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Sample records for hamiltonian efficient numerical

  1. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

    Science.gov (United States)

    Bridges, Thomas J.; Reich, Sebastian

    2001-06-01

    The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

  2. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    Energy Technology Data Exchange (ETDEWEB)

    Habib, K. M. Masum, E-mail: masum.habib@virginia.edu; Ghosh, Avik W. [Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904 (United States); Sajjad, Redwan N. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

    2016-03-14

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  3. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    International Nuclear Information System (INIS)

    Habib, K. M. Masum; Ghosh, Avik W.; Sajjad, Redwan N.

    2016-01-01

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  4. Numerical determination of the magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Kuo-Petravic, G.; Boozer, A.H.

    1986-03-01

    The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories

  5. Numerical Investigations of Post-Newtonian Hamiltonian Dynamics for Spinning Compact Binaries

    Science.gov (United States)

    Zhong, S. Y.

    2012-03-01

    Spinning compact binaries, consisting of neutron stars or black holes, not only have rich dynamic phenomena of resonance and chaos, but also are the most promising source for detecting gravitational waves. There should be a certain relation between the dynamics of the gravitational bodies and the gravitational waveforms. Based on the least-squares correction, several manifold correction schemes like the single-scaling method and the dual-scaling method are designed to suppress numerical errors from 6 integrals of motion in a conservative post-Newtonian (PN) Hamiltonian of spinning compact binaries. Taking a fifth order Runge-Kutta algorithm as a basic integrator, we wonder whether the PN contributions, the spin effects, and the classification of orbits exert some influences on these correction schemes and the Nacozy's approach. It is found that they are almost the same in correcting the integrals for the pure Kepler problem. Once the third-order PN contributions are added to the pure orbital part, there are explicit differences of correction effectiveness among these methods. As an interesting case, the efficiency of correction is better for chaotic eccentric orbits than for quasicircular regular ones. In all cases tested, the new momentum-position dual-scaling scheme does always have the optimal performance. It costs a little but not much expensive additional computational cost when the spin effects exist, and several time-saving techniques are used. The corrected numerical results are more accurate than the uncorrected ones, so that chaos from the numerical errors can be avoided. See Phys. Rev. D 81, 104037 (2010) for more details. Lubich et al. (Phys. Rev. D 81, 104025 (2010)) presented a noncanonically symplectic integrator for the PN Hamiltonian of a spinning compact binary. However, the Euler mixed integrator is problematic because of its bad numerical stability.We improved the work by constructing the second-order and the fourth-order fixed symplectic

  6. Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system

    Science.gov (United States)

    Barrabés, E.; Mondelo, J. M.; Ollé, M.

    2013-10-01

    This paper is devoted to the numerical computation and continuation of families of heteroclinic connections between hyperbolic periodic orbits (POs) of a Hamiltonian system. We describe a method that requires the numerical continuation of a nonlinear system that involves the initial conditions of the two POs, the linear approximations of the corresponding manifolds and a point in a given Poincaré section where the unstable and stable manifolds match. The method is applied to compute families of heteroclinic orbits between planar Lyapunov POs around the collinear equilibrium points of the restricted three-body problem in different scenarios. In one of them, for the Sun-Jupiter mass parameter, we provide energy ranges for which the transition between different resonances is possible.

  7. Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

    Science.gov (United States)

    Schaffer, L.; Burns, J. A.

    1994-01-01

    We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

  8. NON-HAMILTONIAN QUANTUM MECHANICS AND THE NUMERICAL RESEARCHES OF THE ATTRACTOR OF A DYNAMICAL SYSTEM.

    Directory of Open Access Journals (Sweden)

    A. Weissblut

    2012-03-01

    Full Text Available This article – introduction to the structural theory of general view dynamical systems, based on construction of dynamic quantum models (DQM, offered by the author. This model is simply connected with traditional model of quantum mechanics (i.e. with the Schrodinger equation. At the same time obtained thus non – Hamiltonian quantum dynamics is easier than classical one: it allow building the clear structural theory and effective algorithms of research for concrete systems. This article is devoted mainly to such task. The algorithm of search for DQM attractors, based on this approach, is offered here.

