2009-08-01
Wang, G. Haller, A. Banaszuk, and G. Tadmor, Closed-loop Lagrangian separation control in a bluff body shear flow model, Physics of Fluids 15 (2003... separation which depends, in general, on the time interval chosen for assessment of such a measure. Conse- quently, in flows undergoing transitions...straightforward diagnostic tool for uncovering time-dependent flow structures characterised by locally strongest separation of nearby trajectories. Note how
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.
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.
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 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
2016-04-20
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.
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
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.
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.
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
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
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
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
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.
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.
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)
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.
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)
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
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
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.
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
2011-09-05
dependence of the flow and the persistence of stagnation points . Finite-time Lagrangian methods were developed by Haller and coauthors (Haller and Poje , 1997...dimensional steady flows, and present a basic theory of some common finite-time Lagrangian methods and statistical methods. Hyperbolic fixed point ...persistent stagnation points . Finite-time Lagrangian methods avoid this difficulty by find- ing the manifolds directly For a time-dependent flow, con
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.
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.
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).
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 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
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)
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.
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
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.
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
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.
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...
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.
Lagrangian Turbulence and Transport in Semi-enclosed Basins and Coastal Regions
2010-09-30
transport in coastal flows . OBJECTIVES The project has the following specific objectives pursued during the last year of funding: 1) To use...To use HF radar and drifter data to characterize and predict transport properties in coastal flows . 3) To participate to the planning, execution...method ( LAVA ) previously developed in the framework of the present grant and directly based on trajectory information, while the University of Delaware
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.
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.
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
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.
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.
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.
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.
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.
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.
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
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.
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."
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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)
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.
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.
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 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.
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.
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.
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.
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.
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.
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
2012-12-03
they show maximal linear instability for particles located close to the manifolds. The time-dependent analog of a hyperbolic fixed point is called a...stagnation points marking a DHT, finite-time Lagrangian methods may still locate manifolds. For a time-dependent flow, consider two nearby trajectories...and M. T. Montgomery: A Lagrangian analysis during PREDICT 11363 eastern stagnation point of the co-moving frame. Unlike the streamlines, the LCSs
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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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
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
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.
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…
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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-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.
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).
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.
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 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.
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 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 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
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.
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.
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 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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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 .
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.
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.
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.
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.
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.
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
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; 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.
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
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
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.
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)
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.
Lagrangian Transport Signatures in Models and Observations
2011-09-30
6521 email: brucel@udel.edu Award Number: N00014- 10 -1-0522 http://lagrange.ceoe.udel.edu/~helga/lod.html LONG-TERM GOALS A common...S) AND ADDRESS(ES) 10 . SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for...supply 27.6 62 60 6 May – 10 May 2010 14.7 (USF) No new supply 10.6 32 23 15-km new supply 12.7 40 34 15-km new supply + wind 14.2 36 35 80-km new
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.
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.
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.
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.
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...
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.
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.
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.
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. 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.
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)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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 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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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, 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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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 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.
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.
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 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.
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.
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.
{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.
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)
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.
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.
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.
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 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.
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.
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.
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...
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
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)
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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)
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).
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.
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
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...of coastal ocean fields by assimilation of Eulerian and Lagrangian flow data. - Apply our DO and GMM-DO schemes, as well as their theoretical
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
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.
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.
A series solution framework for finite-time optimal feedback control, H-infinity control and games
NASA Astrophysics Data System (ADS)
Sharma, Rajnish
The Bolza-form of the finite-time constrained optimal control problem leads to the Hamilton-Jacobi-Bellman (HJB) equation with terminal boundary conditions and to-be-determined parameters. In general, it is a formidable task to obtain analytical and/or numerical solutions to the HJB equation. This dissertation presents two novel polynomial expansion methodologies for solving optimal feedback control problems for a class of polynomial nonlinear dynamical systems with terminal constraints. The first approach uses the concept of higher-order series expansion methods. Specifically, the Series Solution Method (SSM) utilizes a polynomial series expansion of the cost-to-go function with time-dependent coefficient gains that operate on the state variables and constraint Lagrange multipliers. A significant accomplishment of the dissertation is that the new approach allows for a systematic procedure to generate optimal feedback control laws that exactly satisfy various types of nonlinear terminal constraints. The second approach, based on modified Galerkin techniques for the solution of terminally constrained optimal control problems, is also developed in this dissertation. Depending on the time-interval, nonlinearity of the system, and the terminal constraints, the accuracy and the domain of convergence of the algorithm can be related to the order of truncation of the functional form of the optimal cost function. In order to limit the order of the expansion and still retain improved midcourse performance, a waypoint scheme is developed. The waypoint scheme has the dual advantages of reducing computational efforts and gain-storage requirements. This is especially true for autonomous systems. To illustrate the theoretical developments, several aerospace application-oriented examples are presented, including a minimum-fuel orbit transfer problem. Finally, the series solution method is applied to the solution of a class of partial differential equations that arise in robust
A perturbation-theoretic approach to Lagrangian flow networks
NASA Astrophysics Data System (ADS)
Fujiwara, Naoya; Kirchen, Kathrin; Donges, Jonathan F.; Donner, Reik V.
2017-03-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.
MESOILT2, a Lagrangian trajectory climatological dispersion model
Ramsdell, J.V. Jr.; Burk, K.W.
1991-03-01
The objective of the Hanford Environmental Dose Reconstruction (HEDR) Project is to estimate the radiation dose that individuals could have received as a result of emissions from nuclear operations at the Hanford Site. An independent Technical Steering Panel (TSP) directs the project, which is conducted by the Pacific Northwest Laboratory (PNL). The TSP directed PNL to demonstrate that its recommended approach for dose reconstruction is technically feasible and practical. This demonstration was Phase 1 of the project. This report is specifically concerned with the approach that PNL recommends for dealing with the atmospheric pathway. The TSP established a model domain for the atmospheric pathway for Phase 1 that includes 10 counties in Washington and Oregon and covers several thousand square miles. It is unrealistic to assume that atmospheric models which estimate transport and diffusion based on the meteorological conditions near the point of release of material at the time of release are adequate for a region this large. As a result, PNL recommended use of a Lagrangian trajectory, puff dispersion model for the Phase I study. This report describes the MESOILT2 computer code and the atmospheric transport, diffusion, deposition, and depletion models used in Phase I. The contents of the report include a technical description of the models, a user's guide for the codes, and descriptions of the individual code elements. 53 refs., 17 figs., 5 tabs.
Mars interplanetary trajectory design via Lagrangian points
NASA Astrophysics Data System (ADS)
Eapen, Roshan Thomas; Sharma, Ram Krishan
2014-09-01
With the increase in complexities of interplanetary missions, the main focus has shifted to reducing the total delta-V for the entire mission and hence increasing the payload capacity of the spacecraft. This paper develops a trajectory to Mars using the Lagrangian points of the Sun-Earth system and the Sun-Mars system. The whole trajectory can be broadly divided into three stages: (1) Trajectory from a near-Earth circular parking orbit to a halo orbit around Sun-Earth Lagrangian point L2. (2) Trajectory from Sun-Earth L2 halo orbit to Sun-Mars L1 halo orbit. (3) Sun-Mars L1 halo orbit to a circular orbit around Mars. The stable and unstable manifolds of the halo orbits are used for halo orbit insertion. The intermediate transfer arcs are designed using two-body Lambert's problem. The total delta-V for the whole trajectory is computed and found to be lesser than that for the conventional trajectories. For a 480 km Earth parking orbit, the total delta-V is found to be 4.6203 km/s. Another advantage in the present approach is that delta-V does not depend upon the synodic period of Earth with respect to Mars.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Variational contact symmetries of constrained Lagrangians
NASA Astrophysics Data System (ADS)
Terzis, Petros A.; Dimakis, N.; Christodoulakis, T.; Paliathanasis, Andronikos; Tsamparlis, Michael
2016-03-01
The investigation of contact symmetries of re-parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function N(t) , with the appropriate extension of the dependence in N ˙ (t) of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re-parametrization allows one to appropriately scale N(t) , so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled metric. A rather interesting result is the non-necessity of the gauge function in Noether's theorem due to the presence of the Hamiltonian constraint.
Sigma decomposition: the CP-odd Lagrangian
NASA Astrophysics Data System (ADS)
Hierro, I. M.; Merlo, L.; Rigolin, S.
2016-04-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.
A Theoretical Framework for Lagrangian Descriptors
NASA Astrophysics Data System (ADS)
Lopesino, C.; Balibrea-Iniesta, F.; García-Garrido, V. J.; Wiggins, S.; Mancho, A. M.
This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as n-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors.
Lagrangian relations and linear point billiards
NASA Astrophysics Data System (ADS)
Féjoz, Jacques; Knauf, Andreas; Montgomery, Richard
2017-04-01
Motivated by the high-energy limit of the N-body problem we construct non-deterministic billiard process. The billiard table is the complement of a finite collection of linear subspaces within a Euclidean vector space. A trajectory is a constant speed polygonal curve with vertices on the subspaces and change of direction upon hitting a subspace governed by ‘conservation of momentum’ (mirror reflection). The itinerary of a trajectory is the list of subspaces it hits, in order. (A) Are itineraries finite? (B) What is the structure of the space of all trajectories having a fixed itinerary? In a beautiful series of papers Burago–Ferleger–Kononenko [BFK] answered (A) affirmatively by using non-smooth metric geometry ideas and the notion of a Hadamard space. We answer (B) by proving that this space of trajectories is diffeomorphic to a Lagrangian relation on the space of lines in the Euclidean space. Our methods combine those of BFK with the notion of a generating family for a Lagrangian relation.
Parallel algorithms for semi-lagrangian advection
NASA Astrophysics Data System (ADS)
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Lagrangian coherent structures analysis of gas-liquid flow in a bubble column
NASA Astrophysics Data System (ADS)
Wu, Qin; Wang, GuoYu; Huang, Biao; Bai, ZeYu
2014-06-01
The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water. In the numerical simulations, the standard k- ɛ turbulence model is employed to describe the turbulence phenomenon occurring in the continuous fluid. The Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures (LCS) are applied to analyze the vortex structures in multiphase flow. Reasonable agreements are obtained between the numerical and experimental data. The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages. During the initial stage, the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically. During the periodical developing stage, the bubble hose starts to oscillate periodically, and the vortexes move along the bubble hose to the bottom of column alternately. Compared to the Euler-system-based identification criterion of a vortex, the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles. During the initial stage, the interfaces between the forward and backward flows are highlighted by the LCS. As for the periodical developing stage, the LCS curls near the vortex centers, providing a method of analyzing a flow field from a dynamical system perspective.
GPU-accelerated computing for Lagrangian coherent structures of multi-body gravitational regimes
NASA Astrophysics Data System (ADS)
Lin, Mingpei; Xu, Ming; Fu, Xiaoyu
2017-04-01
Based on a well-established theoretical foundation, Lagrangian Coherent Structures (LCSs) have elicited widespread research on the intrinsic structures of dynamical systems in many fields, including the field of astrodynamics. Although the application of LCSs in dynamical problems seems straightforward theoretically, its associated computational cost is prohibitive. We propose a block decomposition algorithm developed on Compute Unified Device Architecture (CUDA) platform for the computation of the LCSs of multi-body gravitational regimes. In order to take advantage of GPU's outstanding computing properties, such as Shared Memory, Constant Memory, and Zero-Copy, the algorithm utilizes a block decomposition strategy to facilitate computation of finite-time Lyapunov exponent (FTLE) fields of arbitrary size and timespan. Simulation results demonstrate that this GPU-based algorithm can satisfy double-precision accuracy requirements and greatly decrease the time needed to calculate final results, increasing speed by approximately 13 times. Additionally, this algorithm can be generalized to various large-scale computing problems, such as particle filters, constellation design, and Monte-Carlo simulation.
