by near field around observation sites. The ability to resolve variability in atmospheric composition on an hourly time scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and upcoming space-based observations. The coupled model yields increased horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at two sites operated by the National Oceanic and Atmospheric Administration, USA and one site operated by National Institute for Environmental Studies, Japan. As the purpose of this study is limited to demonstration of the new modeling approach, we select a small subset of 3 sites to highlight use of the model in various geographical areas. To explore the capability of the coupled model in simulating synoptic-scale meteorological phenomena, we calculate the correlation coefficients and variance ratios between deseasonalized model-simulated and observed CO2 concentrations. Compared with the Eulerian model alone, the coupled model yields improved agreement between modeled and observed CO2 concentrations.
NASA Astrophysics Data System (ADS)
von Hobe, Marc; Konopka, Paul; Hoffmann, Lars; Griessbach, Sabine; Sumińska-Ebersoldt, Olga; Vernier, Jean-Paul; Plöger, Felix; Tao, Mengchu; Müller, Rolf
2015-04-01
Inverse methods have become widely used tools to infer sources and sinks of atmospheric constituents based on observations. Inversion techniques can also help to better constrain input and process parameters and thus improve the underlying models. While the majority of today's inverse model frameworks use the Eulerian concept of transport, the capability of Lagrangian inversion to infer emissions of even ill constrained sources has been demonstrated (e.g. Stohl et al., 2011). We will discuss Lagrangian inverse modelling as a powerful tool to solve problems on a wide range of scales in terms of spatial and temporal extent as well as complexity. First, two distinct applications on different scales will be presented: i) the retrieval of reaction rates that govern the chlorine catalyzed ozone destruction in the polar winter along individual trajectories connecting airborne observations in the Arctic in 2010, and ii) the derivation of emission altitudes and transport pathways of sulfate aerosol from the 2011 eruption of the Nabro volcano using CALIPSO satellite observations. Second, the potential and requirements for applications at even higher complexity, e.g. simultaneously retrieval of source, sink and process parameters on a global scale, will be explored. Stohl, A., et al. 2011. Atmospheric Chemistry and Physics 11, 4333-4351.
NASA Astrophysics Data System (ADS)
Arnold, S. R.; Chipperfield, M. P.; O'Connor, F. M.; Methven, J.; Law, K. S.; Pyle, J. A.
The transport of pollutants and pollutant precursors from the continental boundary layer to the mid/upper troposphere has been recognised for some time as being po- tentially critical for the photochemistry of this region. Rapid transport by convective systems can transport fresh boundary layer air to the UT in a matter of hours. The ozone production potential of an uplifted air mass may continue to be significant as it is transported far away from its PBL source, due to the increased lifetimes of ozone precursors in the free troposphere. An understanding of the mechanisms which trans- fer boundary layer air to the free troposphere, and the subsequent chemical and mixing processes acting on this air, is therefore vital in order to gain an understanding of the ozone budget of the UT region. Here we use a Lagrangian chemistry transport model (CiTTyCAT) to investigate the chemistry of air masses observed during the NERC supported EXPORT (European eXport of Precursors of Ozone by long-Range Transport) and ACTO (Atmospheric Chemistry and Transport of Ozone) campaigns. The model uses 3 dimensional tra- jectories calculated from large-scale winds output from the ECMWF. The chemical model is initialised using 3D global fields from the TOMCAT CTM, and comprises 80 species and over 200 gas-phase reactions. Surface emissions and deposition pro- cesses are included along the trajectories. The main advantage of the Lagrangian method is the ability to follow individual air masses and study the evolution of chemistry in air masses which have been uplifted by different transport events. The lack of sub-grid transport processes (convection, tur- bulent mixing) in the Lagragian advection has allowed the identification of observed air masses where these processes appear to be important. The relative importance of mixing processes has been derived from tracer correlations in the campaign data. The Lagrangian model allows mixing to be investigateded in a controlled fashion and its 1
NASA Astrophysics Data System (ADS)
Banisch, Ralf; Koltai, Péter
2017-03-01
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a method for extracting coherent sets from possibly sparse Lagrangian trajectory data. Our method can be seen as an extension of diffusion maps to trajectory space, and it allows us to construct "dynamical coordinates," which reveal the intrinsic low-dimensional organization of the data with respect to transport. The only a priori knowledge about the dynamics that we require is a locally valid notion of distance, which renders our method highly suitable for automated data analysis. We show convergence of our method to the analytic transfer operator framework of coherence in the infinite data limit and illustrate its potential on several two- and three-dimensional examples as well as real world data.
Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame
Jobson, Harvey E.
1980-01-01
A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)
NASA Astrophysics Data System (ADS)
Koyama, Y.; Maksyutov, S.; Mukai, H.; Thoning, K.; Tans, P.
2011-04-01
This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, to improve the reproducibility of tracer-gas variations affected by the near-field surface emissions and transport around observation sites. The ability to resolve variability in atmospheric composition on an hourly time-scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and from upcoming space-based observations. The coupled model yields an increase in the horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling computationally efficient global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO2 concentrations with continuous observations at three sites: two operated by the National Oceanic and Atmospheric Administration, USA, and one operated by the National Institute for Environmental Studies, Japan. As the goal of this study is limited to introducing the new modeling approach, we selected a transport simulation at these three sites to demonstrate how the model may perform at various geographical areas. The coupled model provides improved agreement between modeled and observed CO2 concentrations in comparison to the Eulerian model. In an area where variability in CO2 concentration is dominated by a fossil fuel signal, the correlation coefficient between modeled and observed concentrations increases by between 0.05 to 0.1 from the original values of 0.5-0.6 achieved with the Eulerian model.
Lagrangian and Eulerian Methods for the Identification of Water Vapour Sources and Transport
NASA Astrophysics Data System (ADS)
Sodemann, H.; Schwierz, C.; Wernli, H.
2006-12-01
Diagnostics of the hydrological cycle are an important component of detection and attribution of climate variability. The hydrological cycle is a key component of the climate system, but due to the scale of evaporation and condensation processes, NWP models rely heavily on parameterizations. Evaluations of reanalysis datasets show biases of the hydrological cycle that are created during data assimilation, rendering these data one of the less reliable components of reanalysis products. We present two novel approaches to identify the sources and transport paths of atmospheric water vapor from analysis or reanalysis data, one of Lagrangian, and one of Eulerian nature. The Lagrangian method is based on back-trajectories, and diagnoses the evaporative sources of water vapor in high spatial detail. The method is exemplified with an examination of the inter-annual variability of the moisture sources for winter-time precipitation in Greenland, and the seasonality of the moisture sources for Alpine precipitation, based on ECMWF's ERA-40 reanalysis data. The Eulerian method makes use of a regional climate model that has been fitted with a mass-conservative water vapor tracer. This provides a novel possibility to evaluate the representation of the model's hydrological cycle in detail, and on a regional scale. The capabilities of the Eulerian method are exemplified with an identification of the moisture sources of the August 2002 flood, one of the strongest flood events in Central Europe in recent decades. A comparison of the two method indicates different preferential areas of application: the Lagrangian method being more suitable for gaining a large-scale picture, while the Eulerian method could provide detailed process understanding and be useful for NWP model evaluation. This in turn implies that a complementary view could potentially be gained when using such methods for evaluation purposes in combination with new observational data of the atmospheric hydrological cycle.
Finite-time braiding exponents
NASA Astrophysics Data System (ADS)
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.
NASA Astrophysics Data System (ADS)
Hoffmann, L.; Rößler, T.; Griessbach, S.; Heng, Y.; Stein, O.
2016-05-01
Sulfur dioxide (SO2) emissions from strong volcanic eruptions are an important natural cause for climate variations. We applied our new Lagrangian transport model Massive-Parallel Trajectory Calculations to perform simulations for three case studies of volcanic eruption events. The case studies cover the eruptions of Grímsvötn, Iceland, Puyehue-Cordón Caulle, Chile, and Nabro, Eritrea, in May and June 2011. We used SO2 observations of the Atmospheric Infrared Sounder (AIRS/Aqua) and a backward trajectory approach to initialize the simulations. Besides validation of the new model, the main goal of our study was a comparison of simulations with different meteorological data products. We considered three reanalyses, i.e., ERA-Interim, Modern-Era Retrospective Analysis for Research and Applications (MERRA), and National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Reanalysis Project as well as the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis. Qualitatively, the SO2 distributions from the simulations compare well not only with the AIRS data but also with Cloud-Aerosol Lidar with Orthogonal Polarization and Michelson Interferometer for Passive Atmospheric Sounding aerosol observations. Transport deviations and the critical success index (CSI) are analyzed to evaluate the simulations quantitatively. During the first 5 or 10 days after the eruptions we found the best performance for the ECMWF analysis (CSI range of 0.25-0.31), followed by ERA-Interim (0.25-0.29), MERRA (0.23-0.27), and NCAR/NCEP (0.21-0.23). High temporal and spatial resolution of the meteorological data does lead to improved performance of Lagrangian transport simulations of volcanic emissions in the upper troposphere and lower stratosphere.
NASA Astrophysics Data System (ADS)
Tarshish, Nathaniel; Abernathey, Ryan; Dufour, Carolina; Frenger, Ivy; Griffies, Stephen
2017-04-01
Transient ocean mesoscale fluctuations play a central role in the global climate system, transporting climate relevant tracers such as heat and carbon. In satellite observations and numerical simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on Eulerian identification methods, in which vortices are identified by selecting closed contours of Eulerian fields (e.g. sea surface height, or the Okubo-Weiss parameter) that satisfy geometric criteria and anomaly thresholds. In contrast, recent studies employ Lagrangian analysis of virtual particle trajectories initialized within the selected Eulerian contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the Eulerian field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between Eulerian and Lagrangian analyses for the detection of vortices. To do so, we use GFDL's CM2.6 coupled climate model with 5-10km horizontal grid spacing. We identify coherent vortices in CM2.6 by implementing the Rotationally Coherent Lagrangian Vortex (RCLV) framework, which recently emerged from dynamical systems theory. This approach involves the numerical advection of millions of Lagrangian particles and guarantees material coherence by construction. We compute the statistics, spatial distribution, and lifetimes of coherent vortices in addition to calculating the associated mass and tracer transports. We offer compelling evidence that Eulerian vortex methods are poorly suited to answer questions of mass and tracer transport.
NASA Astrophysics Data System (ADS)
Weinzierl, B.; Sauer, D. N.; Walser, A.; Dollner, M.; Reitebuch, O.; Gross, S.; Chouza, F.; Ansmann, A.; Toledano, C.; Freudenthaler, V.; Kandler, K.; Schäfler, A.; Baumann, R.; Tegen, I.; Heinold, B.
2014-12-01
Aerosol particles are regularly transported over long distances impacting air quality, health, weather and climate thousands of kilometers downwind of the source. During transport, particle properties are modified thereby changing the associated impact on the radiation budget. Although mineral dust is of key importance for the climate system many questions such as the change of the dust size distribution during long-range transport, the role of wet and dry removal mechanisms, and the complex interaction between mineral dust and clouds remain open. In June/July 2013, the Saharan Aerosol Long-range Transport and Aerosol-Cloud-Interaction Experiment (SALTRACE: http://www.pa.op.dlr.de/saltrace) was conducted to study the transport and transformation of Saharan mineral dust. Besides ground-based lidar and in-situ instruments deployed on Cape Verde, Barbados and Puerto Rico, the DLR research aircraft Falcon was equipped with an extended aerosol in-situ instrumentation, a nadir-looking 2-μm wind lidar and instruments for standard meteorological parameters. During SALTRACE, five large dust outbreaks were studied by ground-based, airborne and satellite measurements between Senegal, Cape Verde, the Caribbean, and Florida. Highlights included the Lagrangian sampling of a dust plume in the Cape Verde area on 17 June which was again measured with the same instrumentation on 21 and 22 June 2013 near Barbados. Between Cape Verde and Barbados, the aerosol optical thickness (500 nm) decreased from 0.54 to 0.26 and the stratification of the dust layers changed significantly from a rather homogenous structure near Africa to a 3-layer structure with embedded cumulus clouds in the Caribbean. In the upper part of the dust layers in the Caribbean, the aerosol properties were similar to the observations near Africa. In contrast, much more variability in the dust properties was observed between 0.7 and 2.5 km altitude probably due to interaction of the mineral dust with clouds. In our
Applications of Lagrangian Particle Transport Modeling in the Top-Down Regional CO2 Studies
NASA Astrophysics Data System (ADS)
Uliasz, M.; Denning, S.; Lu, L.; Corbin, K.; Zupanski, D.; Miles, N.; Richardson, S.; Davis, K. J.
2007-12-01
Atmospheric transport plays a critical role in top-down studies where observations from towers and/or aircraft are inverted to estimate net sources and sinks of CO2 for the study area over short periods of time. Lagrangian particle dispersion models are well suited for this modeling task since they 1) can be easily linked to any regional scale meteorological model, 2) can be run both forward or backward in time (in an adjoint mode), 3) can accurately resolve any CO2 observational system without limits of gridded transport models, and 4) can be applied to different spatial scales even across grids or domains of meteorological models. In the modeling framework developed at CSU, the Lagrangian Particle Dispersion Model is linked to SiB-RAMS: Regional Atmospheric Modeling System combined with Simple Biosphere model. For our North America studies the SiB-RAMS domain extends over the entire continental US with nested grids centered in the mesoscale area of interest. The CO2 lateral boundary conditions are provided by a global transport model - PCTM (Parameterized Chemistry and Transport Model). Influence functions derived from the LPDM output allow us to quantify each CO2 data point (e.g., concentration at a specific sampling time and tower) in terms of contributions from different sources: 1) surface fluxes, 2) inflow fluxes across domain boundaries and 2) initial CO2 concentration in the domain at the beginning of the analysis period. The surface contributions can be furher quantified by a physical process (respiration, assimilation or fossil fuel emission) and/or land cover type. Therefore, the influence function approach is very useful for interpretation of CO2 observations and source apportionment, designing tower network and, finally, deriving source-receptor information for the inverse studies. We are going to review our modeling efforts based on the SiB-RAMS/ LPDM and the influence function approach to the meso- regional scales from a few tens to several
Local finite time Lyapunov exponent, local sampling and probabilistic source and destination regions
NASA Astrophysics Data System (ADS)
BozorgMagham, A. E.; Ross, S. D.; Schmale, D. G., III
2015-05-01
The time-varying finite time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge between the powerful concept of FTLE and (local) field experiments. In this paper a new interpretation of the local FTLE, the time series of a FTLE field at a fixed location, is proposed. This concept can practically assist in field experiments where samples are collected at a fixed location and it is necessary to attribute long distance transport phenomena and location of source points to the characteristic variation of the sampled particles. Also, results of this study have the potential to aid in planning of optimal local sampling of passive particles for maximal diversity monitoring of assemblages of microorganisms. Assuming a deterministic flow field, one can use the proposed theorem to (i) estimate the differential distances between the source (or destination) points of the collected (or released) particles when consecutive sampling (or releasing) is performed at a fixed location, (ii) estimate the local FTLE as a function of known differential distances between the source (or destination) points. In addition to the deterministic flows, the more realistic case of unresolved turbulence and low resolution flow data that yield the probabilistic source (or destination) regions are studied. It is shown that similar to deterministic flows, Lagrangian coherent structures (LCS) separate probabilistic source (or destination) regions corresponding to consecutive collected (or released) particles.
Turbidity Current Transport using DEM and FEM: a Hybrid Lagrangian-Eulerian Approach
NASA Astrophysics Data System (ADS)
Alves, J. L.; Guevara, N. O., Jr.; Silva, C. E.; Alves, F. T.; Gazoni, L. C.; Coutinho, A.; Camata, J.; Elias, R. N.; Paraizo, P.
2013-05-01
In this work we describe a contribution to the study of turbidity transport in scales smaller than TFM (two-fluid models), The intent of the work, part of a large scale simulation project, is to assess local, small scale parameters and their upscaling. The hybrid model is based on a Lagrangian-Eulerian approach under a class of the so called Unresolved Discrete Particle Method (UDPM). In this approach, a Lagrangian description is used for the particle system employing the Discrete Element Method (DEM) while a fixed Eulerian mesh is used for the fluid phase modeled by finite element method (FEM), Fluid motion is governed by Navier-Stokes equations which are solved by an appropriate FEM implementation. Closure equation are used to compute drag and lift forces over the particles in the DEM framework. Volume averaged momentum sink terms are included in the fluid equations. The resulting coupled DEM-FEM model is integrated in time with a subcycling scheme. The aforementioned scheme was applied in the simulation of a sedimentation basin as depicted in figures 1 and 2 to investigate flow and deposition features of the suspension in a finer scale. For this purpose a submodel of the basin was generated. Mapping variables back and forth the Eulerian (finite element) model and the Lagrangian (discrete element) model were performed during the subcycled integration of the hybrid model. References: [1] Hoomans, B.P.B., Kuipers, J.A.M., Swaaij, van W.P.M," Granular dynamics Simulation of segregation phenomena in bubbling gas-fluidised beds", Powder Technology, V 109, Issues 1-3, 3 April 2000, pp 41-48; [2] Cho, S.H., Choi,H.G, Yoo, J.Y.,"Direct numerical simulation of fluid flow laden with many particles", International Journal of Multiphase Flow, V 31, Issue 4, April 2005, pp 435-451;; Sedimentation basin: sectioning the turbidity plume in the Eulerian FE model for setting up the discrete particle model. ; Sedimentation Basin: section of the turbidity plume displaying the
Lagrangian Turbulence and Transport in Semi-Enclosed Basins and Coastal Regions
2003-09-30
involved in the application of the assimilation methods ; Leonid Piterbarg (USC) in the mathematical formulation of the method; Milena Veneziani (RSMAS...MPO) in the analysis of Lagrangian data; Mike Chin (RSMAS/MPO) in the comparison of the assimilation methods . WORK COMPLETED 1) Application of...Lagrangian statistics even in presence of coherent structures. TRANSITIONS Lagrangian data assimilation methods are planned to be used in the
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-02-01
Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is proposed and applied to find out the origin of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima-derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the 11 March 2011 tsunami that caused heavy damage of the Fukushima Nuclear Power Plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of 134Cs and 137Cs concentrations collected during two research vessel (R/V) cruises in June and July 2011 in the large area of the northwest Pacific (Kaeriyama et al., 2013; Buesseler et al., 2012). It is shown that Lagrangian simulations are useful for finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters that were deployed in the area.
CFD Lagrangian Modeling of Water Droplet Transport for ISS Hygiene Activity Application
NASA Technical Reports Server (NTRS)
Son, Chang H.
2013-01-01
The goal of this study was to assess the impacts of free water propagation in the Waste and Hygiene Compartment (WHC) installed in Node 3. Free water can be generated inside the WHC in small quantities due to crew hygiene activity. To mitigate potential impact of free water in Node 3 cabin the WHC doorway is enclosed by a waterproof bump-out, Kabin, with openings at the top and bottom. At the overhead side of the rack, there is a screen that prevents large drops of water from exiting. However, as the avionics fan in the WHC causes airflow toward the deck side of the rack, small quantities of free water may exit at the bottom of the Kabin. A Computational Fluid Dynamics (CFD) analysis of Node 3 cabin airflow enable identifying the paths of water transport. To simulate the droplet transport the Lagrangian discrete phase approach was used. Various initial droplet distributions were considered in the study. The droplet diameter was varied in the range of 5-20 mm. The results of the computations showed that most of the drops fall to the rack surface not far from the WHC curtain.
Modeling coupled nanoparticle aggregation and transport in porous media: A Lagrangian approach
NASA Astrophysics Data System (ADS)
Taghavy, Amir; Pennell, Kurt D.; Abriola, Linda M.
2015-01-01
Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an Eulerian modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general Lagrangian modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and Eulerian modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media.
NASA Astrophysics Data System (ADS)
Prants, Sergey V.; Budyansky, Maxim V.; Uleysky, Michael Yu.
2017-02-01
Northward near-surface Lagrangian transport of subtropical waters in the Japan Sea frontal zone is simulated and analysed based on altimeter data for the period from 2 January 1993 to 15 June 2015. Computing different Lagrangian indicators for a large number of synthetic tracers launched weekly for 21 years in the southern part of the Sea, we find preferred transport pathways across the Subpolar Front. This cross-frontal transport is statistically shown to be meridionally inhomogeneous with gates
and barriers
whose locations are determined by the local advection velocity field. The gates open
due to suitable dispositions of mesoscale eddies facilitating propagation of subtropical waters to the north. It is documented for the western, central and eastern gates with the help of different kinds of Lagrangian maps and verified by some tracks of available drifters. The transport through the gates occurs by a portion-like manner, i.e. subtropical tracers pass the gates in specific places and during specific time intervals. There are some forbidden
zones in the frontal area where the northward transport has not been observed during all the observation period. They exist due to long-term peculiarities of the advection velocity field.
Examining Lagrangian surface transport during a coastal upwelling in the Gulf of Finland, Baltic Sea
NASA Astrophysics Data System (ADS)
Delpeche-Ellmann, Nicole; Mingelaitė, Toma; Soomere, Tarmo
2017-07-01
We employ in-situ surface drifters and satellite derived sea surface temperature data to examine the impact that an upwelling event may have on mixing and Lagrangian transport of surrounding surface waters. The test area is located near the southern coast of the Gulf of Finland where easterly winds are known to trigger intense coastal upwellings. The analysis is based on the comparison of motions of three drifters that follow the currents in the uppermost layer with a thickness of 2 m with MODIS-based sea surface temperature data and high-quality open sea wind time series. The presence of an upwelling event superseded the classic Ekman-type drift of the surface layer and considerably slowed down the average speed of surface currents in the region affected by the upwelled cold water jet and its filaments. The drifters tended to stay amidst the surrounding surface waters. The properties of mixing were evaluated using the daily rate of temperature change along several transects. The upwelled cooler water largely kept its identity during almost the entire duration of the upwelling event. Intense mixing started at a later stage of the upwelling and continued after the end of the event when the winds that have driven the entire process began to subside.
Parameterizing Urban Canopy Layer transport in an Lagrangian Particle Dispersion Model
NASA Astrophysics Data System (ADS)
Stöckl, Stefan; Rotach, Mathias W.
2016-04-01
The percentage of people living in urban areas is rising worldwide, crossed 50% in 2007 and is even higher in developed countries. High population density and numerous sources of air pollution in close proximity can lead to health issues. Therefore it is important to understand the nature of urban pollutant dispersion. In the last decades this field has experienced considerable progress, however the influence of large roughness elements is complex and has as of yet not been completely described. Hence, this work studied urban particle dispersion close to source and ground. It used an existing, steady state, three-dimensional Lagrangian particle dispersion model, which includes Roughness Sublayer parameterizations of turbulence and flow. The model is valid for convective and neutral to stable conditions and uses the kernel method for concentration calculation. As most Lagrangian models, its lower boundary is the zero-plane displacement, which means that roughly the lower two-thirds of the mean building height are not included in the model. This missing layer roughly coincides with the Urban Canopy Layer. An earlier work "traps" particles hitting the lower model boundary for a recirculation period, which is calculated under the assumption of a vortex in skimming flow, before "releasing" them again. The authors hypothesize that improving the lower boundary condition by including Urban Canopy Layer transport could improve model predictions. This was tested herein by not only trapping the particles, but also advecting them with a mean, parameterized flow in the Urban Canopy Layer. Now the model calculates the trapping period based on either recirculation due to vortex motion in skimming flow regimes or vertical velocity if no vortex forms, depending on incidence angle of the wind on a randomly chosen street canyon. The influence of this modification, as well as the model's sensitivity to parameterization constants, was investigated. To reach this goal, the model was
Kim, Cheol-Hee; Song, Chang-Keun; Lee, Sang-Hyun; Song, Sang-Keun
2008-10-01
In order to simulate the impact of mesoscale wind fields and to assess potential capability of atmospheric Lagrangian particle dispersion model (LPDM) as an emergency response model for the decision supports, two different simulations of LPDM with the mesoscale prognostic model MM5 (Mesoscale Model ver. 5) were driven. The first simulation of radioactive noble gas (85Kr exponent) emitted during JCO accident occurred from 30 September to 3 October 1999 at Tokai, Japan showed that the first arriving short pulse was found in Tsukuba located at 60 km away from the accidental area. However, the released radioactive noble gas was transported back to the origin site about 2 days later due to the mesoscale meteorological wind circulation, enhancing the levels of 85Kr with the secondary peak in Tsukuba. The second simulation of atmospheric dilution factors (the ratio of concentration to the emission rate, chi/Q), during the underground nuclear test (UNT) performed by North Korea showed that high chi/Q moved to the eastward and extended toward southward in accordance with the mesoscale atmospheric circulations generated by mesoscale prognostic model MM5. In comparison with the measurements, the simulated horizontal distribution patterns of 85Kr during the JCO are well accord with that of observation in Tsukuba such as the existence of secondary peak which is associated with the mesoscale circulations. However, the simulated level of 85Kr anomaly was found to be significantly lower than the observations, and some interpretations on these discrepancies were described. Applications of LPDM to two mesoscale emergency response dispersion cases suggest the potential capability of LPDM to be used as a decision support model provided accurate emission rate of accident in case of a large accident.
Gao, Xi; Kong, Bo; Vigil, R Dennis
2017-01-01
A comprehensive quantitative model incorporating the effects of fluid flow patterns, light distribution, and algal growth kinetics on biomass growth rate is developed in order to predict the performance of a Taylor vortex algal photobioreactor for culturing Chlorella vulgaris. A commonly used Lagrangian strategy for coupling the various factors influencing algal growth was employed whereby results from computational fluid dynamics and radiation transport simulations were used to compute numerous microorganism light exposure histories, and this information in turn was used to estimate the global biomass specific growth rate. The simulations provide good quantitative agreement with experimental data and correctly predict the trend in reactor performance as a key reactor operating parameter is varied (inner cylinder rotation speed). However, biomass growth curves are consistently over-predicted and potential causes for these over-predictions and drawbacks of the Lagrangian approach are addressed.
Application of a Lagrangian transport model to organo-mineral aggregates within the Nazaré canyon
NASA Astrophysics Data System (ADS)
Pando, S.; Juliano, M.; Garcia, R.; Mendes, P. A. de Jesus; Thomsen, L.
2013-01-01
In this study, a hydrodynamic model was applied to the Nazaré submarine canyon with boundary forcing provided by an operational forecast model for the West Iberian coast. After validation, a Lagrangian transport model was coupled to the hydrodynamic model to study the transport patterns of the organo-mineral aggregates along the Nazaré canyon comparing three different classes of organo-mineral aggregates. The results showed that the transport in the canyon is neither constant, nor unidirectional and that there are preferential areas where suspended matter is resuspended, transported and deposited. The results showed that the transport of the larger size classes of organo-mineral aggregates is less pronounced, and that there is a decrease in the phytodetrital carbon flux along the canyon. The Nazaré canyon acts as depocenter of sedimentary organic matter and the canyon is not a conduit of organo-mineral aggregates to the deep sea.
GPU and APU computations of Finite Time Lyapunov Exponent fields
NASA Astrophysics Data System (ADS)
Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros
2012-03-01
We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
NASA Astrophysics Data System (ADS)
Hittmeir, Sabine; Philipp, Anne; Seibert, Petra
2017-04-01
In discretised form, an extensive variable usually represents an integral over a 3-dimensional (x,y,z) grid cell. In the case of vertical fluxes, gridded values represent integrals over a horizontal (x,y) grid face. In meteorological models, fluxes (precipitation, turbulent fluxes, etc.) are usually written out as temporally integrated values, thus effectively forming 3D (x,y,t) integrals. Lagrangian transport models require interpolation of all relevant variables towards the location in 4D space of each of the computational particles. Trivial interpolation algorithms usually implicitly assume the integral value to be a point value valid at the grid centre. If the integral value would be reconstructed from the interpolated point values, it would in general not be correct. If nonlinear interpolation methods are used, non-negativity cannot easily be ensured. This problem became obvious with respect to the interpolation of precipitation for the calculation of wet deposition FLEXPART (http://flexpart.eu) which uses ECMWF model output or other gridded input data. The presently implemented method consists of a special preprocessing in the input preparation software and subsequent linear interpolation in the model. The interpolated values are positive but the criterion of cell-wise conservation of the integral property is violated; it is also not very accurate as it smoothes the field. A new interpolation algorithm was developed which introduces additional supporting grid points in each time interval with linear interpolation to be applied in FLEXPART later between them. It preserves the integral precipitation in each time interval, guarantees the continuity of the time series, and maintains non-negativity. The function values of the remapping algorithm at these subgrid points constitute the degrees of freedom which can be prescribed in various ways. Combining the advantages of different approaches leads to a final algorithm respecting all the required conditions. To
Lagrangian Flow Network approach to an open flow model
NASA Astrophysics Data System (ADS)
Ser-Giacomi, Enrico; Rodríguez-Méndez, Víctor; López, Cristóbal; Hernández-García, Emilio
2017-06-01
Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this methodology to open chaotic flows, and check it with numerical results for a model open flow, namely a jet with a localized wave perturbation. We find that network nodes with high values of out-degree and of finite-time entropy in the forward-in-time direction identify the location of the chaotic saddle and its stable manifold, whereas nodes with high in-degree and backwards finite-time entropy highlight the location of the saddle and its unstable manifold. The cyclic clustering coefficient, associated to the presence of periodic orbits, takes non-vanishing values at the location of the saddle itself.
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
NASA Astrophysics Data System (ADS)
Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel
2017-01-01
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and
Speetjens, M. F. M.; Demissie, E. A.; Metcalfe, G.; Clercx, H. J. H.
2014-11-15
Laminar mixing by the inline-mixing principle is a key to many industrial fluids-engineering systems of size extending from micrometers to meters. However, insight into fundamental transport phenomena particularly under the realistic conditions of three-dimensionality (3D) and fluid inertia remains limited. This study addresses these issues for inline mixers with cylindrical geometries and adopts the Rotated Arc Mixer (RAM) as a representative system. Transport is investigated from a Lagrangian perspective by identifying and examining coherent structures that form in the 3D streamline portrait. 3D effects and fluid inertia introduce three key features that are not found in simplified configurations: transition zones between consecutive mixing cells of the inline-mixing flow; local upstream flow (in certain parameter regimes); transition/inertia-induced breaking of symmetries in the Lagrangian equations of motion (causing topological changes in coherent structures). Topological considerations strongly suggest that there nonetheless always exists a net throughflow region between inlet and outlet of the inline-mixing flow that is strictly separated from possible internal regions. The Lagrangian dynamics in this region admits representation by a 2D time-periodic Hamiltonian system. This establishes one fundamental kinematic structure for the present class of inline-mixing flows and implies universal behavior in that all states follow from the Hamiltonian breakdown of one common integrable state. A so-called period-doubling bifurcation is the only way to eliminate transport barriers originating from this state and thus is a necessary (yet not sufficient) condition for global chaos. Important in a practical context is that a common simplification in literature, i.e., cell-wise fully-developed Stokes flow (“2.5D approach”), retains these fundamental kinematic properties and deviates from the generic 3D inertial case only in a quantitative sense. This substantiates its
Finite time stabilization of delayed neural networks.
Wang, Leimin; Shen, Yi; Ding, Zhixia
2015-10-01
In this paper, the problem of finite time stabilization for a class of delayed neural networks (DNNs) is investigated. The general conditions on the feedback control law are provided to ensure the finite time stabilization of DNNs. Then some specific conditions are derived by designing two different controllers which include the delay-dependent and delay-independent ones. In addition, the upper bound of the settling time for stabilization is estimated. Under fixed control strength, discussions of the extremum of settling time functional are made and a switched controller is designed to optimize the settling time. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.
A particle number conserving Lagrangian method for mixing-driven reactive transport
NASA Astrophysics Data System (ADS)
Bolster, Diogo; Paster, Amir; Benson, David A.
2016-02-01
The purely Lagrangian algorithm for chemical reactions introduced by Benson and Meerschaert (2008) suffers from a low-concentration resolution problem. We alleviate the problem by redefining the probabilistic collision/reaction (birth/death) stochastic process as a mass-reduction operation. Theoretically, this corresponds to replacing an on/off particle with a large number of "subparticles" and tracking the number fraction. The new particle reaction process maintains the original particle numbers but adjusts each particle's mass upon reaction. Several simulations show the veracity as well as the gains in low-concentration resolution offered by the algorithm. We also compare the results to those obtained by a traditional finite difference model with suitably defined initial condition, demonstrating that the Lagrangian models match these.
NASA Astrophysics Data System (ADS)
Sato, Tatsuhiro; Tomiyama, Tomoe; Morita, Toyohisa; Murata, Tomohiro
We propose a method for solving the crew rescheduling problem (CRP) and the vehicle rescheduling problem (VRP) based on the Lagrangian relaxation method. The CRP/VRP is formulated as an integer programming problem on the basis of a network flow modeling approach from which a Lagrangian relaxation problem is constructed by relaxing the constraint that links multiple resources. Using two procedures that generate the upper and lower bounds of the primal problem, both of which utilize an efficient shortest path algorithm for the directed acyclic graph (DAG), the proposed method gradually improves the gap between the upper and lower bounds while updating Lagrangian multipliers. Experimental results of real-world vehicle rescheduling data from Japanese railway lines indicated that the proposed method generated feasible solutions that were confirmed to be fairly close to the optimal solutions according to the gap between the upper and lower bounds, and also clarified the quality of the other method's solution by using the gap, which could lead to streamlining and sophisticating real-world rescheduling related activities.
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current-induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide-induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection-dispersion equation in which the convective velocity is the Eulerian residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long-term transport phenomena are closely related to the Lagrangian residual current or the Lagrangian residual transport. In this paper a new formulation of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection-dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first-order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes drift). The remaining dispersion terms are important only in higher-order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment
NASA Astrophysics Data System (ADS)
Cimorelli, L.; Cozzolino, L.; D'Aniello, A.; Morlando, F.; Pianese, D.; Singh, V. P.
2016-07-01
In this paper, a new numerical model for the simulation of constituent transport in both steady and unsteady flow conditions is presented. The transport model is a routing procedure in which the advection process is solved by means of the Lagrangian coordinate transformation, while the dispersion process is approximated within each time step by means of the convolution principle, exploiting a multilinear procedure. In order to facilitate the application of the Lagrangian coordinate transformation during unsteady flow conditions, the unsteady velocity field corresponding to the linearized parabolic approximation of the Saint Venant Equations is provided, taking into account appropriate boundary conditions. Finally, classic BOD-DO relationships are embedded into the routing procedure in order to perform water quality applications with reactive constituents. The model is first demonstrated with respect to a numerical water quality model in both steady and unsteady hydraulic conditions, and is then applied to two real-world cases. Because of its characteristics, the proposed model seems suitable for real time forecast of pollutant concentrations when an emergency event occurs, or for water quality management in real rivers.
NASA Astrophysics Data System (ADS)
Forster, Caroline; Cooper, Owen; Stohl, Andreas; Eckhardt, Sabine; James, Paul; Dunlea, Edward; Nicks, Dennis K.; Holloway, John S.; Hübler, Gerd; Parrish, David D.; Ryerson, Tom B.; Trainer, Michael
2004-04-01
On the basis of Lagrangian tracer transport simulations this study presents an intercontinental transport climatology and tracer forecasts for the Intercontinental Transport and Chemical Transformation 2002 (ITCT 2K2) aircraft measurement campaign, which took place at Monterey, California, in April-May 2002 to measure Asian pollution arriving at the North American West Coast. For the climatology the average transport of an Asian CO tracer was calculated over a time period of 15 years using the particle dispersion model FLEXPART. To determine by how much the transport from Asia to North America during ITCT 2K2 deviated from the climatological mean, the 15-year average for April and May was compared with the average for April and May 2002 and that for the ITCT 2K2 period. It was found that 8% less Asian CO tracer arrived at the North American West Coast during the ITCT 2K2 period compared to the climatological mean. Below 8-km altitude, the maximum altitude of the research aircraft, 13% less arrived. Nevertheless, pronounced layers of Asian pollution were measured during 3 of the 13 ITCT 2K2 flights. FLEXPART was also successfully used as a forecasting tool for the flight planning during ITCT 2K2. It provided 3-day forecasts for three different anthropogenic CO tracers originating from Asia, North America, and Europe. In two case studies the forecast abilities of FLEXPART are analyzed and discussed by comparing the forecasts with measurement data and infrared satellite images. The model forecasts underestimated the measured CO enhancements by about a factor of 4, mainly because of an underestimation of the Asian emissions in the emission inventory and because of biomass-burning influence that was not modeled. Nevertheless, the intercontinental transport and dispersion of pollution plumes were qualitatively well predicted, and on the basis of the model results the aircraft could successfully be guided into the polluted air masses.