  9. Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

    International Nuclear Information System (INIS)

    Kaneko, Yuta; Yoshida, Zensho

    2014-01-01

    Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term −ΔQ, just representing the current density (Q is a Clebsch variable, and Δ is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated

  10. Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

    International Nuclear Information System (INIS)

    Houfek, Karel

    2008-01-01

    Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

  11. Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field

    Science.gov (United States)

    Ohkitani, K.

    2010-05-01

    We study some of the key quantities arising in the theory of [Arnold "Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Annales de l'institut Fourier 16, 319 (1966)] of the incompressible Euler equations both in two and three dimensions. The sectional curvatures for the Taylor-Green vortex and the ABC flow initial conditions are calculated exactly in three dimensions. We trace the time evolution of the Jacobi fields by direct numerical simulations and, in particular, see how the sectional curvatures get more and more negative in time. The spatial structure of the Jacobi fields is compared to the vorticity fields by visualizations. The Jacobi fields are found to grow exponentially in time for the flows with negative sectional curvatures. In two dimensions, a family of initial data proposed by Arnold (1966) is considered. The sectional curvature is observed to change its sign quickly even if it starts from a positive value. The Jacobi field is shown to be correlated with the passive scalar gradient in spatial structure. On the basis of Rouchon's physical-space based expression for the sectional curvature (1984), the origin of negative curvature is investigated. It is found that a "potential" αξ appearing in the definition of covariant time derivative plays an important role, in that a rapid growth in its gradient makes a major contribution to the negative curvature.

  12. Numerical prediction of Pelton turbine efficiency

    Energy Technology Data Exchange (ETDEWEB)

    Jott, D; Mez' nar, P; Lipej, A, E-mail: dragicajost@turboinstitut.s [Turbointtitut, Rovtnikova 7, Ljubljana, 1210 (Slovenia)

    2010-08-15

    This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-{omega} SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

  13. Numerical prediction of Pelton turbine efficiency

    Science.gov (United States)

    Jošt, D.; Mežnar, P.; Lipej, A.

    2010-08-01

    This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

  14. Numerical prediction of Pelton turbine efficiency

    International Nuclear Information System (INIS)

    Jott, D; Mez'nar, P; Lipej, A

    2010-01-01

    This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

  15. Efficient Numerical Simulation of Aerothermoelastic Hypersonic Vehicles

    Science.gov (United States)

    Klock, Ryan J.

    speed and overall solution fidelity. A number of enhancements to this framework are made through 1. the implementation of a publish-subscribe code architecture for rapid prototyping of physics and process models. 2. the implementation of a selection of linearization and model identification methods including high-order pseudo-time forward difference, complex-step, and direct identification from ordinary differential equation inspection. 3. improvements to the aeroheating and thermal models with non-equilibrium gas dynamics and generalized temperature dependent material thermal properties. A variety of model reduction and surrogate model techniques are applied to a representative hypersonic vehicle on a terminal trajectory to enable complete aerothermoelastic flight simulations. Multiple terminal trajectories of various starting altitudes and Mach numbers are optimized to maximize final kinetic energy of the vehicle upon reaching the surface. Surrogate models are compared to represent the variation of material thermal properties with temperature. A new method is developed and shown to be both accurate and computationally efficient. While the numerically efficient simulation of high-speed vehicles is developed within the presented framework, the goal of real time simulation is hampered by the necessity of multiple nested convergence loops. An alternative all-in-one surrogate model method is developed based on singular-value decomposition and regression that is near real time. Finally, the aeroelastic stability of pressurized cylindrical shells is investigated in the context of a maneuvering axisymmetric high-speed vehicle. Moderate internal pressurization is numerically shown to decrease stability, as showed experimentally in the literature, yet not well reproduced analytically. Insights are drawn from time simulation results and used to inform approaches for future vehicle model development.

  16. Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

    OpenAIRE

    Kaneko, Yuta; Yoshida, Zensho

    2014-01-01

    Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensi...