NASA Astrophysics Data System (ADS)
Gibbon, John
2007-06-01
More than 160 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the orientation and paths of moving objects undergoing three-axis rotations. Here it is shown that they provide a natural way of selecting an appropriate orthonormal frame—designated the quaternion-frame—for a particle in a Lagrangian flow, and of obtaining the equations for its dynamics. How these ideas can be applied to the three-dimensional Euler fluid equations is then considered. This work has some bearing on the issue of whether the Euler equations develop a singularity in a finite time. Some of the literature on this topic is reviewed, which includes both the Beale-Kato-Majda theorem and associated work on the direction of vorticity by Constantin, Fefferman, and Majda and by Deng, Hou, and Yu. It is then shown how the quaternion formalism provides an alternative formulation in terms of the Hessian of the pressure.
NASA Astrophysics Data System (ADS)
Palatella, Luigi; Bignami, Francesco; Falcini, Federico; Lacorata, Guglielmo; Lanotte, Alessandra S.; Santoleri, Rosalia
2014-02-01
The interannual variability in the transport of anchovy eggs and larvae in the Sicily Channel, relatively to the period 1999-2012, is studied by means of numerical simulations of the Mediterranean Forecasting System (MFS) circulation model provided by INGV. Subgrid-scale dynamics not resolved by the MFS model is parameterized in terms of kinematic fields. The latter affect small-scale tracer relative dispersion, while leaving the mean large-scale advection substantially unchanged. A Lagrangian Transport Index (LTI) can be defined to characterize the efficiency of the main currents, e.g., the Atlantic Ionian Stream, in connecting spawning and nursery areas to each other. In our case, this indicator comes from the first arrival time statistics of tracers traveling from a spawning area near Sciacca to a nursery area in proximity of Cape Passero. We observe, on the basis of LTI values, that there are years when the Lagrangian connectivity is very efficient (2004, 2008, 2012) and years when it is weak (2000, 2001, 2003, 2010). Lagrangian indicators like the LTI concur to explain observed fluctuations of larval density and, also, can be employed, more in general, in multivariate models of population dynamics.
Arctic sea-ice diffusion from observed and simulated Lagrangian trajectories
NASA Astrophysics Data System (ADS)
Rampal, Pierre; Bouillon, Sylvain; Bergh, Jon; Ólason, Einar
2016-07-01
We characterize sea-ice drift by applying a Lagrangian diffusion analysis to buoy trajectories from the International Arctic Buoy Programme (IABP) dataset and from two different models: the standalone Lagrangian sea-ice model neXtSIM and the Eulerian coupled ice-ocean model used for the TOPAZ reanalysis. By applying the diffusion analysis to the IABP buoy trajectories over the period 1979-2011, we confirm that sea-ice diffusion follows two distinct regimes (ballistic and Brownian) and we provide accurate values for the diffusivity and integral timescale that could be used in Eulerian or Lagrangian passive tracers models to simulate the transport and diffusion of particles moving with the ice. We discuss how these values are linked to the evolution of the fluctuating displacements variance and how this information could be used to define the size of the search area around the position predicted by the mean drift. By comparing observed and simulated sea-ice trajectories for three consecutive winter seasons (2007-2011), we show how the characteristics of the simulated motion may differ from or agree well with observations. This comparison illustrates the usefulness of first applying a diffusion analysis to evaluate the output of modeling systems that include a sea-ice model before using these in, e.g., oil spill trajectory models or, more generally, to simulate the transport of passive tracers in sea ice.
NASA Astrophysics Data System (ADS)
Xu, Chuanju; Pasquetti, Richard
2001-02-01
Classical semi-implicit backward Euler/Adams-Bashforth time discretizations of the Navier-Stokes equations induce, for high-Reynolds number flows, severe restrictions on the time step. Such restrictions can be relaxed by using semi-Lagrangian schemes essentially based on splitting the full problem into an explicit transport step and an implicit diffusion step. In comparison with the standard characteristics method, the semi-Lagrangian method has the advantage of being much less CPU time consuming where spectral methods are concerned. This paper is devoted to the comparison of the semi-implicit and semi-Lagrangian approaches, in terms of stability, accuracy and computational efficiency. Numerical results on the advection equation, Burger's equation and finally two- and three-dimensional Navier-Stokes equations, using spectral elements or a collocation method, are provided. Copyright
MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting - Part 1: Theory
NASA Astrophysics Data System (ADS)
De Dominicis, M.; Pinardi, N.; Zodiatis, G.; Lardner, R.
2013-11-01
The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine surface oil slick numerical model and rewrites the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particle variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998, 2006; Zodiatis et al., 2008a). Part 2 of this paper describes the applications of the model to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
MEDSLIK-II, a Lagrangian marine oil spill model for short-term forecasting - Part 1: Theory
NASA Astrophysics Data System (ADS)
De Dominicis, M.; Pinardi, N.; Zodiatis, G.
2013-03-01
The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine oil slick numerical model and re-writes the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particles variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, so-called MEDSLIK-II. Part 2 of this paper describes the applications of MEDSLIK-II to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
A Vorticity-Divergence Global Semi-Lagrangian Spectral Model for the Shallow Water Equations
Drake, JB
2001-11-30
The shallow water equations modeling flow on a sphere are useful for the development and testing of numerical algorithms for atmospheric climate and weather models. A new formulation of the shallow water equations is derived which exhibits an advective form for the vorticity and divergence. This form is particularly well suited for numerical computations using a semi-Lagrangian spectral discretization. A set of test problems, standard for the shallow water equations on a sphere, are solved and results compared with an Eulerian spectral model. The semi-Lagrangian transport method was introduced into atmospheric modeling by Robert, Henderson, and Turnbull. A formulation based on a three time level integration scheme in conjunction with a finite difference spatial discretization was studied by Ritchie. Two time level grid point schemes were derived by Bates et al. Staniforth and Cote survey developments of the application of semi-Lagrangian transport (SLT) methods for shallow water models and for numerical weather prediction. The spectral (or spherical harmonic transform) method when combined with a SLT method is particularly effective because it allows for long time steps avoiding the Courant-Friedrichs-Lewy (CFL) restriction of Eulerian methods, while retaining accurate (spectral) treatment of the spatial derivatives. A semi-implicit, semi-Lagrangian formulation with spectral spatial discretization is very effective because the Helmholz problem arising from the semi-implicit time integration can be solved cheaply in the course of the spherical harmonic transform. The combination of spectral, semi-Lagrangian transport with a semi-implicit time integration schemes was first proposed by Ritchie. A advective formulation using vorticity and divergence was introduced by Williamson and Olson. They introduce the vorticity and divergence after the application of the semi-Lagrangian discretization. The semi-Lagrangian formulation of Williamson and Olson and Bates et al. has
Defining Lagrangian coherent structures for reactions in time-aperiodic flows
NASA Astrophysics Data System (ADS)
Mitchell, Kevin; Mahoney, John
2014-11-01
Recent theoretical and experimental investigations have highlighted the role of invariant manifolds, termed burning invariant manifolds (BIMs), as one-way barriers to reaction fronts propagating through a flowing medium. Originally, BIM theory was restricted to time-independent or time-periodic flows. The present work extends these ideas to flows with a general time-dependence, thereby constructing coherent structures that organize and constrain the propagation of reaction fronts through general flows. This permits a much broader and physically realistic class of problems to be addressed. Our approach follows the recent work of Farazmand, Blazevski, and Haller [Physica D 44, 278 (2014)], in which Lagrangian coherent structures (LCSs), relevant to purely advective transport, are characterized as curves of minimal Lagrangian shear. Supported by the US National Science Foundation under Grant CMMI-1201236.
Meson-baryon effective chiral Lagrangians at order p4
NASA Astrophysics Data System (ADS)
Jiang, Shao-Zhou; Chen, Qing-Sen; Liu, Yan-Rui
2017-01-01
We construct the three-flavor Lorentz-invariant meson-baryon chiral Lagrangians at the order p4, with which a full one-loop investigation may be performed. One obtains 540 independent terms. The processes with the minimal number of mesons and photons to which this order of Lagrangians may contribute are also presented.
Li, Shuai; Li, Yangming; Wang, Zheng
2013-03-01
This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem.
Bayat, Farhad; Mobayen, Saleh; Javadi, Shamsi
2016-07-01
This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.
NASA Astrophysics Data System (ADS)
Ma, Yuechao; Fu, Lei
2016-10-01
This study employs the multiple Lyapunov-like function method and the average dwell-time concept of switching signal to investigate the finite-time H∞ static output-feedback (SOF) control problem for a class of discrete-time switched singular time-delay systems subject to actuator saturation. First, sufficient conditions are presented to guarantee the discrete-time switched singular time-delay system regular, causal and finite-time boundedness. Meanwhile, sufficient conditions are presented to ensure the H∞ disturbance attenuation level, and the design method of H∞ SOF controller is developed by solving matrix inequalities optimisation problem without any decompositions of system matrices and equivalent transformation. Finally, the effectiveness and merit of the theoretical results are shown through some numerical examples and several vivid illustrations.
Instantons in a Lagrangian model of turbulence
NASA Astrophysics Data System (ADS)
Grigorio, L. S.; Bouchet, F.; Pereira, R. M.; Chevillard, L.
2017-02-01
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the recent fluid deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function (pdf) is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies in the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.
Semigeostrophic moist frontogenesis in a Lagrangian model
NASA Astrophysics Data System (ADS)
Holt, M. W.
1989-01-01
A geometric technique for solving the Lagrangian conservation form of the semigeostrophic equations is extended to study moist frontogenesis. Model elements are required to conserve θE and the frontogenesis is forced by a deformation flow. The boundary-layer elements ahead of the surface front are conditionally unstable but initially unsaturated. As they are forced to ascend at the surface front these elements saturate and appear at a new equilibrium position after implicitly releasing latent heat. This leads to the formation of a 'lens' of moist air at mid-levels some 200 km behind the surface front. In terms of dry potential vorticity, a positive anomaly has been created in the region where the elements saturate and a corresponding negative anomaly is created at the site of the lens. The inclusion of cooling using a simple model to mimic evaporational effects is found to have a significant effect on the overall evolution of the moist front.
Distributed Control by Lagrangian Steepest Descent
NASA Technical Reports Server (NTRS)
Wolpert, David H.; Bieniawski, Stefan
2004-01-01
Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.
Markov Chain Monte Carlo from Lagrangian Dynamics
Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark
2014-01-01
Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper. PMID:26240515
Lagrangian statistics of light particles in turbulence
NASA Astrophysics Data System (ADS)
Mercado, Julián Martínez; Prakash, Vivek N.; Tagawa, Yoshiyuki; Sun, Chao; Lohse, Detlef; (International CollaborationTurbulence Research)
2012-05-01
We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter db = 340 μm and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Reλ) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry. It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23 to 30. The acceleration flatness values show an increasing trend with Reλ, consistent with previous experiments [G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, "Measurement of particle accelerations in fully developed turbulence," J. Fluid Mech. 469, 121 (2002)], 10.1017/S0022112002001842 and numerics [T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, "Small-scale statistics in highresolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics," J. Fluid Mech. 592, 335 (2007)], 10.1017/S0022112007008531. These acceleration PDFs show a higher intermittency compared to tracers [S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, "Modeling inertial particle acceleration statistics in isotropic turbulence," Phys. Fluids. 20, 095104 (2008)], 10.1063/1.2976174 and heavy particles [S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, "Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence," Phys. Rev. Lett. 97, 144507 (2006)], 10.1103/PhysRevLett.97.144507 in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Reλ. We also compare our results with experiments in von Kármán flows and point-particle direct numerical simulations with periodic
The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Kaplan, Carolyn; Oran, Elaine; Boris, Jay
2010-01-01
This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.
A Lagrangian View of Stratospheric Trace Gas Distributions
NASA Technical Reports Server (NTRS)
Schoeberl, M. R.; Sparling, L.; Dessler, A.; Jackman, C. H.; Fleming, E. L.
1998-01-01
As a result of photochemistry, some relationship between the stratospheric age-of-air and the amount of tracer contained within an air sample is expected. The existence of such a relationship allows inferences about transport history to be made from observations of chemical tracers. This paper lays down the conceptual foundations for the relationship between age and tracer amount, developed within a Lagrangian framework. In general, the photochemical loss depends not only on the age of the parcel but also on its path. We show that under the "average path approximation" that the path variations are less important than parcel age. The average path approximation then allows us to develop a formal relationship between the age spectrum and the tracer spectrum. Using the relation between the tracer and age spectra, tracer-tracer correlations can be interpreted as resulting from mixing which connects parts of the single path photochemistry curve, which is formed purely from the action of photochemistry on an irreducible parcel. This geometric interpretation of mixing gives rise to constraints on trace gas correlations, and explains why some observations are do not fall on rapid mixing curves. This effect is seen in the ATMOS observations.