NASA Astrophysics Data System (ADS)
Danesh-Yazdi, Mohammad; Botter, Gianluca; Foufoula-Georgiou, Efi
2017-05-01
Lack of hydro-bio-chemical data at subcatchment scales necessitates adopting an aggregated system approach for estimating water and solute transport properties, such as residence and travel time distributions, at the catchment scale. In this work, we show that within-catchment spatial heterogeneity, as expressed in spatially variable discharge-storage relationships, can be appropriately encapsulated within a lumped time-varying stochastic Lagrangian formulation of transport. This time (variability) for space (heterogeneity) substitution yields mean travel times (MTTs) that are not significantly biased to the aggregation of spatial heterogeneity. Despite the significant variability of MTT at small spatial scales, there exists a characteristic scale above which the MTT is not impacted by the aggregation of spatial heterogeneity. Extensive simulations of randomly generated river networks reveal that the ratio between the characteristic scale and the mean incremental area is on average independent of river network topology and the spatial arrangement of incremental areas.
NASA Astrophysics Data System (ADS)
Doisneau, François; Arienti, Marco; Oefelein, Joseph C.
2017-01-01
For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.
Finite time singularities in the quasigeostrophic model
NASA Astrophysics Data System (ADS)
Scott, Richard
2016-11-01
A finite-time singularity in the evolution of a patch of surface temperature in the quasi-geostrophic equations via two distinct evolution routes is investigated with a grid-free, adaptive numerical scheme. In one case, the singularity proceeds through the formation of a corner, developing infinite curvature in the patch boundary in finite time. The corner is self-similar and the growth of curvature appears to be independent of initial patch shape. In the other case, the singularity proceeds through a self-similar cascade of filament instabilities with geometrically shrinking spatial and temporal scales, and the filament width approaches zero in a finite time. The spatially and temporally adaptive numerical scheme permits the accurate simulation of both corner and cascade singularities over a range of spatial scales spanning ten orders of magnitude. Some aspects of both singularity types exhibit universality, being independent of the initial patch shape and large-scale evolution; however, a simple extension of the initial temperature structure provides evidence that only the instability cascade persists in the case of a continuous initial temperature distribution.
Lagrangian transport near perturbed periodic lines in three-dimensional unsteady flows
NASA Astrophysics Data System (ADS)
Speetjens, Michel
2015-11-01
Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain three-dimensional (3D) time-periodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows
NASA Astrophysics Data System (ADS)
Ploeger, Felix; Konopka, Paul; Diallo, Mohamadou; Birner, Thomas; Hoppe, Charlotte; Müller, Rolf; Haenel, Florian; Stiller, Gabriele; Poshyvailo, Liubov; Garny, Hella; Dietmüller, Simone; Jöckel, Patrick; Engel, Andreas; Boenisch, Harald
2017-04-01
The global stratospheric Brewer-Dobson circulation (BDC) is expected to accelerate with rising Greenhouse gas concentrations, in turn changing the stratospheric trace gas composition and providing an important feedback via radiation on climate change. However, trends in the BDC are largely uncertain, with current climate model results disagreeing with existing observations of mean age of air, the average transit time for an air parcel since entering the stratosphere. We present advances in representing stratospheric trace gas transport caused by the Brewer-Dobson circulation by using the Chemical Lagrangian model of the Stratosphere (CLaMS), a global Lagrangian chemistry transport model with a physically-based parameterization of small-scale mixing. Mean age simulated with CLaMS driven by reanalysis meteorology agrees well with satellite and in-situ observations. Regarding the inter-annual and decadal changes, like increasing age in the Northern hemisphere and decreasing age in the Southern hemisphere during 2002-2012, the natural variability (e.g., QBO, ENSO, volcanic aerosols) is found to play a key role. Age of air spectra simulated with CLaMS provide further insights into the processes involved. Our analysis reveals a crucial effect of mixing on mean age and its decadal change pattern, suggesting that differences between climate models and observations likely involve differences in the effect of mixing. This progress in modelling stratospheric transport has recently been transferred to climate modelling by coupling the Lagrangian transport scheme CLaMS into the global atmosphere-chemistry model EMAC. First results show improvements of stratospheric transport compared to the standard flux-form semi-Lagrangian transport scheme. These improvements are found particularly in regions of strong transport barriers like the polar vortex, with Lagrangian CLaMS transport resulting in a stronger and more realistic transport barrier.
Ganshin, A; Oda, T; Saito, M; Maksyutov, S; Valsala, V; Andres, Robert Joseph; Fischer, R; Lowry, D; Lukyanov, A; Matsueda, H; Nisbet, E; Rigby, M; Sawa, Y; Toumi, R; Tsuboi, K; Varlagin, A; Zhuravlev, R
2012-01-01
Abstract. We designed a method to simulate atmospheric CO2 concentrations at several continuous observation sites around the globe using surface fluxes at a very high spatial resolution. The simulations presented in this study were performed using the Global Eulerian-Lagrangian Coupled Atmospheric model (GELCA), comprising a Lagrangian particle dispersion model coupled to a global atmospheric tracer transport model with prescribed global surface CO2 flux maps at a 1 1 km resolution. The surface fluxes used in the simulations were prepared by assembling the individual components of terrestrial, oceanic and fossil fuel CO2 fluxes. This experimental setup (i.e. a transport model running at a medium resolution, coupled to a high-resolution Lagrangian particle dispersion model together with global surface fluxes at a very high resolution), which was designed to represent high-frequency variations in atmospheric CO2 concentration, has not been reported at a global scale previously. Two sensitivity experiments were performed: (a) using the global transport model without coupling to the Lagrangian dispersion model, and (b) using the coupled model with a reduced resolution of surface fluxes, in order to evaluate the performance of Eulerian-Lagrangian coupling and the role of high-resolution fluxes in simulating high-frequency variations in atmospheric CO2 concentrations. A correlation analysis between observed and simulated atmospheric CO2 concentrations at selected locations revealed that the inclusion of both Eulerian-Lagrangian coupling and highresolution fluxes improves the high-frequency simulations of the model. The results highlight the potential of a coupled Eulerian-Lagrangian model in simulating high-frequency atmospheric CO2 concentrations at many locations worldwide. The model performs well in representing observations of atmospheric CO2 concentrations at high spatial and temporal resolutions, especially for coastal sites and sites located close to sources of
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
NASA Astrophysics Data System (ADS)
Puyguiraud, Alexandre; Dentz, Marco; Gouze, Philippe
2017-04-01
For the past several years a lot of attention has been given to pore-scale flow in order to understand and model transport, mixing and reaction in porous media. Nevertheless we believe that an accurate study of spatial and temporal evolution of velocities could bring important additional information for the upscaling from pore to higher scales. To gather these pieces of information, we perform Stokes flow simulations on pore-scale digitized images of a Berea sandstone core. First, micro-tomography (XRMT) imaging and segmentation processes allow us to obtain 3D black and white images of the sample [1]. Then we used an OpenFoam solver to perform the Stokes flow simulations mentioned above, which gives us the velocities at the interfaces of a cubic mesh. Subsequently, we use a particle streamline reconstruction technique which uses the Eulerian velocity field previously obtained. This technique, based on a modified Pollock algorithm [2], enables us to make particle tracking simulations on the digitized sample. In order to build a stochastic pore-scale transport model, we analyze the Lagrangian velocity series in two different ways. First we investigate the velocity evolution by sampling isochronically (t-Lagrangian), and by studying its statistical properties in terms of one- and two-points statistics. Intermittent patterns can be observed. These are due to the persistance of low velocities over a characteristic space length. Other results are investigated, such as correlation functions and velocity PDFs, which permit us to study more deeply this persistence in the velocities and to compute the correlation times. However, with the second approach, doing these same analysis in space by computing the velocities equidistantly, enables us to remove the intermittency shown in the temporal evolution and to model these velocity series as a Markov process. This renders the stochastic particle dynamics into a CTRW [3]. [1] Gjetvaj, F., A. Russian, P. Gouze, and M. Dentz (2015
Application of a lagrangian transport model to organo-mineral aggregates within the Nazaré canyon
NASA Astrophysics Data System (ADS)
Pando, S.; Juliano, M. F.; García, R.; Mendes, P. A. de Jesus; Thomsen, L.
2013-06-01
In this study, a hydrodynamic model was applied to the Nazaré submarine canyon with boundary forcing provided by an operational forecast model for the west Iberian coast for the spring of 2009. After validation, a lagrangian transport model was coupled to the hydrodynamic model to study and compare the transport patterns of three different classes of organo-mineral aggregates along the Nazaré canyon. The results show that the transport in the canyon is neither constant, nor unidirectional and that there are preferential areas where deposited matter is resuspended and redistributed. The transport of the larger class size of organo-mineral aggregates (2000 μm and 4000 μm) is less pronounced, and a decrease in the phytodetrital carbon flux along the canyon is observed. During the modelled period, the Nazaré canyon acts as a depocentre of sedimentary organic matter rather than a conduit of organo-mineral aggregates to the deep sea, as has been reported by other authors. The results of this study are crucial for the understanding of the oceanic carbon sequestration at the continental margin, and therefore important for evaluating the role of submarine canyons within the global carbon cycle.
Finite-time intercept-angle guidance
NASA Astrophysics Data System (ADS)
Lu, Kunfeng; Xia, Yuanqing; Yu, Chunmei; Chen, Rongfang
2015-02-01
In this paper, new nonsingular terminal sliding mode control guidance laws (NTSMCGLs) to unknown maneuvering target intercept are proposed and their finite-time convergences are proved. A novel nonsingular terminal sliding mode surface based on a predefined angle is designed to improve intercept performance and avoid singularity problem. The presented guidance law requires no information on maneuvering target that is estimated and compensated by extended state observer (ESO), and it can be used in practical systems where the target can evade freely. Also, undesired chattering is restrained effectively by real-time estimation and compensation of ESO. Simulation results show that the NTSMCGLs can achieve exact interception.
A lagrangian-eulerian description of debris transport by a tsunami in the Lisbon waterfront
NASA Astrophysics Data System (ADS)
Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.
2013-04-01
Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (eulerian) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (lagrangian) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the eulerian solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was
The Lagrangian method provides estimates of the chemical and physical evolution of air arriving in the daytime boundary layer at Baltimore. Study results indicate a dominant role for regional transport contributions of those days when sulfate air pollution is highest in Baltimor...
The Lagrangian method provides estimates of the chemical and physical evolution of air arriving in the daytime boundary layer at Baltimore. Study results indicate a dominant role for regional transport contributions of those days when sulfate air pollution is highest in Baltimor...
NASA Astrophysics Data System (ADS)
Maniatis, Georgios
2017-04-01
Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (Eulerian or Lagrangian) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general Eulerian-Lagrangian (E-L) model. This approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D
Finite Time Shock Acceleration at Interplanetary Shocks
NASA Astrophysics Data System (ADS)
Channok, C.; Ruffolo, D.; Desai, M. I.; Mason, G. M.
2004-05-01
Observations of energetic ion acceleration at interplanetary shocks sometimes indicate a spectral rollover at ˜ 0.1 to 1 MeV nucl-1. This rollover is not well explained by finite shock width or thickness effects. At the same time, a typical timescale of diffusive shock acceleration is several days, implying that the process of shock acceleration at an interplanetary shock near Earth usually gives only a mild increase in energy to an existing seed particle population. This is consistent with a recent analysis of ACE observations that argues for a seed population at substantially higher energies than the solar wind. Therefore an explanation of typical spectra of interplanetary shock-accelerated ions requires a theory of finite-time shock acceleration, which for long times (or an unusually fast acceleration timescale) tends to the steady-state result of a power-law spectrum. We present analytic and numerical models of finite-time shock acceleration. For a given injection momentum p0, after a very short time there is only a small boost in momentum, at intermediate times the spectrum is a power law with a hump and steep cutoff at a critical momentum, and at longer times the critical momentum increases and the spectrum approaches the steady-state power law. The composition dependence of the critical momentum is different from that obtained for other cutoff mechanisms. The results are compared with observed spectra. Work in Thailand was supported by the Commission for Higher Education, the Rachadapisek Sompoj Fund of Chulalongkorn University, and the Thailand Research Fund. Work at the University of Maryland was supported by NASA contract NAS5-30927 and NASA grant PC 251428.
Lagrangian Flow networks: a new way to characterize transport and connectivity in geophysical flows
NASA Astrophysics Data System (ADS)
Ser-Giacomi, Enrico; Hernandez-Garcia, Emilio; Lopez, Cristobal; Rossi, Vincent; Vasile, Ruggero
2015-04-01
Water and air transport are among the basic processes shaping the climate of our planet. Heat and salinity fluxes change sea water density, and thus drive the global thermohaline circulation. Atmospheric winds force the ocean motion, and also transport moisture, heat or chemicals, impacting the regional climate. We describe transport among different regions of the ocean or the atmosphere by flow networks, giving a discrete and robust representation of the fluid advection dynamics. We use network-theory tools to gain insights into transport problem. Local and global features of the networks are extracted from many numerical experiments to give a time averaged description of the system. Classical concepts like dispersion, mixing and connectivity are finally related to a set of network-like objects contributing to build a "dictionary" between network measures and physical quantities in geophysical flows.
NASA Astrophysics Data System (ADS)
Brett, G.; Rypina, I.; Pratt, L. J.
2016-12-01
The westernmost part of Mediterranean, the Alboran Sea, sits between the Iberian peninsula and Africa, just east of the Strait of Gibraltar. Atlantic water enters the Alboran through the strait in the form of the Atlantic Jet. After passing through the strait, this jet starts interacting with the Alboran recirculations, most notably with the Western Alboran Gyre - a persistent anticyclonic mesoscale eddy in the western Alboran. Past studies of Finite-Size Lyapunov Exponents in the Alboran (e.g. Sayol et. al 2013) have highlighted the periphery of the Western Alboran Gyre, implying that it has chaotic flow— motion characterized by exponential stretching and folding of fluid parcels. This work examines the near-surface exchange between the Atlantic Jet and the Western Alboran Gyre in a high-resolution regional run of the MIT general circulation model. We use Lagrangian methods from dynamical systems theory, specifically lobe analysis, to define the moving gyre boundary and quantify advective transport in and out of the gyre, avoiding spurious fluxes caused by the gyre moving across its time-mean boundaries. We also identify the stirring region, where exchanges with the Atlantic Jet occur, and the core of the gyre, where they do not. We demonstrate an intermittent path from the north-western upwelling region into the gyre, which may be important for the distribution of both temperature and plankton. Quantifying and qualifying the transport across the boundaries of this modeled mesoscale eddy may contribute to the future design of observational campaigns.
Simulating pollutant transport in complex terrain with a Lagrangian particle dispersion model
NASA Astrophysics Data System (ADS)
Szintai, B.; Kaufmann, P.; Rotach, M. W.
2009-04-01
Lagrangian particle dispersion models (LPDMs) are among the most sophisticated tools to simulate atmospheric dispersion of pollutants, and are widely used in emergency response systems. In these systems, LPDMs should be coupled with a numerical weather prediction (NWP) model, which provides information from the mean wind as well as from the turbulence state of the atmosphere. Mean wind can directly be used from the NWP model, while turbulence characteristics have to be parameterized by a so-called meteorological pre-processor. In most cases, to diagnose turbulence variables, meteorological pre-processors use similarity theory approaches, which are based on turbulence datasets over flat and homogeneous surface. However, turbulence structure in complex terrain, such as in steep and narrow Alpine valleys, can be substantially different from flat conditions. In this study a new scaling approach from Weigel et al. (2007), based on measurements and model simulations of the Riviera Project in the framework of the Mesoscale Alpine Program (MAP), is investigated with respect to pollutant dispersion. In the Riviera Project, analysis of turbulence measurements in a steep and narrow Alpine valley showed that daytime profiles of Turbulent Kinetic Energy (TKE) scale very well if the convective velocity scale w* is obtained from the sunlit eastern slope rather than from the surface directly under the measured profiles. This scaling behaviour was also reproduced by high-resolution Large Eddy Simulation runs. To improve the performance of the dispersion model in complex terrain, this new scaling approach is introduced in the meteorological pre-processor of the LPDM and results are validated with a real tracer experiment. For the evaluation of the dispersion model, the TRANSALP tracer experiment is used. During this experiment passive tracers were released and detected in an Alpine valley in Southern Switzerland on two days in October 1989. To simulate this case the operational
A massively parallel semi-Lagrangian algorithm for solving the transport equation
Manson, Russell; Wang, Dali
2010-01-01
The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.
Geometrical constraints on finite-time Lyapunov exponents in two and three dimensions.
Thiffeault, Jean-Luc; Boozer, Allen H.
2001-03-01
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current. (c) 2001 American Institute of Physics.
Detection of barriers to cross-jet Lagrangian transport and its destruction in a meandering flow
NASA Astrophysics Data System (ADS)
Budyansky, M. V.; Uleysky, M. Yu.; Prants, S. V.
2009-05-01
Cross-jet transport of passive scalars in a kinematic model of the meandering laminar two-dimensional incompressible flow which is known to produce chaotic mixing is studied. We develop a method for detecting barriers to cross-jet transport in the phase space which is a physical space for our model. Using tools from the theory of nontwist maps, we construct a central invariant curve and compute its characteristics that may serve as good indicators of the existence of a central transport barrier, its strength, and topology. Computing fractal dimension, length, and winding number of that curve in the parameter space, we study in detail the change in its geometry and its destruction that is caused by local bifurcations and a global bifurcation known as reconnection of separatrices of resonances. Scenarios of reconnection are different for odd and even resonances. The central invariant curves with rational and irrational (noble) values of winding numbers are arranged into hierarchical series which are described in terms of continued fractions. Destruction of central transport barrier is illustrated for two ways in the parameter space: when moving along resonant bifurcation curves with rational values of the winding number and along curves with noble (irrational) values.
Giudici, Andrea; Soomere, Tarmo
2014-12-15
We explore the possibilities for spontaneous formation of surface patches with high concentrations of contaminants through time correlations of the convergence field and the Lagrangian transport. The test area is the Gulf of Finland, the Baltic Sea, where surface velocity fields show extensive convergence. The flow properties are extracted from 3D velocity fields simulated for 1987-1991 using the OAAS model with a resolution of 1 mile. The focus is on the spatial distribution of the areas in which the values of finite-time flow compressibility of surface velocity fields exceed the threshold for clustering of floats. The distribution of such areas is asymmetric, with likely areas of patch formation located predominantly in the southern and eastern regions of the gulf. Out of nine areas of likely patch formation, six are located along the coast in regions of frequent downwelling, while three are identified in the central region of the gulf. Copyright © 2014 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Rinne, J.; Markkanen, T.; Ruuskanen, T. M.; Petäjä, T.; Keronen, P.; Tang, M. J.; Crowley, J. N.; Rannik, Ü.; Vesala, T.
2012-06-01
In the analyses of VOC fluxes measured above plant canopies, one usually assumes the flux above canopy to equal the exchange at the surface. Thus one assumes the chemical degradation to be much slower than the turbulent transport. We used a stochastic Lagrangian transport model in which the chemical degradation was described as first order decay in order to study the effect of the chemical degradation on above canopy fluxes of chemically reactive species. With the model we explored the sensitivity of the ratio of the above canopy flux to the surface emission on several parameters such as chemical lifetime of the compound, friction velocity, stability, and canopy density. Our results show that friction velocity and chemical lifetime affected the loss during transport the most. The canopy density had a significant effect if the chemically reactive compound was emitted from the forest floor. We used the results of the simulations together with oxidant data measured during HUMPPA-COPEC-2010 campaign at a Scots pine site to estimate the effect of the chemistry on fluxes of three typical biogenic VOCs, isoprene, α-pinene, and β-caryophyllene. Of these, the chemical degradation had a major effect on the fluxes of the most reactive species β-caryophyllene, while the fluxes of α-pinene were affected during nighttime. For these two compounds representing the mono- and sesquiterpenes groups, the effect of chemical degradation had also a significant diurnal cycle with the highest chemical loss at night. The different day and night time loss terms need to be accounted for, when measured fluxes of reactive compounds are used to reveal relations between primary emission and environmental parameters.
Finite-time singularity signature of hyperinflation
NASA Astrophysics Data System (ADS)
Sornette, D.; Takayasu, H.; Zhou, W.-X.
2003-07-01
We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.
Derivation of Transport Equations for a Strongly Interacting Lagrangian in Powers of ħand 1/ Nc
NASA Astrophysics Data System (ADS)
Klevansky, S. P.; Ogura, A.; Hüfner, J.
1997-11-01
Transport theory for an interacting fermionic system is reviewed and applied to the chiral Lagrangian of the Nambu-Jona-Lasinio model. Two expansions must be applied: an expansion in the inverse number of colors, 1/Nc, due to the nature of the strong coupling theory, and a semiclassical expansion, in powers of ħ. The quasiparticle approximation is implemented at an early stage, and spin effects are omitted. The self-energy is evaluated, self-consistently only in the Hartree approximation, and semi-perturbatively in the collision integral. In the Hartree approximation,O((1/Nc)0), the Vlasov equation is recovered toO(ħ1), together with an on-mass shell constraint equation, that is automatically fulfilled by the quasiparticle ansatz. The expressions for the self-energy to orderO((1/Nc)) lead to the collision term. Here one sees explicitly that particle-antiparticle creation and annihilation processes are suppressed that would otherwise be present, should an off-shell energy spectral function be admitted. A clear identification of thes,tanduchannel scattering processes in connection with the self-energy graphs is made and the origin of the mixed terms is made evident. Finally, after ordering according to powers in ħ, a Boltzmann-like form for the collision integral is obtained.
Klaic, Z.
1996-04-01
A Lagrangian receptor-oriented one-layer model has been developed in order to simulate a synoptic-scale transport of airborne sulphur on a daily basis. Mass-balance equations for sulphur dioxide and particulate sulphate were integrated along 3-day backward trajectories. Advective winds were determined from radiosonde reports, taking an average over the ground-based layer up to an 850-hpa level. The mixing height, transformation rate of sulphur dioxide to particulate sulphate, dry deposition velocities, and wet deposition rates for both pollutants were assumed to vary diurnally, depending on meteorological conditions. They were determined from routine synoptic observations. The model was tested for the sulphur dioxide and particulate sulphate data measured at nine and seven measuring sites, respectively. Daily mean calculated concentrations of both pollutants were generally higher than observed values for the test period. Both short- and long-term concentrations were predicted better for sulphur dioxide than for particulate sulphate. In application of the model to real data, problems arose due to incomplete input of meteorological data (particularly in trajectory calculations). 32 refs., 11 figs., 2 tabs.
NASA Astrophysics Data System (ADS)
Garcia, M. H.
2016-12-01
Modeling Sediment Transport Using a Lagrangian Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity Som Dutta1, Paul Fischer2, Marcelo H. Garcia11Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 2Department of Computer Science and Department of MechSE, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 Since the seminal work of Niño and Garcia [1994], one-way coupled Lagrangian particle tracking has been used extensively for modeling sediment transport. Over time, the Lagrangian particle tracking method has been coupled with Eulerian flow simulations, ranging from Reynolds Averaged Navier-Stokes (RANS) based models to Detached Eddy Simulations (DES) [Escauriaza and Sotiropoulos, 2011]. Advent of high performance computing (HPC) platforms and faster algorithms have resulted in the work of Dutta et al. [2016], where Lagrangian particle tracking was coupled with high-resolution Large Eddy Simulations (LES) to model the complex and highly non-linear phenomenon of Bulle-Effect at diversions. Despite all the advancements in using Lagrangian particle tracking, there has not been a study that looks in detail at the limits of the model in the context of sediment transport, and also analyzes the sensitivity of the various force formulation in the force balance equation of the particles. Niño and Garcia [1994] did a similar analysis, but the vertical flow velocity distribution was modeled as the log-law. The current study extends the analysis by modeling the flow using high-resolution LES at a Reynolds number comparable to experiments of Niño et al. [1994]. Dutta et al., (2016), Large Eddy Simulation (LES) of flow and bedload transport at an idealized 90-degree diversion: insight into Bulle-Effect, River Flow 2016 - Constantinescu, Garcia & Hanes (Eds), Taylor & Francis Group, London, 101-109. Escauriaza and Sotiropoulos
Numerical modeling of pollutant transport using a Lagrangian marker particle technique
NASA Technical Reports Server (NTRS)
Spaulding, M.
1976-01-01
A derivation and code were developed for the three-dimensional mass transport equation, using a particle-in-cell solution technique, to solve coastal zone waste discharge problems where particles are a major component of the waste. Improvements in the particle movement techniques are suggested and typical examples illustrated. Preliminary model comparisons with analytic solutions for an instantaneous point release in a uniform flow show good results in resolving the waste motion. The findings to date indicate that this computational model will provide a useful technique to study the motion of sediment, dredged spoils, and other particulate waste commonly deposited in coastal waters.
Till, John E; Rood, Arthur S; Garzon, Caroline D; Lagdon, Richard H
2014-09-01
The suitability of a new facility in terms of potential impacts from routine and accidental releases is typically evaluated using conservative models and assumptions to assure dose standards are not exceeded. However, overly conservative dose estimates that exceed target doses can result in unnecessary and costly facility design changes. This paper examines one such case involving the U.S. Department of Energy's pretreatment facility of the Waste Treatment and Immobilization Plant (WTP). The MELCOR Accident Consequence Code System Version 2 (MACCS2) was run using conservative parameter values in prescribed guidance to demonstrate that the dose from a postulated airborne release would not exceed the guideline dose of 0.25 Sv. External review of default model parameters identified the deposition velocity of 1.0 cm s as being non-conservative. The deposition velocity calculated using resistance models was in the range of 0.1 to 0.3 cm s-1. A value of 0.1 cm s-1 would result in the dose guideline being exceeded. To test the overall conservatism of the MACCS2 transport model, the 95th percentile hourly average dispersion factor based on one year of meteorological data was compared to dispersion factors generated from two state-of-the-art Lagrangian puff models. The 95th percentile dispersion factor from MACCS2 was a factor of 3 to 6 higher compared to those of the Lagrangian puff models at a distance of 9.3 km and a deposition velocity of 0.1 cm s-1. Thus, the inherent conservatism in MACCS2 more than compensated for the high deposition velocity used in the assessment. Applications of models like MACCS2 with a conservative set of parameters are essentially screening calculations, and failure to meet dose criteria should not trigger facility design changes but prompt a more in-depth analysis using probabilistic methods with a defined margin of safety in the target dose. A sample application of the probabilistic approach is provided.
Backward Finite-Time Lyapunov Exponents in Inertial Flows.
Gunther, Tobias; Theisel, Holger
2017-01-01
Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which - given an observation and an initial velocity - allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields.
Joint Statistics of Finite Time Lyapunov Exponents in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry; Meneveau, Charles
2014-11-01
Recently, the notion of Lagrangian Coherent Structures (LCS) has gained attention as a tool for qualitative visualization of flow features. LCS visualize repelling and attracting manifolds marked by local ridges in the field of maximal and minimal finite-time Lyapunov exponents (FTLE), respectively. To provide a quantitative characterization of FTLEs, the statistical theory of large deviations can be used based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms (with finite-size correction). We generalize the formalism to characterize the joint distributions of the two independent FTLEs in 3D. The ``joint Cramér function of turbulence'' is measured from the Johns Hopkins Turbulence Databases (JHTDB) isotropic simulation at Reλ = 433 and results are compared with those computed using only the symmetric part of the velocity gradient tensor, as well as with those of instantaneous strain-rate eigenvalues. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude and the most likely ratio of FTLEs changes from 4:1:-5 to 8:3:-11, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. Supported by NSF Graduate Fellowship (DGE-1232825), a JHU graduate Fellowship, and NSF Grant CMMI-0941530. CM thanks Prof. Luca Biferale for useful discussions on the subject.
NASA Astrophysics Data System (ADS)
Cui, J.; Sprenger, M.; Staehelin, J.; Siegrist, A.; Kunz, M.; Henne, S.; Steinbacher, M.
2009-01-01
The particle dispersion model FLEXPART and the trajectory model LAGRANTO are Lagrangian models which are widely used to study synoptic-scale atmospheric air flows such as stratospheric intrusions (SI) and intercontinental transport (ICT). In this study, we focus on SI and ICT events particularly from the North American planetary boundary layer for the Jungfraujoch (JFJ) measurement site, Switzerland, in 2005. Two representative cases of SI and ICT are identified based on measurements recorded at Jungfraujoch and are compared with FLEXPART and LAGRANTO simulations, respectively. Both models well capture the events, showing good temporal agreement between models and measurements. In addition, we investigate the performance of FLEXPART and LAGRANTO on representing SI and ICT events over the entire year 2005 in a statistical way. We found that the air at JFJ is influenced by SI during 19% (FLEXPART) and 18% (LAGRANTO), and by ICT from the North American planetary boundary layer during 13% (FLEXPART) and 12% (LAGRANTO) of the entire year. Through intercomparsion with measurements, our findings suggest that both FLEXPART and LAGRANTO are well capable of representing SI and ICT events if they last for more than 12 h, whereas both have problems on representing short events. It is also shown that although the long-range transported air is characterized by relatively low NOy/CO ratios and elevated CO concentrations, using a combination of NOy/CO and CO as control parameters still encounters difficulty in distinguishing aged air masses by their source regions. Moreover, a sensitivity study indicates that the agreement between models and measurements depends significantly on the threshold values applied to the individual control parameters. Generally, the less strict the thresholds are, the better the agreement between models and measurements. Although the dependence of the agreement on the threshold values is appreciable, it nevertheless confirms the conclusion that both
NASA Astrophysics Data System (ADS)
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
NASA Astrophysics Data System (ADS)
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents
NASA Astrophysics Data System (ADS)
Doan, T. S.; Karrasch, D.; Nguyen, T. Y.; Siegmund, S.
A hyperbolicity notion for linear differential equations x˙=A(t)x, t∈[t-,t+], is defined which unifies different existing notions like finite-time Lyapunov exponents (Haller, 2001, [13], Shadden et al., 2005, [24]), uniform or M-hyperbolicity (Haller, 2001, [13], Berger et al., 2009, [6]) and (t-,(t+-t-))-dichotomy (Rasmussen, 2010, [21]). Its relation to the dichotomy spectrum (Sacker and Sell, 1978, [23], Siegmund, 2002, [26]), D-hyperbolicity (Berger et al., 2009, [6]) and real parts of the eigenvalues (in case A is constant) is described. We prove a spectral theorem and provide an approximation result for the spectral intervals.
NASA Astrophysics Data System (ADS)
Philipp, Anne; Hittmeir, Sabine; Seibert, Petra
2017-04-01
The distribution of wet deposition as calculated with Lagrangian particle transport models, e.g. FLEXPART (http://flexpart.eu) is governed by the intensity distribution of precipitation. Usually, meteorological input is taken from Eulerian weather forecast models, e.g. ECWMF (European Centre for Medium-Range Weather Forecasts), providing precipitation data as integrated over the time between two output times and over a grid cell. Simple linear interpolation would implicitly assume the integral value to be a point value valid at the grid centre and in the middle of the time interval, and thus underestimate peaks and overestimate local minima. In FLEXPART, a separate pre-processor is used to extract the meteorological input data from the ECMWF archive and prepare them for use in the model. Currently, a relatively simple method prepares the precipitation fields in a way that is consistent with the linear interpolation as applied in FLEXPART. This method is designed to conserve the original amount of precipitation. However, this leads to undesired temporal smoothing of the precipitation time series which even produces nonzero precipitation in dry intervals bordering a precipitation period. A new interpolation algorithm (currently in one dimension) was developed which introduces additional supporting grid points in each time interval (see companion contribution by Hittmeir, Philipp and Seibert). The quality of the algorithm is being tested at first by comparing 1-hourly values derived with the new algorithm from 3- (or 6-)hourly precipitation with the 1-hourly ECMWF model output. As ECWMF provides large-scale and convective precipitation data, the evaluation will be carried out separately as well as for different seasons and climatic zones.
NASA Astrophysics Data System (ADS)
Cui, J.; Sprenger, M.; Staehelin, J.; Siegrist, A.; Kunz, M.; Henne, S.; Steinbacher, M.
2009-05-01
The particle dispersion model FLEXPART and the trajectory model LAGRANTO are Lagrangian models which are widely used to study synoptic-scale atmospheric air flows such as stratospheric intrusions (SI) and intercontinental transport (ICT). In this study, we focus on SI and ICT events particularly from the North American planetary boundary layer for the Jungfraujoch (JFJ) measurement site, Switzerland, in 2005. Two representative cases of SI and ICT are identified based on measurements recorded at Jungfraujoch and are compared with FLEXPART and LAGRANTO simulations, respectively. Both models well capture the events, showing good temporal agreement between models and measurements. In addition, we investigate the performance of FLEXPART and LAGRANTO on representing SI and ICT events over the entire year 2005 in a statistical way. We found that the air at JFJ is influenced by SI during 19% (FLEXPART) and 18% (LAGRANTO), and by ICT from the North American planetary boundary layer during 13% (FLEXPART) and 12% (LAGRANTO) of the entire year. Through intercomparsion with measurements, our findings suggest that both FLEXPART and LAGRANTO are well capable of representing SI and ICT events if they last for more than 12 h, whereas both have problems on representing short events. For comparison with in-situ observations we used O3 and relative humidity for SI events. As parameters to trace ICT events we used a combination of NOy/CO and CO, however these parameters are not specific enough to distinguish aged air masses by their source regions. Moreover, a sensitivity study indicates that the agreement between models and measurements depends significantly on the threshold values applied to the individual control parameters. Generally, the less strict the thresholds are, the better the agreement between models and measurements. Although the dependence of the agreement on the threshold values is appreciable, it nevertheless confirms the conclusion that both FLEXPART and LAGRANTO are
NASA Technical Reports Server (NTRS)
Considine, David B.; Natarajan, Murali; Fairlie, T. D.; Lingenfelser, Gretchen S.; Bernath, Peter
2007-01-01
We use the LaRC Lagrangian Chemistry and Transport Model (LCTM) [Considine et al., 2007; Pierce et al., 2003] to intercompare ACE, Aura, and HALOE observations of long-lived trace species. The LCTM calculates the transport, mixing, and photochemical evolution of an ensemble of parcels that have been initialized from ACE-FTS measurements. Here we focus on late November, 2004 comparisons, due to the previous 3-week period of continuous HALOE observations and MLS v2.2 data on November 29, 2004.
Yeh, Gour-Tsyh; Carpenter, S.L.; Hopkins, P.L.; Siegel, M.D.
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
Finite-time barriers to front propagation in two-dimensional fluid flows.
Mahoney, John R; Mitchell, Kevin A
2015-08-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."
Finite-time barriers to front propagation in two-dimensional fluid flows
NASA Astrophysics Data System (ADS)
Mahoney, John R.; Mitchell, Kevin A.
2015-08-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."
NASA Technical Reports Server (NTRS)
Pavish, D. L.; Spaulding, M. L.
1977-01-01
A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.
Finite Time Blowup for Parabolic Systems in Two Dimensions
NASA Astrophysics Data System (ADS)
Mooney, Connor
2017-03-01
We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.