  17. Numerical calculation of particle collection efficiency in an ...

    Indian Academy of Sciences (India)

    Theoretical and numerical research has been previously done on ESPs to predict the efficiency ... Lagrangian simulations of particle transport in wire–plate ESP were .... The collection efficiency can be defined as the ratio of the number of ...

  18. Power and thermal efficient numerical processing

    DEFF Research Database (Denmark)

    Liu, Wei; Nannarelli, Alberto

    2015-01-01

    Numerical processing is at the core of applications in many areas ranging from scientific and engineering calculations to financial computing. These applications are usually executed on large servers or supercomputers to exploit their high speed, high level of parallelism and high bandwidth...

  19. Lagrangian and Hamiltonian dynamics

    CERN Document Server

    Mann, Peter

    2018-01-01

    An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...

  20. Numerical aspects for efficient welding computational mechanics

    Directory of Open Access Journals (Sweden)

    Aburuga Tarek Kh.S.

    2014-01-01

    Full Text Available The effect of the residual stresses and strains is one of the most important parameter in the structure integrity assessment. A finite element model is constructed in order to simulate the multi passes mismatched submerged arc welding SAW which used in the welded tensile test specimen. Sequentially coupled thermal mechanical analysis is done by using ABAQUS software for calculating the residual stresses and distortion due to welding. In this work, three main issues were studied in order to reduce the time consuming during welding simulation which is the major problem in the computational welding mechanics (CWM. The first issue is dimensionality of the problem. Both two- and three-dimensional models are constructed for the same analysis type, shell element for two dimension simulation shows good performance comparing with brick element. The conventional method to calculate residual stress is by using implicit scheme that because of the welding and cooling time is relatively high. In this work, the author shows that it could use the explicit scheme with the mass scaling technique, and time consuming during the analysis will be reduced very efficiently. By using this new technique, it will be possible to simulate relatively large three dimensional structures.

  1. Hamiltonian ABC

    NARCIS (Netherlands)

    Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.

    2015-01-01

    Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of

  2. Discrete variational Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Lall, S; West, M

    2006-01-01

    The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms

  3. Hamiltonian dynamics

    CERN Document Server

    Vilasi, Gaetano

    2001-01-01

    This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m

  4. Java technology for implementing efficient numerical analysis in intranet

    International Nuclear Information System (INIS)

    Song, Hee Yong; Ko, Sung Ho

    2001-01-01

    This paper introduces some useful Java technologies for utilizing the internet in numerical analysis, and suggests one architecture performing efficient numerical analysis in the intranet by using them. The present work has verified it's possibility by implementing some parts of this architecture with two easy examples. One is based on Servlet-Applet communication, JDBC and swing. The other is adding multi-threads, file transfer and Java remote method invocation to the former. Through this work it has been intended to make the base for the later advanced and practical research that will include efficiency estimates of this architecture and deal with advanced load balancing

  5. Empirical Hamiltonians

    International Nuclear Information System (INIS)

    Peggs, S.; Talman, R.

    1987-01-01

    As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases

  6. Complex Hamiltonian Dynamics

    CERN Document Server

    Bountis, Tassos

    2012-01-01

    This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.  The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...

  7. Numerical conversion efficiency of thermally isolated Seebeck nanoantennas

    Directory of Open Access Journals (Sweden)

    Edgar Briones

    2016-11-01

    Full Text Available In this letter, we evaluate the conversion efficiency of thermally isolated Seebeck nanoantennas by numerical simulations and discuss their uses and scope for energy harvesting applications. This analysis includes the simple case of titanium-nickel dipoles suspended in air above the substrate by a 200 nm silicon dioxide membrane to isolate the heat dissipation. Results show that substantially thermal gradients are induced along the devices leading to a harvesting efficiency around 10-4 %, 400 % higher than the previously reported Seebeck nanoantennas. In the light of these results, different optimizing strategies should be considered in order to make the Seebeck nanoantennas useful for harvesting applications.