Internal wave bolus detection and analysis by a Lagrangian coherent structure method
NASA Astrophysics Data System (ADS)
Allshouse, Michael R.; Salvador-Vieira, G.; Swinney, Harry L.
2015-11-01
The shoaling of vertical mode internal waves on a continental shelf produces boluses, which are trapped regions of fluid that travel up the shelf with the wave. Unlike a propagating solitary wave, these boluses can transport material with the wave. Boluses have been observed to transport oxygen depleted water and induce rapid changes in temperature both of which have potential ramifications for marine biology. We extend a number of two-layer studies by investigating bolus generation and material transport in continuously stratified fluids. Laboratory experiments are conducted in a 4 m long tank and are complemented by 2-dimensional numerical simulations of the Navier-Stokes equations. The boundaries of a bolus are identified using a Lagrangian based coherent structure method relying on trajectory clustering. The time evolution of material transport by the bolus is investigated as a function of the stratification, wave properties, and the angle of the sloping topography. ONR MURI Grant No. N000141110701.
Lagrangian studies of animal swimming and aquatic predator-prey interactions
NASA Astrophysics Data System (ADS)
Dabiri, John
2008-03-01
Experimental studies of animal swimming have been traditionally based on an Eulerian perspective in which the time-dependent flow field surrounding the animal is measured at fixed locations in space. The measured velocity field and its derivatives (e.g. vorticity) can, in principle, be used to deduce the forces, energetics, and fluid transport associated with locomotion in real fluids. However, achieving a connection between measurements of these Eulerian fields and the dynamics of locomotion has proven difficult in practice. We present the application of Lagrangian methods of flow analysis in which the time-dependent trajectories of individual tracer particles in the flow are measured experimentally and subsequently interrogated using dynamical systems tools in order to quantitatively resolve the dynamics of animal swimming. The Lagrangian methods are shown to be readily extended to time-dependent measurements in three spatial dimensions and to in situ field measurements using a recently developed self-contained underwater velocimetry apparatus (SCUVA). Case studies of jellyfish and other aquatic animals observed in the laboratory and in marine environments are used to illustrate the proposed approach. We also show that predator-prey interactions during jellyfish swimming can be addressed using the aforementioned Lagrangian methods in combination with the Maxey-Riley equations for inertial particles in fluid flow.
A reduction of order two for infinite-order Lagrangians
NASA Astrophysics Data System (ADS)
Jaén, X.; Llosa, J.; Molina, A.
1986-10-01
Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.
Lagrangian averaging, nonlinear waves, and shock regularization
NASA Astrophysics Data System (ADS)
Bhat, Harish S.
In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity
Top marine predators track Lagrangian coherent structures
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-01-01
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel. PMID:19416811
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
Disentangling the Cosmic Web with Lagrangian Submanifold
NASA Astrophysics Data System (ADS)
Shandarin, Sergei F.; Medvedev, Mikhail V.
2016-10-01
The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space.
Lagrangian turbulence and the Brownian motion paradox
NASA Astrophysics Data System (ADS)
Viecelli, J. A.
1991-11-01
The unique properties of three-dimensional hydrodynamic turbulence depend on the nature of the long-range time correlations as well as the spatial correlations. Although Kolmogorov's second similarity hypothesis predicts a power-law spatial scaling exponent for the Eulerian velocity fluctuations in agreement with experiments, it also leads, via the Lagrangian velocity time structure function relationship, to particle dispersion predictions that are inconsistent with enhanced diffusion. Recently, a new computational technique has been developed which can generate random power-law correlated fields in any number of dimensions with unlimited scale range. This new method is used to explore the consequences of a proposed set of assumptions about the nature of the time correlations and their relationship to the spatial correlations. In particular, the Brownian motion paradox is examined and it is shown that it can be resolved if the time domain constraint part of Kolmogorov's second hypothesis is relaxed and replaced with an assumption of space-time isotropy. The proposed modification preserves the observed one-dimensional k-5/3 spatial energy spectrum, allows for enhanced diffusion consistent with Richardson's law, is consistent with Taylor's frozen turbulence assumption under the appropriate conditions, and yields an ω-5/3 frequency spectrum for the velocity fluctuations in a frame at rest with respect to the turbulence.
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
NASA Astrophysics Data System (ADS)
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Predicting abrasive wear with coupled Lagrangian methods
NASA Astrophysics Data System (ADS)
Beck, Florian; Eberhard, Peter
2015-05-01
In this paper, a mesh-less approach for the simulation of a fluid with particle loading and the prediction of abrasive wear is presented. We are using the smoothed particle hydrodynamics (SPH) method for modeling the fluid and the discrete element method (DEM) for the solid particles, which represent the loading of the fluid. These Lagrangian methods are used to describe heavily sloshing fluids with their free surfaces as well as the interface between the fluid and the solid particles accurately. A Reynolds-averaged Navier-Stokes equations model is applied for handling turbulences. We are predicting abrasive wear on the boundary geometry with two different wear models taking cutting and deformation mechanisms into account. The boundary geometry is discretized with special DEM particles. In doing so, it is possible to use the same particle type for both the calculation of the boundary conditions for the SPH method as well as the DEM and for predicting the abrasive wear. After a brief introduction to the SPH method and the DEM, the handling of the boundary and the coupling of the fluid and the solid particles are discussed. Then, the applied wear models are presented and the simulation scenarios are described. The first numerical experiment is the simulation of a fluid with loading which is sloshing inside a tank. The second numerical experiment is the simulation of the impact of a free jet with loading to a simplified pelton bucket. We are especially investigating the wear patterns inside the tank and the bucket.
High Order Semi-Lagrangian Advection Scheme
NASA Astrophysics Data System (ADS)
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Sea Fog Forecasting with Lagrangian Models
NASA Astrophysics Data System (ADS)
Lewis, J. M.
2014-12-01
In 1913, G. I. Taylor introduced us to a Lagrangian view of sea fog formation. He conducted his study off the coast of Newfoundland in the aftermath of the Titanic disaster. We briefly review Taylor's classic work and then apply these same principles to a case of sea fog formation and dissipation off the coast of California. The resources used in this study consist of: 1) land-based surface and upper-air observations, 2) NDBC (National Data Buoy Center) observations from moored buoys equipped to measure dew point temperature as well as the standard surface observations at sea (wind, sea surface temperature, pressure, and air temperature), 3) satellite observations of cloud, and 4) a one-dimensional (vertically directed) boundary layer model that tracks with the surface air motion and makes use of sophisticated turbulence-radiation parameterizations. Results of the investigation indicate that delicate interplay and interaction between the radiation and turbulence processes makes accurate forecasts of sea fog onset unlikely in the near future. This pessimistic attitude stems from inadequacy of the existing network of observations and uncertainties in modeling dynamical processes within the boundary layer.
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S.
2014-06-10
We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
de Leon, M.; de Diego, D.M.
1997-06-01
We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}
Improving and applying Lagrangian models of the atmosphere
NASA Astrophysics Data System (ADS)
Lin, John C.; Brunner, Dominik; Gerbig, Christoph
2012-01-01
AGU Chapman Conference on Advances in Lagrangian Modeling of the Atmosphere; Grindelwald, Switzerland, 10-14 October 2011 Under the majestic gaze of the Eiger north face in Switzerland, an international group of researchers met as part of a Chapman Conference to discuss advances in Lagrangian modeling of the atmosphere. Lagrangian models track the movement of air parcels, giving rise to trajectory information and source/receptor linkages that have become increasingly popular as tools used by geoscientists. The conference was an opportunity for a diverse group of researchers developing and applying Lagrangian models to congregate and discuss the use of such models to understand geophysical phenomena and to identify how to further improve the models. The 98 participants (of which 17 were graduate students) hailed from 19 countries around the world.
A semi-analytical Lagrangian dispersion model in inhomogeneous turbulence
Zhuang, Y.
1996-12-31
Probably the most natural method to describe turbulent dispersion in the atmosphere is the Lagrangian trajectory model. In this approach, one builds the joint probability density function (PDF) of particle velocity and position by following a large number of particle trajectories in a turbulent flow given the Eulerian flow statistics. The statistics of the concentration can then be found from the joint PDF. However, the usefulness of the Lagrangian trajectory model in practice has been hindered by the necessary lengthy and stochastic numerical calculations. As a result, few operational models based on the Lagrangian trajectory approach have been proposed. This paper reports the first attempt to solve the Fokker-Planck equation using the function expansion method. The semi-analytical solution retains the characteristics of the Lagrangian trajectory model, but takes little computation effort. The solutions for Gaussian inhomogeneous turbulence and skewed homogeneous turbulence are discussed by comparing them with those calculated using the trajectory simulation method.
Construction of Lagrangians and Hamiltonians from the Equation of Motion
ERIC Educational Resources Information Center
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
Remarks on the Lagrangian representation of bi-Hamiltonian equations
NASA Astrophysics Data System (ADS)
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Lagrangian statistics in forced two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Kamps, Oliver; Friedrich, Rudolf
2007-11-01
In recent years the Lagrangian description of turbulent flows has attracted much interest from the experimental point of view and as well is in the focus of numerical and analytical investigations. We present detailed numerical investigations of Lagrangian tracer particles in the inverse energy cascade of two-dimensional turbulence. In the first part we focus on the shape and scaling properties of the probability distribution functions for the velocity increments and compare them to the Eulerian case and the increment statistics in three dimensions. Motivated by our observations we address the important question of translating increment statistics from one frame of reference to the other [1]. To reveal the underlying physical mechanism we determine numerically the involved transition probabilities. In this way we shed light on the source of Lagrangian intermittency.[1ex] [1] R. Friedrich, R. Grauer, H. Hohmann, O. Kamps, A Corrsin type approximation for Lagrangian fluid Turbulence , arXiv:0705.3132
Scale-dependent relative dispersion measurements from the Grand LAgrangian Deployment (GLAD)
NASA Astrophysics Data System (ADS)
Haza, Angelique; Poje, Andrew; Ozgokmen, Tamay; Griffa, Annalisa; Haus, Brian; Huntley, Helga; Hogan, Patrick; Jacobs, Gregg; Kirwan, Danny; Lipphardt, Bruce; Novelli, Guillaume; Olascoaga, Josefina; Beron-Vera, Francisco; Reniers, Ad; Ryan, Edward
2013-04-01
The scale-dependent Lagrangian dispersion metrics, such as the Finite Scale Lyapunov Exponent, are suitable to study multi-scale interaction of ocean flows. Of particular interest is the possible impact of submesoscale flows on transport in the ocean, for applied problems such as oil spill. Results will be presented from the GLAD experiment, which was configured to optimize in-situ submesoscale relative dispersion measurements in the Gulf of Mexico near DeSoto Canyon from a release of more than 300 surface drifters.
A second order Lagrangian Eulerian momentum bounded method for multiphase flows
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Pitsch, Heinz
2011-11-01
A Lagrangian Eulerian framework relying on both Level Set and Volume of Fluid methods is presented in the context of multiphase flow computations. The resulting interface capturing scheme is shown to preserve planarity, and to conserve mass exactly for solenoidal and linear velocity fields. A novel fractional step approach for the incompressible Navier Stokes equation is also presented. The proposed scheme relies on a consistent transport of volume fraction and momentum fields, which also preserves velocity boundedness. A sharp interface projection step is derived accordingly. The algorithm is shown to conserve momentum exactly for solenoidal linear velocity, and to lead to robust computations. Supported by NASA under Subsonic Fixed Wing project.
Hydrodynamic Lagrangian of relativistic superfluids with crystalline structure
NASA Astrophysics Data System (ADS)
Peletminskii, A. S.
2009-09-01
We propose a relativistic Lagrangian formulation of macroscopic dynamics of superfluid systems. The constructed Lagrangian provides the description of ordinary superfluids and superfluids with a crystalline ordering, where both phase and translational symmetries are simultaneously broken (e.g., supersolids or crystalline superfluids in neutron stars). The covariant conservation laws and equations of motion for the field variables associated with the broken symmetries are obtained. The connection to Khalatnikov-Lebedev relativistic hydrodynamic theory is discussed.