3D Finite Time Lyapunov Exponents in a left ventricle laboratory model
NASA Astrophysics Data System (ADS)
Grazia Badas, Maria; Espa, Stefania; Fortini, Stefania; Querzoli, Giorgio
2015-05-01
Finite Time Lyapunov Exponents (FTLEs) are a powerful means to infer characteristic features of the flow that cannot be revealed by other Eulerian criteria. Recently FTLEs are becoming popular also in the medical context, for instance in the analysis of vascular flow measured by means of Magnetic Resonance Imaging. However, many of the FTLE experimental works are based only on two-dimensional velocity fields, moreover those computed on in-vivo data cannot be obtained under controlled and repeatable conditions. Here we present the 3D FTLE evolution inside a Left Ventricle (LV) laboratory model mimicking physiological human conditions. The investigation of FTLE fields highlights distinctive features of the cardiac flow and gives an insight on the physiological development of the Lagrangian Coherent Structures (LCS) that optimize the LV refill.
NASA Astrophysics Data System (ADS)
Hendabadi, Sahar; Del Alamo, Juan Carlos; Benito, Yolanda; Yotti, Raquel; Bermejo, Javier; Shadden, Shawn
2012-11-01
We discuss work towards understanding human left ventricle (LV) transport and mixing characteristics in normal subjects and patients with dilated cardiomyopathy. Prior studies have shown that the fluid dynamics in the left ventricle (LV) play a major role in dictating overall cardiac health. This study utilizes a noninvasive method to obtain planar velocity data over the apical long-axis view of the LV from color Doppler and B-mode ultrasound measurements. We use a Lagrangian measure to study unsteady behavior of blood transport inside the LV. We compute finite-time Lyapunov exponent (FTLE) fields to extract Lagrangian coherent structures (LCS) from the empirical data. This application presents a particular challenge to Lagrangian computations due to the presence of moving flux, and no-flux, boundaries. We describe a method for unstructured grid generation from the LV motion, and LCS computation on the deforming unstructured grid. Results demonstrate that LCS reveal the moving boundaries confining the blood volume injected to the LV in diastole and ejected into the aorta in systole. We discuss findings related to the quantification of the LV vortex, whose geometry and motion is thought to be an important indicator of cardiac health.
Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.
2015-12-01
Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.
NASA Astrophysics Data System (ADS)
Soltanian, Mohamad Reza; Ritzi, Robert W.; Huang, Chao Cheng; Dai, Zhenxue
2015-03-01
This series of papers addresses the transport of sorbing solutes in groundwater. In part 2, plume dispersion, as quantified by the particle displacement variance, X11R>(t>), is linked to hierarchical sedimentary architecture using a Lagrangian-based transport model. This allows for a fundamental understanding of how dispersion arises from the hierarchical architecture of sedimentary facies, and allows for a quantitative decomposition of dispersion into facies-related contributions at different scales within the hierarchy. As in part 1, the plume behavior is assumed to be controlled by linear-equilibrium sorption and the heterogeneity in both the log permeability, Y=ln>(k>), and the log distribution coefficient, Ξ=ln>(Kd>). Heterogeneity in Y and Ξ arises from sedimentary processes and is structured by the consequent sedimentary architecture. Our goal is to understand the basic science of the dispersion process at this very fundamental level. The spatial auto and cross covariances for the relevant attributes are linear sums of terms corresponding to the probability of transitioning across stratal facies types defined at different scales. Unlike previous studies that used empirical relationships for the spatial covariances, here the model parameters are developed from independent measurements of physically quantifiable attributes of the stratal architecture (i.e., proportions and lengths of facies types, and univariate statistics for Y and Ξ). Nothing is assumed about Y-Ξ point correlation; it is allowed to differ by facies type. However, it is assumed that Y and Ξ variance is small but meaningful, and that pore-scale dispersion is negligible. The time-dependent spreading rate is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each relevant scale of stratal hierarchy. As in part 1, the well-documented perchloroethene (PCE) tracer test at the Borden research site is
Delpeche-Ellmann, Nicole C; Soomere, Tarmo
2013-02-15
The possibility of current-driven propagation of contaminants released along a major fairway polluting the Marine Protected Areas (MPAs) in the Gulf of Finland, the Baltic Sea, is examined using a 3D circulation model, a Lagrangian transport model and statistics. Not surprisingly, the number of hits to the MPA decreases almost linearly with its distance from the fairway. In addition, the potential pollution released during a ship accident with the pollutants carried by currents may affect MPAs at very large distances. Typically, a fairway section approximately 125 km long (covering about 1/3 of the approximate 400-km-long gulf) may serve as a source of pollution for each MPA. The largest MPA (in the Eastern Gulf of Finland) may receive pollution from an approximately 210-km-long section (covering about 1/2 of the entire length of the gulf). This information may be useful in assisting maritime management. Copyright © 2012 Elsevier Ltd. All rights reserved.
Finite-time Control of One-link Mechanical System
NASA Astrophysics Data System (ADS)
Matoba, Shunsuke; Nakamura, Nami; Nakamura, Hisakazu; Akiba, Hideyuki
This paper considers finite-time position control of an one-link mechanical system. The system is modeled by discontinuous differential equations. In this paper, we prove that the Nakamura's local homogeneous controller based on a control Lyapunov function is valid to the position control of the robot manipulators, and show the effectiveness of the controller by experiments.
Finite-time erasing of information stored in fermionic bits
NASA Astrophysics Data System (ADS)
Diana, Giovanni; Bagci, G. Baris; Esposito, Massimiliano
2013-01-01
We address the issue of minimizing the heat generated when erasing the information stored in an array of quantum dots in finite time. We identify the fundamental limitations and trade-offs involved in this process and analyze how a feedback operation can help improve it.
NASA Astrophysics Data System (ADS)
Carlson, Daniel F.; Griffa, Annalisa; Zambianchi, Enrico; Suaria, Giuseppe; Corgnati, Lorenzo; Magaldi, Marcello G.; Poulain, Pierre-Marie; Russo, Aniello; Bellomo, Lucio; Mantovani, Carlo; Celentano, Paolo; Molcard, Anne; Borghini, Mireno
2016-04-01
Surface drifters and virtual particles are used to investigate transport between seven coastal regions in the central and southern Adriatic Sea to estimate the degree to which these regions function as a network. Alongshore coastal currents and cyclonic gyres are the primary circulation features that connected regions in the Adriatic Sea. The historical drifter observations span 25 years and, thus, provide estimates of transport between regions realized by the mean surface circulation. The virtual particle trajectories and a dedicated drifter experiment show that southeasterly Sirocco winds can drive eastward cross-Adriatic transport from the Italian coast near the Gargano Promontory to the Dalmatian Islands in Croatia. Southeasterly winds disrupt alongshore transport on the west coast. Northwesterly Mistral winds enhanced east-to-west transport and resulted in stronger southeastward coastal currents in the western Adriatic current (WAC) and export to the northern Ionian Sea. The central Italian regions showed strong connections from north to south, likely realized by alongshore transport in the WAC. Alongshore, downstream transport was weaker on the east coast, likely due to the more complex topography introduced by the Dalmatian Islands of Croatia. Cross-Adriatic connection percentages were higher for east-to-west transport. Cross-Adriatic transport, in general, occurred via the cyclonic sub-gyres, with westward (eastward) transport observed in the northern (southern) arms of the central and southern gyres.
NASA Astrophysics Data System (ADS)
Park, Young-Gyu; Son, Young Baek; Choi, Byoung-Ju; Kim, Yong Hoon
2014-05-01
Lagrangian particle tracking experiments were conducted to understand the pathway of the floating green algae patches observed in the Yellow Sea (YS) and East China Sea (ECS) in summer 2011. The numerical simulation results indicated that dominant southerly winds during June and July 2011 were related to offshore movement of the floating green algae, especially their eastward extension in the YS/ECS. An infrequent and unusual event occurred in June 2011: a severe Tropical Strom MEARI, caused the green algae to detach from the coast and initiated movement to the east. After the typhoon event, sea surface temperature recovered rapidly enough to grow the floating green algae, and wind and local current controlled the movement of the massive floating algae patches (coastal accumulation or offshore advection in the area). Analysis of the floating green algae movement using satellite images during passage of Typhoon MAON in July 2011 revealed that the floating green algae patches were significantly controlled by both ocean currents and enhanced winds. These findings suggest that the floating green algae bloom off Qingdao, China and in the middle of the YS and ECS in the summer of 2011 occurred due to the combined effects of recent rapid expansion of seaweed aquaculture, strong winds, and the wind patterns in blooming regions. Our combined approach, using satellite data and numerical simulations, provides a robust estimate for tracing and monitoring changes in green algae blooms on a regional scale.
NASA Astrophysics Data System (ADS)
Carlson, D. F.; Novelli, G.; Guigand, C.; Özgökmen, T.; Fox-Kemper, B.; Molemaker, M. J.
2016-02-01
The Consortium for Advanced Research on the Transport of Hydrocarbon in the Environment (CARTHE) will carry out the LAgrangian Submesoscale ExpeRiment (LASER) to study the role of small-scale processes in the transport and dispersion of oil and passive tracers. The Ship-Tethered Aerostat Remote Sensing System (STARRS) will observe small-scale surface dispersion in the open ocean. STARRS is built around a high-lift-capacity (30 kg) helium-filled aerostat. STARRS is equipped with a high resolution digital camera. An integrated GNSS receiver and inertial navigation system permit direct geo-rectification of the imagery. Consortium for Advanced Research on the Transport of Hydrocarbon in the Environment (CARTHE) will carry out the LAgrangian Submesoscale ExpeRiment (LASER) to study the role of small-scale processes in the transport and dispersion of oil and passive tracers. The Ship-Tethered Aerostat Remote Sensing System (STARRS) was developed to produce observational estimates of small-scale surface dispersion in the open ocean. STARRS is built around a high-lift-capacity (30 kg) helium-filled aerostat. STARRS is equipped with a high resolution digital camera. An integrated GNSS receiver and inertial navigation system permit direct geo-rectification of the imagery. Thousands of drift cards deployed in the field of view of STARRS and tracked over time provide the first observational estimates of small-scale (1-500 m) surface dispersion in the open ocean. The STARRS imagery will be combined with GPS-tracked surface drifter trajectories, shipboard observations, and aerial surveys of sea surface temperature in the DeSoto Canyon. In addition to obvious applications to oil spill modelling, the STARRS observations will provide essential benchmarks for high resolution numerical modelsDrift cards deployed in the field of view of STARRS and tracked over time provide the first observational estimates of small-scale (1-100 m) surface dispersion in the open ocean. The STARRS
Finite-Time Shock Acceleration of Energetic Storm Particles
NASA Astrophysics Data System (ADS)
Channok, Chanruangrit; Ruffolo, David; Desai, Mihir I.; Mason, Glenn M.
2005-11-01
Energetic storm particles (ESPs) of various ion species have been shown to arise from suprathermal seed ions accelerated by traveling interplanetary (IP) shocks. The observed spectral rollovers at ~0.1-10 MeV nucleon-1 can be attributed to the finite time available for shock acceleration. Using the locally measured shock strength parameters as inputs, the finite-time shock acceleration model can successfully fit the energy spectra of carbon, oxygen, and iron ions measured by the Ultra Low Energy Isotope Spectrometer (ULEIS) on board the Advanced Composition Explorer (ACE) during three ESP events. The inferred scattering mean free path in the acceleration region ranges from a typical IP value for the weakest ESP event down to 3.0×10-3 AU for the strongest event. This is consistent with the idea that proton-amplified waves result from the very intense particle fluxes in major events.
Finite-time generalization of the thermodynamic uncertainty relation
NASA Astrophysics Data System (ADS)
Pietzonka, Patrick; Ritort, Felix; Seifert, Udo
2017-07-01
For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.
NASA Astrophysics Data System (ADS)
Pisso, I.; Myhre, C. Lund; Platt, S. M.; Eckhardt, S.; Hermansen, O.; Schmidbauer, N.; Mienert, J.; Vadakkepuliyambatta, S.; Bauguitte, S.; Pitt, J.; Allen, G.; Bower, K. N.; O'Shea, S.; Gallagher, M. W.; Percival, C. J.; Pyle, J.; Cain, M.; Stohl, A.
2016-12-01
Methane stored in seabed reservoirs such as methane hydrates can reach the atmosphere in the form of bubbles or dissolved in water. Hydrates could destabilize with rising temperature further increasing greenhouse gas emissions in a warming climate. To assess the impact of oceanic emissions from the area west of Svalbard, where methane hydrates are abundant, we used measurements collected with a research aircraft (Facility for Airborne Atmospheric Measurements) and a ship (Helmer Hansen) during the Summer 2014 and for Zeppelin Observatory for the full year. We present a model-supported analysis of the atmospheric CH4 mixing ratios measured by the different platforms. To address uncertainty about where CH4 emissions actually occur, we explored three scenarios: areas with known seeps, a hydrate stability model, and an ocean depth criterion. We then used a budget analysis and a Lagrangian particle dispersion model to compare measurements taken upwind and downwind of the potential CH4 emission areas. We found small differences between the CH4 mixing ratios measured upwind and downwind of the potential emission areas during the campaign. By taking into account measurement and sampling uncertainties and by determining the sensitivity of the measured mixing ratios to potential oceanic emissions, we provide upper limits for the CH4 fluxes. The CH4 flux during the campaign was small, with an upper limit of 2.5 nmol m-2 s-1 in the stability model scenario. The Zeppelin Observatory data for 2014 suggest CH4 fluxes from the Svalbard continental platform below 0.2 Tg yr-1. All estimates are in the lower range of values previously reported.
NASA Astrophysics Data System (ADS)
Pisso, Ignacio; Myhre, Cathrine Lund; Platt, Stephen Matthew; Eckhardt, Sabine; Hermansen, Ove; Schmidbauer, Norbert; Mienert, Jurgen; Vadakkepuliyambatta, Sunil; Bauguitte, Stephane; Pitt, Joseph; Allen, Grant; Bower, Keith; O'Shea, Sebastian; Gallagher, Martin; Percival, Carl; Pyle, John; Cain, Michelle; Stohl, Andreas
2017-04-01
Methane stored in seabed reservoirs such as methane hydrates can reach the atmosphere in the form of bubbles or dissolved in water. Hydrates could destabilize with rising temperature further increasing greenhouse gas emissions in a warming climate. To assess the impact of oceanic emissions from the area west of Svalbard, where methane hydrates are abundant, we used measurements collected with a research aircraft (FAAM) and a ship (Helmer Hansen) during the Summer 2014, and for Zeppelin Observatory for the full year. We present a model-supported analysis of the atmospheric CH4 mixing ratios measured by the different platforms. To address uncertainty about where CH4 emissions actually occur, we explored three scenarios: areas with known seeps, a hydrate stability model and an ocean depth criterion. We then used a budget analysis and a Lagrangian particle dispersion model to compare measurements taken upwind and downwind of the potential CH4 emission areas. We found small differences between the CH4 mixing ratios measured upwind and downwind of the potential emission areas during the campaign. By taking into account measurement and sampling uncertainties and by determining the sensitivity of the measured mixing ratios to potential oceanic emissions, we provide upper limits for the CH4 fluxes. The CH4 flux during the campaign was small, with an upper limit of 2.5 nmol / m s in the stability model scenario. The Zeppelin Observatory data for 2014 suggests CH4 fluxes from the Svalbard continental platform below 0.2 Tg/yr . All estimates are in the lower range of values previously reported.
Myhre, C. Lund; Platt, S. M.; Eckhardt, S.; Hermansen, O.; Schmidbauer, N.; Mienert, J.; Vadakkepuliyambatta, S.; Bauguitte, S.; Pitt, J.; Allen, G.; Bower, K. N.; O'Shea, S.; Gallagher, M. W.; Percival, C. J.; Pyle, J.; Cain, M.; Stohl, A.
2016-01-01
Abstract Methane stored in seabed reservoirs such as methane hydrates can reach the atmosphere in the form of bubbles or dissolved in water. Hydrates could destabilize with rising temperature further increasing greenhouse gas emissions in a warming climate. To assess the impact of oceanic emissions from the area west of Svalbard, where methane hydrates are abundant, we used measurements collected with a research aircraft (Facility for Airborne Atmospheric Measurements) and a ship (Helmer Hansen) during the Summer 2014 and for Zeppelin Observatory for the full year. We present a model‐supported analysis of the atmospheric CH4 mixing ratios measured by the different platforms. To address uncertainty about where CH4 emissions actually occur, we explored three scenarios: areas with known seeps, a hydrate stability model, and an ocean depth criterion. We then used a budget analysis and a Lagrangian particle dispersion model to compare measurements taken upwind and downwind of the potential CH4 emission areas. We found small differences between the CH4 mixing ratios measured upwind and downwind of the potential emission areas during the campaign. By taking into account measurement and sampling uncertainties and by determining the sensitivity of the measured mixing ratios to potential oceanic emissions, we provide upper limits for the CH4 fluxes. The CH4 flux during the campaign was small, with an upper limit of 2.5 nmol m−2 s−1 in the stability model scenario. The Zeppelin Observatory data for 2014 suggest CH4 fluxes from the Svalbard continental platform below 0.2 Tg yr−1. All estimates are in the lower range of values previously reported. PMID:28261536
Pisso, I; Myhre, C Lund; Platt, S M; Eckhardt, S; Hermansen, O; Schmidbauer, N; Mienert, J; Vadakkepuliyambatta, S; Bauguitte, S; Pitt, J; Allen, G; Bower, K N; O'Shea, S; Gallagher, M W; Percival, C J; Pyle, J; Cain, M; Stohl, A
2016-12-16
Methane stored in seabed reservoirs such as methane hydrates can reach the atmosphere in the form of bubbles or dissolved in water. Hydrates could destabilize with rising temperature further increasing greenhouse gas emissions in a warming climate. To assess the impact of oceanic emissions from the area west of Svalbard, where methane hydrates are abundant, we used measurements collected with a research aircraft (Facility for Airborne Atmospheric Measurements) and a ship (Helmer Hansen) during the Summer 2014 and for Zeppelin Observatory for the full year. We present a model-supported analysis of the atmospheric CH4 mixing ratios measured by the different platforms. To address uncertainty about where CH4 emissions actually occur, we explored three scenarios: areas with known seeps, a hydrate stability model, and an ocean depth criterion. We then used a budget analysis and a Lagrangian particle dispersion model to compare measurements taken upwind and downwind of the potential CH4 emission areas. We found small differences between the CH4 mixing ratios measured upwind and downwind of the potential emission areas during the campaign. By taking into account measurement and sampling uncertainties and by determining the sensitivity of the measured mixing ratios to potential oceanic emissions, we provide upper limits for the CH4 fluxes. The CH4 flux during the campaign was small, with an upper limit of 2.5 nmol m(-2) s(-1) in the stability model scenario. The Zeppelin Observatory data for 2014 suggest CH4 fluxes from the Svalbard continental platform below 0.2 Tg yr(-1). All estimates are in the lower range of values previously reported.
A finite-time exponent for random Ehrenfest gas
Moudgalya, Sanjay; Chandra, Sarthak; Jain, Sudhir R.
2015-10-15
We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.
Lagrangian coherent structures are associated with fluctuations in airborne microbial populations
NASA Astrophysics Data System (ADS)
Tallapragada, P.; Ross, S. D.; Schmale, D. G.
2011-09-01
Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.
Are Atmospheric Rivers Lagrangian Coherent Structures?
NASA Astrophysics Data System (ADS)
Garaboa, Daniel; Eiras, Jorge; Huhn, Florian; Miguez-Macho, Gonzalo; Pérez-Muñuzuri, Vicente
2014-05-01
Most of the advective moisture transport from the tropics (main planetary precipitable water source) to mid-latitudes is not smooth and uniform. More than 90% of poleward water vapor transport is accomplished by narrow and elongated (longer than 2000 km and narrower than 1000 km) structures within the pre-cold frontal Warm Conveyor Belt (WCB) and Low Level Jet (LLJ) of extratropical cyclones, mostly associated to the polar front. These structures, labeled as Tropospheric or Atmospheric Rivers (ARs), are defined as areas of Integrated Water Vapor (IWV) column over 2 cm and strong winds, transporting water vapor whitin the lower troposphere (close to 1 km above the sea level). Due to their nature, we analyzed these structures in terms of Lagrangian Coherent Structures (LCS), using the Finite-Time Lyapunov Exponents (FTLE). In order to develop such analysis, we extract 2D-velocity field from vector flux fields over the North Atlantic Ocean, using vertical integrals of water vapor (Q) and eastward/northward water vapor flux (ΦΛ,Φφ), retrieved from the ECMWF Reanalysis (ERA-Interim) at a 0.7°× 0.7° horizontal resolution. Such 2D-velocity fields are dominated by those layers with high water vapor flux content. We carry out an Atmospheric River analysis in terms of the FTLE for a set of 10 strong events whit different shape (7 of them have a clear water transport filament shape and the rest have a scattered one) over the North Atlantic Ocean. To that end, we compare the LCS extracted from the FTLE fields computed backward and forward for 5 days with the ridge extracted from the vertical integral Q. We find that repelling LCS derived from the forward FTLE do not show any connection with the ARs. However, for the well defined AR there is a strong correlation between AR ridges and the attracting LCS and both present similar structures, whereas for the other ARs with scattered shape we do not find a principal LCS derived from the AR event.
NASA Technical Reports Server (NTRS)
Cram, Thomas A.; Persing, John; Montgomery, Michael T.; Braun, Scott A.
2006-01-01
The transport and mixing characteristics of a large sample of air parcels within a mature and vertically sheared hurricane vortex is examined. Data from a high-resolution (2 km grid spacing) numerical simulation of "real-case" Hurricane Bonnie (1998) is used to calculate Lagrangian trajectories of air parcels in various subdomains of the hurricane (namely, the eye, eyewall, and near-environment) to study the degree of interaction (transport and mixing) between these subdomains. It is found that 1) there is transport and mixing from the low-level eye to the eyewall that carries high- Be air which can enhance the efficiency of the hurricane heat engine; 2) a portion of the low-level inflow of the hurricane bypasses the eyewall to enter the eye, that both replaces the mass of the low-level eye and lingers for a sufficient time (order 1 hour) to acquire enhanced entropy characteristics through interaction with the ocean beneath the eye; 3) air in the mid- to upper-level eye is exchanged with the eyewall such that more than half the air of the eye is exchanged in five hours in this case of a sheared hurricane; and 4) that one-fifth of the mass in the eyewall at a height of 5 km has an origin in the mid- to upper-level environment where thet(sub e) is much less than in the eyewall, which ventilates the ensemble average eyewall theta(sub e) by about 1 K. Implications of these findings to the problem of hurricane intensity forecasting are discussed.
Optimal finite-time processes in stochastic thermodynamics.
Schmiedl, Tim; Seifert, Udo
2007-03-09
For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicit solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and at the end of the process.
NASA Technical Reports Server (NTRS)
Taylor, John A.; Brasseur, G. P.; Zimmerman, P. R.; Cicerone, R. J.
1991-01-01
Sources and sinks of methane and methyl chloroform are investigated using a global three-dimensional Lagrangian tropospheric tracer transport model with parameterized hydroxyl and temperature fields. Using the hydroxyl radical field calibrated to the methyl chloroform observations, the globally averaged release of methane and its spatial and temporal distribution were investigated. Two source function models of the spatial and temporal distribution of the flux of methane to the atmosphere were developed. The first model was based on the assumption that methane is emitted as a proportion of net primary productivity (NPP). The second model identified source regions for methane from rice paddies, wetlands, enteric fermentation, termites, and biomass burning based on high-resolution land use data. The most significant difference between the two models were predictions of methane fluxes over China and South East Asia, the location of most of the world's rice paddies, indicating that either the assumption that a uniform fraction of NPP is converted to methane is not valid for rice paddies, or that NPP is underestimated for rice paddies, or that present methane emission estimates from rice paddies are too high.
Lagrangian coherent structures in hurricanes
NASA Astrophysics Data System (ADS)
Lipinski, Doug; Mohseni, Kamran
2011-11-01
We present the results of a ``surface tracking'' algorithm for efficiently computing Lagrangian coherent structure (LCS) surfaces in three dimensions. The algorithm is applied to data from a Weather Research and Forecasting simulation of hurricane Rita. The highly complicated LCS surfaces reveal complex dynamics and transport in the hurricane, particularly in the lower atmosphere boundary layer and the upper level outflow. The lower level transport in the hurricane is of particular importance for accurate intensity prediction in hurricane forecasts due to the uncertainty in the ocean-atmosphere interaction. Understanding the lower level transport and mixing behavior in hurricanes could lead to significant advances in hurricane intensity prediction.
Volkmar, E.C.; Dahlgren, R.A.; Stringfellow, W.T.; Henson, S.S.; Borglin, S.E.; Kendall, C.; Van Nieuwenhuyse, E. E.
2011-01-01
To investigate the mechanism for diel (24h) changes commonly observed at fixed sampling locations and how these diel changes relate to downstream transport in hypereutrophic surface waters, we studied a parcel of agricultural drainage water as it traveled for 84h in a concrete-lined channel having no additional water inputs or outputs. Algal fluorescence, dissolved oxygen, temperature, pH, conductivity, and turbidity were measured every 30min. Grab samples were collected every 2h for water quality analyses, including nutrients, suspended sediment, and chlorophyll/pheophytin. Strong diel patterns were observed for dissolved oxygen, pH, and temperature within the parcel of water. In contrast, algal pigments and nitrate did not exhibit diel patterns within the parcel of water, but did exhibit strong diel patterns for samples collected at a fixed sampling location. The diel patterns observed at fixed sampling locations for these constituents can be attributed to algal growth during the day and downstream transport (washout) of algae at night. Algal pigments showed a rapid daytime increase during the first 48h followed by a general decrease for the remainder of the study, possibly due to sedimentation and photobleaching. Algal growth (primarily diatoms) was apparent each day during the study, as measured by increasing dissolved oxygen concentrations, despite low phosphate concentrations (<0.01mgL-1). ?? 2011 Elsevier B.V.
Finite-time thermodynamics of port-Hamiltonian systems
NASA Astrophysics Data System (ADS)
Delvenne, Jean-Charles; Sandberg, Henrik
2014-01-01
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second Laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell’s demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.
Finite-time thermodynamic analysis of the Stirling engine
Ibrahim, O.M.; Ladas, H.G.
1995-12-31
This paper presents a finite-time thermodynamic analysis of the Stirling engine cycle. A lumped-parameter thermodynamic model is used to describe the dynamic behavior of the Stirling engine. The mathematical formulation of this model is based on mass and energy balances with associated heat transfer rate equations. These governing equations are formulated into a set of ordinary differential equations, which are then solved numerically to obtain the dynamic behavior of the Stirling engine. Close inspection of the governing equations reveals that the time to complete on cycle, {tau} and the engine time constant, {tau}{sub c} always appear together in a dimensionless ratio. This ratio, {tau}/{tau}{sub c}, is defined here as the Finite-Time Parameter, FTP. The effects of FTP upon power output and efficiency, are studied. The results show that there exists an optimum power output for a given engine design, based on engine speed and heat-transfer contact time. The results also provide an engineering evaluation procedure to improve the efficiency and power output of Stirling engines.
Finite time future singularities in the interacting dark sector
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Chimento, Luis P.; Richarte, Martín G.
2017-03-01
We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter-dark energy framework, with the latter in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-dominated universe until the sudden future singularity occurs. Then, an expanding branch emerges from a past singularity, reaches a maximum, reverses its expansion, and possibly collapses into itself while another expanding branch emerges from the latter singularity and has a de Sitter phase which is intrinsically stable. We obtain a different piecewise scale factor which describes a contracting de Sitter universe in the distant past until the finite-time future singularity happens. It emerges and continues in a contracting phase, bounces at the minimum, reverses, and enters into a stable de Sitter phase without a dramatic final. Also, we explore the aforesaid cosmic scenarios by focusing on the leading contributions of some physical quantities near the sudden future singularity and applying the geometric Tipler and Królak criteria in order to inspect the behavior of timelike geodesic curves around such singularity.
NASA Astrophysics Data System (ADS)
Curcoll Masanes, Roger; Rodó, Xavier; Anton, Jordi; Ballester, Joan; Jornet, Albert; Nofuentes, Manel; Sanchez-Manubens, Judith; Morguí, Josep-Anton
2015-04-01
Kawasaki disease (KD) is an acute, coronary artery vasculitis of young children, and still a medical mystery after more than 40 years. A former study [Rodó et al. 2011] demonstrated that certain patterns of winds in the troposphere above the earth's surface flowing from Asia were associated with the times of the annual peak in KD cases and with days having anomalously high numbers of KD patients. In a later study [Rodó et al. 2014], we used residence times from an Air Transport Model to pinpoint the source region for KD. Simulations were generated from locations spanning Japan from days with either high or low KD incidence. In order to cope with stationarity of synoptic situations, only trajectories for the winter months, when there is the maximum in KD cases, were considered. Trajectories traced back in time 10 days for each dataset and location were generated using the flexible particle Lagrangian dispersion model (FLEXPART Version 8.23 [Stohl et al. 2005]) run in backward mode. The particles modeled were air tracers, with 10,000 particles used on each model run. The model output used was residence time, with an output grid of 0.5° latitude × longitude and a time resolution of 3 h. The data input used for the FLEXPART model was gridded atmospheric wind velocity from the European Center for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim at 1°). Aggregates of winter period back-trajectories were calculated for three different regions of Japan. A common source of wind air masses was located for periods with High Kawasaki disease. Knowing the trajectories of winds from the air transport models, a sampling methodology was developed in order to capture the possible etiological agent or other tracers that could have been released together. This methodology is based on the sterilized filtering of high volumes of the transported air at medium tropospheric levels by aircraft sampling and a later analyze these filters with adequate techniques. High purity
Onsager coefficients of a finite-time Carnot cycle.
Izumida, Yuki; Okuda, Koji
2009-08-01
We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T(h)-T(c) --> 0 where T(h) and T(c) are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power eta(max) of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.
Onsager coefficients of a finite-time Carnot cycle
NASA Astrophysics Data System (ADS)
Izumida, Yuki; Okuda, Koji
2009-08-01
We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of Th-Tc→0 where Th and Tc are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power ηmax of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.
Sliding mode control method having terminal convergence in finite time
NASA Technical Reports Server (NTRS)
Venkataraman, Subramanian T. (Inventor); Gulati, Sandeep (Inventor)
1994-01-01
An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters.
Parisian ruin over a finite-time horizon
NASA Astrophysics Data System (ADS)
Dębicki, Krzysztof; Hashorva, Enkelejd; Ji, LanPeng
2016-03-01
For a risk process $R_u(t)=u+ct-X(t), t\\ge 0$, where $u\\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \\[ \\mathcal{P}_S(u,T_u)=\\mathbb{P}\\{\\inf_{t\\in[0,S]} \\sup_{s\\in[t,t+T_u]} R_u(s)<0\\}, \\] with a given positive constant $S$ and a positive measurable function $T_u$. We derive asymptotic expansion of $\\mathcal{P}_S(u,T_u)$, as $u\\to\\infty$, for the aggregate claim process $X$ modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a standard Brownian motion with drift over a finite-time interval.
Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
Kanno, Kazutaka; Uchida, Atsushi
2014-03-01
We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.
Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems.
Wang, Tianbo; Zhao, Shouwei; Zhou, Wuneng; Yu, Weiqin
2014-07-01
This paper investigates the finite-time master-slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master-slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Hasebe, Fumio; Noguchi, Taisuke
2016-04-01
The sudden decrease in stratospheric water vapor at around the year 2000 to 2001 is relatively well accepted in spite of the difficulty to quantify the long-term variations. This stepwise change is studied by examining the entry value of water to the stratosphere ([H2O]e) and some Lagrangian diagnostics of dehydration taking place in the tropical tropopause layer (TTL). The analysis is made using the backward kinematic trajectories initialized every ˜ 10 days from January 1997 to December 2002 at 400 K potential temperature surface in the tropics. The [H2O]e is estimated by the ensemble mean value of the water saturation mixing ratio (SMR) at the Lagrangian cold point (LCP) where SMR becomes minimum (SMR
Lagrangian coherent structures and turbulence characteristics downstream of prosthetic aortic valves
NASA Astrophysics Data System (ADS)
de Tullio, Marco D.
2015-11-01
The flowfield through prosthetic heart valves is investigated by means of direct numerical simulations, considering the fully coupled fluid-structure interaction problem. Two different aortic valve models are modeled: a bileaflet mechanical and a biological one. In order to reveal fluid flow structures and to better understand the transport mechanics, Lagrangian coherent structures (LCS) are used. LCS are distinguished material surfaces that can be identified as boundaries to regions with dynamically distinct behavior, and are revealed as hypersurfaces that locally maximize the finite-time Lyapunov exponent (FTLE) fields. Post-processing the flow simulation data, first FTLE fields are calculated integrating dense meshes of Lagrangian particles backward in time, and then attracting LCS are extracted. A three-jet configuration is distinctive of bi-leaflet mechanical valves, with higher turbulent shear stresses immediately distal to the valve leaflets, while a jet-like flow emerges from the central orifice of bio-prosthetic valves, with high turbulent shear stresses occurring at the edge of the jet. Details of the numerical methodology along with a thorough analysis of the different flow structures developing during the cardiac cycle for the two configurations will be provided.
Characteristic distributions of finite-time Lyapunov exponents.
Prasad, A; Ramaswamy, R
1999-09-01
We study the probability densities of finite-time or local Lyapunov exponents in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections, which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has a characteristic shape. For intermittent dynamics, and at crises, dynamical correlations lead to distributions with stretched exponential tails, while for fully developed chaos the probability density has a cusp. Exact results are presented for the logistic map, x-->4x(1-x). At intermittency the density is markedly asymmetric, while for "typical" chaos, it is known that the central limit theorem obtains and a Gaussian density results. Local analysis provides information on the variation of predictability on dynamical attractors. These densities, which are used to characterize the nonuniform spatial organization on chaotic attractors, are robust to noise and can, therefore, be measured from experimental data.
Finite time convergent learning law for continuous neural networks.
Chairez, Isaac
2014-02-01
This paper addresses the design of a discontinuous finite time convergent learning law for neural networks with continuous dynamics. The neural network was used here to obtain a non-parametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties was the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on discontinuous algorithms was used to adjust the weights of the neural network. The adaptive algorithm was derived by means of a non-standard Lyapunov function that is lower semi-continuous and differentiable in almost the whole space. A compensator term was included in the identifier to reject some specific perturbations using a nonlinear robust algorithm. Two numerical examples demonstrated the improvements achieved by the learning algorithm introduced in this paper compared to classical schemes with continuous learning methods. The first one dealt with a benchmark problem used in the paper to explain how the discontinuous learning law works. The second one used the methane production model to show the benefits in engineering applications of the learning law proposed in this paper.
Effects of finite-time singularities on gravitational waves
NASA Astrophysics Data System (ADS)
Kleidis, K.; Oikonomou, V. K.
2016-10-01
We analyze the impact of finite-time singularities on gravitational waves, in the context of F(R) gravity. We investigate which singularities are allowed to occur during the inflationary era, when gravitational waves are considered, and we discuss the quantitative implications of each allowed singularity. As we show, only a pressure singularity, the so-called Type II and also a Type IV singularity are allowed to occur during the inflationary era. In the case of a Type II, the resulting amplitude of the gravitational wave is zero or almost zero, hence this pressure singularity has a significant impact on the primordial gravitational waves. The case of a Type IV singularity is more interesting since as we show, the singularity has no effect on the amplitude of the gravitational waves. Therefore, this result combined with the fact that the Type IV singularity affects only the dynamics of inflation, leads to the conclusion that the Universe passes smoothly through a Type IV singularity.
A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows
NASA Astrophysics Data System (ADS)
Garaboa-Paz, D.; Pérez-Muñuzuri, V.
2015-10-01
The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Thus, the inertial FTLEs (iFTLEs) are defined in terms of the maximum stretching between infinitesimally close trajectories that have different initial velocities. The advantages of this improvement, if compared to the standard method (Shadden et al., 2005), are discussed for the double-gyre flow and the meandering jet flow. The new method allows one to identify the initial velocity that inertial particles must have in order to maximize their dispersion.