  8. Efficient numerical simulations of many-body localized systems

    Energy Technology Data Exchange (ETDEWEB)

    Pollmann, Frank [Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden (Germany); Khemani, Vedika; Sondhi, Shivaji [Physics Department, Princeton University, Princeton, NJ 08544 (United States)

    2016-07-01

    Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new, efficient numerical methods to find highly excited eigenstates is essential. We introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate-large disorder. This method explicitly takes advantage of the local spatial structure characterizing MBL eigenstates.

  9. Numerical study of particle capture efficiency in fibrous filter

    Directory of Open Access Journals (Sweden)

    Fan Jianhua

    2017-01-01

    Full Text Available Numerical simulations are performed for transport and deposition of particles over a fixed obstacle in a fluid flow. The effect of particle size and Stokes number on the particle capture efficiency is investigated using two methods. The first one is one-way coupling combining Lattice Boltzmann (LB method with Lagrangian point-like approach. The second one is two-way coupling based on the coupling between Lattice Boltzmann method and discrete element (DE method, which consider the particle influence on the fluid. Then the single fiber collection efficiency characterized by Stokes number (St are simulated by LB-DE methods. Results show that two-way coupling method is more appropriate in our case for particles larger than 8 μm. A good agreement has also been observed between our simulation results and existing correlations for single fiber collection efficiency. The numerical simulations presented in this work are useful to understand the particle transport and deposition and to predict the capture efficiency.

  10. Efficient numerical method for district heating system hydraulics

    International Nuclear Information System (INIS)

    Stevanovic, Vladimir D.; Prica, Sanja; Maslovaric, Blazenka; Zivkovic, Branislav; Nikodijevic, Srdjan

    2007-01-01

    An efficient method for numerical simulation and analyses of the steady state hydraulics of complex pipeline networks is presented. It is based on the loop model of the network and the method of square roots for solving the system of linear equations. The procedure is presented in the comprehensive mathematical form that could be straightforwardly programmed into a computer code. An application of the method to energy efficiency analyses of a real complex district heating system is demonstrated. The obtained results show a potential for electricity savings in pumps operation. It is shown that the method is considerably more effective than the standard Hardy Cross method still widely used in engineering practice. Because of the ease of implementation and high efficiency, the method presented in this paper is recommended for hydraulic steady state calculations of complex networks

  11. Interleaved numerical renormalization group as an efficient multiband impurity solver

    Science.gov (United States)

    Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.

    2016-06-01

    Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

  12. Efficient numerical solution to vacuum decay with many fields

    Energy Technology Data Exchange (ETDEWEB)

    Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

    2017-01-01

    Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

  13. A Numerical and Experimental Study of Local Exhaust Capture Efficiency

    DEFF Research Database (Denmark)

    Madsen, U.; Breum, N. O.; Nielsen, Peter Vilhelm

    1993-01-01

    Direct capture efficiency of a local exhaust system is defined by introducing an imaginary control box surrounding the contaminant source and the exhaust opening. The imaginary box makes it possible to distinguish between contaminants directly captured and those that escape. Two methods for estim...... location is less important for the case studied. The choice of sampling strategy to obtain a representative background concentration is essential as substantial differences on direct capture efficiency are found. Recommendations are given......Direct capture efficiency of a local exhaust system is defined by introducing an imaginary control box surrounding the contaminant source and the exhaust opening. The imaginary box makes it possible to distinguish between contaminants directly captured and those that escape. Two methods...... for estimation of direct capture efficiency are given: (1) a numerical method based on the time-averaged Navier-Stokes equations for turbulent flows; and (2) a field method based on a representative background concentration. Direct capture efficiency is sensitive to the size of the control box, whereas its...

  14. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1981-11-01

    A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions

  15. Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows

    Science.gov (United States)

    Moitra, Stuti; Gatski, Thomas B.

    1997-01-01

    A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.

  16. Flow Structures and Efficiency of Swimming Fish school: Numerical Study

    Science.gov (United States)

    Yatagai, Yuzuru; Hattori, Yuji

    2013-11-01

    The flow structure and energy-saving mechanism in fish school is numerically investigated by using the volume penalization method. We calculate the various patterns of configuration of fishes and investigate the relation between spatial arrangement and the performance of fish. It is found that the down-stream fish gains a hydrodynamic advantage from the upstream wake shed by the upstream fish. The most efficient configuration is that the downstream fish is placed in the wake. It reduces the drag force of the downstream fish in comparison with that in solo swimming.