A Lagrangian theory of the classical spinning electron
NASA Technical Reports Server (NTRS)
Nash, P. L.
1984-01-01
A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
2014-09-30
that survives the summer melt season in each of the Arctic peripheral seas. The Lagrangian Model is forced with weekly mean satellite-derived sea- ice ...GCM to drive the Lagrangian code and map the regions for the multi-year ice surviving the summer melt in each of the Arctic peripheral seas in todays...1995, Emery et al. 1997, Meier et al. 2000, Tschudi et al. 2010) 3- Assess whether the source region of sea ice melting in peripheral seas in the
Semi-Lagrangian integration schemes for atmospheric models - A review
Staniforth, A.; Cote, J. )
1991-09-01
The semi-Lagrangian methodology is described for a hierarchy of applications (passive advection, forced advection, and coupled sets of equation) of increasing complexity, in one, two, and three dimensions. Attention is focused on its accuracy, stability, and efficiency properties. Recent developments in applying semi-Lagrangian methods to 2D and 3D atmospheric flows in both Cartesian and spherical geometries are then reviewed. Finally, the current status of development is summarized, followed by a short discussion of future perspectives. 80 refs.
Dynamical systems analysis of fluid transport in time-periodic vortex ring flows
NASA Astrophysics Data System (ADS)
Shariff, Karim; Leonard, Anthony; Ferziger, Joel H.
2006-04-01
It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization experiments of turbulent vortex rings suggests that a similar process might be at play. However, what precise modes of unsteadiness are responsible for stirring in a turbulent vortex ring is left as an open question. The second situation is that of two leapfrogging rings. The unstable manifold shows striking agreement with even the fine features of smoke visualization photographs, suggesting that fluid elements in the vicinity of the manifold are drawn out along it and begin to reveal its structure. We suggest that interpretations of these photographs that argue for complex vorticity dynamics ought to be reconsidered. Recently, theoretical and computational tools have been developed to locate structures analogous to stable and unstable manifolds in aperiodic, or finite-time systems. The usefulness of these analogs is demonstrated, using vortex ring flows as an example, in the paper by Shadden, Dabiri, and Marsden [Phys. Fluids 18, 047105 (2006)].
Grid adaptation and remapping for arbitrary lagrangian eulerian (ALE) methods
Lapenta, G. M.
2002-01-01
Methods to include automatic grid adaptation tools within the Arbitrary Lagrangian Eulerian (ALE) method are described. Two main developments will be described. First, a new grid adaptation approach is described, based on an automatic and accurate estimate of the local truncation error. Second, a new method to remap the information between two grids is presented, based on the MPDATA approach. The Arbitrary Lagrangian Eulerian (ALE) method solves hyperbolic equations by splitting the operators is two phases. First, in the Lagrangian phase, the equations under consideration are written in a Lagrangian frame and are discretized. In this phase, the grid moves with the solution, the velocity of each node being the local fluid velocity. Second, in the Eulerian phase, a new grid is generated and the information is transferred to the new grid. The advantage of considering this second step is the possibility of avoiding mesh distortion and tangling typical of pure Lagrangian methods. The second phase of the ALE method is the primary topic of the present communication. In the Eulerian phase two tasks need to be completed. First, a new grid need to be created (we will refer to this task as rezoning). Second, the information is transferred from the grid available at the end of the Lagrangian phase to the new grid (we will refer to this task as remapping). New techniques are presented for the two tasks of the Eulerian phase: rezoning and remapping.
Generalized Lagrangian dynamics of physical and non-physical systems
NASA Astrophysics Data System (ADS)
Sandler, U.
2014-12-01
In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1-dimensional space, where n is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics. We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to non-physical systems. An example of such an application is presented as well.
NASA Astrophysics Data System (ADS)
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
NASA Astrophysics Data System (ADS)
Seyrich, Maximilian; Sornette, Didier
2016-04-01
We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a>1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modeling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.
Sampath, Ramgopal; Mathur, Manikandan; Chakravarthy, Satyanarayanan R
2016-12-01
This paper quantitatively examines the occurrence of large-scale coherent structures in the flow field during combustion instability in comparison with the flow-combustion-acoustic system when it is stable. For this purpose, the features in the recirculation zone of the confined flow past a backward-facing step are studied in terms of Lagrangian coherent structures. The experiments are conducted at a Reynolds number of 18600 and an equivalence ratio of 0.9 of the premixed fuel-air mixture for two combustor lengths, the long duct corresponding to instability and the short one to the stable case. Simultaneous measurements of the velocity field using time-resolved particle image velocimetry and the CH^{*} chemiluminescence of the flame along with pressure time traces are obtained. The extracted ridges of the finite-time Lyapunov exponent (FTLE) fields delineate dynamically distinct regions of the flow field. The presence of large-scale vortical structures and their modulation over different time instants are well captured by the FTLE ridges for the long combustor where high-amplitude acoustic oscillations are self-excited. In contrast, small-scale vortices signifying Kelvin-Helmholtz instability are observed in the short duct case. Saddle-type flow features are found to separate the distinct flow structures for both combustor lengths. The FTLE ridges are found to align with the flame boundaries in the upstream regions, whereas farther downstream, the alignment is weaker due to dilatation of the flow by the flame's heat release. Specifically, the FTLE ridges encompass the flame curl-up for both the combustor lengths, and thus act as the surrogate flame boundaries. The flame is found to propagate upstream from an earlier vortex roll-up to a newer one along the backward-time FTLE ridge connecting the two structures.
NASA Astrophysics Data System (ADS)
Sampath, Ramgopal; Mathur, Manikandan; Chakravarthy, Satyanarayanan R.
2016-12-01
This paper quantitatively examines the occurrence of large-scale coherent structures in the flow field during combustion instability in comparison with the flow-combustion-acoustic system when it is stable. For this purpose, the features in the recirculation zone of the confined flow past a backward-facing step are studied in terms of Lagrangian coherent structures. The experiments are conducted at a Reynolds number of 18600 and an equivalence ratio of 0.9 of the premixed fuel-air mixture for two combustor lengths, the long duct corresponding to instability and the short one to the stable case. Simultaneous measurements of the velocity field using time-resolved particle image velocimetry and the C H* chemiluminescence of the flame along with pressure time traces are obtained. The extracted ridges of the finite-time Lyapunov exponent (FTLE) fields delineate dynamically distinct regions of the flow field. The presence of large-scale vortical structures and their modulation over different time instants are well captured by the FTLE ridges for the long combustor where high-amplitude acoustic oscillations are self-excited. In contrast, small-scale vortices signifying Kelvin-Helmholtz instability are observed in the short duct case. Saddle-type flow features are found to separate the distinct flow structures for both combustor lengths. The FTLE ridges are found to align with the flame boundaries in the upstream regions, whereas farther downstream, the alignment is weaker due to dilatation of the flow by the flame's heat release. Specifically, the FTLE ridges encompass the flame curl-up for both the combustor lengths, and thus act as the surrogate flame boundaries. The flame is found to propagate upstream from an earlier vortex roll-up to a newer one along the backward-time FTLE ridge connecting the two structures.
An Application of Lagrangian Coherent Structures to Harmful Algal Blooms
NASA Astrophysics Data System (ADS)
Olascoaga, M. J.; Beron-Vera, F. J.; Brand, L. E.; Kocak, H.
2009-04-01
Karenia brevis is present in low concentrations in vast areas of the Gulf of Mexico (GoM). This toxic dinoflagellate sporadically develops blooms anywhere in the GoM, except in the southern portion of West Florida Shelf (WFS). There, these harmful algal blooms (HABs) are recurrent events whose frequency and intensity are increasing. HABs on the WFS are usually only evident once they have achieved high concentrations that can be detected by observation of discolored water, which may be apparent in satellite imagery; by ecological problems such as fish kills; or human health problems. Because the early development stages of HABs are usually not detected, there is limited understanding of the environmental conditions that lead to their development. Analysis of simulated surface ocean currents reveals the presence of a persistent large-scale Lagrangian coherent structure (LCS) on the southern portion of the WFS. A LCS can be regarded as a distinguished material line which divides immiscible fluid regions with distinct advection properties. Consistent with satellite-tracked drifter trajectories, this LCS on the WFS constitutes a cross-shelf barrier for the lateral transport of passive tracers. We hypothesize that such a LCS provides favorable conditions for the development of HABs. LCSs are also employed to trace the early location of an observed HAB on the WFS. Using a simplified population dynamics model we infer the factors that could possibly lead to the development of this HAB. The population dynamics model determines nitrogen in two components, nutrients and phytoplankton, which are assumed to be passively advected by simulated surface ocean currents. Two nutrient sources are inferred for the HAB whose evolution is found to be strongly tied to the simulated LCSs. These nutrient sources are found to be located near shore and likely due to land runoff.
Parameterization of Submesoscale Particle Transport in the Gulf of Mexico
NASA Astrophysics Data System (ADS)
Haza, A. C.; Ozgokmen, T. M.; Griffa, A.; Poje, A. C.; Hogan, P. J.; Jacobs, G. A.
2014-12-01
Submesoscale flows have a significant impact on the transport at their own scales, yet require extensive data sets and numerical computations, making them challenging to approach deterministically. A recent Lagrangian parametrization to correct particle transport at the submesoscales is implemented to an eddy permitting ocean model at 1/25 degree grid for the surface circulation of the Gulf of Mexico. It combines mesoscale transport from the deterministic Lagrangian Coherent Structures (LCS) and statistical Lagrangian subgridscale (LSGS) models over the submesoscale range. Comparison to a 1km submesoscale-permitting ocean model shows a significant improvement of the scale-dependent relative dispersion and particle distribution.
Post-Newtonian cosmological dynamics in Lagrangian coordinates
NASA Astrophysics Data System (ADS)
Matarrese, Sabino; Terranova, David
1996-11-01
We study the non-linear dynamics of self-gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of light. To lowest order, the Newtonian approximation - in Lagrangian form - is derived and written in a transparent way; the corresponding Lagrangian Newtonian metric is obtained. Post-Newtonian corrections are then derived and their physical meaning clarified. A number of results are obtained: (i) the master equation of Lagrangian Newtonian dynamics, the Raychaudhuri equation, can be interpreted as an equation for the evolution of the Lagrangian-to-Eulerian Jacobian matrix, complemented by the irrotationality constraint; (ii) the Lagrangian spatial metric reduces, in the Newtonian limit, to that of Euclidean 3-space written in time-dependent curvilinear coordinates, with non-vanishing Christoffel symbols, but vanishing spatial curvature (a particular example of it is given within the Zel'dovich approximation); (iii) a Lagrangian version of the Bernoulli equation for the evolution of the `velocity potential' is obtained. (iv) The Newtonian and post-Newtonian content of the electric and magnetic parts of the Weyl tensor is clarified. (v) At the post-Newtonian level, an exact and general formula is derived for gravitational-wave emission from non-linear cosmological perturbations; (vi) a straightforward application to the anisotropic collapse of homogeneous ellipsoids shows that the ratio of these postNewtonian terms to the Newtonian ones tends to diverge at least like the mass density. (vii) It is argued that a stochastic gravitational wave background is produced by non-linear cosmic structures, with present-day closure density Ωgw ˜10-5-10-6 on 1-10 Mpc scales.