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Wiggins, Stephen; Curbelo, Jezabel; Mendoza, Carolina
2013-11-01
Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a ``heuristic argument'' that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (``time averages''). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We thank CESGA for computing facilities. This research was supported by MINECO grants: MTM2011-26696, I-Math C3-0104, ICMAT Severo Ochoa project SEV-2011-0087, and CSIC grant OCEANTECH. SW acknowledges the support of the ONR (Grant No. N00014-01-1-0769).
Nonstandard Lagrangian cosmology
NASA Astrophysics Data System (ADS)
El-Nabulsi, Rami Ahmad
2013-11-01
We show that many independent scenarios as the `accelerated expansion of the universe', `eternal inflation', `eternally oscillating universe', `nonsingular oscillating universe', and `collapse of an oscillating universe' may occur without modifying the gravity theory or introducing scalar fields of any type. This is achieved by replacing the standard Lagrangian in the Friedmann-Robertson-Walker spacetime model by an exponentially nonstandard Lagrangian which modify the Euler-Lagrange equation although the standard variational approach is used.
Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems
NASA Astrophysics Data System (ADS)
Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei
2016-07-01
This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.
Finite-time consensus for leader-following second-order multi-agent system
NASA Astrophysics Data System (ADS)
Sun, Fenglan; Guan, Zhi-Hong
2013-04-01
The finite-time consensus problems of second-order multi-agent system under fixed and switching network topologies are studied in this article. Based on the graph theory, LaSalle's invariance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. The leader-following finite-time consensus is analysed in detail. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Finite-Time Control by Observer-Based Output Feedback for Linear Discrete-Time Systems
NASA Astrophysics Data System (ADS)
Ichihara, Hiroyuki; Katayama, Hitoshi
In this paper we consider finite-time stabilization and finite-time boundedness control problems for time-varying discrete-time systems. We give a set of sufficient conditions, in terms of difference LMIs, for the existence of observer-based output feedback controllers that make the system finite-time stable and finite-time bounded. We then reduce the obtained results to the ones for time-invariant discrete-time systems and derive numerically tractable sufficient conditions given by LMIs. We also show numerical examples to illustrate the design methods of observer-based output feedback controllers.
Higher order finite-time consensus protocol for heterogeneous multi-agent systems
NASA Astrophysics Data System (ADS)
Zhou, Yingjiang; Yu, Xinghuo; Sun, Changyin; Yu, Wenwu
2015-02-01
This paper studies the higher order finite-time consensus protocol for heterogeneous multi-agent systems (HMASs). By adding a power integrator method and using heterogeneous domination method, two kinds of consensus protocols are proposed with state feedback and output feedback, respectively. First, for the leaderless and leader-follower HMASs, the continuous finite-time consensus protocols are proposed. Then, by designing a finite-time observer, the output-feedback finite-time consensus protocol is developed. Finally, simulations are performed to illustrate the effectiveness of the theoretical results.
Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation.
Yu, Jinpeng; Zhao, Lin; Yu, Haisheng; Lin, Chong; Dong, Wenjie
2017-08-22
This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Finite time control of a class of time-varying unified chaotic systems.
Ying, Yang; Guopei, Chen
2013-09-01
This paper considers the problem of finite time control for a class of time-varying unified chaotic system. First, based on the finite-time stability theory, a novel adaptive control technique is presented to achieve finite-time stabilization for time-varying unified chaotic system. Comparing with the existing methods, the proposed controller only need to be added on one state variable of systems and it is easy to be implemented. Then, a finite time control technique is provided to realize the tracking of any target function with second-order derivatives. Finally, Simulation results are provided to show the effectiveness of the proposed method.
Euler-Lagrangian computation for estuarine hydrodynamics
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
Robust control of post-stall pitching maneuver based on finite-time observer.
Wu, Dawei; Chen, Mou; Gong, Huajun
2017-09-01
This article presents a robust finite-time maneuver control scheme for the longitudinal attitude dynamic of the aircraft with unsteady aerodynamic disturbances and input saturation. To efficiently eliminate the influence of unsteady aerodynamic disturbances, nonlinear finite-time observers are developed. Despite the existence of the nonlinearity and the coupling between aircraft states and unsteady aerodynamic disturbances, the proposed observers can still precisely estimate the unmeasurable unsteady aerodynamic disturbances in finite time. To attenuate the effect caused by input saturation, a finite-time auxiliary system is constructed. With the error between the desired control input and saturation input as the input of the auxiliary system, the additional signals are generated to compensate for the effect of input saturation. Combined with the finite-time observers and the finite-time auxiliary system, a robust finite-time backstepping attitude control design is developed. The finite-time convergence of all closed-loop system signals is rigorously proved via Lyapunov analysis method under the developed robust attitude control schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed attitude control approaches. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Continuous composite finite-time convergent guidance laws with autopilot dynamics compensation.
He, Shaoming; Lin, Defu
2015-09-01
This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.
Hu, Qinglei; Zhang, Jian
2015-01-01
This paper investigates finite-time relative position coordinated tracking problem by output feedback for spacecraft formation flying without velocity measurement. By employing homogeneous system theory, a finite-time relative position coordinated tracking controller by state feedback is firstly developed, where the desired time-varying trajectory given in advance can be tracked by the formation. Then, to address the problem of lack of velocity measurements, a finite-time output feedback controller is proposed by involving a novel filter to recover unknown velocity information in a finite time. Rigorous proof shows that the proposed control law ensures global stability and guarantees the position of spacecraft formation to track a time-varying reference in finite time. Finally, simulation results are presented to illustrate the performance of the proposed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
NASA Astrophysics Data System (ADS)
Johnson, Perry L.; Meneveau, Charles
2015-08-01
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:-5, compared to about 8:3:-11 when using only the strain-rate tensor for calculating fluid volume deformations. The results
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
Johnson, Perry L. Meneveau, Charles
2015-08-15
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
Effective Lagrangian for supersymmetric QCD
Peskin, M.E.
1983-02-01
I present a Lagrangian which describes the spontaneous breaking of chiral symmetries in strongly interacting supersymmetric Yang-Mills theory with matter fields. This Lagrangian predicts that supersymmetry is spontaneously broken if the matter fields have precisely zero mass.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Finite time measurements by Unruh-DeWitt detector and Landauer's principle
NASA Astrophysics Data System (ADS)
Shevchenko, V.
2017-06-01
The model of Unruh-DeWitt detector coupled to the scalar field for finite time is studied. A systematic way of computing finite time corrections in various cases is suggested and nonperturbative effects like thermalization are discussed. It is shown in particular that adiabatic switching off the coupling between the detector and the thermal bath leaves non-vanishing corrections to the detector's levels distribution. Considering the two level detector as an information bearing degree of freedom encoding one bit of information, limits on external work for the detector's (de)coupling in finite time following from the Landauer's bound are formulated.
Sun, Yongzheng; Li, Wang; Zhao, Donghua
2012-06-01
In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.
Wu, Yuanyuan; Cao, Jinde; Alofi, Abdulaziz; Al-Mazrooei, Abdullah; Elaiw, Ahmed
2015-09-01
This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.
Liu, Xiaoyang; Ho, Daniel W C; Cao, Jinde; Xu, Wenying
2016-08-24
This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.
Finite-time consensus for heterogeneous multi-agent systems with mixed-order agents
NASA Astrophysics Data System (ADS)
Sun, Fenglan; Zhu, Wei
2015-08-01
This paper studies the finite-time consensus for heterogeneous multi-agent systems composed of mixed-order agents over fixed and switching topologies. The control protocol of each agent using local information is designed and the detailed analysis of the finite-time consensus for fixed and switching interaction topologies is presented. The design of the finite-time consensus protocol is based on graph theory, matrix theory, and LaSalle's invariance principle. Both theoretical studies and simulation results show the effectiveness of the proposed method and the correctness of the obtained theoretical results.
Wu, Yuanyuan; Cao, Jinde; Li, Qingbo; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-01-01
This paper deals with the finite-time synchronization problem for a class of uncertain coupled switched neural networks under asynchronous switching. By constructing appropriate Lyapunov-like functionals and using the average dwell time technique, some sufficient criteria are derived to guarantee the finite-time synchronization of considered uncertain coupled switched neural networks. Meanwhile, the asynchronous switching feedback controller is designed to finite-time synchronize the concerned networks. Finally, two numerical examples are introduced to show the validity of the main results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Finite time control of uncertain networked switched linear systems with quantizations
NASA Astrophysics Data System (ADS)
Chen, Xiaoling; Zhou, Guopeng; Tian, Fengxia; Liu, Hao
2017-01-01
This paper is concerned with the finite-time control problem for uncertain networked switched linear systems with both state and control input quantizations. By employing average well dwell time (ADT) and Lyapunov-like function method, a feedback controller is designed to guarantee that the dynamic augment closed-loop system is finite-time boundedness. Then based on this, some sufficient conditions which ensure the finite-time boundedness of networked switched systems are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach.
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2014-01-01
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in Castro et al. (Splash singularity for water waves, http://arxiv.org/abs/1106.2120v2, 2011), wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.
2010-09-30
the vertical interpolation adjustment given by Equation 8 (SL OMT ), NOGAPS SL/SI with non-interpolation in the vertical (SL NIV), and the non semi...interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV) and the non semi-Lagrangian NOGAPS (EULER). Figures 4 and...2009 comparing the control NOGAPS SL/SI with the adjusted vertical interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
New physical Lagrangian tracer
Zak, B.D.
1984-01-01
A physical Lagrangian tracer will be operational and available for use within the near future. The tracer is an adjustable buoyancy constant volume balloon with an onboard microprocessor to serve an appropriate array of sensors, and to control buoyancy. Tracking and data reporting is to be accomplished via the ARGOS satellite-borne data system, yielding both a local and a world-wide capability. 5 references, 1 figure.
Compressible Lagrangian hydrodynamics without Lagrangian cells
NASA Astrophysics Data System (ADS)
Clark, Robert A.
The partial differential Eqs [2.1, 2.2, and 2.3], along with the equation of state 2.4, which describe the time evolution of compressible fluid flow can be solved without the use of a Lagrangian mesh. The method follows embedded fluid points and uses finite difference approximations to ěc nablaP and ěc nabla · ěc u to update p, ěc u and e. We have demonstrated that the method can accurately calculate highly distorted flows without difficulty. The finite difference approximations are not unique, improvements may be found in the near future. The neighbor selection is not unique, but the one being used at present appears to do an excellent job. The method could be directly extended to three dimensions. One drawback to the method is the failure toexplicitly conserve mass, momentum and energy. In fact, at any given time, the mass is not defined. We must perform an auxiliary calculation by integrating the density field over space to obtain mass, energy and momentum. However, in all cases where we have done this, we have found the drift in these quantities to be no more than a few percent.
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Sathishkumar, M.; Kaviarasan, B.; Anthoni, S. Marshal
2016-04-01
This article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov-Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time
NASA Astrophysics Data System (ADS)
Nguyen, V. T.
2017-01-01
In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation
Nonsmooth finite-time stabilization of neural networks with discontinuous activations.
Liu, Xiaoyang; Park, Ju H; Jiang, Nan; Cao, Jinde
2014-04-01
This paper is concerned with the finite-time stabilization for a class of neural networks (NNs) with discontinuous activations. The purpose of the addressed problem is to design a discontinuous controller to stabilize the states of such neural networks in finite time. Unlike the previous works, such stabilization objective will be realized for neural networks when the activations and controllers are both discontinuous. Based on the famous finite-time stability theorem of nonlinear systems and nonsmooth analysis in mathematics, sufficient conditions are established to ensure the finite-time stability of the dynamics of NNs. Then, the upper bound of the settling time for stabilization can be estimated in two forms due to two different methods of proof. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method. Copyright © 2014 Elsevier Ltd. All rights reserved.
Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.
Chen, Qiang; Ren, Xuemei; Na, Jing
2015-09-01
In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method.
NASA Astrophysics Data System (ADS)
Ran, Dechao; Chen, Xiaoqian; Misra, Arun K.
2017-07-01
This paper investigates the finite time coordinated formation control problem for spacecraft formation flying (SFF) under the assumption of directed communication topology. By using the neighborhood state measurements, a robust finite time coordinated formation controller is firstly designed based on the nonsingular terminal sliding mode surface. To address the special case that the desired trajectory of the formation is only accessible to a subset of spacecraft in the formation, an adaptive finite time coordinated formation controller is also proposed by designing a novel sliding mode surface. In both cases, the external disturbances are explicitly taken into account. Rigorous theoretical analysis proves that the proposed control schemes ensure that the closed-loop system can track the desired time-varying trajectory in finite time. Numerical simulations are presented that not only highlights the closed-loop performance benefits from the proposed control algorithms, but also illustrates the effectiveness in the presence of external disturbances when compared with the existing coordinated formation control schemes.
Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions.
Meng, Deyuan; Jia, Yingmin; Du, Junping
2016-04-01
This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.
Finite-Time Control for Robust Tracking Consensus in MASs With an Uncertain Leader.
Lu, Xiaoqing; Wang, Yaonan; Yu, Xinghuo; Lai, Jingang
2016-03-31
This paper investigates the finite-time control for robust tracking consensus problems of multiagent systems with an uncertain leader for situations where the state of the considered active leader may not be measured and the directed network topology is time-varying. Based on the neighbor-based state-estimation rule and a new Lyapunov stability analysis method, a continuous and nonlinear distributed tracking protocol using only relative position information is designed, under which each agent can follow the leader in finite time if the input (acceleration) of the leader is known, and the tracking errors can converge to a bounded region in finite time if the input of the leader is unknown. In particular, a special continuous distributed tracking protocol with bounded control inputs is introduced to track the active leader in finite time. Numerical simulations are also given to illustrate the effectiveness of the theoretic results.
Distributed finite-time containment control for double-integrator multiagent systems.
Wang, Xiangyu; Li, Shihua; Shi, Peng
2014-09-01
In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.
Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation
NASA Astrophysics Data System (ADS)
Pan, Huihui; Jing, Xingjian; Sun, Weichao
2017-05-01
This paper focuses on the finite-time tracking control with external disturbance for active suspension systems. In order to compensate unknown disturbance efficiently, a disturbance compensator with finite-time convergence property is studied. By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance. According to the finite-time separation principle, the design procedures of the nominal controller for the suspension system without disturbance and the disturbance compensator can be implemented in a completely independent manner. Therefore, the overall control law for the closed-loop system is continuous, which offers some distinct advantages over the existing discontinuous ones. From the perspective of practical implementation, the continuous controller can avoid effectively the unexpected chattering in active suspension control. Comparative experimental results are presented and discussed to illustrate the advantage and effectiveness of the proposed control strategy.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Lagrangian coherent structures and the dynamics of inertial particles
NASA Astrophysics Data System (ADS)
Madhavan, Sudharsan
Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley equations have been employed to track particles. Patterns formed by inertial particles are reported along with their dependance on Strokes number and density of particles relative to the carrier-fluid density. Our results distinguish patterns formed by particles denser than the fluid (aerosols) from those formed by particles lighter than the fluid (bubbles). Preferential concentration of these particles at specific regions of the flow have been observed. The attenuating, low-pass filter effect of Stokes drag on bubbles are reported for the first time. The results from this part of the work motivated further investigations into the underlying organizing structures of the flow, namely the Lagrangian coherent structures (LCS). LCS is traditionally evaluated using FTLE. In the next part of the work, our objective was to interpret the dynamics of inertial particles by evaluating finite-time Lyapunov exponents on their trajectories. A main result is that aerosols were found to be attracted and preferentially concentrated along ridges of negative finite-time Lyapunov exponents (nFTLE) of the underlying flow. On the other hand bubbles were found to be repelled from these structures and were therefore observed preferentially concentrating away from these zones. These results, being reported for the first time, supplement the existing literature on preferential concentration of inertial particles. Despite having an effect on particle trajectories, increasing the Stokes number had very little effect on inertial finite-time Lyapunov exponents (iFTLE). Furthermore, increasing Stokes number resulted in an increase in the ridges of iFTLE contours for aerosols, whereas for bubbles the opposite was observed. These findings indicate that optimum mixing occurs at
Finite-time consensus for leader-following multi-agent systems over switching network topologies
NASA Astrophysics Data System (ADS)
Sun, Feng-Lan; Zhu, Wei
2013-11-01
Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper. Based on the graph theory, matrix theory, homogeneity with dilation, and LaSalle's invariance principle, the control protocol of each agent using local information is designed, and the detailed analysis of the leader-following finite-time consensus is provided. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control.
Liu, Xiwei; Chen, Tianping
2016-12-06
In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.
Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil
NASA Astrophysics Data System (ADS)
Wu, Qin; Huang, Biao; Wang, Guoyu
2016-02-01
The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equation γ {-Re}_θ transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re=7.5× 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.
Introduction to Focus Issue: Lagrangian Coherent Structures.
Peacock, Thomas; Dabiri, John
2010-03-01
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.
Chaotic Lagrangian models for turbulent relative dispersion
NASA Astrophysics Data System (ADS)
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
NASA Astrophysics Data System (ADS)
Schamel, Hans
2004-03-01
The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D
Multiplicative form of the Lagrangian
NASA Astrophysics Data System (ADS)
Surawuttinack, K.; Yoo-Kong, S.; Tanasittikosol, M.
2016-12-01
We obtain an alternative class of Lagrangians in the so-called the multiplicative form for a system with one degree of freedom in the nonrelativistic and the relativistic cases. This new form of the Lagrangian can be regarded as a one-parameter class with the parameter λ obtained using an extension of the standard additive form of the Lagrangian because both forms yield the same equation of motion. We note that the multiplicative form of the Lagrangian can be regarded as a generating function for obtaining an infinite hierarchy of Lagrangians that yield the same equation of motion. This nontrivial set of Lagrangians confirms that the Lagrange function is in fact nonunique.
NASA Astrophysics Data System (ADS)
Kim, Y. H.; Choi, B.; Son, Y. B.; Shim, W. J.; Hwang, J. H.; Park, Y.
2012-12-01
Series of satellite images show that the development and migration of green macroalgal bloom (known as Ulva prolifera) in the Yellow Sea (YS) and Eastern China Sea (ECS). This presentation will utilize the Lagrangian Coherent Structures (LCS) analysis to demonstrate the dispersion pattern of algal bloom patches. Analyzing LCS such as stable and unstable manifolds is one of emerging technologies for characterizing Lagrangian pathways in aquatic environments. This approach is based on the assumption that unstable manifolds such as ridges (i.e., high values) in the finite-time Lyapunov exponent (FTLE) fields coincide with material transport barriers. In this study, the FTLE fields were computed from gridded trajectories using flow fields provided by Regional Ocean Modeling System (ROMS) in the YS/ECS during summer 2011. The results show that there exist two strong transport barriers that lie along the east-west direction, at least, for the simulation period; one is located from the north of Changjiang River mouth to the middle of the Yellow Sea and the other one is stretched from the south of Shandong Peninsular toward east/southeast. This LCS analysis suggests that patches of green algae developed in the coastal region of Jiangsu Province during summer may migrate toward east into the middle of the YS or even toward Korean coast rather than extending along the Jiangsu coast, which is consistent with the observation results derived from the satellite ocean color data. In the very same manner, the utilization of LCS results to evaluate the distribution/transport pattern of marine debris in the YS/ECS will also be discussed during the presentation.
NASA Astrophysics Data System (ADS)
Short, Cody R.; Howell, Kathleen C.
2014-02-01
The Finite-Time Lyapunov Exponent (FTLE) has been demonstrated as an effective metric for revealing distinct, bounded regions within a flow. The dynamical differential equations derived in multi-body gravitational environments model a flow that governs the motion of a spacecraft. Specific features emerge in an FTLE map, denoted Lagrangian Coherent Structures (LCS), that define the extent of regions that bound qualitatively different types of behavior. Consequently, LCS supply effective barriers to transport in a generic system, similar to the notion of invariant manifolds in autonomous systems. Unlike traditional invariant manifolds associated with solutions in an autonomous system, LCS evolve with the flow in time-dependent systems while continuing to bound distinct regions of behavior. Moreover, in general, FTLE values supply information describing the relative sensitivity in the neighborhood of a trajectory. Here, different models and variable representations are used to generate maps of FTLE, and the resulting structures are applied to design and analysis within an astrodynamical context. Application of FTLE and LCS to transfers from LEO to the L1 region in the Earth-Moon system are presented and discussed. In an additional example, an FTLE analysis is offered of a few stationkeeping maneuvers from the Earth-Moon mission ARTEMIS (Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun).
NASA Astrophysics Data System (ADS)
Griffa, Annalisa; Carlson, Daniel; Berta, Maristella; Sciascia, Roberta; Corgnati, Lorenzo; Mantovani, Carlo; Fredji, Erick; Magaldi, Marcello; Zambianchi, Enrico; Poulain, Pierre Marie; Russo, Aniello; Carniel, Sandro
2017-04-01
Surface transport in the Adriatic Sea is investigated using data from historic drifter data, HF radar and virtual particles computed from a numerical model. Alongshore coastal currents and cyclonic gyres are the primary circulation features that connect regions in the Adriatic Sea. Their strength is highly dependent on the wind, with Southeasterly Sirocco winds driving eastward cross-Adriatic transport from the Italian coasts and Northwesterly Mistral winds enhancing east-to-west transport. Results from the analysis show that Cross-Adriatic connection percentages were higher for east-to-west transport, with westward (eastward) transport observed mostly in the northern (southern) arms of the central and southern gyres. These pathways of patterns influence the connection between Marine Protected Areas (MPAs) and between spawning and nursery areas for small pelagic fish. Percentage connections between MPAs are computed, showing that while the highest percentages occur through boundary currents, significant percentages also occur through cross-gyre transport, suggesting the concept of cell-based ecosystems. The nursery area of the Manfredonia Gulf has limited retention properties, and eggs and larvae are likely to reach the Gulf mostly from remote spawning areas through current transport
Lagrangian statistics in laboratory 2D turbulence
NASA Astrophysics Data System (ADS)
Xia, Hua; Francois, Nicolas; Punzmann, Horst; Shats, Michael
2014-05-01
Turbulent mixing in liquids and gases is ubiquitous in nature and industrial flows. Understanding statistical properties of Lagrangian trajectories in turbulence is crucial for a range of problems such as spreading of plankton in the ocean, transport of pollutants, etc. Oceanic data on trajectories of the free-drifting instruments, indicate that the trajectory statistics can often be described by a Lagrangian integral scale. Turbulence however is a state of a flow dominated by a hierarchy of scales, and it is not clear which of these scales mostly affect particle dispersion. Moreover, coherent structures often coexist with turbulence in laboratory experiments [1]. The effect of coherent structures on particle dispersion in turbulent flows is not well understood. Recent progress in scientific imaging and computational power made it possible to tackle this problem experimentally. In this talk, we report the analysis of the higher order Lagrangian statistics in laboratory two-dimensional turbulence. Our results show that fluid particle dispersion is diffusive and it is determined by a single measurable Lagrangian scale related to the forcing scale [2]. Higher order moments of the particle dispersion show strong self-similarity in fully developed turbulence [3]. Here we introduce a new dispersion law that describes single particle dispersion during the turbulence development [4]. These results offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales are persistent. It may help better understanding of drifter Lagrangian statistics in the regions of the ocean where small scale coherent eddies are present [5]. Reference: 1. H. Xia, H. Punzmann, G. Falkovich and M. Shats, Physical Review Letters, 101, 194504 (2008) 2. H. Xia, N. Francois, H. Punzmann, and M. Shats, Nature Communications, 4, 2013 (2013) 3. R. Ferrari, A.J. Manfroi , W.R. Young, Physica D 154 111 (2001) 4. H. Xia, N. Francois, H. Punzmann and M. Shats, submitted (2014
NASA Astrophysics Data System (ADS)
Babaee, Hessam; Farazmand, Mohamad; Haller, George; Sapsis, Themistoklis P.
2017-06-01
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.
Babaee, Hessam; Farazmand, Mohamad; Haller, George; Sapsis, Themistoklis P
2017-06-01
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.
Bamba, Kazuharu; Nojiri, Shin'ichi; Odintsov, Sergei D E-mail: nojiri@phys.nagoya-u.ac.jp
2008-10-15
We investigate the future evolution of the dark energy universe in modified gravities, including F(R) gravity, and string-inspired scalar Gauss-Bonnet and modified Gauss-Bonnet ones, and ideal fluid with an inhomogeneous equation of state (EoS). The modified Friedmann-Robertson-Walker dynamics for all of these theories may be presented in a universal form by using the effective ideal fluid with an inhomogeneous EoS without specifying its explicit form. We construct several examples of a modified gravity which produces accelerating cosmologies ending at the finite-time future singularities of all four known types by applying a reconstruction program. Some scenarios for resolving a finite-time future singularity are presented. Among these scenarios, the most natural one is related to additional modification of the gravitational action in the early universe. In addition, late-time cosmology in the non-minimal Maxwell-Einstein theory is considered. We investigate the forms of non-minimal gravitational coupling which generate finite-time future singularities and the general conditions for this coupling such that the finite-time future singularities cannot emerge. Furthermore, it is shown that the non-minimal gravitational coupling can remove the finite-time future singularities or make the singularity stronger (or weaker) in modified gravity.
NASA Technical Reports Server (NTRS)
Eluszkiewicz, Janusz; Nehrkorn, Thomas; Wofsy, Steven C.; Matross, Daniel; Gerbig, Christoph; Lin, John C.; Freitas, Saulo; Longo, Marcos; Andrews, Arlyn E.; Peters, Wouter
2007-01-01
This paper evaluates simulations of atmospheric CO2 measured in 2004 at continental surface and airborne receptors, intended to test the capability to use data with high temporal and spatial resolution for analyses of carbon sources and sinks at regional and continental scales. The simulations were performed using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by the Weather Forecast and Research (WRF) model, and linked to surface fluxes from the satellite-driven Vegetation Photosynthesis and Respiration Model (VPRM). The simulations provide detailed representations of hourly CO2 tower data and reproduce the shapes of airborne vertical profiles with high fidelity. WRF meteorology gives superior model performance compared with standard meteorological products, and the impact of including WRF convective mass fluxes in the STILT trajectory calculations is significant in individual cases. Important biases in the simulation are associated with the nighttime CO2 build-up and subsequent morning transition to convective conditions, and with errors in the advected lateral boundary condition. Comparison of STILT simulations driven by the WRF model against those driven by the Brazilian variant of the Regional Atmospheric Modeling System (BRAMS) shows that model-to-model differences are smaller than between an individual transport model and observations, pointing to systematic errors in the simulated transport. Future developments in the WRF model s data assimilation capabilities, basic research into the fundamental aspects of trajectory calculations, and intercomparison studies involving other transport models, are possible venues for reducing these errors. Overall, the STILT/WRF/VPRM offers a powerful tool for continental and regional scale carbon flux estimates.
NASA Technical Reports Server (NTRS)
Eluszkiewicz, Janusz; Nehrkorn, Thomas; Wofsy, Steven C.; Matross, Daniel; Gerbig, Christoph; Lin, John C.; Freitas, Saulo; Longo, Marcos; Andrews, Arlyn E.; Peters, Wouter
2007-01-01
This paper evaluates simulations of atmospheric CO2 measured in 2004 at continental surface and airborne receptors, intended to test the capability to use data with high temporal and spatial resolution for analyses of carbon sources and sinks at regional and continental scales. The simulations were performed using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by the Weather Forecast and Research (WRF) model, and linked to surface fluxes from the satellite-driven Vegetation Photosynthesis and Respiration Model (VPRM). The simulations provide detailed representations of hourly CO2 tower data and reproduce the shapes of airborne vertical profiles with high fidelity. WRF meteorology gives superior model performance compared with standard meteorological products, and the impact of including WRF convective mass fluxes in the STILT trajectory calculations is significant in individual cases. Important biases in the simulation are associated with the nighttime CO2 build-up and subsequent morning transition to convective conditions, and with errors in the advected lateral boundary condition. Comparison of STILT simulations driven by the WRF model against those driven by the Brazilian variant of the Regional Atmospheric Modeling System (BRAMS) shows that model-to-model differences are smaller than between an individual transport model and observations, pointing to systematic errors in the simulated transport. Future developments in the WRF model s data assimilation capabilities, basic research into the fundamental aspects of trajectory calculations, and intercomparison studies involving other transport models, are possible venues for reducing these errors. Overall, the STILT/WRF/VPRM offers a powerful tool for continental and regional scale carbon flux estimates.
Applications the Lagrangian description in aperiodic flows
NASA Astrophysics Data System (ADS)
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities.
Wang, Zhuo; Xu, Yong; Lu, Renquan; Peng, Hui
2017-03-01
This paper investigates the issue of finite-time state estimation for coupled Markovian neural networks subject to sensor nonlinearities, where the Markov chain with partially unknown transition probabilities is considered. A Luenberger-type state estimator is proposed based on incomplete measurements, and the estimation error system is derived by using the Kronecker product. By using the Lyapunov method, sufficient conditions are established, which guarantee that the estimation error system is stochastically finite-time bounded and stochastically finite-time stable, respectively. Then, the estimator gains are obtained via solving a set of coupled linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design method.
Finite-Time Consensus of Multiagent Systems With a Switching Protocol.
Liu, Xiaoyang; Lam, James; Yu, Wenwu; Chen, Guanrong
2016-04-01
In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.
Finite-time boundedness and stabilisation of networked control systems with bounded packet dropout
NASA Astrophysics Data System (ADS)
Sun, Yeguo
2014-09-01
In this paper, the finite-time boundedness and stabilisation problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilisation of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.
Passivity control with practically finite-time convergence for large space structures
NASA Astrophysics Data System (ADS)
Hu, Quan; Li, Jinyue; Zhang, Jingrui
2017-02-01
A nonlinear output feedback control law based on passivity is proposed to reduce the vibration of large space structures. The considered system is assumed to be equipped with collocated actuators and sensors. The concept of practically finite-time stability is first developed to describe the finite-time convergence of a passive system. Then, an output feedback is introduced to drive the trajectories of a passive system into a small set around the origin in finite time. Finally, the proposed control strategy is applied to the vibration suppression of large space structures with distributed thrusters and velocity sensors or torque outputting devices and angular rate sensors. Numerical simulations are conducted to validate the effectiveness of the proposed controller.
Finite-time consensus of time-varying nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Liu, Qingrong; Liang, Zhishan
2016-08-01
This paper investigates the problem of leader-follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader-follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.
Finite-time H∞ synchronization for complex networks with semi-Markov jump topology
NASA Astrophysics Data System (ADS)
Shen, Hao; Park, Ju H.; Wu, Zheng-Guang; Zhang, Zhengqiang
2015-07-01
This paper investigates the problem of finite-time H∞ synchronization for complex networks with time-varying delays and semi-Markov jump topology. The network topologies are assumed to switch from one to another at different instants. Such a switching is governed by a semi-Markov process which are time-varying and dependent on the sojourn-time h. Attention is focused on proposing some synchronization criteria guaranteeing the underlying network is stochastically finite-time H∞ synchronized. By using the properties of Kronecker product combined with the Lyapunov-Krasovskii method, the solutions to the finite-time H∞ synchronization problem are formulated in the form of low-dimensional linear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of our proposed approach.
Lagrangian computation of inviscid compressible flows
NASA Technical Reports Server (NTRS)
Klopfer, G. H.
1978-01-01
A Lagrangian method is developed to solve the Euler equations of gas dynamics. The solution of the equations is obtained by a numerical computation with the well-known Flux-Corrected-Transport (FCT) numerical method. This procedure is modified so that the boundary treatment is accurate and relatively simple. Shock waves and other flow discontinuities are captured monotonically without any type of fitting procedures. The Lagrangian method is employed so that the problem of mesh generation is completely avoided. The method is applicable to all Mach numbers except the low subsonic range where compressibility effects are small. The method is applied to a one-dimensional Riemann problem (shock tube) and to a two-dimensional supersonic channel flow with reflecting shock waves.
Finite-time control of DC-DC buck converters via integral terminal sliding modes
NASA Astrophysics Data System (ADS)
Chiu, Chian-Song; Shen, Chih-Teng
2012-05-01
This article presents novel terminal sliding modes for finite-time output tracking control of DC-DC buck converters. Instead of using traditional singular terminal sliding mode, two integral terminal sliding modes are introduced for robust output voltage tracking of uncertain buck converters. Different from traditional sliding mode control (SMC), the proposed controller assures finite convergence time for the tracking error and integral tracking error. Furthermore, the singular problem in traditional terminal SMC is removed from this article. When considering worse modelling, adaptive integral terminal SMC is derived to guarantee finite-time convergence under more relaxed stability conditions. In addition, several experiments show better start-up performance and robustness.
Finite-time thin film rupture driven by modified evaporative loss
NASA Astrophysics Data System (ADS)
Ji, Hangjie; Witelski, Thomas P.
2017-03-01
Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with modified evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term. Several different types of finite-time singularities are observed due to balances between conservative and non-conservative terms. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.
NASA Astrophysics Data System (ADS)
Zhai, Jun-Yong
2014-03-01
This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.
Finite-time synchronization control of a class of memristor-based recurrent neural networks.
Jiang, Minghui; Wang, Shuangtao; Mei, Jun; Shen, Yanjun
2015-03-01
This paper presents a global and local finite-time synchronization control law for memristor neural networks. By utilizing the drive-response concept, differential inclusions theory, and Lyapunov functional method, we establish several sufficient conditions for finite-time synchronization between the master and corresponding slave memristor-based neural network with the designed controller. In comparison with the existing results, the proposed stability conditions are new, and the obtained results extend some previous works on conventional recurrent neural networks. Two numerical examples are provided to illustrate the effective of the design method.
An integral equation representation approach for valuing Russian options with a finite time horizon
NASA Astrophysics Data System (ADS)
Jeon, Junkee; Han, Heejae; Kim, Hyeonuk; Kang, Myungjoo
2016-07-01
In this paper, we first describe a general solution for the inhomogeneous Black-Scholes partial differential equation with mixed boundary conditions using Mellin transform techniques. Since Russian options with a finite time horizon are usually formulated into the inhomogeneous free-boundary Black-Scholes partial differential equation with a mixed boundary condition, we apply our method to Russian options and derive an integral equation satisfied by Russian options with a finite time horizon. Furthermore, we present some numerical solutions and plots of the integral equation using recursive integration methods and demonstrate the computational accuracy and efficiency of our method compared to other competing approaches.
Finite-time synchronization of fractional-order simplest two-component chaotic oscillators
NASA Astrophysics Data System (ADS)
Kengne, Romanic; Tchitnga, Robert; Mezatio, Anicet; Fomethe, Anaclet; Litak, Grzegorz
2017-05-01
The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractional-order systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.
A novel recurrent neural network with finite-time convergence for linear programming.
Liu, Qingshan; Cao, Jinde; Chen, Guanrong
2010-11-01
In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.
Global generalised exponential/finite-time control for course-keeping of ships
NASA Astrophysics Data System (ADS)
Sun, Xifang; Chen, Weisheng
2016-06-01
This paper addresses the global generalised exponential/finite-time control of the nonlinear ship course system with an unknown control coefficient. Different from the well-known Nussbaum-gain adaptive rule, a new Lyapunov-based adaptive logic switching rule is proposed to seek the correct control direction of the ship course system. The main advantage of the proposed controller is that it guarantees the global generalised exponential/finite-time control of closed-loop systems. Theoretical analysis and simulation results show the effectiveness of the developed control method.
Lagrangian Observations and Modeling of Marine Larvae
NASA Astrophysics Data System (ADS)
Paris, Claire B.; Irisson, Jean-Olivier
2017-04-01
Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a Lagrangian platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed Lagrangian behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source Lagrangian tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive Lagrangian trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.
Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow
NASA Astrophysics Data System (ADS)
Chabreyrie, Rodolphe; Llewellyn Smith, Stefan
2012-11-01
Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this talk, we use a set of classical (i.e. Poincaré section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time. This research was funded by the ONR MURI Dynamical Systems Theory and Lagrangian Data Assimilation in 3D+1 Geophysical Fluid Dynamics.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang Wenbo; Mahalov, Alex
2013-03-15
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
NASA Astrophysics Data System (ADS)
Tang, Wenbo; Mahalov, Alex
2013-03-01
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology—the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
NASA Astrophysics Data System (ADS)
Cassiani, Massimo; Stohl, Andreas; Olivié, Dirk; Seland, Øyvind; Bethke, Ingo; Pisso, Ignacio; Iversen, Trond
2016-11-01
The offline FLEXible PARTicle (FLEXPART) stochastic dispersion model is currently a community model used by many scientists. Here, an alternative FLEXPART model version has been developed and tailored to use with the meteorological output data generated by the CMIP5-version of the Norwegian Earth System Model (NorESM1-M). The atmospheric component of the NorESM1-M is based on the Community Atmosphere Model (CAM4); hence, this FLEXPART version could be widely applicable and it provides a new advanced tool to directly analyse and diagnose atmospheric transport properties of the state-of-the-art climate model NorESM in a reliable way. The adaptation of FLEXPART to NorESM required new routines to read meteorological fields, new post-processing routines to obtain the vertical velocity in the FLEXPART coordinate system, and other changes. These are described in detail in this paper. To validate the model, several tests were performed that offered the possibility to investigate some aspects of offline global dispersion modelling. First, a comprehensive comparison was made between the tracer transport from several point sources around the globe calculated online by the transport scheme embedded in CAM4 and the FLEXPART model applied offline on output data. The comparison allowed investigating several aspects of the transport schemes including the approximation introduced by using an offline dispersion model with the need to transform the vertical coordinate system, the influence on the model results of the sub-grid-scale parameterisations of convection and boundary layer height and the possible advantage entailed in using a numerically non-diffusive Lagrangian particle solver. Subsequently, a comparison between the reference FLEXPART model and the FLEXPART-NorESM/CAM version was performed to compare the well-mixed state of the atmosphere in a 1-year global simulation. The two model versions use different methods to obtain the vertical velocity but no significant difference
Lagrangian Coherent Structures in the Trieste Gulf
NASA Astrophysics Data System (ADS)
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Lagrangian Coherent Structures in a Non-Euclidean Global Thermosphere
NASA Astrophysics Data System (ADS)
Wang, N.; Ramirez, U.; Flores, F.; Datta-Barua, S.
2016-12-01
Lagrangian Coherent Structures (LCSs) are manifolds of maximum divergence or convergence in 2D or 3D time-varying flow fields. The study of LCSs has been used to predict material transport in numerous geophysical flows. The most commonly used computational method for finding LCSs is to compute the finite time Lyapunov exponent (FTLE), a scalar field measuring the ratio of stretching after a given interval of time among neighboring particles, relative to their initial separation. LCS ridges are located at the local maxima of the FTLE. The LCS must be objective (frame-invariant for different observers), and the technique for computing the FTLE that determines the LCS typically assumes a Euclidean domain. Previous work showed that LCSs are likely to exist globally at high latitudes using the Euclidean norm. Here we refine that calculation by deriving the FTLE calculation for the Riemannian manifold of a spherical surface, and applying it to the thermospheric layer of the atmosphere globally. The thermosphere is treated as a closed spherical 2D domain on which the fluid flows, assuming negligible vertical flow. The domain is discretized in longitude and latitude, and the Horizontal Wind Model 2014 (HWM14) is used to generate the 2D velocity field at each grid point, each of which is a ground speed in the local east-north-up (ENU) frame. To make the LCS objective, the ground speed in each local ENU frame is converted to angular velocity in the earth-centered earth-fixed (ECEF) coordinates. Using bilinear interpolation and including the rotational velocity of Earth to transform to an inertial frame, we trace the trajectory of each particle to compute the final positions after the integration time. Replacing the Euclidean distance between particles with the great circle distance gives the FTLE scalar field from which the LCSs can be identified. We find and illustrate objective LCSs in the neutral wind flow field at high latitudes by applying this algorithm for the
Finite-time Lyapunov stability analysis and its application to atmospheric predictability
Yoden, Shigeo; Nomura, Masako )
1993-06-01
Finite-time Lyapunov stability, analysis is reviewed and applied to a low-order spectral model of barotropic flow in a midlatitude [beta] channel. The tangent linear equations of the model are used to investigate the growth of small perturbations superposed on a reference solution for a prescribed time interval. Three types of reference solutions of the model, stationary, periodic, and chaotic, are investigated to demonstrate usefulness of the analysis in the study of the atmospheric predictability problem. The finite-time Lyapunov exponents, which give the growth rate of small perturbations, depend upon the reference solution as well as the preturbation for time interval. The finite-time Lyapunov vector corresponding to the largest Lyapunov exponent gives the streamfunction field of the fastest growing perturbation for the time interval. In the case of the chaotic reference solution, the streamfunction field has large amplitudes in limited areas for a small time interval. The areas of the large perturbation growth have some relation to the reference streamfunction field. A possible application of the finite-time Lyapunov exponents and vectors to the atmospheric predictability problem is discussed. These quantities might be used as several forecast measures of the time-dependent predictability in numerical weather predictions. 29 refs., 14 figs.
Finite-time tracking control for multiple non-holonomic mobile robots based on visual servoing
NASA Astrophysics Data System (ADS)
Ou, Meiying; Li, Shihua; Wang, Chaoli
2013-12-01
This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.
NASA Astrophysics Data System (ADS)
Liu, Huiyang; Cheng, Long; Tan, Min; Hou, Zengguang; Wang, Yunpeng
2015-02-01
In this paper, exponential finite-time coordination problems of multi-agent systems are investigated, including containment control and consensus. The theoretical basis is that a class of nonlinear systems has favourable finite-time convergence characteristic. For the objective of containment control, the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time. For the objective of consensus, a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time. The distinguished features of this paper lie in the following two points: (1) a smaller settling time of the Lyapunov function is obtained, which manifests in a faster convergence rate than the traditional one and (2) the weakly connected topology considered in this paper is more general than the ones (a spanning tree, a spanning forest, and so on) in other coordination problems. All the results are illustrated by some simulations.
A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence
NASA Astrophysics Data System (ADS)
Li, Guilin; Ji, Haibo
2016-05-01
This paper presents a novel three-dimensional nonlinear terminal guidance law with finite-time convergence for intercepting manoeuvring targets. Different from the usual method of decoupling the missile-target relative motion into two-dimensional planes, this law is designed via using the coupled dynamics. The guidance law is derived based on the theory of finite-time input-to-state stability (ISS), which needs no assumption of the linearisation and the estimation of target accelerations. Under this law, the line-of-sight angular rates can be stabilised to a small domain of convergence around zero in finite time. The convergence rate and convergence domain can be adjusted by changing the guidance parameters. First, a sufficient condition on finite-time ISS of the guidance system is given, and is subsequently used to design the guidance law. Finally, simulation results are provided to show that the proposed guidance law possesses fast convergence rate and strong robustness to target manoeuvres.
Almost global finite-time stabilization of rigid body attitude motion
NASA Astrophysics Data System (ADS)
Bohn, Jan
This dissertation considers continuous finite-time stabilization of rigid body attitude dynamics using a coordinate-free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). First a general methodology to construct control Lyapunov functions that are Holder continuous and that can be used to show finite-time stability of the feedback controlled system, is presented. The dynamics is represented by generalized (local) coordinates. This methodology is then extended, using a Holder continuous Morse-Lyapunov function, to obtain a finite-time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback. The feedback control law designed here leads to almost global finite-time stabilization of the attitude motion of a rigid body with Holder continuous feedback, to the desired attitude. Furthermore, using the finite-time feedback stabilization scheme, a state observer is proposed for rigid body attitude motion with a given attitude dynamics model that in the absence of measurement noise and disturbance torques leads to almost global finite-time stable convergence of attitude motion state estimates to the actual states for a rigid body whose inertia is known. Subsequently this state observer is combined with a deterministic filter scheme that utilizes a set of sigma points obtained from the unscented transform based on exponential coordinates. This estimation scheme uses discrete-time state measurements of inertially known vectors along with rate gyro measurements of the angular velocity, to obtain state estimates in the filtering stage. Additionally, a set of sigma points is obtained from the unscented transform, with re-sampling centered at the current state estimate at each measurement instant. The state estimates along with sampled sigma points are propagated between measurement instants, using the discrete-time attitude state observer that is almost globally finite-time
Lagrangian Coherent Structures in Blood Flow
NASA Astrophysics Data System (ADS)
Shadden, Shawn
2008-11-01
Knowledge of fluid transport is particularly compelling in understanding the function of cardiovascular processes. Transport of chemicals, cells, and compounds in the vascular system is influenced by local flow structures in large vessels. Local flow features can also induce cell-signaling pathways and biologic response critical to maintaining health or disease progression. Complex vessel geometry, the pulsatile pumping of blood, and low Reynolds number turbulence leads to complex flow features in large vessels. However, we are gaining the ability to study transport in large vessels with unprecedented detail, which is in part allowing us to broaden the ``shear-centric'' view of hemodynamics. In this talk we will describe the application of computational fluid mechanics and the computation of Lagrangian coherent structures (LCS) to study transport in various cardiovascular applications. We will discuss some of the challenges of this work and some results of computing LCS in several regions of the vascular system. In collaboration with Charles Taylor, Stanford University.
Gwo, J.P.; Jardine, P.M.; Yeh, G.T.; Wilson, G.V.
1995-04-01
Matrix diffusion, a diffusive mass transfer process,in the structured soils and geologic units at ORNL, is believe to be an important subsurface mass transfer mechanism; it may affect off-site movement of radioactive wastes and remediation of waste disposal sites by locally exchanging wastes between soil/rock matrix and macropores/fractures. Advective mass transfer also contributes to waste movement but is largely neglected by researchers. This report presents the first documented 2-D multiregion solute transport code (MURT) that incorporates not only diffusive but also advective mass transfer and can be applied to heterogeneous porous media under transient flow conditions. In this report, theoretical background is reviewed and the derivation of multiregion solute transport equations is presented. Similar to MURF (Gwo et al. 1994), a multiregion subsurface flow code, multiplepore domains as suggested by previous investigators (eg, Wilson and Luxmoore 1988) can be implemented in MURT. Transient or steady-state flow fields of the pore domains can be either calculated by MURF or by modelers. The mass transfer process is briefly discussed through a three-pore-region multiregion solute transport mechanism. Mass transfer equations that describe mass flux across pore region interfaces are also presented and parameters needed to calculate mass transfer coefficients detailed. Three applications of MURT (tracer injection problem, sensitivity analysis of advective and diffusive mass transfer, hillslope ponding infiltration and secondary source problem) were simulated and results discussed. Program structure of MURT and functions of MURT subroutiness are discussed so that users can adapt the code; guides for input data preparation are provided in appendices.
Exact stabilization of entangled states in finite time by dissipative quantum circuits
NASA Astrophysics Data System (ADS)
Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza
2017-07-01
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly noncanonical) commuting parent Hamiltonian may be found. Aside from graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi [Quantum Inf. Comput. 5, 187 (2005)]. Extensions to representative classes of mixed graph-product and thermal states are also discussed.
NASA Astrophysics Data System (ADS)
Nakata, H.; Fujihara, M.; Suenaga, Y.; Nagasawa, T.; Fujii, T.
2000-10-01
The transportation of eggs and larvae of brown sole in a shelf region of the Sea of Japan was explored using a 3D Euler-Lagrangian model, with special interest in the effect of wind blows on the larval retention. The general pattern of egg and larval transport from the spawning ground to the nursery was well reproduced under a constant westerly wind (4 m s -1), by assuming vertical movement of the eggs and larvae (upward in the earlier phase and downward in the later phase of the drift period). Using this model, the effect of westerly wind speed on egg and larval retention in the shelf was evaluated, and it was shown that when the wind speed exceeded a critical value (>5 m s -1), the retention rate could be rapidly reduced. An exploratory simulation of the effect of a one-day westerly blow with a speed of 15 m s -1 on the retention further indicated that the westerly blow induced strong offshore drift of the shelf water at the subsurface, and that it could markedly reduce the retention rate in the earlier phase of the drift period when eggs stay in the lower layer, and in the final phase when larvae stay near the bottom before settlement. The numbers of juveniles which successfully settled on the nursery in the study area showed a significant negative correlation with the frequency of strong westerlies in April. This suggests that wind blows could seriously reduce the retention of the larvae just before settlement, providing field evidence to support the model results. Recent declines in the fishery catch can therefore be partly explained by recruitment failure due to the increase in the frequency of strong westerly blows.
NASA Astrophysics Data System (ADS)
Su, Zhan; Zhang, Qingling; Ai, Jun; Sun, Xin
2015-01-01
For nonlinear descriptor systems, this paper presents an approach to obtain a fuzzy controller with guaranteed finite-time stability and finite-time boundedness with non-zero initial state, which outperforms some recent work and additionally provides a precision estimation of model approximation. We prove necessary and sufficient conditions of finite-time stability and finite-time boundedness with non-zero initial state for nonlinear descriptor systems. Using Takagi-Sugeno fuzzy dynamic models and proposed sufficient conditions, we define fuzzy sets and use linear matrix inequalities to satisfy differential linear matrix inequalities. A simulation confirms efficiency and precision of the given method.
Lagrangian postprocessing of computational hemodynamics
Shadden, Shawn C.; Arzani, Amirhossein
2014-01-01
Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889
Lagrangian Modeling of the Atmosphere
NASA Astrophysics Data System (ADS)
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
Softened Lagrangian hydrodynamics for cosmology
NASA Astrophysics Data System (ADS)
Gnedin, Nickolay Y.
1995-04-01
A new approach to cosmological hydrodynamics is discussed that is based on a moving, quasi-Lagrangian mesh. The softened Lagrangian hydrodynamics (SLH) method utilizes a high-resolution Lagrangian hydrodynamic code combined with a low-resolution Eulerian solver to deal with severe mesh distortions. Most of the volume of a simulation is treated with the Lagrangian code and only in sites where the Lagrangian approach fails, due to mesh distortions, does the Eulerian part of the code step in. This approach utilizes a high-resolution gravity solver without use of TREE or P3M methods; Poisson's equation is solved on the moving baryonic mesh using a simple relaxation technique. The dark matter is included by means of the cloud-in-cell method on the Lagrangian mesh. All three components of the cosmological code--gravity, dark matter, and baryons--are thus treated selft-consistently with exactly the same resolution. The computer code based on the SLH approach is described in detail, and comparison with existing Eulerian and smooth particle hydrodynamics (SPH) codes is presented. For most purposes the SLH approach turns out to be the intermediate between Eulerian and SPH codes, but it outperforms both of these approaches in resolving caustics. Thus, it may turn out to be a valuable tool to study galaxy formation.
NASA Astrophysics Data System (ADS)
Davis, William E.; Olsen, Anthony R.; Erb, Trudy A.
1989-01-01
The 1987 Across North America Tracer Experiment (ANATEX), for the study of regional to continental-scale transport and diffusion, released perfluorocarbon tracers for three hours every 2.5 days in January, February and March (Draxler et. al. 1985, 1987). The experiment resulted in 33 days of releases at two sites; Glasgow, Montana and St. Cloud, Minnesota. Each release consisted of approximately 50 kg of perfluoro ortho-dimenthoyl cyclohexane (PDCH) at St. Cloud and 83 kg of perfluoro trimethyl cyclohexane (PTCH) at Glasgow. The experiment included the release of a third tracer, 50 kg of perfluoro methyl cyclohexane (PMCH), every five days from St. Cloud; designed to serve as a means to distinguish consecutive releases from St. Cloud. A surface sampling network of 77 sampling sites, located east of 105 degree longitude in the United States and Canada, measured 24-hour average tracer concentrations out to a distance of 3000 km from Glasgow. The network, organized in eight arcs east of Glasgow, collected daily concentrations of each tracer from January 5 through March 29, 1987. The network design provides average daily surface footprint information for the three tracers.
Davis, W.E.; Olsen, A.R.; Erb, T.A.
1989-01-01
The 1987 Across North America Tracer Experiment (ANATEX), for the study of regional to continental-scale transport and diffusion, released perfluorocarbon tracers for three hours every 2.5 days in January, February and March (Draxler et. al. 1985, 1987). The experiment resulted in 33 days of releases at two sites; Glasgow, Montana and St. Cloud, Minnesota. Each release consisted of approximately 50 kg of perfluoro-ortho-dimenthoyl-cyclohexane (PDCH) at St. Cloud and 83 kg of perfluoro-trimethyl-cyclohexane (PTCH) at Glasgow. The experiment included the release of a third tracer, 50 kg of perfluoro-methyl-cyclohexane (PMCH), every five days from St. Cloud; designed to serve as a means to distinguish consecutive releases from St. Cloud. A surface sampling network of 77 sampling sites, located east of 105/degree/ longitude in the United States and Canada, measured 24-hour average tracer concentrations out to a distance of 3000 km from Glasgow. The network, organized in eight arcs east of Glasgow, collected daily concentrations of each tracer from January 5 through March 29, 1987. The network design provides average daily surface footprint information for the three tracers. 8 refs., 2 figs.
DG-FTLE: Lagrangian coherent structures with high-order discontinuous-Galerkin methods
NASA Astrophysics Data System (ADS)
Nelson, Daniel A.; Jacobs, Gustaaf B.
2015-08-01
We present an algorithm for the computation of finite-time Lyapunov exponent (FTLE) fields using discontinuous-Galerkin (dG) methods in two dimensions. The algorithm is designed to compute FTLE fields simultaneously with the time integration of dG-based flow solvers of conservation laws. Fluid tracers are initialized at Gauss-Lobatto quadrature nodes within an element. The deformation gradient tensor, defined by the deformation of the Lagrangian flow map in finite time, is determined per element with high-order dG operators. Multiple flow maps are constructed from a particle trace that is released at a single initial time by mapping and interpolating the flow map formed by the locations of the fluid tracers after finite time integration to a unit square master element and to the quadrature nodes within the element, respectively. The interpolated flow maps are used to compute forward-time and backward-time FTLE fields at several times using dG operators. For a large finite integration time, the interpolation is increasingly poorly conditioned because of the excessive subdomain deformation. The conditioning can be used in addition to the FTLE to quantify the deformation of the flow field and identify subdomains with material lines that define Lagrangian coherent structures. The algorithm is tested on three benchmarks: an analytical spatially periodic gyre flow, a vortex advected by a uniform inviscid flow, and the viscous flow around a square cylinder. In these cases, the algorithm is shown to have spectral convergence.
Eulerian-Lagrangian solution of the convection-dispersion equation in natural co-ordinates.
Cheng, R.T.; Casulli, V.; Milford, S.N.
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system.-from Authors
Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique.
Song, Zhankui; Li, Hongxing; Sun, Kaibiao
2014-01-01
In this paper, a fast terminal sliding mode control (FTSMC) scheme with double closed loops is proposed for the spacecraft attitude control. The FTSMC laws are included both in an inner control loop and an outer control loop. Firstly, a fast terminal sliding surface (FTSS) is constructed, which can drive the inner loop tracking-error and the outer loop tracking-error on the FTSS to converge to zero in finite time. Secondly, FTSMC strategy is designed by using Lyaponov's method for ensuring the occurrence of the sliding motion in finite time, which can hold the character of fast transient response and improve the tracking accuracy. It is proved that FTSMC can guarantee the convergence of tracking-error in both approaching and sliding mode surface. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
NASA Astrophysics Data System (ADS)
Lee, Daero; Vukovich, George; Gui, Haichao
2017-05-01
This paper presents an adaptive variable-structure finite-time control for spacecraft proximity maneuvers under parameter uncertainties, external disturbances and actuator saturation. The coupled six degrees-of-freedom dynamics are modeled for spacecraft relative motion, where the exponential coordinates on the Lie group SE(3) are employed to describe relative configuration. No prior knowledge of inertia matrix and mass of the spacecraft is required for the proposed control law, which implies that the proposed control scheme can be applied in spacecraft systems with large parametric uncertainties in inertia matrix and mass. Finite-time convergence of the feedback system with the proposed control law is established. Numerical simulation results are presented to illustrate the effectiveness of the proposed control law for spacecraft proximity operations with actuator saturation.
Finite-time synchronization of fractional-order memristor-based neural networks with time delays.
Velmurugan, G; Rakkiyappan, R; Cao, Jinde
2016-01-01
In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.
Finite-time thermodynamics and the gas-liquid phase transition
NASA Astrophysics Data System (ADS)
Santoro, M.; Schön, J. C.; Jansen, M.
2007-12-01
In this paper, we study the application of the concept of finite-time thermodynamics to first-order phase transitions. As an example, we investigate the transition from the gaseous to the liquid state by modeling the liquification of the gas in a finite time. In particular, we introduce, state, and solve an optimal control problem in which we aim at achieving the gas-liquid first-order phase transition through supersaturation within a fixed time in an optimal fashion, in the sense that the work required to supersaturate the gas, called excess work, is minimized by controlling the appropriate thermodynamic parameters. The resulting set of coupled nonlinear differential equations is then solved for three systems, nitrogen N2 , oxygen O2 , and water vapor H2O .
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
NASA Astrophysics Data System (ADS)
Zuo, Zongyu; Tie, Lin
2016-04-01
This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.
Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction
NASA Astrophysics Data System (ADS)
Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George
2016-11-01
We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.
Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva
2016-08-01
It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite- and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.
Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements
NASA Astrophysics Data System (ADS)
Song, Jun; Niu, Yugang; Jia, Tinggang
2016-09-01
This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.
Global finite-time stabilisation of a class of switched nonlinear systems
NASA Astrophysics Data System (ADS)
Liang, Ying-Jiu; Ma, Ruicheng; Wang, Min; Fu, Jun
2015-12-01
This paper is concerned with the global finite-time stabilisation problem for a class of switched nonlinear systems under arbitrary switchings. All subsystems of the studied switched system under consideration are in lower triangular form. Based on the adding one power integrator technique, both a class of non-Lipschitz continuous state feedback controllers and a common Lyapunov function are simultaneously constructed such that the closed-loop switched system is global finite-time stable under arbitrary switchings. In the controller design process, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for subsystems. Finally, two examples are given to show the effectiveness of the proposed method.
Proof of the finite-time thermodynamic uncertainty relation for steady-state currents
NASA Astrophysics Data System (ADS)
Horowitz, Jordan M.; Gingrich, Todd R.
2017-08-01
The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations. Our proof is based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies.
Some properties of asymmetric Hopfield neural networks with finite time of transition between states
NASA Astrophysics Data System (ADS)
Suleimenov, Ibragim; Mun, Grigoriy; Panchenko, Sergey; Pak, Ivan
2016-11-01
There were implemented samples of asymmetric Hopfield neural networks which have finite time of transition from one state to another. It was shown that in such systems, various oscillation modes could occur. It was revealed that the oscillation of the output signal of certain neuron could be treated as extra logical variable, which describes the state of the neuron. Asymmetric Hopfield neural networks are described in terms of ternary logic. Such logic may be employed in image recognition procedure.
Jammazi, Chaker
2009-03-05
The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.
NASA Astrophysics Data System (ADS)
Uglietti, C.; Leuenberger, M.; Brunner, D.
2011-08-01
The University of Bern monitors carbon dioxide (CO2) and oxygen (O2) at the High Altitude Research Station Jungfraujoch since the year 2000 by means of flasks sampling and since 2005 using a continuous in situ measurement system. This study investigates the transport of CO2 and O2 towards Jungfraujoch using backward Lagrangian Particle Dispersion Model (LPDM) simulations and utilizes CO2 and O2 signatures to classify air masses. By investigating the simulated transport patterns associated with distinct CO2 concentrations it is possible to decipher different source and sink areas over Europe. The highest CO2 concentrations, for example, were observed in winter during pollution episodes when air was transported from Northeastern Europe towards the Alps, or during south Foehn events with rapid uplift of polluted air from Northern Italy, as demonstrated in two case studies. To study the importance of air-sea exchange for variations in O2 concentrations at Jungfraujoch the correlation between CO2 and APO (Atmospheric Potential Oxygen) deviations from a seasonally varying background was analyzed. Anomalously high APO concentrations were clearly associated with air masses originating from the Atlantic Ocean, whereas low APO concentrations were found in air masses advected either from the east from the Eurasian continent in summer, or from the Eastern Mediterranean in winter. Those air masses with low APO in summer were also strongly depleted in CO2 suggesting a combination of CO2 uptake by vegetation and O2 uptake by dry summer soils. Other subsets of points in the APO-CO2 scatter plot investigated with respect to air mass origin included CO2 and APO background values and points with regular APO but anomalous CO2 concentrations. Background values were associated with free tropospheric air masses with little contact with the boundary layer during the last few days, while high or low CO2 concentrations reflect the various levels of influence of anthropogenic emissions and
Optimum neural tuning curves for information efficiency with rate coding and finite-time window
Han, Fang; Wang, Zhijie; Fan, Hong; Sun, Xiaojuan
2015-01-01
An important question for neural encoding is what kind of neural systems can convey more information with less energy within a finite time coding window. This paper first proposes a finite-time neural encoding system, where the neurons in the system respond to a stimulus by a sequence of spikes that is assumed to be Poisson process and the external stimuli obey normal distribution. A method for calculating the mutual information of the finite-time neural encoding system is proposed and the definition of information efficiency is introduced. The values of the mutual information and the information efficiency obtained by using Logistic function are compared with those obtained by using other functions and it is found that Logistic function is the best one. It is further found that the parameter representing the steepness of the Logistic function has close relationship with full entropy, and that the parameter representing the translation of the function associates with the energy consumption and noise entropy tightly. The optimum parameter combinations for Logistic function to maximize the information efficiency are calculated when the stimuli and the properties of the encoding system are varied respectively. Some explanations for the results are given. The model and the method we proposed could be useful to study neural encoding system, and the optimum neural tuning curves obtained in this paper might exhibit some characteristics of a real neural system. PMID:26089793
Optimum neural tuning curves for information efficiency with rate coding and finite-time window.
Han, Fang; Wang, Zhijie; Fan, Hong; Sun, Xiaojuan
2015-01-01
An important question for neural encoding is what kind of neural systems can convey more information with less energy within a finite time coding window. This paper first proposes a finite-time neural encoding system, where the neurons in the system respond to a stimulus by a sequence of spikes that is assumed to be Poisson process and the external stimuli obey normal distribution. A method for calculating the mutual information of the finite-time neural encoding system is proposed and the definition of information efficiency is introduced. The values of the mutual information and the information efficiency obtained by using Logistic function are compared with those obtained by using other functions and it is found that Logistic function is the best one. It is further found that the parameter representing the steepness of the Logistic function has close relationship with full entropy, and that the parameter representing the translation of the function associates with the energy consumption and noise entropy tightly. The optimum parameter combinations for Logistic function to maximize the information efficiency are calculated when the stimuli and the properties of the encoding system are varied respectively. Some explanations for the results are given. The model and the method we proposed could be useful to study neural encoding system, and the optimum neural tuning curves obtained in this paper might exhibit some characteristics of a real neural system.
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
Yang, Yana; Hua, Changchun; Guan, Xinping
2016-03-01
Due to the cognitive limitations of the human operator and lack of complete information about the remote environment, the work performance of such teleoperation systems cannot be guaranteed in most cases. However, some practical tasks conducted by the teleoperation system require high performances, such as tele-surgery needs satisfactory high speed and more precision control results to guarantee patient' health status. To obtain some satisfactory performances, the error constrained control is employed by applying the barrier Lyapunov function (BLF). With the constrained synchronization errors, some high performances, such as, high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. Nevertheless, like many classical control schemes only the asymptotic/exponential convergence, i.e., the synchronization errors converge to zero as time goes infinity can be achieved with the error constrained control. It is clear that finite time convergence is more desirable. To obtain a finite-time synchronization performance, the terminal sliding mode (TSM)-based finite time control method is developed for teleoperation system with position error constrained in this paper. First, a new nonsingular fast terminal sliding mode (NFTSM) surface with new transformed synchronization errors is proposed. Second, adaptive neural network system is applied for dealing with the system uncertainties and the external disturbances. Third, the BLF is applied to prove the stability and the nonviolation of the synchronization errors constraints. Finally, some comparisons are conducted in simulation and experiment results are also presented to show the effectiveness of the proposed method.
Xu, Xiaole; Chen, Shengyong; Gao, Lixin
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.
Topological detection of Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Thiffeault, Jean-Luc; Allshouse, Michael
2011-11-01
In many applications, particularly in geophysics, we often have fluid trajectory data from floats, but little or no information about the underlying velocity field. The standard techniques for finding transport barriers, based for example on finite-time Lyapunov exponents, are then inapplicable. However, if there are invariant regions in the flow this will be reflected by a `bunching up' of trajectories. We show that this can be detected by tools from topology. The method relies on examining a large number of topological loops, encoded symbolically. These loops wrap around the trajectories, which are viewed as topological obstacles. As the trajectories move around, they cause most loops to grow. The few loops that do not grow, or grow slowly, can be associated with coherent structures. Supported by NSF grant DMS-0806821
Semi-Lagrangian modelling of tropospheric ozone
NASA Astrophysics Data System (ADS)
Pudykiewicz, Janusz A.; Kallaur, A.; Smolarkiewicz, Piotr K.
1997-07-01
The occurrence of high concentrations of ozone in the lower part of the troposphere is considered as one of the most important issues of tropospheric chemistry. The chemical mechanisms of tropospheric ozone formation are complex, and highly variable meteorological conditions contribute additionally to difficulties in an accurate prediction of ozone episodes. An effective way to increase our understanding of the problem and eventually improve our ability to predict the concentration of tropospheric ozone and to formulate emission control strategies is by applying a comprehensive model representing accurately the interaction between meteorological processes and chemical reactions. This paper presents a 3-dimensional semi-Lagrangian, chemical tracer model (CTM) featuring an accurate transport algorithm, comprehensive oxidants chemistry and deposition modules. The CTM is executed in off line mode with a semi-Lagrangian, nonhydrostatic, mesoscale meteorological model that contains an extensive parameterization of physical processes (including a boundary layer scheme and clouds). The system of models was run for a time period of 6days in order to generate a tropospheric ozone field during a smog episode observed in the eastern part of North America, in the beginning of August 1988. The numerical simulation was performed on grids with resolution of 20 and 40km with 25 vertical levels. The emissions inventory considered in the simulation included point sources, surface biogenic sources, surface mobile sources and surface non-mobile sources. An evaluation of the model results against observations clearly indicates the ability of the system to simulate regional aspects of a tropospheric ozone episode. The model performance compares well to other models' results reported in the literature. An important achievement of this work is improving the physical realism of simulations by using highly accurate, nonoscillatory semi-Lagrangian advection transport algorithms.
Integrated computation of Lagrangian coherent structures during DNS of unsteady and turbulent flows
NASA Astrophysics Data System (ADS)
Finn, Justin; Apte, Sourabh
2012-11-01
The computation of Lagrangian coherent structures (LCS) typically involves post processing of experimentally or numerically obtained fluid velocity fields to obtain the finite time Lyapunov exponent (FTLE) via a sequence of flow maps (vector fields which describe fluid displacement patterns over a finite time interval, t0 +/- T). However, this procedure can be prohibitively expensive for large-scale complex flows of engineering interest. In this work, an alternative approach involving computation of the FTLE on the fly during direct numerical simulation (DNS) of the 3D Navier-Stokes equations is developed. This incorporation of the FTLE computations into a parallel DNS solver relies on Lagrangian particle tracking to compose forward time flow maps, and an Eulerian treatment of the backward time flow map [Leung, J. Comp. Physics 2011] coupled with a semi-Lagrangian advection scheme. The time T flow maps are accurately constructed from smaller sub-steps [Brunton & Rowley, Chaos 2010], resulting in low CPU and memory requirements for computing evolving FTLE fields. Illustrative examples will be presented to demonstrate the capability of the approach including the evolution of a turbulent vortex ring and turbulent flows in complex porous media. Funding: NSF project #0933857, Inertial Effects in Flow Through Porous Media.
NASA Astrophysics Data System (ADS)
BozorgMagham, Amir E.; Ross, Shane D.; Schmale, David G.
2013-09-01
The language of Lagrangian coherent structures (LCSs) provides a new means for studying transport and mixing of passive particles advected by an atmospheric flow field. Recent observations suggest that LCSs govern the large-scale atmospheric motion of airborne microorganisms, paving the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. In addition, having reliable predictions of the timing of hyperbolic LCSs may contribute to improved aerobiological sampling of microorganisms with unmanned aerial vehicles and LCS-based early warning systems. Chaotic atmospheric dynamics lead to unavoidable forecasting errors in the wind velocity field, which compounds errors in LCS forecasting. In this study, we reveal the cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters. Objectives of this paper are to (a) quantify the accuracy of prediction of FTLE-LCS features and (b) determine the sensitivity of such predictions to forecasting parameters. Results indicate that forecasts of attracting LCSs exhibit less divergence from the archive-based LCSs than the repelling features. This result is important since attracting LCSs are the backbone of long-lived features in moving fluids. We also show under what circumstances one can trust the forecast results if one merely wants to know if an LCS passed over a region and does not need to precisely know the passage time.
Lagrangian Mixing in an Axisymmetric Hurricane Model
2010-07-23
particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents , rel- ative...mixing derived from finite-time Lyapunov exponents , relative dispersion, and a measured mixing rate are applied to distinct regions representing...field varies slowly both in space and time. Some of the local techniques currently in use are finite-time Lyapunov exponents , (Haller, 2002; Haller
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
Finite-time Stückelberg interferometry with nanomechanical modes
NASA Astrophysics Data System (ADS)
Seitner, Maximilian J.; Ribeiro, Hugo; Kölbl, Johannes; Faust, Thomas; Weig, Eva M.
2017-03-01
Stückelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we investigate finite-time effects in Stückelberg interferometry and discuss the exact analytical solution of the double passage Stückelberg problem by expanding the finite-time solution of the Landau–Zener problem. Approximating the return probability amplitudes of the double passage in distinct limits reveals uncharted parameter regimes of Stückelberg interferometry where finite-time effects affect the coherent exchange of energy. We find the long-time limit of the exact solution to formally coincide with the well-established adiabatic impulse model which is, to the best of our knowledge, the only regime of Stückelberg interferometry reported so far. Experimentally, we study all predicted regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. We exploit our experimental and theoretical findings by studying the onset of Stückelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented findings are not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit.
Finite-time control for asteroid hovering and landing via terminal sliding-mode guidance
NASA Astrophysics Data System (ADS)
Yang, Hongwei; Bai, Xiaoli; Baoyin, Hexi
2017-03-01
This paper proposes a new nonlinear guidance algorithm applicable for asteroid both hovering and landing. With the new guidance, a spacecraft achieves its target position and velocity in finite-time without the requirement of reference trajectories. The global stability is proven for the controlled system. A parametric analysis is conducted to illustrate the parameters' effects on the guidance algorithm. Simulations of straight landing, hovering to hovering and landing with a prior hovering phase of the highly irregular asteroid 2063 Bacchus are presented and the effectiveness of the proposed method is demonstrated.
NASA Astrophysics Data System (ADS)
Estrada, Antonio; Efimov, Denis; Perruquetti, Wilfrid
2016-09-01
The present work focuses on the problem of velocity and position estimation. A solution is presented for a class of oscillating systems in which position, velocity and acceleration are zero mean signals. The proposed scheme considers that the dynamic model of the system is unknown. Only noisy acceleration measurements, that may be contaminated by zero mean noise and constant bias, are considered to be available. The proposal uses the periodic nature of the signals obtaining finite-time estimations while tackling integration drift accumulation.
NASA Astrophysics Data System (ADS)
Dasgupta, Sambarta
Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of
NASA Astrophysics Data System (ADS)
Wang, Ronghao; Xing, Jianchun; Li, Juelong; Xiang, Zhengrong
2016-10-01
This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results.
A Student's Guide to Lagrangians and Hamiltonians
NASA Astrophysics Data System (ADS)
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Galilean invariance in Lagrangian mechanics
NASA Astrophysics Data System (ADS)
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
On the Lagrangian description of unsteady boundary layer separation. Part 2: The spinning sphere
NASA Technical Reports Server (NTRS)
Vandommelen, Leon L.