  17. Optimal control methods for rapidly time-varying Hamiltonians

    International Nuclear Information System (INIS)

    Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.

    2011-01-01

    In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.

  18. Efficient numerical simulation of heat storage in subsurface georeservoirs

    Science.gov (United States)

    Boockmeyer, A.; Bauer, S.

    2015-12-01

    The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and

  19. Nested Sampling with Constrained Hamiltonian Monte Carlo

    OpenAIRE

    Betancourt, M. J.

    2010-01-01

    Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.

  20. Hamiltonian Algorithm Sound Synthesis

    OpenAIRE

    大矢, 健一

    2013-01-01

    Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

  1. Contact Hamiltonian mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

    2017-01-15

    In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

  2. Robust online Hamiltonian learning

    International Nuclear Information System (INIS)

    Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G

    2012-01-01

    In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)

  3. Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning

    Science.gov (United States)

    Bradley, Ben K.

    Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and

  4. Hamiltonian closures in fluid models for plasmas

    Science.gov (United States)

    Tassi, Emanuele

    2017-11-01

    This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

  5. Spectral and resonance properties of the Smilansky Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)

    2017-02-26

    We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.

  6. Witnessing eigenstates for quantum simulation of Hamiltonian spectra

    Science.gov (United States)

    Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

    2018-01-01

    The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796

  7. Renormalization of Hamiltonian QCD

    International Nuclear Information System (INIS)

    Andrasi, A.; Taylor, John C.

    2009-01-01

    We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

  8. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-03-01

    The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

  9. Geometry of Hamiltonian chaos

    DEFF Research Database (Denmark)

    Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

    2007-01-01

    The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

  10. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1985-02-01

    The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined

  11. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  12. Diagonalization of Hamiltonian; Diagonalization of Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Garrido, L M; Pascual, P

    1960-07-01

    We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.

  13. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

    KAUST Repository

    Happola, Juho

    2017-09-19

    Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

  14. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

    KAUST Repository

    Happola, Juho

    2017-01-01

    Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

  15. Energy efficient process planning based on numerical simulations

    OpenAIRE

    Neugebauer, Reimund; Hochmuth, C.; Schmidt, G.; Dix, M.

    2011-01-01

    The main goal of energy-efficient manufacturing is to generate products with maximum value-added at minimum energy consumption. To this end, in metal cutting processes, it is necessary to reduce the specific cutting energy while, at the same time, precision requirements have to be ensured. Precision is critical in metal cutting processes because they often constitute the final stages of metalworking chains. This paper presents a method for the planning of energy-efficient machining processes ...

  16. Efficient approximation of random fields for numerical applications

    KAUST Repository

    Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus

    2015-01-01

    We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

  17. Numerical analyses for efficient photoionization by nonmonochromatic fields

    International Nuclear Information System (INIS)

    Hasegawa, Shuichi; Suzuki, Atsuyuki

    2000-01-01

    Numerical analyses on excitation and ionization probabilities of atoms with hyperfine structures were performed in order to compare two different excitation methods, adiabatic excitation and broadband excitation. The lifetime of the intermediate states was considered in order to investigate the effect of the absorption line broadening. The dependences of the two excitation methods on the lifetime were found to be quite different. The ionization probability by the adiabatic excitation is higher than that by the broadband excitation for identical excitation laser intensity. (author)

  18. Efficient approximation of random fields for numerical applications

    KAUST Repository

    Harbrecht, Helmut

    2015-01-07

    We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

  19. Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures

    Science.gov (United States)

    2017-10-04

    to the memory architectures of CPUs and GPUs to obtain good performance and result in good memory performance using cache management. These methods ...Accomplishments: The PI and students has developed new methods for path and ray tracing and their Report Date: 14-Oct-2017 INVESTIGATOR(S): Phone...The efficiency of our method makes it a good candidate for forming hybrid schemes with wave-based models. One possibility is to couple the ray curve

  20. Numerical simulation of energy efficiency measures: control and operational strategies

    International Nuclear Information System (INIS)

    Ardehali, M. M.