Development of a Lagrangian-Lagrangian methodology to predict brownout dust clouds
NASA Astrophysics Data System (ADS)
Syal, Monica
A Lagrangian-Lagrangian dust cloud simulation methodology has been developed to help better understand the complicated two-phase nature of the rotorcraft brownout problem. Brownout conditions occur when rotorcraft land or take off from ground surfaces covered with loose sediment such as sand and dust, which decreases the pilot's visibility of the ground and poses a serious safety of flight risk. The present work involved the development of a comprehensive, computationally efficient three-dimensional sediment tracking method for dilute, low Reynolds number Stokes-type flows. The flow field generated by a helicopter rotor in ground effect operations over a mobile sediment bed was modeled by using an inviscid, incompressible, Lagrangian free-vortex method, coupled to a viscous semi-empirical approximation for the boundary layer flow near the ground. A new threshold model for the onset of sediment mobility was developed by including the effects of unsteady pressure forces that are induced in vortically dominated rotor flows, which can significantly alter the threshold conditions for particle motion. Other important aspects of particle mobility and uplift in such vortically driven dust flows were also modeled, including bombardment effects when previously suspended particles impact the bed and eject new particles. Bombardment effects were shown to be a particularly significant contributor to the mobilization and eventual suspension of large quantities of smaller-sized dust particles, which tend to remain suspended. A numerically efficient Lagrangian particle tracking methodology was developed where individual particle or clusters of particles were tracked in the flow. To this end, a multi-step, second-order accurate time-marching scheme was developed to solve the numerically stiff equations that govern the dynamics of particle motion. The stability and accuracy of this scheme was examined and matched to the characteristics of free-vortex method. One-way coupling of the
NASA Astrophysics Data System (ADS)
Ross, Shane; Tallapragada, Phanindra; Schmale, David
2010-11-01
The atmospheric transport of airborne microorganisms (e.g., plant pathogens) is poorly understood, yet necessary to assess their ecological roles in agricultural ecosystems and to evaluate risks posed by invasive species. The atmospheric transport of plant pathogens can be roughly divided into three phases: liberation of pathogen spores, drift (transport in the atmosphere) and deposition. If liberated spores escape into the planetary boundary layer, they could be transported over thousands of kilometers before being deposited. The drift phase is poorly understood, due to the complex nature of atmospheric transport and relative lack of observational data. In this talk, we present a framework of Lagrangian coherent structures to determine the important atmospheric transport barriers (ATBs) that partition the atmosphere and systematically organize the mesoscale transport problem. Using autonomous unmanned aerial vehicles, we measure the concentration of spores of a plant pathogenic fungus (Fusarium) sampled in the atmosphere above Virginia Tech's Kentland Farm. We report correlations between concentrations of Fusarium with the local movement of ATBs determined from archived meteorological data.
A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows
NASA Astrophysics Data System (ADS)
Owkes, Mark; Desjardins, Olivier
2017-03-01
In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas-liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.
Lagrangian tracking of an instrumented particule in Rayleigh-Benard flow
NASA Astrophysics Data System (ADS)
Seychelles, Fanny; Riedinger, Xavier; Salort, Julien; Rusaouen, Eleonore; Gibert, Matthieu; Gasteuil, Yoann; Liot, Olivier; Castaing, Bernard; Chilla, Francesca
2012-11-01
Thermal convection is present in different systems from astrophysical to geophysical flows. Most experiments and numerical studies are carried from eulerian point of view. The heat transfer from a local perspective is not well understood. Lagrangian description could provide the missing insights on the local mixing and transport mechanisms in thermal convection. We present here a lagrangian measurement in a Rayleigh Bénard convection. To be more precise, we have conceived a sphere particle with embarked thermometers and radio emitter. Our experimental setup is a rectangular vessel with height H=40 cm and section 40 cm × 10 cm filled with water. The walls are made of polymethylmetacrylate, the top plate is cooled by controlled thermal bath, and the bottom plate is heated by electrical resistance. Using a camera for optical tracking, we obtain at the same time the position and temperature measurement of the particle. We present here the results of a new sensor on statistics of temperature, velocity and heat transport in an original Rayleigh Benard convection, where the top plate is smooth and the bottom plate is rough.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
NASA Astrophysics Data System (ADS)
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Forms of null Lagrangians in field theories of continuum mechanics
NASA Astrophysics Data System (ADS)
Kovalev, V. A.; Radaev, Yu. N.
2012-02-01
The divergence representation of a null Lagrangian that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null Lagrangian can contain up to 15 independent elements in total. The general form of a null Lagrangian in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null Lagrangian for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null Lagrangians are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
Lagrangian Displacement Ensembles for Aerosol Data Assimilation (Invited)
NASA Astrophysics Data System (ADS)
da Silva, A.; Colarco, P. R.; Govindaraju, R. C.
2010-12-01
A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely-sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentractions for initializing a prognostic model. This problem is exarcebated in the the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols). An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meterorological fields and realistc emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from innacurate emissions, and the Lagrangian misplacement of plumes induced by errors in the driving meterorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of errors is no longer the main order of business. We will describe and aerosol data assimilation scheme in which the anaysis update step is conducted in observation space, using an adaptive maximum-likelihood scheme for estimating background errors in AOD space. This scheme includes explicit sequential bias estimation as in Dee and da Silva (1998). Unlikely existing aerosol data assimiltion schemes we do not obtain analysis increments of the 3D concentrations by scalling the background profiles. Instead, we explore the Langrangian characteristics of the problem for generating local displacement ensembles. These high-resolution, state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity comparable to the forecasting step by the aerosol transport model
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.
A new approach to Lagrangian investigations of isotropic turbulence
NASA Astrophysics Data System (ADS)
Barjona, Manuel; B. da Silva, Carlos; Idmec Team
2016-11-01
A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.
Lagrangian statistics and flow topology in forced 2-D turbulence
Kadoch, B.; Del-Castillo-Negrete, Diego B; Bos, W.J.T.; Schneider, Kai
2011-01-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order - 2.
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
Large N Duality, Lagrangian Cycles, and Algebraic Knots
NASA Astrophysics Data System (ADS)
Diaconescu, D.-E.; Shende, V.; Vafa, C.
2013-05-01
We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Generalized extended Lagrangian Born-Oppenheimer molecular dynamics
Niklasson, Anders M. N. Cawkwell, Marc J.
2014-10-28
Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.
Lagrangian dimensionality reduction of convection dominated nonlinear flows
NASA Astrophysics Data System (ADS)
Balajewicz, Maciej; Mojgani, Rambod
2016-11-01
We introduce a new projection-based model reduction approach for convection dominated nonlinear fluid flows. In this method the evolution of the fluid is approximated in the Lagrangian frame of reference. More specifically, global basis functions are utilized for both the state of the system and the positions of the Lagrangian computational domain. In this approach, wave-like solutions exhibit low-rank structure and thus, can be approximated efficiently using a small number of reduced bases. The proposed approach is successfully demonstrated for the reduction of several simple but representative flow problems.
Functional Lagrange formalism for time-non-local Lagrangians
NASA Astrophysics Data System (ADS)
Ferialdi, L.; Bassi, A.
2012-05-01
We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.
Lagrangian-Hamiltonian unified formalism for field theory
NASA Astrophysics Data System (ADS)
Echeverría-Enríquez, Arturo; López, Carlos; Marín-Solano, Jesús; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
2004-01-01
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.
Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
NASA Astrophysics Data System (ADS)
García-Toraño Andrés, E.; Guzmán, E.; Marrero, J. C.; Mestdag, T.
2014-06-01
In this paper, we will see that the symplectic creed by Weinstein ‘everything is a Lagrangian submanifold’ also holds for Hamilton-Poincaré and Lagrange-Poincaré reduction. In fact, we show that solutions of the Hamilton-Poincaré equations and of the Lagrange-Poincaré equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction.
A Spectral Clustering Approach to Lagrangian Vortex Detection
NASA Astrophysics Data System (ADS)
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2015-11-01
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.
Spectral-clustering approach to Lagrangian vortex detection.
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2016-06-01
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.
Spectral-clustering approach to Lagrangian vortex detection
NASA Astrophysics Data System (ADS)
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2016-06-01
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.
An effective Lagrangian description of supernova-core bounce
NASA Astrophysics Data System (ADS)
Rodrigues, H.; Deavila, V.; Duarte, S. J. B.; Kodama, T.
1990-08-01
The global dynamical aspects of a supernova event are studied in terms of an effective Lagrangian formulation. The equation of motion derived from this Lagrangian is solved numerically for different supernova core masses. An equation of state for cold matter is introduced by means of an adiabatic index parametrization which is a smooth function of the matter density. The energy transfer from the inner to the outer core is estimated in the context of the hydrodynamic bounce mechanism. It is found that only a very restricted mass distribution to pre-supernova core configuration generate a strong enough shock wave leading to a prompt bounce ejection.
Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.; Metcalfe, G.
2015-10-15
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
Lagrangian Analysis of Kerguelen's Naturally Iron-fertilised Phytoplankton Bloom
NASA Astrophysics Data System (ADS)
Della Penna, A.; Trull, T. W.; Grenier, M.; Wotherspoon, S.; Johnson, C.; De Monte, S.; d'Ovidio, F.
2015-12-01
The role of iron as a limiting micro-nutrient for primary production in High Nutrient Low Chlorophyll regions has been highlighted by paleoceanography, artificial fertilisation experiments and observed naturally fertilised systems. Examples of natural fertilisation have suggested that (sub-)mesoscale (1-100 km, days-months) horizontal transport modulates and structures the spatial and temporal extent of iron enrichment, phytoplankton production and biogeography. Here we combine different satellite products (altimetry, ocean color, PHYSAT), in-situ sampling, drifting floats and autonomous profilers to analyse the naturally iron-fertilised phytoplankton bloom of the Kerguelen region (Southern Ocean). Considering the Kerguelen Plateau as the main local source of iron, we compute two Lagrangian diagnostics: the "age" - how long before a water parcel has touched the plateau- and the "origin" - the latitude where a water parcel has left the plateau. First, we verify that these altimetry-defined diagnostics' spatial patterns -computed using geostrophic and Ekman corrected velocity fields- are coherent with the ones structuring the trajectories of more than 100 drifters and that trends in surface Chlorophyll (Chl) present an overall agreement with total column content (yet with ~2-3x differences in dynamic ranges likely due to the varying presence of Chl below the mixed layer). Second, assuming a first-order removal, we fit "age" with iron measurements and we estimate removal rates for bloom and abiotic conditions of respectively 0.058 and 0.041 1/d. Then, we relate "age" and "origin" with locations of high Chl concentrations and diatom-dominance. We find out that locations of high Chl concentration correspond to water parcels that have recently left the plateau. Furthermore, general additive models reveal that recently enriched waters are more likely to present a diatom dominance. However, the expected exponential fit varies within the geographic domain suggesting that
Compatible, energy and symmetry preserving 2D Lagrangian hydrodynamics in rz-cylindrical coordinates
Shashkov, Mikhail; Wendroff, Burton; Burton, Donald; Barlow, A; Hongbin, Guo
2009-01-01
We present a new discretization for 2D Lagrangian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, energy conserving and symmetry preserving. We describe discretization of the basic Lagrangian hydrodynamics equations.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Lagrangian Approach to Study Catalytic Fluidized Bed Reactors
NASA Astrophysics Data System (ADS)
Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration
2013-03-01
Lagrangian approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a Lagrangian approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The Lagrangian perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the Lagrangian approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)
Singular Lagrangians. Classical dynamics and quantization. Lectures for young scientists
NASA Astrophysics Data System (ADS)
Nesterenko, V. V.; Chervyakov, A. M.
The lectures are devoted to the classical and quantum dynamics of the systems described by singular (or degenerate) Lagrangians. The complete set of the Hamiltonian constraints is constructed in the framework of the Lagrangian formalism. The equations of motion in the phase space are derived by taking into account all the constraints in the theory. It is proved that the dynamic on the physical submanifold of the phase space has the Hamiltonian form. On lectures the second Noether theorem is widely used. On its basis the properties of the Poisson brackets of the primary constraints are investigated and the invariance of the Lagrangian constraints during evolution is proved. The setting of the Cauchy problem in the theories with singular Lagrangians is discussed. The quantization of the systems with constraints is carried out by the functional integration in the phase space. There is considered the most general case of the first class and the second class constraints with an explicit time dependence. The gauge conditions may be noninvoluntary and time dependent. The material is illustrated by some examples (relativistic point particle, relativistic string, electromagnetic field, and Yang-Mills fields).
Some examples related to the method of Lagrangian descriptors
NASA Astrophysics Data System (ADS)
Ruiz-Herrera, Alfonso
2015-06-01
We provide families of counter-examples, including Hamiltonian systems, to the method of Lagrangian descriptors developed by Mancho, Wiggins, and their co-workers. A detailed mathematical discussion on why that methodology fails together with some pathological phenomena are given as well.