1989-01-01
A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.
On the Lagrangian description of unsteady boundary-layer separation. II - The spinning sphere
NASA Technical Reports Server (NTRS)
Van Dommelen, Leon L.
1990-01-01
A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.
On the Lagrangian description of unsteady boundary-layer separation. II - The spinning sphere
NASA Technical Reports Server (NTRS)
Van Dommelen, Leon L.
1990-01-01
A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.
Lagrangian clustering detection of internal wave boluses
NASA Astrophysics Data System (ADS)
Allshouse, M.; Salvador Vieira, G.; Swinney, H. L.
2016-02-01
The shoaling of internal waves on a continental slope or shelf produces boluses that travel up the slope with the wave. The boluses are regions of trapped fluid that are transported along with the wave, unlike fluid in the bulk that is temporarily pertubed by a passing wave. Boluses have been observed to transport oxygen-depleted water and induce rapid changes in temperature (Walter et al, JGR, 2012), both of which have potential ramifications for marine biology. Several previous studies have investigated boluses in systems with two layers of different density (e.g., Helfrich, JFM, 1992, and Sutherland et al., JGR, 2013). We conduct laboratory and computational studies of bolus generation and material transport in continuously stratified fluids with a pycnocline, as in the oceans. Our laboratory experiments in a 4 m long tank are complemented by 2-dimensional direct numerical simulations of the Navier-Stokes equations. Efforts have been made to identify boluses with Eularian measures in the past, but a Lagrangian perspective is necessary to objectively identify the bolus over its lifespan. Here we use a Lagrangian based coherent structure method relying on trajectory clustering using the fuzzy c-means approach (Froyland and Padberg-Gehle, Chaos, 2015). The objective detection of a bolus enables examination of the volume, distance traveled, and increased available potential energy of a bolus, as a function of the stratification, wave properties, and the angle of the sloping topography. The decay of a bolus through turbulent mixing is investigated by locating where the Richardson number drops below ¼, where velocity shear overcomes the tendency of a stratified fluid to remain stratified. (supported by ONR MURI grant N000141110701)
Finite-time quantum-to-classical transition for a Schroedinger-cat state
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
2011-07-15
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
Zong, Qun; Shao, Shikai
2016-11-01
This paper investigates decentralized finite-time attitude synchronization for a group of rigid spacecraft by using quaternion with the consideration of environmental disturbances, inertia uncertainties and actuator saturation. Nonsingular terminal sliding mode (TSM) is used for controller design. Firstly, a theorem is proven that there always exists a kind of TSM that converges faster than fast terminal sliding mode (FTSM) for quaternion-descripted attitude control system. Controller with this kind of TSM has faster convergence and reduced computation than FTSM controller. Then, combining with an adaptive parameter estimation strategy, a novel terminal sliding mode disturbance observer is proposed. The proposed disturbance observer needs no upper bound information of the lumped uncertainties or their derivatives. On the basis of undirected topology and the disturbance observer, decentralized attitude synchronization control laws are designed and all attitude errors are ensured to converge to small regions in finite time. As for actuator saturation problem, an auxiliary variable is introduced and accommodated by the disturbance observer. Finally, simulation results are given and the effectiveness of the proposed control scheme is testified.
Optimal initial condition of passive tracers for their maximal mixing in finite time
NASA Astrophysics Data System (ADS)
Farazmand, Mohammad
2017-05-01
The efficiency of fluid flow for mixing passive tracers is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here we address the natural corollary question: Given a fluid flow, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small length-scale threshold ℓν under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of two-dimensional turbulence. Evaluating the optimal initial condition through this framework requires only the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data are available through numerical simulations or experimental measurements.
Finite-time scaling via linear driving: application to the two-dimensional Potts model.
Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli
2010-04-01
We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.
Finite-time quantum-to-classical transition for a Schrödinger-cat state
NASA Astrophysics Data System (ADS)
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
2011-07-01
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schrödinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a “sudden death.” In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu
2011-08-01
A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.
NASA Astrophysics Data System (ADS)
Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhao, Hui
2016-09-01
In this paper, we study the finite-time stability and synchronization problem of a class of memristor-based fractional-order Cohen-Grossberg neural network (MFCGNN) with the fractional order α ∈ (0,1 ]. We utilize the set-valued map and Filippov differential inclusion to treat MFCGNN because it has discontinuous right-hand sides. By using the definition of Caputo fractional-order derivative, the definitions of finite-time stability and synchronization, Gronwall's inequality and linear feedback controller, two new sufficient conditions are derived to ensure the finite-time stability of our proposed MFCGNN and achieve the finite-time synchronization of drive-response systems which are constituted by MFCGNNs. Finally, two numerical simulations are presented to verify the rightness of our proposed theorems.
NASA Astrophysics Data System (ADS)
Cai, Zuo-Wei; Huang, Jian-Hua; Huang, Li-Hong
2017-02-01
The aim of this paper is to provide a novel switching control design to solve finite-time stabilization issues of a discontinuous or switching dynamical system. In order to proceed with our analysis, we first design two kinds of switching controllers: switching adaptive controller and switching state-feedback controller. Then, we apply the proposed switching control technique to stabilize the states of delayed memristor-based neural networks (DMNNs) in finite time. Based on a famous finite-time stability theorem, the theory of differential inclusion and the generalized Lyapunov functional method, some sufficient conditions are obtained to guarantee the finite-time stabilization control of DMNNs. The feedback functions of our model are allowed to be unbounded, and the upper bounds of the settling time for stabilization are also given. Finally, the validity of designed method and the theoretical results are illustrated by numerical examples.
Transport and mixing of microbial population by atmospheric coherent structures
NASA Astrophysics Data System (ADS)
Bozorg Magham, A.; Ross, S. D.
2012-12-01
Lagrangian coherent structures (LCSs) provide a new means for discussion of spatiotemporal characteristics of the passive transport and mixing of atmospheric pathogen populations, paving the way for new management strategies regarding the spread of infectious diseases affecting plants, domestic animals, and humans, including identification of probable source regions and forecasts of regions at high risk. We report on the relationship of coherent structures to the patchiness of pathogen populations, and the effects of imperfect forecast wind data on the resultant LCSs. Regarding forecasting LCSs, our main contributions are to quantify the accuracy and sensitivity of such predictions with respect to the forecasting parameters. To obtain more reliable atmospheric LCS features, we have incorporated two more concepts. First is the effect of unresolved turbulent motion; this consideration leads to the stochastic finite-time Lyapunov exponent (SFTLE) field and the resultant stochastic LCS. The second concept is ensemble FTLE/LCS forecasting using individual members of the ensemble wind field forecasts.
LSPRAY-V: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2015-01-01
LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.
LSPRAY-III: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2008-01-01
LSPRAY-III is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-III, we have advanced the state-of-the-art in spray computations in several important ways.
Parallelization of the Lagrangian Particle Dispersion Model
Buckley, R.L.; O`Steen, B.L.
1997-08-01
An advanced stochastic Lagrangian Particle Dispersion Model (LPDM) is used by the Atmospheric Technologies Group (ATG) to simulate contaminant transport. The model uses time-dependent three-dimensional fields of wind and turbulence to determine the location of individual particles released into the atmosphere. This report describes modifications to LPDM using the Message Passing Interface (MPI) which allows for execution in a parallel configuration on the Cray Supercomputer facility at the SRS. Use of a parallel version allows for many more particles to be released in a given simulation, with little or no increase in computational time. This significantly lowers (greater than an order of magnitude) the minimum resolvable concentration levels without ad hoc averaging schemes and/or without reducing spatial resolution. The general changes made to LPDM are discussed and a series of tests are performed comparing the serial (single processor) and parallel versions of the code.
LSPRAY-II: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2004-01-01
LSPRAY-II is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-II, we have advanced the state-of-the-art in spray computations in several important ways.
An ambitwistor Yang Mills Lagrangian
NASA Astrophysics Data System (ADS)
Mason, L. J.; Skinner, D.
2006-04-01
We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory.
Characterization of the transport topology in patient-specific abdominal aortic aneurysm models
NASA Astrophysics Data System (ADS)
Arzani, Amirhossein; Shadden, Shawn C.
2012-08-01
Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.
Characterization of the transport topology in patient-specific abdominal aortic aneurysm models.
Arzani, Amirhossein; Shadden, Shawn C
2012-08-01
Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.
Finite-time arbitrary-motion unsteady cascade airfoil theory for helicopter rotors in hover
NASA Technical Reports Server (NTRS)
Dinyavari, M. A. H.; Friedmann, P. P.
1985-01-01
A complete and detailed derivation of finite-time arbitrary-motion cascade theory is presented for both Laplace and frequency domains. This theory includes the effect of returning wakes for both single- and multibladed rotors. The generalized cascade lift-deficiency function (CLDF) is shown to be consistent with the generalized Theodorsen lift-deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity. This function predicts correct zero-reduced-frequency limit. Accurate and efficient numerical procedures are presented for the evaluation of the CLDF. Numerical examples comparing the CLDF with Loewy's lift deficiency function in frequency domain are presented. Accurate Pade approximants of the CLDF are constructed using a Bode-plot approach which allows for complex poles.
Efficiency at maximum power output of quantum heat engines under finite-time operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Efficiency, Power and Period of a model quantum heat engine working in a finite time
NASA Astrophysics Data System (ADS)
Bekele, Mulugeta; Dima, Tolasa A.; Alemye, Mekuannent; Chegeno, Warga
We take a spin-half quantum particle undergoing Carnot type cyclic process in a finite time assisted by two heat reservoirs and an external magnetic field. We find that the power of the heat engine is maximum at a particular period of the cyclic process and efficiency at the maximum power is at least half of the Carnot efficiency. We further apply the Omega-criterion for a figure of merit representing a compromise between useful power and lost power determining the corresponding efficiency for the optimization criterion to be at least three fourth of the Carnot efficiency. The authers are thankful to the International Science programme, IPS, Uppsala, Sweden for their support to our research lab.
On the thermal efficiency of power cycles in finite time thermodynamics
NASA Astrophysics Data System (ADS)
Momeni, Farhang; Morad, Mohammad Reza; Mahmoudi, Ashkan
2016-09-01
The Carnot, Diesel, Otto, and Brayton power cycles are reconsidered endoreversibly in finite time thermodynamics (FTT). In particular, the thermal efficiency of these standard power cycles is compared to the well-known results in classical thermodynamics. The present analysis based on FTT modelling shows that a reduction in both the maximum and minimum temperatures of the cycle causes the thermal efficiency to increase. This is antithetical to the existing trend in the classical references. Under the assumption of endoreversibility, the relation between the efficiencies is also changed to {η }{{Carnot}}\\gt {η }{{Brayton}}\\gt {η }{{Diesel}}\\gt {η }{{Otto}}, which is again very different from the corresponding classical results. The present results benefit a better understanding of the important role of irreversibility on heat engines in classical thermodynamics.
Efficiency at maximum power output of quantum heat engines under finite-time operation
NASA Astrophysics Data System (ADS)
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1-Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2-ηC) and from below by ηC/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ηCA=1-Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Time-dependent modes associated with finite time instabilities in unstable fluid flows
NASA Astrophysics Data System (ADS)
Babaee, Hessam; Sapsis, Themistoklis
2015-11-01
We apply a recently developed variational formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures the directions associated with finite-time instabilities. We demonstrate the capability of the method for two problems: the Orr-Sommerfeld/Squire operator and the vertical jet in crossflow. In the first problem we demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short time regime), while for longer times the modes capture the expected asymptotic behavior of the dynamics. We also consider the vertical jet in crossflow at the jet Reynolds number of Rej = 900 . We demonstrate that the subspace instantaneously captures the most unstable directions of the time-dependent flow. We explore the connection between the shear flow, non-normal growth and persistent instabilities. Supported by ARO Award # 66710-EG-YIP.
Liu, Xiaoyang; Su, Housheng; Chen, Michael Z Q
2016-02-01
This paper is concerned with the finite-time synchronization issue of nonlinear coupled neural networks by designing a new switching pinning controller. For the fixed network topology and control strength, the newly designed controller could optimize the synchronization time by regulating a parameter α (0 ≤ α < 1). The control law presented in this paper covers both continuous controllers and discontinuous ones, which were studied separately in the past. Some criteria are discussed in detail on how to shorten the synchronization time for the strongly connected networks. Finally, the results are generalized to any network topologies containing a directed spanning tree, and one numerical example is given to demonstrate the effectiveness of the theoretical results.
Shocks and finite-time singularities in Hele-Shaw flow
Teodorescu, Razvan; Wiegmann, P; Lee, S-y
2008-01-01
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.
NASA Astrophysics Data System (ADS)
Xu, Chang-Jin; Li, Pei-Luan; Pang, Yi-Cheng
2017-02-01
This paper is concerned with fractional-order bidirectional associative memory (BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag-Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. Supported by National Natural Science Foundation of China under Grant Nos.~61673008, 11261010, 11101126, Project of High-Level Innovative Talents of Guizhou Province ([2016]5651), Natural Science and Technology Foundation of Guizhou Province (J[2015]2025 and J[2015]2026), 125 Special Major Science and Technology of Department of Education of Guizhou Province ([2012]011) and Natural Science Foundation of the Education Department of Guizhou Province (KY[2015]482)
Finite-Time Effects and Ultraweak Ergodicity Breaking in Superdiffusive Dynamics
NASA Astrophysics Data System (ADS)
Godec, Aljaž; Metzler, Ralf
2013-01-01
We study the ergodic properties of superdiffusive, spatiotemporally coupled Lévy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement δx2¯ around the ensemble value 3-α (1<α<2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of δx2¯ over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.
Quantum Otto cycle with inner friction: finite-time and disorder effects
NASA Astrophysics Data System (ADS)
Alecce, A.; Galve, F.; Lo Gullo, N.; Dell'Anna, L.; Plastina, F.; Zambrini, R.
2015-07-01
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.
Finite Time Extinction for Stochastic Sign Fast Diffusion and Self-Organized Criticality
NASA Astrophysics Data System (ADS)
Gess, Benjamin
2015-04-01
We prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space-time noise, corresponding to the Bak-Tang-Wiesenfeld model for self-organized criticality. This solves a problem posed and left open in several works: (Barbu, Methods Appl Sci 36:1726-1733, 2013; Röckner and Wang, J Lond Math Soc (2) 87:545-560, 2013; Barbu et al. J Math Anal Appl 389:147-164, 2012; Barbu and Röckner, Comm Math Phys 311:539-555, 2012; Barbu et al., Comm Math Phys 285:901-923, 2009, C R Math Acad Sci Paris 347(1-2):81-84, 2009). The highly singular-degenerate nature of the drift in interplay with the stochastic perturbation causes the need for new methods in the analysis of mass diffusion, and several new estimates and techniques are introduced.
Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon
Grandits, Peter
2013-04-15
We construct {epsilon}-optimal strategies for the following control problem: Maximize E[{integral}{sub [0,{tau})}e{sup -{beta}s} dC{sub s}+e{sup -{beta}{tau}}X{sub {tau}}] , where X{sub t}=x+{mu}t+{sigma}W{sub t}-C{sub t}, {tau}{identical_to}inf{l_brace}t>0|X{sub t}=0{r_brace} Logical-And T, T>0 is a fixed finite time horizon, W{sub t} is standard Brownian motion, {mu}, {sigma} are constants, and C{sub t} describes accumulated consumption until time t. It is shown that {epsilon}-optimal strategies are given by barrier strategies with time-dependent barriers.
Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach
Elie, R.
2008-12-15
We consider the optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model and we consider a general class of utility functions. On an infinite time horizon, Elie and Touzi (Preprint, [2006]) provided the value function as well as the optimal consumption and investment strategy in explicit form. In a more realistic setting, we consider here an agent optimizing its consumption-investment strategy on a finite time horizon. The value function interprets as the unique discontinuous viscosity solution of its corresponding Hamilton-Jacobi-Bellman equation. This leads to a numerical approximation of the value function and allows for a comparison with the explicit solution in infinite horizon.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro E-mail: mwhite@berkeley.edu
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models
NASA Technical Reports Server (NTRS)
Lin, Shian-Jiann
2003-01-01
A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.
Performance of Lagrangian descriptors and their variants in incompressible flows.
Ruiz-Herrera, Alfonso
2016-10-01
The method of Lagrangian Descriptors has been applied in many different contexts, specially in geophysical flows. In this paper, we analyze their performance in incompressible flows. We construct broad families of systems where this diagnostic fails in the detection of barriers to transport. Another aim of this manuscript is to illustrate the same deficiencies in the recent diagnostic proposed by Craven and Hernández.
Modeling electrokinetic flow by Lagrangian particle-based method
NASA Astrophysics Data System (ADS)
Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre; Parks, Mike
2015-11-01
This work focuses on mathematical models and numerical schemes based on Lagrangian particle-based method that can effectively capture mesoscale multiphysics (hydrodynamics, electrostatics, and advection-diffusion) associated in applications of micro-/nano-transport and technology. The order of accuracy is significantly improved for particle-based method with the presented implicit consistent numerical scheme. Specifically, we show simulation results on electrokinetic flows and microfluidic mixing processes in micro-/nano-channel and through semi-permeable porous structures.
Using Lagrangian Coherent Structures to understand coastal water quality
NASA Astrophysics Data System (ADS)
Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.
2012-09-01
The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a Lagrangian circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.
Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.
Holzner, M; Morales, V L; Willmann, M; Dentz, M
2015-07-01
Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.
Korayem, M H; Nekoo, S R
2015-01-01
This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Wang, Yujuan; Song, Yongduan; Krstic, Miroslav
2016-12-14
This paper investigates the problem of achieving rotating formation and containment simultaneously via finite time control schemes for multiagent systems. It is nontrivial to maintain rotating formation where the desired formation structure is time-varying and only neighboring information is available. The underlying problem becomes even more complicated if containment is imposed yet finite time convergence is required at the same time. To tackle this problem, a polar coordinate-based approach is exploited in this paper. Finite time control protocols are established for leader agents and follower agents, respectively, such that three goals are achieved in finite time concurrently: 1) all the agents maintain a stable rotating motion around a common circular center with a common (possibly time-varying) angular velocity; 2) the leader agents form and maintain a prespecified rotating formation structure; and 3) the follower agents converge to the shifting convex hull shaped by the dynamically moving (circling) leaders. It is the polar coordinate expression that simplifies the formulation of the rotating formation-containment problem and facilitates the finite time control design process. The effectiveness of the proposed control scheme is illustrated via both formative mathematical analysis and numerical simulation.
Lagrangian tracing of Sahelian Sudan moisture sources
NASA Astrophysics Data System (ADS)
Salih, Abubakr A. M.; Zhang, Qiong; Tjernström, Michael
2013-04-01
Sahelian Sudan, 10° to 16°N, is an arid to semi-arid zone that separates the Saharan to the north and the wet Savannah to the south. The region is characterized by, relatively, limited water resources, and hence has a high dependency on the annual rainfall. According to the latest IPCC report, regions that have such limited water resources are highly vulnerable to the ongoing climate change and variability. Taking into account that the agriculture is the main economical activity, the variability in annual rainfall is of direct soci-economical relevance. Similar to the rest of the African Sahel, the rainy season, June through September, across Sahelian Sudan is connected to the annual march of the Intertropical Convergence Zone (ITCZ). However, there still a limited understanding of the actual sources of moisture that supplies this region with water vapor during the rainy season. Broadly speaking, the Atlantic, the Congo rain forest, the Read Sea and the Indian Ocean are the main potential sources. In this study we use Lagrangian tracing technique to indentify the sources of moisture of Sahelian Sudan and attempt quantifying their contribution to the total annual moisture convergence. For this we utilized output from the Lagrangian trajectory model FLEXPART driven by the meteorological fields from the European Center for Medium range Weather Forecast ERA-interim for period of ten years 2000 to 2009. We trace back, for ten days each mass element to indentify the source region. The models also accounts for precipitation and moisture uptakes through the course of the transport of the air parcel from source to destination. Identifying the sources of moisture is of great importance, and can help in two connected directions. First, identifying sources of moisture will help in understanding the variability and will provide insight about the drought causes and mechanisms. Second, revealing the moisture sources would enhance ongoing efforts in seasonal forecasting.
Xu, Yong; Lu, Renquan; Shi, Peng; Li, Hongyi; Xie, Shengli
2016-12-15
This paper considers finite-time distributed state estimation for discrete-time nonlinear systems over sensor networks. The Round-Robin protocol is introduced to overcome the channel capacity constraint among sensor nodes, and the multiplicative noise is employed to model the channel fading. In order to improve the performance of the estimator under the situation, where the transmission resources are limited, fading channels with different stochastic properties are used in each round by allocating the resources. Sufficient conditions of the average stochastic finite-time boundedness and the average stochastic finite-time stability for the estimation error system are derived on the basis of the periodic system analysis method and Lyapunov approach, respectively. According to the linear matrix inequality approach, the estimator gains are designed. Finally, the effectiveness of the developed results are illustrated by a numerical example.
Foam on troubled water: Capillary induced finite-time arrest of sloshing waves
NASA Astrophysics Data System (ADS)
Viola, Francesco; Brun, P.-T.; Dollet, Benjamin; Gallaire, François
2016-09-01
Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid's oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.
Characteristic distribution of finite-time Lyapunov exponents for chimera states
Botha, André E.
2016-01-01
Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators – certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed. PMID:27374473
Characteristic distribution of finite-time Lyapunov exponents for chimera states.
Botha, André E
2016-07-04
Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators - certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed.
Characteristic distribution of finite-time Lyapunov exponents for chimera states
NASA Astrophysics Data System (ADS)
Botha, André E.
2016-07-01
Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators - certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed.
Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula
NASA Astrophysics Data System (ADS)
Garaboa-Paz, Daniel; Lorenzo, Nieves; Pérez-Muñuzuri, Vicente
2017-05-01
Seasonal forecasts have improved during the last decades, mostly due to an increase in understanding of the coupled ocean-atmosphere dynamics, and the development of models able to predict the atmosphere variability. Correlations between different teleconnection patterns and severe weather in different parts of the world are constantly evolving and changing. This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain. To understand the mechanisms behind this correlation, summer anomalies of the FTLE have also been correlated with other climatic variables such as the sea surface temperature (SST), the sea level pressure (SLP) or the geopotential. The East Atlantic (EA) teleconnection index correlates with the summer FTLE anomalies, confirming their role as a seasonal predictor for winter precipitation over the Iberian Peninsula.
Finite-time singularity in the dynamics of the world population, economic and financial indices
NASA Astrophysics Data System (ADS)
Johansen, Anders; Sornette, Didier
2001-05-01
Contrary to common belief, both the Earth's human population and its economic output have grown faster than exponential, i.e., in a super-Malthusian mode, for most of the known history. These growth rates are compatible with a spontaneous singularity occurring at the same critical time 2052±10 signaling an abrupt transition to a new regime. The degree of abruptness can be infered from the fact that the maximum of the world population growth rate was reached in 1970, i.e., about 80 years before the predicted singular time, corresponding to approximately 4% of the studied time interval over which the acceleration is documented. This rounding-off of the finite-time singularity is probably due to a combination of well-known finite-size effects and friction and suggests that we have already entered the transition region to a new regime. As theoretical support, a multivariate analysis coupling population, capital, R&D and technology shows that a dramatic acceleration in the population growth during most of the timespan can occur even though the isolated dynamics do not exhibit it. Possible scenarios for the cross-over and the new regime are discussed.
Finite time attitude takeover control for combination via tethered space robot
NASA Astrophysics Data System (ADS)
Lu, Yingbo; Huang, Panfeng; Meng, Zhongjie; Hu, Yongxin; Zhang, Fan; Zhang, Yizhai
2017-07-01
Up to April 6, 2016, there are 17,385 large debris in orbit around the Earth, which poses a serious hazard to near-Earth space activities. As a promising on-orbit debris capture strategy, tethered space robots (TSRs) have wide applications in future on-orbit service owing to its flexibility and great workspace. However, lots of problems may arise in the Tethered Space Robots (TSRs) system from the approaching, capturing, postcapturing and towing phases. The postcapture combination attitude takeover control by the TSR is studied in this paper. Taking control constraints, tether oscillations and external disturbances into consideration, a fast terminal sliding mode control (FTSMC) methodology with dual closed loops for the flexible combination attitude takeover control is designed. The unknown upper bounds of the uncertainties, external disturbances are estimated through adaptive techniques. Stability of the dual closed loop control system and finite time convergence of system states are proved via Lyapunov stability theory. Besides, null space intersection control allocation was adopted to distribute the required control moment over TSR's redundant thrusters. Simulation studies have been conducted to demonstrate the effectiveness of the proposed controller with the conventional sliding mode control(SMC).
A game theoretic approach to a finite-time disturbance attenuation problem
NASA Technical Reports Server (NTRS)
Rhee, Ihnseok; Speyer, Jason L.
1991-01-01
A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.
A game theoretic approach to a finite-time disturbance attenuation problem
NASA Technical Reports Server (NTRS)
Rhee, Ihnseok; Speyer, Jason L.
1991-01-01
A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.
Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2014-03-15
We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.
Finite-time normal mode disturbances and error growth during Southern Hemisphere blocking
NASA Astrophysics Data System (ADS)
Wei, Mozheng; Frederiksen, Jorgen S.
2005-01-01
The structural organization of initially random errors evolving in a barotropic tangent linear model, with time-dependent basic states taken from analyses, is examined for cases of block development, maturation and decay in the Southern Hemisphere atmosphere during April, November, and December 1989. The statistics of 100 evolved errors are studied for six-day periods and compared with the growth and structures of fast growing normal modes and finite-time normal modes (FTNMs). The amplification factors of most initially random errors are slightly less than those of the fastest growing FTNM for the same time interval. During their evolution, the standard deviations of the error fields become concentrated in the regions of rapid dynamical development, particularly associated with developing and decaying blocks. We have calculated probability distributions and the mean and standard deviations of pattern correlations between each of the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. The mean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases with increasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but not always, gives the largest mean pattern correlation with error fields. Corresponding pattern correlations with the fast growing normal modes of the instantaneous basic state flow are significant but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increase further when the time interval is increased beyond six days.
Sheng, Shiqi; Tu, Z C
2014-01-01
The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [ M. Esposito, R. Kawai, K. Lindenberg and C. Van den Broeck Phys. Rev. Lett. 105 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.
Finite-time Properties of the Navier-Stokes Equations Under Lebesque Space Disturbances
NASA Astrophysics Data System (ADS)
Bobba, Kumar
2006-11-01
A complete understanding of the stability characteristics of the Navier-Stokes equations involve understanding both the transient response and the steady state response. The steady state (or infinite-time) response of the Navier-Stokes equations is characterized by the point spectrum and has been well studied. In this work, we study the transient (or finite-time) response of the unsteady Navier-Stokes equations linearized about plane Couette base flow under spatial and temporal varying disturbance forcing. The forcing and response are assumed to belong to infinite-dimensional Lebesque function spaces, L2 and L∞. An analytical characterization is given for the induced norms that characterize the response. It is shown that the L2 induced norm is tightly bounded by the H∞ norm of the transfer function operator and the L∞ induced norm is upper bounded by the L1 norm of the impulse response operator. The structure of the worst case disturbances and their amplification rates are computed using spectral methods---with Fourier modes in homogeneous direction and Chebyshev collocation in non-homogeneous direction. The relevance of the present results to the channel flow laminar-turbulent transition experiments will be discussed.
Finite-time vortex singularity and Kolmogorov spectrum in a symmetric three-dimensional spiral model
NASA Astrophysics Data System (ADS)
Bhattacharjee, A.; Ng, C. S.; Wang, Xiaogang
1995-11-01
A recent analytical model of three-dimensional Euler flows [Phys. Rev. Lett. 69, 2196 (1992)] which exhibits a finite-time vortex singularity is developed further. The initial state is symmetric and contains a velocity null (stagnation point) which is collinear with two vorticity nulls. Under some assumptions, it is shown by asymptotic analysis of the Euler equation that the vorticity blows up at the stagnation point as inverse time in a locally self-similar manner. The spatial structure of the inviscid flow in the vicinity of the singularity involves disparate small scales. The effect of a small but finite viscosity is shown to arrest the formation of the singularity. The presence of spiral structure in the initial conditions leads naturally to the model developed by Lundgren [Phys. Fluids 25, 2193 (1982)] in which the gradual tightening of spirals by differential rotation provides a mechanism for transfer of energy to small spatial scales. It is shown by asymptotic analysis of the Navier-Stokes equation, that a time-average over the lifetime of the spiral vortex in the present model yields the Kolmogorov spectrum.
Protecting a quantum state from environmental noise by an incompatible finite-time measurement
Brasil, Carlos Alexandre; Castro, L. A. de; Napolitano, R. d. J.
2011-08-15
We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.
Visual servo walking control for humanoids with finite-time convergence and smooth robot velocities
NASA Astrophysics Data System (ADS)
Delfin, Josafat; Becerra, Hector M.; Arechavaleta, Gustavo
2016-07-01
In this paper, we address the problem of humanoid locomotion guided from information of a monocular camera. The goal of the robot is to reach a desired location defined in terms of a target image, i.e., a positioning task. The proposed approach allows us to introduce a desired time to complete the positioning task, which is advantageous in contrast to the classical exponential convergence. In particular, finite-time convergence is achieved while generating smooth robot velocities and considering the omnidirectional waking capability of the robot. In addition, we propose a hierarchical task-based control scheme, which can simultaneously handle the visual positioning and the obstacle avoidance tasks without affecting the desired time of convergence. The controller is able to activate or inactivate the obstacle avoidance task without generating discontinuous velocity references while the humanoid is walking. Stability of the closed loop for the two task-based control is demonstrated theoretically even during the transitions between the tasks. The proposed approach is generic in the sense that different visual control schemes are supported. We evaluate a homography-based visual servoing for position-based and image-based modalities, as well as for eye-in-hand and eye-to-hand configurations. The experimental evaluation is performed with the humanoid robot NAO.
Fan, Xiaofei; Zhang, Xian; Wu, Ligang; Shi, Michael
2016-04-11
This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad- slope integrations, we establish delay-dependent finite-time stabil- ity criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction- diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Zhong, Qishui; Cheng, Jun; Zhao, Yuqing
2015-07-01
In this paper, a novel method is developed for delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. New sufficient condition for stochastic boundness of Markovian jumping neural networks is presented and proved by an newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, the state trajectory remains in a bounded region of the state space over a given finite-time interval. Finally, a numerical example is given to illustrate the efficiency and less conservative of the proposed method.
DDI-based finite-time stability analysis for nonlinear switched systems with time-varying delays
NASA Astrophysics Data System (ADS)
Xue, Wenping; Li, Kangji; Liu, Guohai
2016-09-01
This paper investigates the finite-time stability (FTS) analysis problem for switched systems with both nonlinear perturbation and time-varying delays. For the system to be finite-time stable, a sufficient condition is proposed based on some delay differential inequalities (DDIs), rather than the Lyapunov-like functions which are commonly used in the FTS analysis of switched systems. Compared with the Lyapunov-like function method, the FTS conditions based on the DDI method are easier for checking and do not require FTS of each subsystem. Two examples are given to illustrate the effectiveness of the developed theory.
NASA Astrophysics Data System (ADS)
Qi, Wenhai; Gao, Xianwen
2016-01-01
This paper focuses on the problem of finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. By employing an appropriate Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is designed to ensure H∞ finite-time boundedness of the resulting closed-loop system that contains time-varying delay, admissible external disturbance, It ?-type stochastic disturbance and nonlinearity. All the proposed conditions are established in the form of linear matrix inequalities. Finally, an example is given to demonstrate the validity of the main results.
Lagrangian based methods for coherent structure detection
Allshouse, Michael R.; Peacock, Thomas
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen
2017-04-01
Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A
A Lagrangian approach to the Loop Current eddy separation
NASA Astrophysics Data System (ADS)
Andrade-Canto, F.; Sheinbaum, J.; Zavala, L.
2013-05-01
Determining when and how a Loop Current eddy (LCE) in the Gulf of Mexico will finally separate is a difficult task, since several detachment re-attachment processes can occur during one of these events. Separation is usually defined based on snapshots of Eulerian fields such as sea surface height (SSH) but here we suggest that a Lagrangian view of the LCE separation process is more appropriate and objective. The basic idea is very simple: separation should be defined whenever water particles from the cyclonic side of the Loop Current move swiftly from the Yucatan Peninsula to the Florida Straits instead of penetrating into the NE Gulf of Mexico. An Eulerian metric is defined, based on the slope of the strain direction of the instantaneous hyperbolic point of the Loop Current anticyclone that provides useful information to forecast final LCE detachments. We highlight cases in which an LCE separation metric based on SSH contours (Leben, 2005) suggests there is a separated LCE that later reattaches, whereas the slope method and the Finite Time Lyapunov Exponent structure indicate the eddy remains dynamically connected to the Loop Current during the process.
A Lagrangian approach to the Loop Current eddy separation
NASA Astrophysics Data System (ADS)
Andrade-Canto, F.; Sheinbaum, J.; Zavala Sansón, L.
2013-01-01
Determining when and how a Loop Current eddy (LCE) in the Gulf of Mexico will finally separate is a difficult task, since several detachment re-attachment processes can occur during one of these events. Separation is usually defined based on snapshots of Eulerian fields such as sea surface height (SSH) but here we suggest that a Lagrangian view of the LCE separation process is more appropriate and objective. The basic idea is very simple: separation should be defined whenever water particles from the cyclonic side of the Loop Current move swiftly from the Yucatan Peninsula to the Florida Straits instead of penetrating into the NE Gulf of Mexico. The properties of backward-time finite time Lyapunov exponents (FTLE) computed from a numerical model of the Gulf of Mexico and Caribbean Sea are used to estimate the "skeleton" of flow and the structures involved in LCE detachment events. An Eulerian metric is defined, based on the slope of the strain direction of the instantaneous hyperbolic point of the Loop Current anticyclone that provides useful information to forecast final LCE detachments. We highlight cases in which an LCE separation metric based on SSH contours (Leben, 2005) suggests there is a separated LCE that later reattaches, whereas the slope method and FTLE structure indicate the eddy remains dynamically connected to the Loop Current during the process.
A Lagrangian analysis of sea ice dynamics in the Arctic
NASA Astrophysics Data System (ADS)
Szanyi, S.; Lukovich, J. V.; Haller, G.; Barber, D. G.
2014-12-01
Recent studies have highlighted acceleration in sea ice drift and deformation in the Arctic over the last several decades, underlining the need for improved understanding of sea ice dynamics and dispersion. In this study we present Lagrangian diagnostics to quantify changes in the dynamical characteristics of the Arctic sea ice cover from 1979 to 2012 during the transition from a predominantly multi-year to a first-year ice regime. Examined in particular is the evolution in finite-time Lyapunov exponents (FTLEs), which monitor the rate at which neighboring particle trajectories diverge, and stretching rates throughout the Arctic. In this analysis we compute FTLEs for the Arctic ice drift field using National Snow and Ice Data Centre (NSIDC) Polar Pathfinder Daily 25 km EASE-Grid weekly sea ice motion vectors for the annual cycle beginning both from the sea ice minimum in September, and maximum in March. Sensitivity analyses show that maximal FTLEs, or ridges, are robust even with the introduction of significant noise. Probability density functions and mean values of FTLEs show a trend towards higher FTLE values characteristic of increased mixing in the Arctic in the last decade, in keeping with a transition to a weaker, thinner ice cover.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Pratt, Kenneth R.; Meiss, James D.; Crimaldi, John P.
2015-03-01
Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
Pratt, Kenneth R. Crimaldi, John P.; Meiss, James D.
2015-03-15
Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement.
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
NASA Astrophysics Data System (ADS)
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Finite-time singularities in the dynamics of hyperinflation in an economy.
Szybisz, Martín A; Szybisz, Leszek
2009-08-01
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t), changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time t(c). By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t) approximately (t(c)-t)(-alpha) (with alpha>0 ) and the other exhibits a logarithmic divergence, p(t) approximately ln[1/(t(c)-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.