Lagrangian fluid dynamics using the Voronoi-Delauanay mesh
Dukowicz, J.K.
1981-01-01
A Lagrangian technique for numerical fluid dynamics is described. This technique makes use of the Voronoi mesh to efficiently locate new neighbors, and it uses the dual (Delaunay) triangulation to define computational cells. This removes all topological restrictions and facilitates the solution of problems containing interfaces and multiple materials. To improve computational accuracy a mesh smoothing procedure is employed.
The complete HEFT Lagrangian after the LHC Run I
NASA Astrophysics Data System (ADS)
Brivio, I.; Gonzalez-Fraile, J.; Gonzalez-Garcia, M. C.; Merlo, L.
2016-07-01
The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge-boson coupling data from the LHC Run I. The operators' basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the SU(2)_L doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact SU(2)_L doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing (i) anomalous signals present only in the chiral Lagrangian and not expected in the linear one, that are potentially relevant for LHC searches, and (ii) decorrelation effects between observables that are predicted to be correlated in the linear case and not in the chiral one. The global analysis presented here, which includes several kinematic distributions, is crucial for reducing the allowed parameter space and for controlling the correlations between parameters. This improves previous studies aimed at investigating the Higgs Nature and the origin of the electroweak symmetry breaking.
The quasi-Lagrangian nature of SOFAR floats
NASA Astrophysics Data System (ADS)
Riser, Stephen C.
1982-12-01
From several simple numerical and analytical model experiments, estimates are made of the times over which quasi-Lagrangian (constant pressure) SOFAR floats are useful followers of truly Lagrangian fluid parcels. A simple, three-dimensional, analytical, time-dependent model, the MCWILLIAMS and FLIERL (1976 Deep-Sea Research, 23, 285-300) Rossby wave fit to the MODE data set, is used as the prototype mid-ocean eddy field. Twenty initially coincident Lagrangian-quasi-Lagrangian pairs of tracers were released at random locations in the field and tracked as a function of time and the root-mean-square amplitude of the field. When the field has an r.m.s. amplitude of 20 cm s -1 at 700 m, an isobaric SOFAR float represents fluid parcel motion for times of the order of the period of the fastest Rossby wave in the field, 129 days. When a field of internal gravity waves (a spectrum of inertial oscillations and baroclinic semidiurnal tides) is added to the Rossby wave field, the representative time is reduced by about 30%. The 700-m results provide a lower bound on estimates of the time that float motion is representative of parcel motion at greater depths.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the
Lipsius, Kai; Wilhelm, Ralf; Richter, Otto; Schmalstieg, Klaus Jürgen; Schiemann, Joachim
2006-01-01
Modeling pollen dispersal to predict cross-pollination is of great importance for the ongoing discussion of adventitious presence of genetically modified material in food and feed. Two different modeling approaches for pollen dispersal were used to simulate two years of data for the rate of cross-pollination of non-GM maize (Zea mays (L.)) fields by pollen from a central 1 ha transgenic field. The models combine the processes of wind pollen dispersal (transport) and pollen competition. Both models used for the simulation of pollen dispersal were Lagrangian approaches: a stochastic particle Lagrange model and a Lagrangian transfer function model. Both modeling approaches proved to be appropriate for the simulation of the cross-pollination rates. However, model performance differed significantly between years. We considered different complexity in meteorological input data. Predictions compare well with experimental results for all simplification steps, except that systematic deviations occurred when only main wind direction was used. Concluding, it can be pointed out that both models might be adapted to other pollen dispersal experiments of different crops and plot sizes, when wind direction statistics are available. However, calibration of certain model parameters is necessary.
Detecting and tracking eddies in oceanic flows: A vorticity based Euler-Lagrangian method
NASA Astrophysics Data System (ADS)
Vortmeyer-Kley, Rahel; Gräwe, Ulf; Feudel, Ulrike
2016-04-01
Algae blooms as recurrent events in the Baltic Sea are an increasing natural hazard. Sandulescu et al. show in numerical simulation in [1] that eddies can play the role of an incubator for an algae bloom. Inside the eddy nutrients and plankton are trapped and can then be transported across rather long distances. To gain insight in mechanisms of algae bloom evolution detection and tracking of eddies is of interest. Based on the idea to interpret an eddy as a region that is bounded by manifolds and has an elliptic fixed point inside them, we develop an Euler-Lagrangian eddytracking tool using the idea of Lagrangian descriptors [2] and the vorticity. To test how well the tool detects eddy tracks and shapes, and estimates eddy lifetimes, the method is applied to a synthetic van Karman-Vortex Street. The results are compared to an eddytracking tool by Nencioli et al. [3]. Even velocity fields incorporated with different types of noise are taken into account to test the robustness of the tool. Finally, both methods are applied to velocity fields of the Baltic Sea. [1] M. Sandulescu, C. Lopez, E. Hernandez-Garcia and U. Feudel, Nonlinear Proc. Geophys., 14, 443-454, (2007). [2] J. Jimenez-Madrid and A. Mancho, Chaos, 19, 013111-1-18, (2009). [3] F. Nencioli, C. Dong, T. Dickey, L. Washburn, and J.C. McWilliams, J. Atmos. Ocean Tech., 27, 564-579, (2010).
Lee, R.L.; Naeslund, E.
1995-07-01
This paper describes a numerical modeling approach that can be used to provide estimates of air concentrations due to emissions at industrial sites or other sites where buildings may have an important impact on the dispersion patterns. The procedure consists of two sequential steps: (i) Prediction of mean flow and turbulence fields via a turbulent flow model; and, (ii) Employment of the calculated flow and Turbulence fields to drive a Lagrangian Stochastic Particle Model. Two flow scenarios in which the approaching mean wind is assumed to be at 90{degrees} and 30{degrees} to the building complex are used as input to the Lagrangian model. The first calculation is based on an earlier transport and diffusion simulation that employed an existing particle-in-cell flux-gradient dispersion model. The second simulation is used to demonstrate the strong spatial variations that the concentration field exhibit within the highly complex separation zones of building wakes. The relationship between concentration levels and toxic load are discussed for the case of a chemical spill.
NASA Astrophysics Data System (ADS)
Orjuela, H. R.; Leon, G. E.; Jimenez-Pizarro, R.
2012-12-01
The ongoing transformation of the Colombian Orinoquia (Eastern Plains) due to the rapid expansion of the agricultural frontier and oil production implies a series of new atmospheric emissions, which might negatively impact human health and ecosystems in different ways. Some air pollutants have already been detected in the region. This is the case of Persistent Organic Pollutants (POPs), which are sampled in a site of the Global Atmospheric Passive Sampling (GAPS) network located in Arauca, Colombia. The current understanding on the origin and transport of pollutants is limited due to the lack of information on the atmospheric circulation in the Colombian Orinoquia. This research aims at generating new knowledge on the meteorology of this region mainly for weather forecasting and atmospheric pollution impact assessment. We present a conceptual model of the atmospheric circulation in the Colombian Orinoquia, including the main synoptic and mesoscale factors governing its meteorology. In order to identify the source of air masses and synoptic scale disturbances, we used Lagrangian back trajectories obtained with the model HYSPLIT 4.9 over the period 2000-2010. NCEP/NCAR and Global Data Assimilation System (GDAS) reanalysis results were used as meteorological input to HYSPLIT. Prior to the Lagrangian simulation, these global datasets were evaluated for their capability to reproduce meteorological observations in the region, particularly for rain and flood-triggering conditions. The observational data included satellite images and ground level network measurements by the Colombian Institute of Hydrology, Meteorology and Environmental Research (IDEAM). Windgridds and other data analysis tools were used.
A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing
Chang, Chong; Stagg, Alan K
2012-01-01
We present a Lagrangian time integration scheme and compatible discretization for total energy conservation in multicomponent mixing simulations. Mixing behavior results from relative motion between species. Species velocities are determined by solving species momentum equations in a Lagrangian manner. Included in the species momentum equations are species artificial viscosity (since each species can undergo compression) and inter-species momentum exchange. Thermal energy for each species is also solved, including compression work and thermal dissipation caused by momentum exchange. The present procedure is applicable to mixing of an arbitrary number of species that may not be in pressure or temperature equilibrium. A traditional staggered stencil has been adopted to describe motion of each species. The computational mesh for the mixture is constructed in a Lagrangian manner using the mass-averaged mixture velocity. Species momentum equations are solved at the vertices of the mesh, and temporary species meshes are constructed and advanced in time using the resulting species velocities. Following the Lagrangian step, species quantities are advected (mapped) from the species meshes to the mixture mesh. Momentum exchange between species introduces work that must be included in an energy-conserving discretization scheme. This work has to be transformed to dissipation in order to effect a net change in species thermal energy. The dissipation between interacting species pairs is obtained by combining the momentum exchange work. The dissipation is then distributed to the species involved using a distribution factor based on species specific heats. The resulting compatible discretization scheme provides total energy conservation of the whole mixture. In addition, the numerical scheme includes conservative local energy exchange between species in mixture. Due to the relatively large species interaction coefficients, both the species momenta and energies are calculated
2014-11-01
Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories by JD Clayton ARL-RP-0513...of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories JD Clayton Weapons and Materials Research Directorate, ARL...SUBTITLE Shock Compression of Metal Crystals: A Comparison of Eulerian and Lagrangian Elastic- Plastic Theories 5a. CONTRACT NUMBER 5b. GRANT
Sepúlveda-Gálvez, Alfonso; Agustín Badillo-Corona, Jesús; Chairez, Isaac
2017-03-17
Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes. In this scheme, super-twisting algorithm was proposed to recover the derivative of all the proteins and mRNA of E. coli associated to changes in the concentration of oxygen available in the growth media. The 75 identified parameters in this study maintain the biological coherence of the system and they were estimated with no more than 20% error with respect to the real ones included in the proposed model.
NASA Technical Reports Server (NTRS)
Hall, Philip; Balakumar, P.
1990-01-01
A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2014-11-01
We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
NASA Astrophysics Data System (ADS)
Sun, Zhe; Zhou, Longwen; Xiao, Gaoyang; Poletti, Dario; Gong, Jiangbin
2016-01-01
We investigate Landau-Zener processes modeled by a two-level quantum system, with its finite bias energy varied in time and in the presence of a single broadened cavity mode at zero temperature. By applying the hierarchy equation method to the Landau-Zener problem, we computationally study the survival fidelity of adiabatic states without Born, Markov, rotating-wave, or other perturbative approximations. With this treatment it also becomes possible to investigate cases with very strong system-bath coupling. Different from a previous study of infinite-time Landau-Zener processes, the fidelity of the time-evolving state as compared with instantaneous adiabatic states shows nonmonotonic dependence on the system-bath coupling and on the sweep rate of the bias. We then consider the effect of applying a counterdiabatic driving field, which is found to be useful in improving the fidelity only for sufficiently short Landau-Zener processes. Numerically exact results show that different counterdiabatic driving fields can have very different robustness against environment effects. Lastly, using a case study, we discuss the possibility of introducing a dynamical decoupling field in order to eliminate the decoherence effect of the environment and, at the same time, to retain the positive role of a counterdiabatic field. Our work indicates that finite-time Landau-Zener processes with counterdiabatic driving offer a fruitful testbed to understand controlled adiabatic processes in open systems.
NASA Astrophysics Data System (ADS)
Vinkovic, Ivana; Aguirre, Cesar; Simoëns, Serge
A large-eddy simulation (LES) with the dynamic Smagorinsky Germano subgrid scale (SGS) model is used to study the passive scalar dispersion in a turbulent boundary layer. Instead of resolving the passive scalar transport equation, fluid particles containing scalar are tracked in a Lagrangian way. The Lagrangian velocity of each fluid particle is considered to have a large-scale part (directly computed by the LES) and a small-scale part. The movement of fluid elements containing scalar at a subgrid level is given by a three-dimensional Langevin model. The stochastic model is written in terms of SGS statistics at a mesh level. The results of the LES are compared with the wind-tunnel experiments of Fackrell and Robins (1982, Journal of Fluid Mechanics, 117, 1 26) and with the LES results of Sykes and Henn (1992, Atmospheric Environment A, 26, 3127 3144), who used a completely Eulerian approach with a non-dynamic SGS model. Our simulations predict the quantitative features of the experiments of Fackrell and Robins (1982, Journal Fluid Mechanics, 117, 1 26). Moreover, by using the Lagrangian approach, scalar fluxes are computed with no additional modeling assumptions and show good agreement with the experimental data. A classic mean-gradient model of the scalar flux is calculated from the computed results. The agreement between the directly computed fluxes and the classic mean-gradient model calculation is remarkable.
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
NASA Astrophysics Data System (ADS)
Cameron, Alexandre; Raynaud, Raphaël; Dormy, Emmanuel
2016-12-01
Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \\& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.
Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver
NASA Astrophysics Data System (ADS)
Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind
2016-09-01
Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid Eulerian- Lagrangian approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.
Subedi, P.; Chhiber, R.; Tessein, J. A.; Wan, M.; Matthaeus, W. H.
2014-12-01
The Minimal Multiscale Lagrangian Mapping procedure developed in the context of neutral fluid turbulence is a simple method for generating synthetic vector fields. Using a sequence of low-pass filtered fields, fluid particles are displaced at their rms speed for some scale-dependent time interval, and then interpolated back to a regular grid. Fields produced in this way are seen to possess certain properties of real turbulence. This paper extends the technique to plasmas by taking into account the coupling between the velocity and magnetic fields. We examine several possible applications to plasma systems. One use is as initial conditions for simulations, wherein these synthetic fields may efficiently produce a strongly intermittent cascade. The intermittency properties of the synthetic fields are also compared with those of the solar wind. Finally, studies of cosmic ray transport and modulation in the test particle approximation may benefit from improved realism in synthetic fields produced in this way.
The Lagrangian particle dispersion model FLEXPART-WRF VERSION 3.1
Brioude, J.; Arnold, D.; Stohl, A.; Cassiani, M.; Morton, Don; Seibert, P.; Angevine, W. M.; Evan, S.; Dingwell, A.; Fast, Jerome D.; Easter, Richard C.; Pisso, I.; Bukhart, J.; Wotawa, G.
2013-11-01
The Lagrangian particle dispersion model FLEXPART was originally designed for cal- culating long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant. In the meantime FLEXPART has evolved into a comprehensive tool for atmospheric transport modeling and analysis at different scales. This multiscale need from the modeler community has encouraged new developments in FLEXPART. In this document, we present a version that works with the Weather Research and Forecasting (WRF) mesoscale meteoro- logical model. Simple procedures on how to run FLEXPART-WRF are presented along with special options and features that differ from its predecessor versions. In addition, test case data, the source code and visualization tools are provided to the reader as supplementary material.
High-Fidelity Lagrangian Coherent Structures Analysis and DNS with Discontinuous-Galerkin Methods
NASA Astrophysics Data System (ADS)
Nelson, Daniel Alan Wendell
High-fidelity numerical tools based on high-order Discontinuous-Galerkin (DG) methods and Lagrangian Coherent Structure (LCS) theory are developed and validated for the study of separated, vortex-dominated flows over complex geometry. The numerical framework couples prediction of separated turbulent flows using DG with time-dependent analysis of the flow through LCS and is intended for the development of separation control strategies for aerodynamic surfaces. The compressible viscous flow over a NACA 65-(1)412 airfoil is solved with a DG based Navier-Stokes solver in two and three dimensions. A method is presented in which high-order polynomial element edges adjacent to curved boundaries are matched to boundaries defined by non-smooth splines. Artificial surface roughness introduced by the piecewise-linear boundary approximation of straight-sided meshes results in the simulation of incorrect physics, including wake instabilities and spurious time-dependent modes. Spectral accuracy in the boundary approximation is not achieved for non-analytic boundary functions, particularly in high curvature regions. An algorithm is developed for the high-order computation of Finite-Time Lyapunov Exponent (FTLE) fields simultaneously and efficiently with two and three dimensional DG-based flow solvers. Fluid tracers are initialized at Gauss-Lobatto quadrature nodes within an element and form the high-order basis for a flow map at later time. Gradients of the flow map and FTLE are evaluated with DG operators. Multiple flow maps are determined from a single particle trace by remapping the flow map to the quadrature nodes on deformed mesh elements. For large integration times, excessive subdomain deformation deteriorates the interpolating conditioning. The conditioning provides information on the fluid deformation and identifies subdomains that contain LCS. An exponential filter smooths the flow map in highly deformed areas. The algorithm is tested on several benchmarks and is shown
NASA Astrophysics Data System (ADS)
Winschall, A.; Pfahl, S.; Sodemann, H.; Wernli, H.
2014-07-01
Moisture convergence from different sources is an important prerequisite for a heavy-precipitation event. The contributions from different source regions can, however, hardly be quantified from observations, and their assessment based on model results is complex. Two conceptually different numerical methods are widely used for the quantification of moisture sources: Lagrangian approaches based on the analysis of humidity variations along backward trajectories and Eulerian methods based on the implementation of moisture tracers into a numerical model. In this study the moisture sources for a high-impact, heavy-precipitation event that affected eastern Europe in May 2010 are studied with both Eulerian and Lagrangian moisture source diagnostics. The precipitation event was connected to a cyclone that developed over northern Africa, moved over the Mediterranean towards eastern Europe and induced transport of moist air towards the Carpathian Mountains. Heavy precipitation and major flooding occurred in Poland, the Czech Republic and Slovakia between 16 and 18 May 2010. The Lagrangian and Eulerian diagnostics consistently indicate a wide spatial and temporal range of moisture sources contributing to the event. The source with the largest share is local evapotranspiration from the European land surface, followed by moisture from the North Atlantic. Further contributions come from tropical western Africa (10-20° N) and the Mediterranean Sea. Contrary to what could be expected, the Mediterranean contribution of about 10% is relatively small. A detailed analysis of exemplary trajectories corroborates the general consistency of the two approaches, and underlines their complementarity. The Lagrangian method allows for mapping out moisture source regions with computational efficiency, whereas the more elaborate Eulerian model requires predefined moisture sources, but includes also processes such as precipitation, evaporation and turbulent mixing. However, in the Eulerian model
Lagrangian modelling of turbulent spray combustion under liquid rocket engine conditions
NASA Astrophysics Data System (ADS)
Gomet, Laurent; Robin, Vincent; Mura, Arnaud
2014-01-01
In the field of liquid rocket propulsion, the use of computational design tools, such as computational fluid dynamics (CFD) solvers, may provide a great deal of help to proceed with the primary design choice. Considering the complexity of rocket engine geometries, as well as associated fluid flow conditions, the use of Reynolds-Averaged Navier-Stokes (RANS) numerical simulations remains very popular. Important modelling efforts are therefore still required to provide reliable computational models able to describe the complex interaction that takes place between turbulence and chemistry in such cryogenic high-speed flows. The present manuscript reports the results of some recent investigations conducted in this field. The modelling analysis relies on a Lagrangian framework, the salient features of which consist in approximating the Lagrangian path in a reduced composition space made up of the mixture fraction variable, i.e. a conserved scalar introduced to represent the variations of composition, and a progress variable, i.e. a reactive scalar to follow the departures from chemical equilibrium. The retained methodology allows to presume the joint probability density function of the two scalar fields without invoking the assumption of statistical independence between them. Equivalence ratio fluctuations induced by the vaporization of the liquid phase are considered as additional sources terms appearing in the transport equation of the mixture fraction variance. The transport of the corresponding mean scalar dissipation rate (SDR), which is a key quantity in the corresponding closure, is also affected by the vaporization processes. The proposed model has been implemented into the U-RANS CFD code N3S_Natur, while the liquid phase is described using a Lagrangian module. The capabilities of the computation model are evaluated through a detailed comparison with the experimental databases gathered on the ONERA Mascotte test bench. The corresponding test rig consists of a
Chiral Lagrangian for baryons in the 1/Nc expansion
NASA Astrophysics Data System (ADS)
Jenkins, Elizabeth
1996-03-01
A 1/Nc expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet π, K, η, and η' in a combined expansion in chiral symmetry breaking and 1/Nc. Strong CP violation is included. The chiral Lagrangian correctly implements nonet symmetry and contracted spin-flavor symmetry for baryons in the large Nc limit. The implications of nonet symmetry for low-energy baryon-pion interactions are described in detail. The procedure for calculating nonanalytic pion-loop corrections to baryon amplitudes in the 1/Nc expansion for finite Nc is explained. Flavor-27 baryon mass splittings are calculated at leading order in chiral perturbation theory as an example.
A non-conventional discontinuous Lagrangian for viscous flow
Marner, F.
2017-01-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415
Lagrangian Frequency Spectrum as a Diagnostic for Magnetohydrodynamic Turbulence Dynamics
Busse, Angela; Mueller, Wolf-Christian; Gogoberidze, Grigol
2010-12-03
For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations {tau}{sub ac} and the associated cascade time scale {tau}{sub cas}. Thus, the Lagrangian energy spectrum can serve to identify weak ({tau}{sub ac}<<{tau}{sub cas}) and strong ({tau}{sub ac{approx}{tau}cas}) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.
On singular Lagrangian underlying the Schrödinger equation
NASA Astrophysics Data System (ADS)
Deriglazov, A. A.
2009-10-01
We analyze the properties that manifest Hamiltonian nature of the Schrödinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian formulation). It is used to show that any solution of the Schrödinger equation with time independent potential can be presented in the form Ψ=(-ℏ/2m Δ+V)ϕ+iℏ∂ϕ, where the real field ϕ(t,x) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field ϕ. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
NASA Astrophysics Data System (ADS)
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
A non-conventional discontinuous Lagrangian for viscous flow
NASA Astrophysics Data System (ADS)
Scholle, M.; Marner, F.
2017-02-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
Lagrangian space consistency relation for large scale structure
Horn, Bart; Hui, Lam; Xiao, Xiao E-mail: lh399@columbia.edu
2015-09-01
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias and Riotto and Peloso and Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.
Second order upwind Lagrangian particle method for Euler equations
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
2016-06-01
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.
Second order upwind Lagrangian particle method for Euler equations
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
2016-06-01
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Singular Lorentz-violating Lagrangians and associated Finsler structures
NASA Astrophysics Data System (ADS)
Colladay, Don; McDonald, Patrick
2015-10-01
Several Lagrangians associated with classical limits of Lorentz-violating fermions in the standard model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin couplings are present, the Lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive-definite quadratic form defined on a desingularized variety.
A Lagrangian stochastic model of surf zone drifter dispersion
NASA Astrophysics Data System (ADS)
Spydell, Matthew S.; Feddersen, Falk
2012-03-01
Drifter-derived cross-shore and alongshore surf zone diffusivities were previously estimated on an alongshore uniform beach over 1000 s for five Huntington Beach, California, 2006 (HB06) experiment release days. The cross-shore diffusivity Kx had a nonmonotonic time dependence, potentially due to the shoreline or to weaker diffusivity seaward of the surf zone. The alongshore diffusivities Ky were qualitatively consistent with shear dispersion but differed from the classic Taylor laminar theory. Here, modeled and analytic diffusivities for the five release days are derived from a Lagrangian stochastic model (LSM) that uses the drifter-derived bulk (cross-shore averaged) velocity variance and cross-shore-dependent mean alongshore current. The LSM modeled and analytic cross-shore diffusivities are nonmonotonic due to the shoreline and strongly suggest that the observed cross-shore diffusivity is shoreline affected. The LSM typically reproduce well the observed Kx with Lagrangian time scale between 75 and 200 s, consistent with surf zone eddy time scales. HB06 drifter trajectories were too short to observe the analytic long-time Kx limit, and weaker diffusivity seaward of the surf zone may be important at longer times (>1000 s). On all release days, the LSM model and analytic alongshore diffusivity reproduce well the observed Ky with alongshore Lagrangian time scales between 95 and 155 s. The isolated shear-induced diffusivity is very well represented by an analytic theory which incorporates a nonzero Lagrangian time scale. Many of the stochastic model parameters can be specified a priori with reasonable assumptions to predict surf zone dispersion of an initial value problem pollution spill.
A semi-Lagrangian approach to the shallow water equation
NASA Technical Reports Server (NTRS)
Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad
1993-01-01
We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.