Finite-time Lyapunov exponent-based analysis for compressible flows
NASA Astrophysics Data System (ADS)
González, D. R.; Speth, R. L.; Gaitonde, D. V.; Lewis, M. J.
2016-08-01
The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.
Finite-time singularities in the dynamics of hyperinflation in an economy
NASA Astrophysics Data System (ADS)
Szybisz, Martín A.; Szybisz, Leszek
2009-08-01
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective “adaptive inflation expectations” with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t) , changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time tc . By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t)≈(tc-t)-α (with α>0 ) and the other exhibits a logarithmic divergence, p(t)≈ln[1/(tc-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.
Finite-time Lyapunov exponent-based analysis for compressible flows.
González, D R; Speth, R L; Gaitonde, D V; Lewis, M J
2016-08-01
The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.
Peng, Xiao; Wu, Huaiqin; Song, Ka; Shi, Jiaxin
2017-07-10
This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Ghabraei, Soheil; Moradi, Hamed; Vossoughi, Gholamreza
2016-06-01
Large amplitude oscillation of the power transmission lines, which is also known as galloping phenomenon, has hazardous consequences such as short circuiting and failure of transmission line. In this article, to suppress the undesirable vibrations of the transmission lines, first the governing equations of transmission line are derived via mode summation technique. Then, due to the occurrence of large amplitude vibrations, nonlinear quadratic and cubic terms are included in the derived linear equations. To suppress the vibrations, arbitrary number of the piezoelectric actuators is assumed to exert the actuation forces. Afterwards, a Lyapunov based approach is proposed for the robust adaptive suppression of the undesirable vibrations in the finite time. To compensate the supposed parametric uncertainties with unknown bands, proper adaption laws are introduced. To avoid the vibration devastating consequences as quickly as possible, appropriate control laws are designed. The vibration suppression in the finite time with supposed adaption and control laws is mathematically proved via Lyapunov finite time stability theory. Finally, to illustrate and validate the efficiency and robustness of the proposed finite time control scheme, a parametric case study with three piezoelectric actuators is performed. It is observed that the proposed active control strategy is more efficient and robust than the passive control methods.
A Lagrangian approach to classical thermodynamics
NASA Astrophysics Data System (ADS)
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
Gao, Lijun; Jiang, Xiaoxiao; Wang, Dandan
2016-03-01
This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.
NASA Astrophysics Data System (ADS)
Lindner, Michael; Donner, Reik V.
2017-03-01
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.
Lindner, Michael; Donner, Reik V
2017-03-01
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.
Gulf Stream transport and mixing processes via coherent structure dynamics
NASA Astrophysics Data System (ADS)
Wilson, Chris; Liu, Yi; Green, Melissa; Hughes, Chris
2017-04-01
The Gulf Stream has been characterized as either a barrier or blender to fluid transfer, involving processes relevant to the material exchange of heat, freshwater and carbon between the subtropical and subpolar gyres. However, previous characterization has depended on relatively sparse, in-situ Lagrangian float and drifter observations. The elegant kinematic model of Gulf Stream exchange developed by Bower (1991) is re-examined within a new diagnostic framework. The finite-time Lyapunov exponent (FTLE) is calculated from satellite altimetry to identify Lagrangian coherent structures (LCS) in the Gulf Stream region. The method provides dense sampling of the flow, the LCS capture dynamically-distinct regions associated with transport and mixing, and even represent some flow structure at finer spatial scale than the observational grid. Structures seen in independent observations of ocean colour match the LCS identified purely from surface velocity. The 22-year timeseries of diagnosed LCS supports the existing Bower kinematic model of the Gulf Stream, but also highlights fascinating new processes of comparable importance. Additionally, vortex pinch-off and formation of spiral eddies are clearly identified by LCS and may only be explained by considering changes to flow topology and the dynamics of shear-flow instability at both small and large Rossby number. Such processes, seen though LCS may enhance validation of climate models. Bower, A. S. (1991), A simple kinematic mechanism for mixing fluid parcels across a meandering jet, Journal of Physical Oceanography, 21(1), 173-180.
Buoyancy-induced Lagrangian chaos: the differentially-heated cavity revisited
NASA Astrophysics Data System (ADS)
Contreras, P. S.; Speetjens, M. F. M.; Clercx, H. J. H.
2016-09-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially-heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside differentially-heated cavities. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. First results reveal that the convective terms in the momentum and energy balances cause non-trivial (and potentially chaotic) Lagrangian transport.
LSPRAY-IV: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2012-01-01
LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1994-01-01
In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.
Lagrangian tracing of Sahelian Sudan moisture sources
NASA Astrophysics Data System (ADS)
Salih, Abubakr A. M.; Zhang, Qiong; Tjernström, Michael
2015-07-01
The Sahelian Sudan is an arid to semiarid region that depends on the seasonal rainfall as the main source of water, but its rainfall has large interannual variability. Such dry regions usually have their main moisture sources elsewhere; thus, the rainfall variability is directly related to the moisture transport. This study seeks to identify source regions of water vapor for Sahelian Sudan during the monsoon period, from July to September. We have used the Lagrangian trajectory model FLEXPART driven by ERA-Interim reanalysis for the time period 1998 to 2008. The results show that most of the air masses that reach this region during the monsoon period have their major origins over the Arabian Peninsula, Central Africa, or are associated with the tropical easterly jet. Flow associated with Intertropical Convergence Zone contributes almost half of the total precipitated water; most of it comes from Central Africa. This suggests that moisture recycling is the major contributor, compared to Oceanic sources. The flows from the northeast (Arabian Peninsula and north Asia) and east (Horn of Africa and north Indian Ocean) contribute about one third of the precipitated water. The rest of precipitated water comes from the Mediterranean, subtropical Atlantic, and western Sahel, all with smaller contribution. Our results also indicate that different subregions of Sahelian Sudan have different moisture sources. Such result needs to be taken into account in seasonal forecasting practices.
Surface transport in the Ria de Vigo - Transport barriers in a tidal estuary with a complex geometry
NASA Astrophysics Data System (ADS)
Huhn, F.; von Kameke, A.; Montero, P.; Allen-Perkins, S.; Venancio, A.; Pérez-Muñuzuri, V.
2012-04-01
We study the submesoscale surface transport in the Ria de Vigo, NW Spain, an estuary with tidal and wind-driven circulation, analyzing the output of the coastal model MOHID with state-of-the-art Lagrangian methods, and comparing the results to drifter experiments. We extract Lagrangian Coherent Structures (LCS) as ridges in fields of the Finite-Time Lyapunov Exponent (FTLE) that can be identified with transport barriers. The LCS reveal the fundamental structure of the modelled circulation in the estaury that is a superposition of the tidal inflow and outflow, the wind-driven currents and the long-term drift on the shelf. In the Ria de Vigo, LCS are attached to prominent coastal boundaries, as islands or capes, indicating that the geometry of the flow patterns is dominated by bathymetry. Although the vertical flow which is not represented in the horizontal surface flow can be important at the coast, the found transport patterns can be seen as the surface footprint of the 3D circulation in the estaury. Comparing the trajectories of real surface drifters from four deployments to the computed transport barriers in different typical meteorological sitiations, we find that the drifter trajectories are in agreement with the different coherent water masses predicted by the model. The knowledge of the global transport patterns of water masses in this highly populated coastal region is indispensable for the assessment of the fate of contaminations, like possible oil spills or released waste water, but also for biological studies that deal with the drift of eggs and larvae of fish and other marine species, or investigate plankton blooms.
Currents in the Dead Sea: Lagrangian and Eulerian observations
NASA Astrophysics Data System (ADS)
Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav
2015-04-01
The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (Eulerian) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.
Nonlinear E -mode clustering in Lagrangian space
NASA Astrophysics Data System (ADS)
Yu, Hao-Ran; Pen, Ue-Li; Zhu, Hong-Ming
2017-02-01
We study the nonlinear E -mode clustering in Lagrangian space by using large scale structure N -body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the E -mode displacement fields in Lagrangian space improves the cross-correlation scale k with initial density field by a factor of 6-7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation measurements from current and future large scale structure surveys.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching Yuen
1991-01-01
A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.
An Augmented Lagrangian Approach for Scheduling Problems
NASA Astrophysics Data System (ADS)
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
Liu, Qingshan; Dang, Chuangyin; Cao, Jinde
2010-07-01
In this paper, based on a one-neuron recurrent neural network, a novel k-winners-take-all ( k -WTA) network is proposed. Finite time convergence of the proposed neural network is proved using the Lyapunov method. The k-WTA operation is first converted equivalently into a linear programming problem. Then, a one-neuron recurrent neural network is proposed to get the kth or (k+1)th largest inputs of the k-WTA problem. Furthermore, a k-WTA network is designed based on the proposed neural network to perform the k-WTA operation. Compared with the existing k-WTA networks, the proposed network has simple structure and finite time convergence. In addition, simulation results on numerical examples show the effectiveness and performance of the proposed k-WTA network.
Dong, Hongyang; Hu, Qinglei; Ma, Guangfu
2016-03-01
Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Lagrangian treatment of magnetic dielectrics
NASA Astrophysics Data System (ADS)
Nelson, D. F.; Chen, B.
1994-07-01
A general Lagrangian-based long-wavelength theory of ordered magnetic dielectric crystals (ferromagnetic, antiferromagnetic, and ferrimagnetic) is formulated. Our classical treatment of intrinsic spin uses the anticommuting Grassmann algebra G3 developed by Berezin and Marinov and by Casalbuoni. The Grassmann formulation of classical spin gives by the Dirac quantization procedure the usual nonrelativistic spin-1/2 quantum theory. The treatment begins at the microscopic level before a long-wavelength limit is performed to obtain a macroscopic theory so as to incorporate all long-wavelength modes of motion (acoustic, optic, electromagnetic, and spin) and their interaction to all orders of nonlinearity. The crystals can have any symmetry, anisotropy, and structural complexity. The equations of motion for all the modes are obtained and the energy, momentum, pseudomomentum, angular momentum, and spin conservation laws are found. The magnetizations arising from spin and from the motion of bound charge are found to enter the energy conservation law distinguishably. This theory should be particularly useful for the study of magneto-optical phenomena.
NASA Astrophysics Data System (ADS)
Yagasaki, Kazuyuki
2007-08-01
In experiments for single and coupled pendula, we demonstrate the effectiveness of a new control method based on dynamical systems theory for stabilizing unstable aperiodic trajectories defined on infinite- or finite-time intervals. The basic idea of the method is similar to that of the OGY method, which is a well-known, chaos control method. Extended concepts of the stable and unstable manifolds of hyperbolic trajectories are used here.
Homology class of a Lagrangian Klein bottle
NASA Astrophysics Data System (ADS)
Nemirovski, Stefan Yu
2009-08-01
It is shown that an embedded Lagrangian Klein bottle realises a non-zero mod 2 homology class in a compact symplectic four-manifold (X,\\omega) such that c_1(X,\\omega)\\cdot \\lbrack \\omega \\rbrack > 0.
Alternative Expression for the Electromagnetic Lagrangian
NASA Astrophysics Data System (ADS)
Saldanha, Pablo L.
2016-06-01
We reintroduce an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields, proposed by Livens about one century ago. This Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. Here, we show that the total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. We also show that the alternative Lagrangian is equivalent to the traditional one in their domain of validity and that it provides an interesting description of the Aharonov-Bohm effect.
Van, Mien; Ge, Shuzhi Sam; Ren, Hongliang
2016-04-28
In this paper, a novel finite time fault tolerant control (FTC) is proposed for uncertain robot manipulators with actuator faults. First, a finite time passive FTC (PFTC) based on a robust nonsingular fast terminal sliding mode control (NFTSMC) is investigated. Be analyzed for addressing the disadvantages of the PFTC, an AFTC are then investigated by combining NFTSMC with a simple fault diagnosis scheme. In this scheme, an online fault estimation algorithm based on time delay estimation (TDE) is proposed to approximate actuator faults. The estimated fault information is used to detect, isolate, and accommodate the effect of the faults in the system. Then, a robust AFTC law is established by combining the obtained fault information and a robust NFTSMC. Finally, a high-order sliding mode (HOSM) control based on super-twisting algorithm is employed to eliminate the chattering. In comparison to the PFTC and other state-of-the-art approaches, the proposed AFTC scheme possess several advantages such as high precision, strong robustness, no singularity, less chattering, and fast finite-time convergence due to the combined NFTSMC and HOSM control, and requires no prior knowledge of the fault due to TDE-based fault estimation. Finally, simulation results are obtained to verify the effectiveness of the proposed strategy.
Wang, Yujuan; Song, Yongduan
2017-03-01
In this paper, the problem of containment control of networked multiagent systems is considered with special emphasis on finite-time convergence. A distributed neural adaptive control scheme for containment is developed, which, different from the current state of the art, is able to achieve dynamic containment in finite time with sufficient accuracy despite unknown nonaffine dynamics and mismatched uncertainties. Such a finite-time feature, highly desirable in practice, is made possible by the fraction dynamic surface control design technique based on the concept of virtual fraction filter. In the proposed containment protocol, only the local information from the neighbor followers and the local position information from the neighbor leaders are required. Furthermore, since the available information utilized is local and is embedded into the control scheme through fraction power feedback, rather than direct linear or regular nonlinear feedback, the resultant control scheme is truly distributed. In addition, although mismatched uncertainties and external disturbances are involved, only one single generalized neural parameter needs to be updated in the control scheme, making its design and implementation straightforward and inexpensive. The effectiveness of the developed method is also confirmed by numerical simulation.
Wang, Licheng; Wang, Zidong; Wei, Guoliang; Alsaadi, Fuad E
2017-02-06
This paper deals with the event-based finite-time state estimation problem for a class of discrete-time stochastic neural networks with mixed discrete and distributed time delays. In order to mitigate the burden of data communication, a general component-based event-triggered transmission mechanism is proposed to determine whether the measurement output should be released to the estimator at certain time-point according to a specific triggering condition. A new concept of finite-time boundedness in the mean square is put forward to quantify the estimation performance by introducing a settling-like time function. The objective of the addressed problem is to construct an event-based state estimator to estimate the neuron states such that, in the presence of both mixed time delays and external noise disturbances, the dynamics of the estimation error is finite-time bounded in the mean square with a prescribed error upper bound. Sufficient conditions are established, via stochastic analysis techniques, to guarantee the desired estimation performance. By solving an optimization problem with some inequality constraints, the explicit expression of the estimator gain matrix is characterized to minimize the settling-like time. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design scheme.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2011-06-01
We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube Ω=[0 can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. The new system is amenable to being integrated numerically using similar methods as in Euler equations. We propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite-time singularity problem of Euler equations, based on the conservation of quantities directly related to energy and circulation. The method of mapping to a regular system can be extended to any fluid equation that admits a Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of 2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the mapping, we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1D inviscid Burgers equation.
Relativistic Lagrangian displacement field and tensor perturbations
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Wiegand, Alexander
2014-12-01
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating tensor artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Lagrangian Simulation of Taylor-Couette Flow.
1981-07-22
4. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability , Clarendon Press, 428 (1961). 5. J. L. Synge, Trans. of the Roy. Soc. of Canada 27, 1... hydrodynamics code designed for the Lagrangian simulation of transient rotational flow phenomena. The code solves the incompressible, inviscid fluid...COUETVE FLOW I. Introduction We report here on the development of the hydrodynamics code SPLASH which is designed for the Lagrangian simulation of
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
NASA Astrophysics Data System (ADS)
Ferrero, Enrico; Mortarini, Luca; Purghè, Federico
2017-04-01
A model for the evaluation of the concentration fluctuation variance is coupled with a one-particle Lagrangian stochastic model and results compared to a wind-tunnel simulation experiment. In this model the concentration variance evolves along the particle trajectories according to the same Langevin equation used for the simulation of the velocity field, and its dissipation is taken into account through a decay term with a finite time scale. Indeed, while the mean concentration is conserved, the concentration variance is not and our model takes into account its dissipation. A simple parametrization for the dissipation time scale is proposed and it is found that it depends linearly on time and on the ratio between the size and the height of the source through a scaling factor of 1 / 3.
Lagrangian Coherent Structures in a coastal upwelling environment
NASA Astrophysics Data System (ADS)
Gough, Matt K.; Reniers, Ad; Olascoaga, M. Josefina; Haus, Brian K.; MacMahan, Jamie; Paduan, Jeff; Halle, Chris
2016-10-01
A unique spatiotemporal perspective of evolving surface currents off the northern California coast is provided with Lagrangian Coherent Structures (LCSs) determined from attracting Finite-Time Lyapunov Exponents (FTLEs). The FTLEs are calculated from hourly 2-D surface current velocities obtained with HF radars. Attracting FTLE field maxima can identify confluence and shear in flows which can be useful in mapping dynamics associated with fronts. FTLE and SST fields are compared during three time periods in 2009: late March, early September, and late September. During strong upwelling-favorable winds in late March the FTLE and SST fields were not strongly related indicating that frontal dynamics were not strongly influencing surface circulation. Exceptions to this occurred when FTLE ridges calculated from a shorter integration period captured the evolution of a cold water filament and when a FTLE ridge migrated offshore along with an upwelling front. During the two September cases an improved relationship between the FTLE and SST fields was found although occasionally they became shifted. The shifts occurred when the FTLE integration period spanned backwards in time through periods of relaxed and upwelling-favorable winds. This suggests that frontal dynamics captured by LCSs during relaxed winds can subsequently become advected after the onset of wind-forcing by a surface mixed layer decoupled from stably stratified water below the surface mixed layer. Additionally, the LCSs were found to be useful in mapping the origin and destination of surface trajectories, the confluence associated with a persistent eddy-like feature, and retention zones off coastal promontories.
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
Holm, Darryl D.
2002-06-01
We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.
Aguilar-López, Ricardo
2016-01-01
This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme. PMID:27738651
Duc, Luu Hoang; Chávez, Joseph Páez; Son, Doan Thai; Siegmund, Stefan
2016-01-01
In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.
Yan, Zhiguo; Song, Yunxia; Park, Ju H
2017-05-01
This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Aguilar-López, Ricardo; Mata-Machuca, Juan L
2016-01-01
This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.
Relating surface pressure to Lagrangian wake topology around a circular cylinder in cross flow
NASA Astrophysics Data System (ADS)
Rockwood, Matthew; Green, Melissa
2016-11-01
The tracks of Lagrangian saddles, identified as non-parallel intersections of positive and negative-time finite-time Lyapunov exponent (FTLE) ridges, have been shown to indicate the timing of von Karman vortex shedding in the wake of bluff bodies. The saddles are difficult to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the topological changes without direct access to the FTLE, the saddle dynamics are correlated to measurable surface quantities on a circular cylinder in cross flow. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex has been shown to accelerate away from the cylinder surface as the vortex sheds. In previous numerical results at Re = 150 , this acceleration coincides with the peak in lift force over the cylinder, and also with a minimum in the static pressure at a location slightly upstream of the mean separation location. In the current work, this result is compared with experimental data at Re = O (10 , 000) . Successful validation would provide a strategy for locating sensitive regions on the cylinder surface where vortex shedding could be detected using simple pressure transducers. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.
Lagrangian coherent structures in the wake of a streamwise oscillating cylinder
NASA Astrophysics Data System (ADS)
Cagney, Neil; Balabani, Stavroula
2015-11-01
Lagrangian analysis of experimental flow measurements has the ability to reveal complex coherent structures and identify phenomena that may not be apparent from standard Eulerian descriptors, such as vorticity. We measure the wake of a cylinder undergoing streamwise vortex-induced vibrations (VIVs) using Particle-Image Velocimetry, and examine the wake dynamics throughout the response regime in terms of the phase-averaged vorticity fields. The Finite-Time Lyapunov exponent (FTLE) fields are also computed in backward- and forward-time in order to identify the Lagrangian Coherent Structures. We examine four distinct wake modes that occur at various points in the response regime. The roll up of the shear layers and the vortex formation process are examined using the FTLE fields. This analysis allows the fluid-structure interaction and dynamics in the near wake to be examined in much greater detail than would be possible using the vorticity fields alone. Particular attention is paid to the symmetric vortex-shedding mode, which is characteristic to streamwise VIV; the forward-time FTLE fields show that the wake is organised into discreet ``vortex cells,'' which enclose each vortex and define its boundary. Finally, the advection of tracers in the wake is studied in order to examine how the different wake modes promote/inhibit mixing. The alternate wake modes tend to promote mixing, particularly in the second response branch, but the symmetric shedding tends to reduce the lateral mixing across the wake.
A Lagrangian approach to study flow topology around a flapping flat-plate wing
NASA Astrophysics Data System (ADS)
Krishna, Swathi; Mulleners, Karen; Green, Melissa
2015-11-01
The incredible flight performance of insects can be attributed in part to the generation and maintenance of stable regions of vorticity, which is achieved by manipulating the wing kinematics. Along with the prolonged attachment of the leading edge vortex during translation of the wing, the rotational motion at the end of the stroke is critical as it generates large amounts of lift required for the insect to remain air-borne while hovering. The wing reversal entails a change in the flow-field around the wing which is closely tied to variations in force production. Based on phase-averaged particle image velocimetry data we analyze the effect of a shift in the rotational phase of a flapping wing on the flow characteristics. A topological study is conducted using Lagrangian vortex detection techniques in order to characterize the shear layer formation, vortex interactions and flow separation. The Lagrangian analysis includes the calculation of Finite Time Lyapunov Exponents based on particle trajectories. An objective approach is employed to trace the location of separation or attachment points as an indication for changes in the strength, stability and shedding frequencies of vortices. These trajectories are correlated with fluctuations in aerodynamic force coefficients.
Lagrangian measurement in fully developed turbulence
NASA Astrophysics Data System (ADS)
Pinton, J.-F.; Michel, O.; Mordant, N.; Metz, P.
2002-07-01
We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number Rlambda = 1200. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentz form EL(omega = urms2TL/(1 + (TLomega2, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.
Lagrangian measurement in fully developed turbulence
NASA Astrophysics Data System (ADS)
Mordant, N.; Metz, P.; Pinton, J.-F.; Michel, O.
2002-07-01
We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number Rλ = 1200. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentz form EL(ω) = urms2TL/(1 + (TLω)2), in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.
The recursion relation in Lagrangian perturbation theory
Rampf, Cornelius
2012-12-01
We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter density contrast is in one-to-one correspondence with standard perturbation theory (SPT) at any order. This correspondence has been recently shown to be valid up to fourth order for a non-relativistic, irrotational and dust-like component. Assuming it to be valid at arbitrary (higher) order, we express the Lagrangian displacement field in terms of the perturbative kernels of SPT, which are itself given by their own and well-known recursion relation. We argue that the Lagrangian solution always contains more non-linear information in comparison with the SPT solution, (mainly) if the non-perturbative density contrast is restored after the displacement field is obtained.
Lagrangian methods in nonlinear plasma wave interaction
NASA Technical Reports Server (NTRS)
Crawford, F. W.
1980-01-01
Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.
Lagrangian solution of supersonic real gas flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.
Effective Lagrangian in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Kitamoto, Hiroyuki; Kitazawa, Yoshihisa
2017-01-01
Scale invariant fluctuations of metric are a universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating superhorizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
Ik Han, Seong; Lee, Jangmyung
2016-11-01
This paper presents finite-time sliding mode control (FSMC) with predefined constraints for the tracking error and sliding surface in order to obtain robust positioning of a robot manipulator with input nonlinearity due to an unknown deadzone and external disturbance. An assumed model feedforward FSMC was designed to avoid tedious identification procedures for the manipulator parameters and to obtain a fast response time. Two constraint switching control functions based on the tracking error and finite-time sliding surface were added to the FSMC to guarantee the predefined tracking performance despite the presence of an unknown deadzone and disturbance. The tracking error due to the deadzone and disturbance can be suppressed within the predefined error boundary simply by tuning the gain value of the constraint switching function and without the addition of an extra compensator. Therefore, the designed constraint controller has a simpler structure than conventional transformed error constraint methods and the sliding surface constraint scheme can also indirectly guarantee the tracking error constraint while being more stable than the tracking error constraint control. A simulation and experiment were performed on an articulated robot manipulator to validate the proposed control schemes.
Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model
NASA Astrophysics Data System (ADS)
Paga, Pierre; Kühn, Reimer
2017-08-01
We study the large deviations of the magnetization at some finite time in the Curie-Weiss random field Ising model with parallel updating. While relaxation dynamics in an infinite-time horizon gives rise to unique dynamical trajectories [specified by initial conditions and governed by first-order dynamics of the form mt +1=f (mt) ] , we observe that the introduction of a finite-time horizon and the specification of terminal conditions can generate a host of metastable solutions obeying second-order dynamics. We show that these solutions are governed by a Newtonian-like dynamics in discrete time which permits solutions in terms of both the first-order relaxation ("forward") dynamics and the backward dynamics mt +1=f-1(mt) . Our approach allows us to classify trajectories for a given final magnetization as stable or metastable according to the value of the rate function associated with them. We find that in analogy to the Freidlin-Wentzell description of the stochastic dynamics of escape from metastable states, the dominant trajectories may switch between the two types (forward and backward) of first-order dynamics. Additionally, we show how to compute rate functions when uncertainty in the quenched disorder is introduced.
NASA Astrophysics Data System (ADS)
Wessel, Niels; Ziehmann, Christine; Kurths, Jürgen; Meyerfeldt, Udo; Schirdewan, Alexander; Voss, Andreas
2000-01-01
Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.
NASA Astrophysics Data System (ADS)
Dadić, I.
2001-01-01
We study out of equilibrium thermal field theories with switching on the interaction occurring at finite time using the Wigner transforms of two-point functions. For two-point functions we define the concept of a projected function: it is zero if any of the times refers to the time before switching on the interaction; otherwise it depends only on the relative coordinates. This definition includes bare propagators, one-loop self-energies, etc. For the infinite-average-time limit of the Wigner transforms of projected functions we define the analyticity assumptions: (1) The function of energy is analytic above (below) the real axis. (2) The function goes to zero as the absolute value of energy approaches infinity in the upper (lower) semiplane. Without use of the gradient expansion, we obtain the convolution product of projected functions. We sum the Schwinger-Dyson series in closed form. In the calculation of the Keldysh component (both resummed and single self-energy insertion approximation) contributions appear which are not the Fourier transforms of projected functions, signaling the limitations of the method. In the Feynman diagrams there is no explicit energy conservation at vertices; there is an overall energy-smearing factor taking care of the uncertainty relations. The relation between the theories with the Keldysh time path and with the finite time path enables one to rederive the results, such as the cancellation of pinching, collinear, and infrared singularities, hard thermal loop resummation, etc.
NASA Technical Reports Server (NTRS)
Methven, J.; Arnold, S. R.; Stohl, A.; Evans, M. J.; Avery, M.; Law, K.; Lewis, A. C.; Monks, P. S.; Parrish, D.; Reeves, C.; Schlager, H.; Atlas, E.; Blake, D.; Coe, H.; Cohen, R. C.; Crosier, J.; Flocke, F.; Holloway, J. S.; Hopkins, J. R.; Huber, G.; McQuaid, J.; Purvis, R.; Rappengluck, B.; Ryerson, T. B.; Sachse, G. W.
2006-01-01
The International Consortium for Atmospheric Research on Transport and Transformation (ICARTT)-Lagrangian experiment was conceived with an aim to quantify the effects of photochemistry and mixing on the transformation of air masses in the free troposphere away from emissions. To this end attempts were made to intercept and sample air masses several times during their journey across the North Atlantic using four aircraft based in New Hampshire (USA), Faial (Azores) and Creil (France). This article begins by describing forecasts using two Lagrangian models that were used to direct the aircraft into target air masses. A novel technique is then used to identify Lagrangian matches between flight segments. Two independent searches are conducted: for Lagrangian model matches and for pairs of whole air samples with matching hydrocarbon fingerprints. The information is filtered further by searching for matching hydrocarbon samples that are linked by matching trajectories. The quality of these coincident matches is assessed using temperature, humidity and tracer observations. The technique pulls out five clear Lagrangian cases covering a variety of situations and these are examined in detail. The matching trajectories and hydrocarbon fingerprints are shown and the downwind minus upwind differences in tracers are discussed.
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
NASA Astrophysics Data System (ADS)
Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba
2017-07-01
In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.
Lagrangian water quality dynamics in the San Luis Drain, California.
NASA Astrophysics Data System (ADS)
Volkmar, E. C.; Dahlgren, R. A.; Stringfellow, W. T.; Henson, S. S.; Borglin, S. E.; Kendall, C.
2007-12-01
Integration of temporal changes in biological and water quality constituents during downstream transport is critical to understanding aquatic ecosystem and biogeochemical dynamics of rivers, estuaries, and the near- coastal waters into which rivers flow. Changes in chemical, physical, and biological water quality constituents during downstream transport can be evaluated by following a specific parcel of water, known as a Lagrangian study. The objective of this study was to differentiate changes in water quality constituents occurring within a parcel of water as it travels downstream to the changes observed at a fixed sampling location. We sampled a parcel of agricultural drainage water as it traveled downstream for 84 h in a concrete-lined channel (San Luis Drain in San Joaquin Valley) with no additional water inputs or outputs. The Lagrangian sampling occurred in August 2006 and June 2007. Data from the Lagrangian study was compared to data collected at a fixed point using an automatic pump sampler and water quality sonde. Fluorescence (a measure of algal pigments), dissolved oxygen, temperature, pH, and conductivity were measured every 30 minutes, as well as collecting grab samples every 2 h for nutrient and suspended sediment analyses. Sinusoidal diel (24 h) patterns were observed for dissolved oxygen, pH, and temperature within the parcel of water. Algal pigments, nutrients, suspended solids, and turbidity did not exhibit sinusoidal diel patterns, generally observed at a fixed sampling location. The diel patterns observed indicated changes that would occur during downstream transport. Algal pigments showed a rapid day time increase during the first 24 to 48 h followed by a plateau or decrease for the remainder of the study. Algal growth was apparent each day during the study, as measured by increasing dissolved oxygen concentrations, in spite of non-detectable phosphate concentrations (<5 ppb) and nearly complete consumption of soluble silica during the 2007
NASA Astrophysics Data System (ADS)
Fu, Junjie; Wang, Jinzhi
2016-06-01
In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.
NASA Astrophysics Data System (ADS)
Zhang, Yong; Meerschaert, Mark M.; Baeumer, Boris; LaBolle, Eric M.
2015-08-01
This study develops an explicit two-step Lagrangian scheme based on the renewal-reward process to capture transient anomalous diffusion with mixed retention and early arrivals in multidimensional media. The resulting 3-D anomalous transport simulator provides a flexible platform for modeling transport. The first step explicitly models retention due to mass exchange between one mobile zone and any number of parallel immobile zones. The mobile component of the renewal process can be calculated as either an exponential random variable or a preassigned time step, and the subsequent random immobile time follows a Hyper-exponential distribution for finite immobile zones or a tempered stable distribution for infinite immobile zones with an exponentially tempered power-law memory function. The second step describes well-documented early arrivals which can follow streamlines due to mechanical dispersion using the method of subordination to regional flow. Applicability and implementation of the Lagrangian solver are further checked against transport observed in various media. Results show that, although the time-nonlocal model parameters are predictable for transport with retention in alluvial settings, the standard time-nonlocal model cannot capture early arrivals. Retention and early arrivals observed in porous and fractured media can be efficiently modeled by our Lagrangian solver, allowing anomalous transport to be incorporated into 2-D/3-D models with irregular flow fields. Extensions of the particle-tracking approach are also discussed for transport with parameters conditioned on local aquifer properties, as required by transient flow and nonstationary media.
{eta}-{eta}{sup '}--glue Mixing from the Chiral Lagrangian
Mathieu, Vincent; Vento, Vicente
2011-05-23
The {eta}-{eta}{sup '} mixing from the chiral Lagrangian is reviewed. It is shown how the Feldman-Kroll-Stech ansatz can be derived from the chiral Lagrangian. The inclusion of the glueball is also discussed.
Lorentz-covariant dissipative Lagrangian systems
NASA Technical Reports Server (NTRS)
Kaufman, A. N.
1985-01-01
The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.
Lorentz-covariant dissipative Lagrangian systems
NASA Technical Reports Server (NTRS)
Kaufman, A. N.
1985-01-01
The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.
Lagrangian tetragons and instabilities in Hamiltonian dynamics
NASA Astrophysics Data System (ADS)
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Examination of Eulerian and Lagrangian Coordinate Systems.
ERIC Educational Resources Information Center
Remillard, Wilfred J.
1978-01-01
Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)
Peierls brackets in non-Lagrangian field theory
NASA Astrophysics Data System (ADS)
Sharapov, A. A.
2014-10-01
The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.
NASA Astrophysics Data System (ADS)
Sawford, B. L.; Yeung, P. K.
2001-09-01
Direct numerical simulation calculations of Lagrangian statistics for homogeneous turbulence in uniform shear flow are used to test the performance of two different Lagrangian stochastic models of turbulent dispersion. These two models differ in their representation of Eulerian acceleration statistics. In particular one of the models imparts an excessively large mean rotation to the trajectories in the plane of the shear, while the other is nonrotational. We show that this rotation degrades the model's prediction of Lagrangian statistics such as the velocity correlation function and the dispersion. Compared with the predictions of the nonrotational model, the excessive rotation reduces dispersion in the shear plane by up to a factor of 2 and introduces spurious oscillations into the velocity covariance. These differences are typical of those for shear flows at equilibrium, and may be even greater for flows not at equilibrium. The Eulerian differences thus also serve as a useful indication of the performance of these models in predicting Lagrangian statistics. We also show that for the present shear flow the behavior of the Lagrangian velocity structure function for time lags between the Kolmogorov and energy-containing time scales is consistent with corresponding analyses of forced isotropic turbulence. The present results are consistent with a revised value C0≈6 for the universal constant in the inertial subrange of the Lagrangian velocity structure function. This finding suggests that the artificial forcing of the isotropic turbulence simulations does not distort estimates of C0.
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
NASA Astrophysics Data System (ADS)
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
A Quasi-Conservative Adaptive Semi-Lagrangian Advection-Diffusion Scheme
NASA Astrophysics Data System (ADS)
Behrens, Joern
2014-05-01
Many processes in atmospheric or oceanic tracer transport are conveniently represented by advection-diffusion type equations. Depending on the magnitudes of both components, the mathematical representation and consequently the discretization is a non-trivial problem. We will focus on advection-dominated situations and will introduce a semi-Lagrangian scheme with adaptive mesh refinement for high local resolution. This scheme is well suited for pollutant transport from point sources, or transport processes featuring fine filamentation with corresponding local concentration maxima. In order to achieve stability, accuracy and conservation, we combine an adaptive mesh refinement quasi-conservative semi-Lagrangian scheme, based on an integral formulation of the underlying advective conservation law (Behrens, 2006), with an advection diffusion scheme as described by Spiegelman and Katz (2006). The resulting scheme proves to be conservative and stable, while maintaining high computational efficiency and accuracy.
Agoritsas, Elisabeth; Bustingorry, Sebastian; Lecomte, Vivien; Schehr, Grégory; Giamarchi, Thierry
2012-09-01
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length ξ and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the directed polymer, described by its roughness, and the fluctuations of its free energy, characterized by its two-point correlator. Analytical arguments are provided in favor of a generic scaling law between those quantities, at finite time, nonvanishing ξ, and explicit temperature dependence. Numerical results are in good agreement both for simulations on the discrete directed polymer and on a continuous directed polymer (with short-range correlated disorder). Applications to recent experiments on liquid crystals are discussed.
Liu, Chongxin; Liu, Hang
2017-01-01
This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme. PMID:28406966
NASA Technical Reports Server (NTRS)
Dinyavari, M. A. H.; Friedmann, P. P.
1984-01-01
Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.
NASA Astrophysics Data System (ADS)
Wen, Guoguang; Yu, Yongguang; Peng, Zhaoxia; Rahmani, Ahmed
2016-06-01
This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.