Solitary waves in a Skyrmion-quark Lagrangian
NASA Astrophysics Data System (ADS)
Kälbermann, G.
1986-04-01
We investigate nontopological solitary wave solutions of a Skyrmion-quark Lagrangian. The quark wave functions are of the hedgehog type and the chiral angle corresponding to the classical pionic field goes to zero both at the origin and infinity. The Skyrme parameter is varied and nontopological solutions are found in a restricted range of values. The mass of the system is calculated and explicit solutions are shown for nodeless quark wave functions. The properties of the states are investigated.
Strong WW scattering chiral lagrangians, unitarity and resonances
Pelaez, J.R.
1996-08-01
Chiral lagrangians provide a model independent description of the strongly interacting symmetry breaking sector. In this work, first we review the LHC sensitivity to the chiral parameters (in the hardest case of non-resonant low-energy WW scattering). Later we show how to reproduce or predict the resonance spectrum by means of dispersion theory and the inverse amplitude method. We present a parameter space scan that covers many different strong WW scattering scenarios.
Accelerated augmented Lagrangian method for few-view CT reconstruction
NASA Astrophysics Data System (ADS)
Wu, Junfeng; Mou, Xuanqin
2012-03-01
Recently iterative reconstruction algorithms with total variation (TV) regularization have shown its tremendous power in image reconstruction from few-view projection data, but it is much more demanding in computation. In this paper, we propose an accelerated augmented Lagrangian method (ALM) for few-view CT reconstruction with total variation regularization. Experimental phantom results demonstrate that the proposed method not only reconstruct high quality image from few-view projection data but also converge fast to the optimal solution.
Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact
2015-03-01
Lagrangian marker method to ballistic impact problems relevant to defense applications. impact, penetration, plasticity , fracture, computer...shown in Eqs. 2 and 3 provides a representa- tion of the dynamic yield strength of metals as a function of equivalent plastic strain (εp), plastic ...and body- 3 centered-cubic (bcc) metals and takes the general form of Eq. 4, in which εp is the equivalent plastic strain, ε̇p is the plastic strain
Tsunami intrusion in wide meandering channels: a Lagrangian numerical experiment
NASA Astrophysics Data System (ADS)
Couston, L. A.; Alam, M. R.
2015-12-01
Among the many difficulties of tsunami forecast, wave runup on sloped beaches remains a major obstacle in numerical simulations. Traditional Eulerian models must adjust the fluid flow domain continuously due to the moving shorelines, which can significantly affect the computational cost and results accuracy. An efficient though uncommon alternative for accurate runup predictions still exists, consisting in using a Lagrangian model as recently shown by e.g. Couston et al. (2015) who studied the runup of landslide tsunamis in lakes with a non-dispersive Lagrangian model. Here we introduce a fully-nonlinear Boussinesq-type model derived in the Lagrangian framework to investigate various cases of long-wave runup on curved beaches and meandering channels. The governing equations are expressed in terms of curvilinear Lagrangian coordinates, making the model suitable for accurate runup computations at shorelines of arbitrary geometry while retaining the inherent simplicity of a physical model discretized on a fixed and structured grid. We implement an elliptic grid generation algorithm to map the physical space to the computational space, and a high-order finite-difference scheme for time integration. The numerical model has a linear complexity in the number of unknowns when neglecting dispersive effects. We show that the formation of edge waves due to the sloped banks of a wide channel has a significant influence on the capability of a meander or constriction in reflecting the intruding tsunami, and we investigate the effect of dispersion. Reference: Couston, L.-A., Mei, C. C., & Alam, M.-R. (2015). Landslide tsunamis in lakes. Journal of Fluid Mechanics, 772, 784-804.
Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
NASA Astrophysics Data System (ADS)
Montenegro, David; Torrieri, Giorgio
2016-09-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear dissipation forces the inclusion of the Israel-Stewart term into the theory, thereby providing an additional justification for the form of this term.
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
Suk, Heejun
2016-07-01
MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices
NASA Astrophysics Data System (ADS)
Huhn, F.; van Rees, W. M.; Gazzola, M.; Rossinelli, D.; Haller, G.; Koumoutsakos, P.
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
NASA Astrophysics Data System (ADS)
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-11-01
Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Ruiz, D. E.; Dodin, I. Y.
2015-07-29
Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an (N^{2} - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Ruiz, D. E.; Dodin, I. Y.
2015-07-29
Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less
Variational Lagrangian data assimilation in open channel networks
NASA Astrophysics Data System (ADS)
Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.
2015-04-01
This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of Lagrangian data, a time series of positions as the sensors moved through the water. Measurements were also taken from Eulerian sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate Lagrangian and Eulerian measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.
Charnoz, Sebastien; Aleon, Jerome
2011-08-10
In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study here the dust-diffusive transport using Lagrangian numerical simulations using the popular 'turbulent diffusion' formalism. However, it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. We present a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form that overcomes these difficulties. We show that a net diffusive flux F of the dust appears and that it is proportional to the gas density ({rho}) gradient and the dust diffusion coefficient D{sub d}: (F = D{sub d} /{rho} x grad({rho})). It induces an inward transport of dust in the disk's midplane, while favoring outward transport in the disk's upper layers. We present tests and applications comparing dust diffusion in the midplane and upper layers as well as sample trajectories of particles with different sizes. We also discuss potential applications for cosmochemistry and smoothed particle hydrodynamic codes.
NASA Astrophysics Data System (ADS)
Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Dlugokencky, E. J.; Tans, P. P.; Maksyutov, S. S.
2013-12-01
Global monthly CO2 flux distributions for 2001-2011 were estimated using an atmospheric inverse modeling system, which is based on combination of two transport models, called GELCA (Global Eulerian-Lagrangian Coupled Atmospheric model). This coupled model approach has several advantages over inversions to a single model alone: the use of Lagrangian particle dispersion model (LPDM) to simulate the transport in the vicinity of the observation points enables us to avoid numerical diffusion of Eulerian models, and is suitable to represent observations at high spatial and temporal resolutions. The global background concentration field generated by an Eulerian model is used as time-variant boundary conditions for an LPDM that performs backward simulations from each receptor point (observation event). In the GELCA inversion system, National Institute for Environmental Studies-Transport Model (NIES-TM) version 8.1i was used as an Eulerian global transport model coupled with FLEXPART version 8.0 as an LPDM. The meteorological fields for driving both models were taken from JMA Climate Data Assimilation System (JCDAS) with a spatial resolution of 1.25° x 1.25°, 40 vertical levels and a temporal resolution of 6 hours. Our prior CO2 fluxes consist of daily terrestrial biospheric fluxes, monthly oceanic fluxes, monthly biomass burning emissions, and monthly fossil fuel CO2 emissions. We employed a Kalman Smoother optimization technique with fixed lag of 3 months, estimating monthly CO2 fluxes for 42 land and 22 ocean regions. We have been using two different global networks of CO2 observations. The Observation Package (ObsPack) data products contain more measurement information in space and time than the NOAA global cooperative air sampling network which basically consists of approximately weekly sampling at background sites. The global total flux and its large-scale distribution optimized with two different global observation networks agreed overall with other previous
Differential geometry based solvation model II: Lagrangian formulation
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-01-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Lagrangian-based Backtracking of Oil Spill Dynamics from SAR Images: Application to Montara Case
NASA Astrophysics Data System (ADS)
Gautama, Budhi Gunadharma; Mercier, Gregoire; Fablet, Ronan; Longepe, Nicolas
2016-08-01
Within the framework of INDESO project (Infrastructure Development Space Oceanography), we address the issue of oilspill and aim at developing an operational SAR- based system for monitoring this issue in Indonesian waters from space. In this work, we focus on the backtrack- ing of an oilspill detected from SAR observations. As a case-study, we consider one large oil spill event that happened in Indonesian waters in 2009, referred to as the Montara oilspill. On 21 August 2009, the Montara Wellhead Platform had an uncontrolled release of hydrocarbons from one of the platform wells. It was estimated that 400 barrels (or approximately 64 tonnes) of crude oil were being lost per day. The uncontrolled release continued until 3 November 2009 and response operations continued until 3 December 2009. In this work, we develop a Langragian analysis and associated numerical inversion tools with a view to further analyzing the oil spread due to the Montara Wellhead Platform. Our model relies on a 2D Lagrangian transport model developed by CLS (Collecte Localisation Satellite). Our model involves four main parameters : the weights of wind- related and current-related advection, the origin and the duration of the oil leakage. Given SAR oilspill detections, we propose a numerical inversion of the parameters of the Lagrangian model, so that the simulated drift match the SAR observations of the oil spill. We demonstrate the relevance of the proposed model and numerical scheme for the Montara oilspill and further discuss their operational interest for the space-based oilspill backtracking and forecasting.
NASA Astrophysics Data System (ADS)
Vérèmes, H.; Cammas, J.-P.; Baray, J.-L.; Keckhut, P.; Barthe, C.; Posny, F.; Tulet, P.; Dionisi, D.; Bielli, S.
2016-12-01
Signatures of multiple stratospheric intrusions were observed on simultaneous and collocated ozone and water vapor profiles retrieved by lidars and radiosondes at the Maïdo Observatory, Reunion Island (21°S, 55°E, 2160 m above sea level), during MAïdo LIdar Calibration CAmpaign in April 2013. A singular structure of the ozone vertical profile with three peaks (in excess of 90 ppbv, at 8, 10, and 13 km altitude) embedded in a thick dry layer of air suggested stratospheric intrusions with multiple origins. The hypothesis is corroborated by a synoptic analysis based on re-analyses. European Centre for Medium-Range Weather Forecasts ERA-Interim temporal series associated with 5 days Lagrangian back trajectories initialized on each ozone peak allows to capture their stratospheric origin. The ozone peak at the lowest altitude is associated with an irreversible tropopause folding process along the polar jet stream during an extratropical cutoff low formation. Simultaneous lidar water vapor profiles of this peak show that the anticorrelation with ozone has been removed, due to mixing processes. Back trajectories indicate that the two other ozone peaks observed at higher altitudes are associated with the dynamics of the subtropical jet stream and the lower stratosphere. The observations confirm the recent stratospheric origins. The highest ozone peak is explained by the horizontal distribution of the intrusion. Use of a Lagrangian Reverse Domain Filling model and of the Meso-NH Eulerian mesoscale model with a passive stratospheric tracer allow to further document the stratosphere-troposphere transport processes and to describe the detailed potential vorticity and ozone structures in which are embedded in the observed multiple stratospheric intrusions.
A macroscopic plasma Lagrangian and its application to wave interactions and resonances
NASA Technical Reports Server (NTRS)
Peng, Y. K. M.
1974-01-01
The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-01-01
Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.
Effective Lagrangians and Current Algebra in Three Dimensions
NASA Astrophysics Data System (ADS)
Ferretti, Gabriele
In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.
A Lagrangian fluctuation-dissipation relation for scalar turbulence
NASA Astrophysics Data System (ADS)
Drivas, Theodore; Eyink, Gregory
2016-11-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation but simple examples show that a distinct mechanism of non-vanishing dissipation can be thin scalar boundary layers near the walls. As an example, we consider turbulent Rayleigh-Benard convection. We here obtain an exact relation between steady-state thermal dissipation and the time for diffusive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an "ultimate regime" of turbulent convection as predicted by Kraichnan (1962) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the large-scale circulation time.
Lagrangian chaos and small scale structure of passive scalars
NASA Astrophysics Data System (ADS)
Vulpiani, Angelo
1989-09-01
We revise the classical theory of Batchelor, which gives a k-1 law for the power spectrum of a passive scalar at wavenumbers k, for which the molecular diffusion is unimportant and much smaller than the fluid viscosity. Using some ideas borrowed from the theory of dynamical systems, we show that this power law is related to the chaotic motion of marker particles (Lagrangian chaos) and to the incompressibility constraint. Moreover our approach permits showing that the k-1 regime is present in fluids which are not turbulent and it is valid for all dimensionalities d⩾2.
k Spectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows
NASA Astrophysics Data System (ADS)
Antonsen, Thomas M., Jr.; Fan, Zhencan Frank; Ott, Edward
1995-08-01
An eikonal-type description for the evolution of k spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar k spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law k spectrum and its diffusive cutoff.