Mazinan, A H; Pasand, M; Soltani, B
2015-09-01
In the aspect of further development of investigations in the area of spacecraft modeling and analysis of the control scheme, a new hybrid finite-time robust three-axis cascade attitude control approach is proposed via pulse modulation synthesis. The full quaternion based control approach proposed here is organized in association with both the inner and the outer closed loops. It is shown that the inner closed loop, which consists of the sliding mode finite-time control approach, the pulse width pulse frequency modulator, the control allocation and finally the dynamics of the spacecraft is realized to track the three-axis referenced commands of the angular velocities. The pulse width pulse frequency modulators are in fact employed in the inner closed loop to accommodate the control signals to a number of on-off thrusters, while the control allocation algorithm provides the commanded firing times for the reaction control thrusters in the overactuated spacecraft. Hereinafter, the outer closed loop, which consists of the proportional linear control approach and the kinematics of the spacecraft is correspondingly designed to deal with the attitude angles that are presented by quaternion vector. It should be noted that the main motivation of the present research is to realize a hybrid control method by using linear and nonlinear terms and to provide a reliable and robust control structure, which is able to track time varying three-axis referenced commands. Subsequently, a stability analysis is presented to verify the performance of the overall proposed cascade attitude control approach. To prove the effectiveness of the presented approach, a thorough investigation is presented compared to a number of recent corresponding benchmarks.
An advection scheme based on the combination of particle mesh method and pure Lagrangian approach
NASA Astrophysics Data System (ADS)
Arsenic, Ilija; Mihailovic, Dragutin T.; Kapor, Darko
2011-11-01
Possibility of using pure Lagrangian approach in modeling transport phenomena is described in this paper. The application of pure Lagrangian approach in real atmospheric field induces highly irregular spatial distribution of grid points, after only a few time steps. In order to avoid problems caused by that irregularity, a quasi interpolation procedure is proposed. Proposed interpolation procedure is similar to the radial basis functions interpolation and does not impose any demands about spatial distribution of the grid points or about continuity and differentiability of the field that needs to be interpolated. Besides that, proposed procedure is explicitly mass conserving. Combination of particle mesh method and pure Lagrangian approach creates efficient transport scheme that does not produce any new local maxima and minima in advected field. In proposed advection scheme motion of points are performed in Lagrangian manner while spatial derivatives are evaluated on the basis of values interpolated onto regular grid. Applicability of proposed advection scheme in an unambiguous way is proved by performing "standard" numerical tests with (i) the slotted cylinder under solid body rotation, (ii) the test with Doswell's idealized cyclogenesis as well as (iii) integration of shallow water equations.
A Lagrangian Turbulent Dispersion Model of Evolving Sea Spray Droplets Over the Ocean
NASA Astrophysics Data System (ADS)
Mueller, James; Veron, Fabrice
2004-11-01
Lagrangian models for the dispersion of heavy particles have consistently proven to be useful in atmospheric studies. Our Spray Lagrangian Turbulent Transport and Evaporation model (SpLaTTE), while sharing many common aims with the aforementioned atmospheric models, is distinguished both by its targeted location, the oceanic surface-wave zone, and by its level of detail. Although there have also been previous models of sea-spray, none of them have been exclusively Lagrangian. SpLaTTE simultaneously models the transport of droplets, by solving the complete equations of motion numerically, and the evolution of the droplets in temperature, salinity, volume, and density; consequently, it has already produced interesting results. For instance, we have found that the Lagrangian frequency spectrum for the droplet's velocity in the inertial subrange does not follow a perfect ω -4 dependence, as expected for a Stokes flow. Furthermore, we have also observed a phase shift between the air and droplet velocity. Finally, the sensible heat flux reverses as a droplet falls back through the surface boundary layer.
Lagrangian modelling of OPALE dataset.
NASA Astrophysics Data System (ADS)
Gil, Jaime E.; Thomas, Jennie; Bekki, Slimane; Kukui, Alexandre; Ancellet, Gerad; Preunkert, Susanne; Legrand, Michel; Frey, Markus; Savarino, Joel; Jourdain, Bruno; Kerbrat, Michel; France, James; King, Martin; Toumi, Ralf
2013-04-01
The OPALE measurement campaign aimed to characterize the atmospheric chemistry of the East Antarctic Plateau making a range of measurements at two sites, a coastal one, Dumont d'Urville (DDU) (From December 2010 until March 2011, 66o S, 123oE, coastal site) and on top of the Antarctic plateau Dome C (From December 2011 until January 2012 at Dome C, 75oS, 123o E, 3233 m a.s.l.). There are relatively few observations of chemistry occurring inland and coastal sites Antarctic sites. During the campaign air masses originating from the marine boundary layer, the free troposphere, the Antarctic continent, and of mixed origins were observed. We present analyses of chemical measurements (including O3, NO2, OH, RO2, hydrocarbons) using the CiTTyCAT photochemical trajectory model. The model simulates the chemistry of air masses over multiple (~5) days back trajectories provided by a stochastic trajectory model (FLEXPART). In some cases, the initial chemical conditions are taken from a chemistry-transport model (MOZART). The effect of clouds on the photolysis rates is also accounted for using MODIS satellite data. The model results are compared with measurements performed during both OPALE campaign years. Differences between the reactive nitrogen and hydroxyl radical chemistry at DDU and Dome C and the strong influence of reactive exchanges of trace gases between the snow and the atmosphere at Dome C are highlighted. The implications for the oxidizing capacity of the Antarctic boundary layer are also discussed.
Lagrangian descriptors and their applications to oceanic and atmospheric flows
NASA Astrophysics Data System (ADS)
Mancho, A. M.
2012-12-01
Geometry has been a very useful approach for studying dynamical systems. At the basis are Poincare ideas of seeking structures on the phase space that divide it into regions corresponding to trajectories with different dynamical fates. These ideas have demonstrated to be very powerful for the description of transport in purely advective flows and important applications have been found in geophysics. This presentation explores the performance of new Lagrangian tools, so called, Lagrangian descriptors [1,2,3], which are based on the integration along trajectories of bounded positive scalars which express an intrinsic geometrical or physical property of the trajectory. We analyze the convenience of different descriptors from several points of view and compare outputs with other methods proposed in the literature. We discuss applications of these new tools on oceanic datasets taken from altimeter satellites on the Kuroshio region, and on reanalysis data on the Antarctic polar vortex [4,5,6]. This research has been supported by MINECO under grants MTM2011-26696 and ICMAT Severo Ochoa project SEV-2011-0087 and CSIC under grant ILINK-0145. Computational support from CESGA and CCC-UAM is acknowledged. [1] J. A. J. Madrid, A. M. Mancho. Distinguished trajectories in time dependent vector fields. Chaos 19 (2009), 013111-1-013111-18. [2] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [3], A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. In preparation. [4] A. de la Cámara, A. M. Mancho, K. Ide, E. Serrano, C.R. Mechoso. Routes of transport across the Antarctic polar vortex in the southern spring. Journal of Atmospheric Sciences 69, 2 (2012). [5] C. Mendoza, A. M. Mancho, M. H. Rio. The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields. Nonlinear Proc. Geoph 17 (2010), 2, 103-111. [6] Carolina Mendoza, Ana M. Mancho. The Lagrangian description of
Lagrangian modeling of global atmospheric methane (1990-2012)
NASA Astrophysics Data System (ADS)
Arfeuille, Florian; Henne, Stephan; Brunner, Dominik
2016-04-01
In the MAIOLICA-II project, the lagrangian particle model FLEXPART is used to simulate the global atmospheric methane over the 1990-2012 period. In this lagrangian framework, 3 million particles are permanently transported based on winds from ERA-interim. The history of individual particles can be followed allowing for a comprehensive analysis of transport pathways and timescales. The link between sources (emissions) and receptors (measurement stations) is then established in a straightforward manner, a prerequisite for source inversion problems. FLEXPART was extended to incorporate the methane loss by reaction with OH, soil uptake and stratospheric loss reactions with prescribed Cl and O(1d) radicals. Sources are separated into 245 different tracers, depending on source origin (anthropogenic, wetlands, rice, biomass burning, termites, wild animals, oceans, volcanoes), region of emission, and time since emission (5 age classes). The inversion method applied is a fixed-lag Kalman smoother similar to that described in Bruhwiler et al. [2005]. Results from the FLEXPART global methane simulation and from the subsequent inversion will be presented. Results notably suggest: - A reduction in methane growth rates due to diminished wetland emissions and anthropogenic European emission in 1990-1993. - A second decrease in 1995-1996 is also mainly attributed to these two emission categories. - A reduced increase in Chinese anthropogenic emissions after 2003 compared to EDGAR inventories. - Large South American wetlands emissions during the entire period. Bruhwiler, L. M. P., Michalak, A. M., Peters, W., Baker, D. F. & Tans, P. 2005: An improved Kalman smoother fore atmospheric inversions, Atmos Chem Phys, 5, 2691-2702.
The Lagrangian description of oceanic and atmospheric flows
NASA Astrophysics Data System (ADS)
Mancho, A. M.
2012-04-01
Geometry has been a very useful approach for studying dynamical systems. At the basis are Poincare ideas of seeking structures on the phase space that divide it into regions corresponding to trajectories with different dynamical fates. These ideas have demonstrated to be very powerful for the description of transport in purely advective flows and important applications have been found in geophysics. However realistic flows as those obtained by altimeter satellites or from numerical simulations are highly non-periodic and to deal with these flows is a challenge because traditional methods can be used only in autonomous and time periodic dynamical systems. We describe new Lagrangian tools that are applied to general time dependent flows. First we propose a generalisation of the concept of fixed point to aperiodic dynamical systems: the distinguished trajectory [1]. The definition is based on a function called M for which we show is a powerful Lagrangian descriptor [2]. We discuss applications of these new tools on oceanic datasets taken from altimeter satellites on the Kuroshio region, and on reanalysis data on the Antarctic polar vortex [3,4]. This research is supported by the Spanish Ministry of Science under grants MTM2011-26696 and Spanish CSIC under grant ILINK-0145. We acknowledge computational support from CESGA and CCC-UAM. [1] J. A. J. Madrid, A. M. Mancho. Distinguished trajectories in time dependent vector fields. Chaos 19 (2009), 013111-1-013111-18. [2] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [3] C. Mendoza, A. M. Mancho, M. H. Rio. The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields. Nonlinear Proc. Geoph 17 (2010), 2, 103-111. [4] A. de la Cámara, A. M. Mancho, K. Ide, E. Serrano, C.R. Mechoso. Routes of transport across the Antarctic polar vortex in the southern spring. Journal of Atmospheric Sciences 69, 2 (2012)
Alternative refined Gribov-Zwanziger Lagrangian
Gracey, J. A.
2010-10-15
We consider the implications of the condensation of a general local Becchi-Rouet-Stora-Tyutin invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different color tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.
Functional integral for non-Lagrangian systems
Kochan, Denis
2010-02-15
A functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The approach, which we call ''stringy quantization,'' is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -{kappa}q{sup A}. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
A Lagrangian particle level set method
NASA Astrophysics Data System (ADS)
Hieber, Simone E.; Koumoutsakos, Petros
2005-11-01
We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Enhanced Predictability Through Lagrangian Observations and Analysis
2008-09-30
forecast EAS-16 model velocities. Matlab code for computing direct Lyapunov exponents (provided by A. C. Poje, College of Staten Island) using the...Explore the near-surface Lagrangian dispersion characteristics of the EAS-16 model, which includes a number of distinct dynamical regimes, including...include the following: • Inflowing/outflowing manifolds • Gridded trajectories • Relative dispersion • Finite-scale and direct Lyapunov
Simulating Fibre Suspensions: Lagrangian versus Statistical Approach
NASA Astrophysics Data System (ADS)
Zhao, L. H.; Andersson, H. I.; Gillissen, J. J. J.; Boersma, B. J.
Fibre suspensions exhibit complex dynamical flow phenomena and are at the same time of immense practical importance, notably in the pulp and paper industries. NTNU and TU Delft have in a collaborative research project adopted two alternative strategies in the simulation of dilute fibre suspensions, namely a statistical approach [2] and a Lagrangian particle treatment [4]. The two approaches have their own advantages and disadvantages. In this paper we aim for the first time to compare the performance of the two.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1995-01-01
In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
Measuring non-local Lagrangian peak bias
NASA Astrophysics Data System (ADS)
Biagetti, Matteo; Chan, Kwan Chuen; Desjacques, Vincent; Paranjape, Aseem
2014-06-01
We investigate non-local Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the non-local ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a one-point cross-correlation technique to measure bias factors associated with χ2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order non-local contributions -2χ _{10}(k_1\\cdot k_2) and χ _{01}[3(k_1\\cdot k_2)^2-k_1^2 k_2^2], where k_1, k_2 are wave modes. We can reproduce our measurement of χ10 if we allow for an offset between the Lagrangian halo centre-of-mass and the peak position. The sign and magnitude of χ10 is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 1013 M⊙ h-1, but could become relevant at larger halo masses. For the second non-local bias χ01 however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from non-local Lagrangian contributions induced by non-spherical collapse.
Phenomenological Lagrangians, gauge models and branes
NASA Astrophysics Data System (ADS)
Zheltukhin, A. A.
2017-03-01
Phenomenological Lagrangians for physical systems with spontaneously broken symmetries are reformulated in terms of gauge field theory. Description of the Dirac p-branes in terms of the Yang-Mills- Cartan gauge multiplets interacting with gravity, is proved to be equivalent to their description as a closed dynamical system with the symmetry ISO(1, D - 1) spontaneously broken to ISO(1, p) × SO( D - p - 1).
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
cyclones B. Rutherford,a* T. J. Dunkertona and M. T. Montgomeryb aNorthwest Research Associates, Redmond, WA, USA bNaval Postgraduate School, Monterey...article has been contributed to by a US Government employee and his work is in the public domain in the USA. Tracking pre-genesis tropical cyclones is...season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones . The
Augmented Lagrangian method for optimal laser control
NASA Astrophysics Data System (ADS)
Shen, Hai; Dussault, Jean-Pierre; Bandrauk, Andre D.
1994-06-01
We use penalty methods derived from Augmented Lagrangians coupled with unitary exponential operator methods to solve the optimal control problem for molecular time-dependent Schodinger equations involving laser pulse excitations. A stable numerical algorithm is presented which propagates directly from initial states to given final states. Results are reported for an analytically solvable model for the complete inversion of a three-state system.
On the Lagrangian Description of Vorticity
1991-01-01
Iow% OF TWIS PA09GSIU Dow Bae...E Arch. Rational Mech. Anal. 115 (1991) 1-14. ( Springer -Verlag 1991 On the Lagrangian Description of Vorticity J. CASEY...der Physik, Vol. VIII/1, Springer -Verlag, 1959. 8. TRUESDELL, C., & TouwiN, R. A., The classical field theories. S. FLOOGS’S Handbuch der Physik, Vol...VIII/1, Springer -Verlag, 1960. 9. BATCHELOR, G. K., An Introduction to Fluid Mechanics, Cambridge University Press, 1967. 10. BELTRAM!, E., Sui
NASA Astrophysics Data System (ADS)
Hegarty, J. D.; Draxler, R.; Stein, A. F.; Brioude, J.; Eluszkiewicz, J.; Mountain, M.; Nehrkorn, T.; Andrews, A. E.
2012-12-01
The accuracy of greenhouse gas (GHG) fluxes estimated using inverse methods is highly dependent on the fidelity of the atmospheric transport model employed. Lagrangian particle dispersion models (LPDMs) driven by customized meteorological output from mesoscale models have emerged as a powerful tool in inverse GHG estimates at policy-relevant regional and urban scales, for several reasons: 1) Mesoscale meteorology can be available at higher resolution than in most global models, and therefore has the potential to be more realistic, 2) the Lagrangian approach minimizes numerical diffusion present in Eulerian models and is thus better able to represent transport in the near-field of measurement locations, and 3) the Lagrangian approach offers an efficient way to compute the grid-scale adjoint of the transport model ("footprints") by running transport backwards in time. Motivated by these considerations, we intercompare three widely used LPDMs (HYSPLIT, STILT, and FLEXPART) driven by identical meteorological input from the Weather Research and Forecasting (WRF) model against measurements from the controlled tracer release experiments (ready-testbed.arl.noaa.gov/HYSPLIT_datem.php). Our analysis includes statistical assessments of each LPDM in terms of its ability to simulate the observed tracer concentrations, reversibility, and sensitivity to the WRF configuration, particularly with regard to the simulation of the planetary boundary layer.
Lagrangian predictability characteristics of an Ocean Model
NASA Astrophysics Data System (ADS)
Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia
2014-11-01
The Mediterranean Forecasting System (MFS) Ocean Model, provided by INGV, has been chosen as case study to analyze Lagrangian trajectory predictability by means of a dynamical systems approach. To this regard, numerical trajectories are tested against a large amount of Mediterranean drifter data, used as sample of the actual tracer dynamics across the sea. The separation rate of a trajectory pair is measured by computing the Finite-Scale Lyapunov Exponent (FSLE) of first and second kind. An additional kinematic Lagrangian model (KLM), suitably treated to avoid "sweeping"-related problems, has been nested into the MFS in order to recover, in a statistical sense, the velocity field contributions to pair particle dispersion, at mesoscale level, smoothed out by finite resolution effects. Some of the results emerging from this work are: (a) drifter pair dispersion displays Richardson's turbulent diffusion inside the [10-100] km range, while numerical simulations of MFS alone (i.e., without subgrid model) indicate exponential separation; (b) adding the subgrid model, model pair dispersion gets very close to observed data, indicating that KLM is effective in filling the energy "mesoscale gap" present in MFS velocity fields; (c) there exists a threshold size beyond which pair dispersion becomes weakly sensitive to the difference between model and "real" dynamics; (d) the whole methodology here presented can be used to quantify model errors and validate numerical current fields, as far as forecasts of Lagrangian dispersion are concerned.
Identifying Lagrangian fronts with favourable fishery conditions
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-08-01
Lagrangian fronts (LFs) in the ocean are defined as boundaries between surface waters with strongly different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps for displacements of synthetic tracers and other Lagrangian indicators. We use Pacific saury catch and location data for a number of commercial fishery seasons in the region of the northwest Pacific with one of the richest fishery in the world. It is shown statistically that the saury fishing grounds with maximal catches are not randomly distributed over the region but located mainly along the sharp LFs where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts in altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions LF locations may serve as good indicators of potential fishing grounds. Possible biophysical reasons for saury aggregation near sharp LFs are discussed. We propose a mechanism for effective export of nutrient rich waters based on stretching of material lines in the vicinity of hyperbolic objects in the ocean. The developed method, based on identifying LFs in any velocity fields, is quite general and may be applied to find potential fishing grounds for the other pelagic fish.
Lagrangian methods of cosmic web classification
NASA Astrophysics Data System (ADS)
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
Effective Lagrangian for low-scale technicolor
Lane, Kenneth; Martin, Adam
2009-12-01
We present an effective Lagrangian for low-scale technicolor. It describes the interactions at energies < or approx. M{sub {rho}{sub T}} of the lowest-lying bound states of the lightest technifermion doublet--the spin-one {rho}{sub T}, {omega}{sub T}, a{sub T}, f{sub T}, and the corresponding technipions {pi}{sub T}. This Lagrangian is intended to put on firmer ground the technicolor straw man phenomenology used for collider searches of low-scale technicolor. The technivectors are described using the hidden local symmetry (HLS) formalism of Bando, et al. The Lagrangian is based on SU(2) x U(1) x U(2){sub L} x U(2){sub R}, where SU(2) x U(1) is the electroweak gauge group and U(2){sub L} x U(2){sub R} is the HLS gauge group. Special attention is paid to the higher-derivative standard HLS and Wess-Zumino-Witten interactions needed to describe radiative and other decays of a{sub T} and {rho}{sub T}/{omega}{sub T}, respectively.
A chiral effective lagrangian for nuclei
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Serot, Brian D.; Tang, Hua-Bin
1997-02-01
An effective hadronic lagrangian consistent with the symmetries of quantum chromodynamics and intended for applications to finite-density systems is constructed. The degrees of freedom are (valence) nucleons, pions and the low-lying non-Goldstone bosons, which account for the intermediate-range nucleon-nucleon interactions and conveniently describe the nonvanishing expectation values of nucleon bilinears. Chiral symmetry is realized nonlinearly, with a light scalar meson included as a chiral singlet to describe the mid-range nucleon-nucleon attraction. The low-energy electromagnetic structure of the nucleon is described within the theory using vector-meson dominance, so that external form factors are not needed. The effective lagrangian is expanded in powers of the fields and their derivatives, with the terms organized using Georgi's "naive dimensional analysis". Results are presented for finite nuclei and nuclear matter at one-baryon-loop order, using the single-nucleon structure determined within the model. Parameters obtained from fits to nuclear properties show that naive dimensional analysis is a useful principle and that a truncation of the effective lagrangian at the first few powers of the fields and their derivatives is justified.
Inverse Variational Problem for Nonstandard Lagrangians
NASA Astrophysics Data System (ADS)
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
NASA Astrophysics Data System (ADS)
Tang, Wenbo; Chan, Pak Wai; Haller, George
2010-03-01
Locating Lagrangian coherent structures (LCS) for dynamical systems defined on a spatially limited domain present a challenge because trajectory integration must be stopped at the boundary for lack of further velocity data. This effectively turns the domain boundary into an attractor, introduces edge effects resulting in spurious ridges in the associated finite-time Lyapunov exponent (FTLE) field, and causes some of the real ridges of the FTLE field to be suppressed by strong spurious ridges. To address these issues, we develop a finite-domain FTLE method that renders LCS with an accuracy and fidelity that is suitable for automated feature detection. We show the application of this technique to the analysis of velocity data from aircraft landing at the Hong Kong International Airport.
Presentation outline: transport principles, effective solubility; gasoline composition; and field examples (plume diving).
Presentation conclusions: MTBE transport follows from - phyiscal and chemical properties and hydrology. Field examples show: MTBE plumes > benzene plu...
Dynamics of Multibody Systems Near Lagrangian Points
NASA Astrophysics Data System (ADS)
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term
Turbulence Interface Simulation by Lagrangian Blocks
NASA Astrophysics Data System (ADS)
Chu, V. H.
2015-12-01
Most computational fluid-dynamics codes are developed using the Eulerian description. To find the numerical solution, fluxes are estimated on the surface of the finite volume using a truncation series. Spurious numerical oscillations and artificial numerical diffusion are consequences, particularly in regions across flow discontinuities. Diffusion often is introduced synthetically in many schemes to gain computational stability. Occasional switching to a diffusive upwind scheme, for example, is one classic strategy to manage the numerical oscillations [see e.g., Ghannadi & Chu 2015]. Lagrangian-block simulation offers an alternative that could minimize the spurious oscillations and false diffusive error. The blocks move in the direction of the flow. The squares of the block widths expand in proportion to the diffusivities. The block simulation procedure consists of (i) Lagrangian advection and diffusion, (ii) division into portions, and (iii) reassembly of the portions into new blocks. The blocks are renewed in each time increment to prevent excessive distortion. Details of the Lagrangian-block simulations method have been given in a series of papers by Tan & Chu (2012), Chu & Altai (2012, 2015}. In this paper, the exchanges across turbulence interfaces are considered for two problems. The first series of the simulations are conducted to find the mass and momentum exchanges across a shallow flow of two different depth. In the simulations, the advection and diffusion of three separated systems of blocks that contain the mass, momentum and potential vorticity are carried out using the Lagrangian-block simulation method. The simulation results are compared with data obtained from a previous laboratory investigation and related to the shear instability problem in rotating shear flow previously considered by Chu (2014). The second problem involves the turbulence generation across the interface of an internal waves. The simulation shows the development of gravitational
NASA Astrophysics Data System (ADS)
Zhang, Feng; Duan, Guang-Ren
2014-05-01
This paper tackles the problem of integrated translation and rotation finite-time control of a rigid spacecraft with actuator misalignment and unknown mass property. Due to the system natural couplings, the coupled translational and rotational dynamics of the spacecraft is developed, where a thruster configuration with installation misalignment and unknown mass property are taken into account. By solving an equivalent designated trajectory tracking problem via backstepping philosophy, a robust adaptive integrated finite-time control scheme is proposed to enable the spacecraft track command position and attitude in a pre-determined time, despite of external disturbance, unknown mass property and thruster misalignment. The finite-time closed-loop stability is guaranteed within the Lyapunov framework. Two scenario numerical simulations demonstrate the effect of the designed controller.
NASA Astrophysics Data System (ADS)
Zavala-Río, A.; Fantoni, I.; Sanahuja, G.
2016-05-01
In this work, an output-feedback scheme for the global stabilisation of the planar vertical take-off and landing aircraft with bounded inputs is developed taking into account the positive nature of the thrust. The global stabilisation objective is proven to be achieved avoiding input saturation and by exclusively considering the system positions in the feedback. To cope with the lack of velocity measurements, the proposed algorithm involves a finite-time observer. The generalised versions of the involved finite-time stabilisers have not only permitted to solve the output-feedback stabilisation problem avoiding input saturation, but also provide additional flexibility in the control design that may be used in aid of performance improvements. With respect to previous approaches, the developed finite-time observer-based scheme guarantees the global stabilisation objective disregarding velocity measurements in a bounded input context. Simulation tests corroborate the analytical developments. The study includes further experimental results on an actual flying device.
Lagrangian and Eulerian description of bed-load particle kinematics
NASA Astrophysics Data System (ADS)
Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio
2016-04-01
The motion of bed-load sediment particles transported by a flow can be analyzed within a Lagrangian or an Eulerian framework. In the former case, we consider the particles as individual objects in motion and we study their kinematic properties. The latter approach is instead referred to suitably chosen control volumes. Quantities describing sediment motion in the two frameworks are different, and the relationships among the two approaches are not straightforward. In this work, we intend to discuss the kinematic properties of sediment transport: first, a set of quantities is univocally defined; then, relationships among different representations are explored. Proof-of-concept results presented in the study are from a recent experiment involving weak bed-load sediment transport, where the moving particles were released over a fixed rough bed. The bulk flow velocity was 1.4 times the critical value for incipient particle motion, and particles were mostly moving by rolling and sliding, with limited saltation. The particle motion was filmed from the top and the measurements were conducted by image-based methods, obtaining extensive samples of virtually-instantaneous quantities.
Invariant-tori-like Lagrangian coherent structures in geophysical flows.
Beron-Vera, Francisco J; Olascoaga, María J; Brown, Michael G; Koçak, Huseyin; Rypina, Irina I
2010-03-01
The term "Lagrangian coherent structure" (LCS) is normally used to describe numerically detected structures whose properties are similar to those of stable and unstable manifolds of hyperbolic trajectories. The latter structures are invariant curves, i.e., material curves of fluid that serve as transport barriers. In this paper we use the term LCS to describe a different type of structure whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. Like stable and unstable manifolds, invariant tori are invariant curves that serve as transport barriers. There are many differences, however, between traditional LCSs and invariant-tori-like LCSs. These differences are discussed with an emphasis on numerical techniques that can be used to identify invariant-tori-like LCSs. Structures of this type are often present in geophysical flows where zonal jets are present. A prime example of an invariant-torus-like LCS is the transport barrier near the core of the polar night jet in the Earth's lower and middle stratospheres in the austral winter and early spring; this is the barrier that traps ozone-depleted air inside the ozone hole. This example is investigated using both a simple analytically prescribed flow and a velocity field produced by a general circulation model of the Earth's atmosphere.
Correlating Lagrangian structures with forcing in two-dimensional flow
NASA Astrophysics Data System (ADS)
Ouellette, Nicholas T.; Hogg, Charlie A. R.; Liao, Yang
2016-01-01
Lagrangian coherent structures (LCSs) are the dominant transport barriers in unsteady, aperiodic flows, and their role in organizing mixing and transport has been well documented. However, nearly all that is known about LCSs has been gleaned from passive observations: they are computed in a post-processing step after a flow has been observed and used to understand why the mixing and transport proceeded as it did. In many applications, the ability instead to control the presence or location of LCSs via imposed forcing would be valuable. With this goal in mind, we study the relationship between LCSs and external forcing in an experimental quasi-two-dimensional weakly turbulent flow. We find that the likelihood of finding a repelling LCS at a given location is positively correlated with the mean strain rate injected at that point and negatively correlated with the mean speed, and that it is not correlated with the vorticity. We also find that mean time between successive LCSs appearing at a fixed location is related to the structure of the forcing field. Finally, we demonstrate a surprising difference in our results between LCSs computed forward and backward in time, with forward-time (repelling) LCSs showing much more correlation with the forcing than backwards-time (attracting) LCSs.
NASA Astrophysics Data System (ADS)
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
NASA Astrophysics Data System (ADS)
Dallaston, M. C.; Tseluiko, D.; Zheng, Z.; Fontelos, M. A.; Kalliadasis, S.
2017-07-01
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, \\Pi(h)\\propto -1/h3 , where h is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485 . We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, n_cplane≈ 1.499 . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.
NASA Astrophysics Data System (ADS)
Sapsis, T.
2012-04-01
We examine the geometry of the inertial manifold associated with fluid flows described by Navier-Stokes equations and we relate its nonlinear dimensionality to energy exchanges between the mean flow and stochastic modes of the flow. Specifically, we employ a stochastic framework based on the dynamically orthogonal field equations to perform efficient order-reduction in terms of time-dependent modes and describe the inertial manifold in the reduced-order phase space in terms of the associated probability measure. We introduce the notion of local fractal dimensionality and we establish a connection with the finite-time Lyapunov exponents of the reduced-order dynamics. Based on this tool we illustrate in 2D Navier-Stokes equations that the underlying mechanism responsible for the finite dimensionality of the inertial manifold is, apart from the viscous dissipation, the reverse flow of energy from the stochastic fluctuations (containing in general smaller lengthscales) back to the mean flow (which is characterized by larger spatial scales).
Hybrid Eulerian-Lagrangian Vortex Model for Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Royero, John; Ahmed, Kareem
2016-11-01
A hybrid Eulerian-Lagrangian model for three dimensional large eddy simulations of turbulent reacting flows is presented. The method utilizes a Eulerian grid to resolve large scale flow features and the Lagrangian vortex element method to capture smaller subgrid scale effects and carry out reactions which are then communicated back to the Eulerian grid after a set number of Lagrangian time steps. Lagrangian influences are localized in order to reduce computational cost. The Lagrangian vortex method which utilizes the Helmholtz decomposition of the velocity into potential, expansive, and solenoidal components allows the separation of the various mechanisms contributing to vorticity including gas expansion, diffusion, external body forces and baroclinic torque and is coupled with the Eulerian solver allowing easier implementation in arbitrary reacting flows at a reduced computational cost compared to a pure Lagrangian solver.
Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology
NASA Astrophysics Data System (ADS)
Wang, Xin; Szalay, Alex
2016-03-01
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.
STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY
Wang, Xin; Szalay, Alex
2016-03-20
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.
The Lagrangian analysis tool LAGRANTO - version 2.0
NASA Astrophysics Data System (ADS)
Sprenger, M.; Wernli, H.
2015-02-01
Lagrangian trajectories are widely used in the atmospheric sciences, for instance to identify flow structures in extratropical cyclones (e.g., warm conveyor belts) and long-range transport pathways of moisture and trace substances. Here a new version of the Lagrangian analysis tool LAGRANTO (Wernli and Davies, 1997) is introduced, which offers considerably enhanced functionalities: (i) trajectory starting positions can be described easily based on different geometrical and/or meteorological conditions; e.g., equidistantly spaced within a prescribed region and on a stack of pressure (or isentropic) levels; (ii) a versatile selection of trajectories is offered based on single or combined criteria; these criteria are passed to LAGRANTO with a simple command language (e.g., "GT:PV:2" readily translates into a selection of all trajectories with potential vorticity (PV) greater than 2 PVU); and (iii) full versions are available for global ECMWF and regional COSMO data; core functionality is also provided for the regional WRF and UM models, and for the global 20th Century Reanalysis data set. The intuitive application of LAGRANTO is first presented for the identification of a warm conveyor belt in the North Atlantic. A further case study then shows how LAGRANTO is used to quasi-operationally diagnose stratosphere-troposphere exchange events over Europe. Whereas these example rely on the ECMWF version, the COSMO version and input fields with 7 km horizontal resolution are needed to adequately resolve the rather complex flow structure associated with orographic blocking due to the Alps. Finally, an example of backward trajectories presents the tool's application in source-receptor analysis studies. The new distribution of LAGRANTO is publicly available and includes simple tools, e.g., to visualize and merge trajectories. Furthermore, a detailed user guide exists, which describes all LAGRANTO capabilities.
The LAGRANTO Lagrangian analysis tool - version 2.0
NASA Astrophysics Data System (ADS)
Sprenger, M.; Wernli, H.
2015-08-01
Lagrangian trajectories are widely used in the atmospheric sciences, for instance to identify flow structures in extratropical cyclones (e.g., warm conveyor belts) and long-range transport pathways of moisture and trace substances. Here a new version of the Lagrangian analysis tool LAGRANTO (Wernli and Davies, 1997) is introduced, which offers considerably enhanced functionalities. Trajectory starting positions can be defined easily and flexibly based on different geometrical and/or meteorological conditions, e.g., equidistantly spaced within a prescribed region and on a stack of pressure (or isentropic) levels. After the computation of the trajectories, a versatile selection of trajectories is offered based on single or combined criteria. These criteria are passed to LAGRANTO with a simple command language (e.g., "GT:PV:2" readily translates into a selection of all trajectories with potential vorticity, PV, greater than 2 PVU; 1 PVU = 10-6 K m2 kg-1 s-1). Full versions of this new version of LAGRANTO are available for global ECMWF and regional COSMO data, and core functionality is provided for the regional WRF and MetUM models and the global 20th Century Reanalysis data set. The paper first presents the intuitive application of LAGRANTO for the identification of a warm conveyor belt in the North Atlantic. A further case study then shows how LAGRANTO can be used to quasi-operationally diagnose stratosphere-troposphere exchange events. Whereas these examples rely on the ECMWF version, the COSMO version and input fields with 7 km horizontal resolution serve to resolve the rather complex flow structure associated with orographic blocking due to the Alps, as shown in a third example. A final example illustrates the tool's application in source-receptor analysis studies. The new distribution of LAGRANTO is publicly available and includes auxiliary tools, e.g., to visualize trajectories. A detailed user guide describes all LAGRANTO capabilities.
Lagrangian coherent structures and inertial particle dynamics.
Sudharsan, M; Brunton, Steven L; Riley, James J
2016-03-01
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.
Lagrangian coherent structures and inertial particle dynamics
NASA Astrophysics Data System (ADS)
Sudharsan, M.; Brunton, Steven L.; Riley, James J.
2016-03-01
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.
AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)
Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...
AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)
Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...
Lagrangian form of Schrödinger equation
NASA Astrophysics Data System (ADS)
Arsenović, D.; Burić, N.; Davidović, D. M.; Prvanović, S.
2014-07-01
Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.
An Unconditionally Stable Fully Conservative Semi-Lagrangian Method (PREPRINT)
2010-08-07
An Unconditionally Stable Fully Conservative Semi- Lagrangian Method Michael Lentine∗, Jón Tómas Grétarsson∗, Ronald Fedkiw∗ Stanford University...353 Serra Mall Room 207, Stanford, CA 94305 Abstract Semi- Lagrangian methods have been around for some time, dating back at least to [3]. Researchers...the typical semi- Lagrangian interpolation step in order to guarantee that the amount of the con- servative quantity does not increase during this
Hamiltonian and Lagrangian theory of viscoelasticity
NASA Astrophysics Data System (ADS)
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Stabilization by modification of the Lagrangian
NASA Technical Reports Server (NTRS)
Baumgarte, J. W.
1975-01-01
In order to reduce the error growth during a numerical integration, a method of stabilization of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as an independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Liapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi; Nakano, Kunihiko; Suzuki, Takafumi
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Lagrangian flows within reflecting internal waves at a horizontal free-slip surface
Zhou, Qi; Diamessis, Peter J.
2015-12-15
In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes drift cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.