    2006-01-01

    The inherent limitation in performance of building envelop components and heating ventilating and air conditioning (HVAC) equipment necessitates the examination of operational strategies for improvement in energy-efficient operation of buildings. Due to the ease of installation and increasing availability of electronic controllers, operational strategies that could be programmed are of particular interest. The Iowa Energy Center in the US has taken the initiative to conduct the necessary assessment of current HVAC technology and the commonly-used operational strategies for commercial and industrial buildings, as applied to the midwestern part of the country, with weather and energy cost data for Des Moines, Iowa. The first part of this study focused on the energy consumption and cost effectiveness of HVAC systems. The objectives of the second part is concerned with examination of various operational strategies, namely, night purge (NP), fan optimum start and stop (OSS), condenser water reset (CWR), and chilled water reset (CHWR) applied to order and newer-type commercial office buildings. The indoor air quality requirement are met and the latest applicable energy rates from local utility companies are used. The results show that, in general, NP is not an effective strategy in buildings with low thermal mass storage, OSS reduced fan energy, and CWR and CHWR could be effective and require chillers with multi-stage unloading characteristics. The most operationally efficient strategies are the combination of OSS, CWR, and CHWR for the older-type building, and OSS for the newer-type building. Economically, the most effective is the OSS strategy for the older-type building and the CHWR strategy for the newer-type building.(Author)

  1. Mesh-free Hamiltonian implementation of two dimensional Darwin model

    Science.gov (United States)

    Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul

    2017-08-01

    A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.

  2. An efficient numerical approach to electrostatic microelectromechanical system simulation

    International Nuclear Information System (INIS)

    Pu, Li

    2009-01-01

    Computational analysis of electrostatic microelectromechanical systems (MEMS) requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed on an undeformed geometry. However, the electrostatic analysis is performed on the deformed position of microstructures. In this paper, a new efficient approach to self-consistent analysis of electrostatic MEMS in the small deformation case is presented. In this approach, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures. This algorithm is based on the linear mode shapes of a microstructure as basis functions. A boundary integral equation for the electrostatic problem is expanded into a Taylor series around the undeformed configuration, and a new coupled-field equation is presented. This approach is validated by comparing its results with the results available in the literature and ANSYS solutions, and shows attractive features comparable to ANSYS. (general)

  3. Renormalization of Hamiltonians

    International Nuclear Information System (INIS)

    Glazek, S.D.; Wilson, K.G.

    1993-01-01

    This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

  4. Theory of collective Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Qingying

    1982-02-01

    Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

  5. Time dependent drift Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1982-04-01

    The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

  6. Bäcklund transformations and Hamiltonian flows

    International Nuclear Information System (INIS)

    Zullo, Federico

    2013-01-01

    In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)

  7. Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

    International Nuclear Information System (INIS)

    Reiher, Markus; Wolf, Alexander

    2004-01-01

    In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented

  8. Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

    Science.gov (United States)

    Reiher, Markus; Wolf, Alexander

    2004-12-08

    In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

  9. Hamiltonian Chaos and Fractional Dynamics

    International Nuclear Information System (INIS)

    Combescure, M

    2005-01-01

    This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

  10. Effective Hamiltonian for travelling discrete breathers

    Science.gov (United States)

    MacKay, Robert S.; Sepulchre, Jacques-Alexandre

    2002-05-01

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

  11. Quantum bootstrapping via compressed quantum Hamiltonian learning

    International Nuclear Information System (INIS)

    Wiebe, Nathan; Granade, Christopher; Cory, D G

    2015-01-01

    A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)

  12. Effective magnetic Hamiltonians

    Czech Academy of Sciences Publication Activity Database

    Drchal, Václav; Kudrnovský, Josef; Turek, I.

    2013-01-01

    Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013

  13. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.

    2015-01-01

    We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or

  14. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.

    A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity

  15. Hamiltonian formulation of reduced magnetohydrodynamics

    International Nuclear Information System (INIS)

    Morrison, P.J.; Hazeltine, R.D.

    1983-07-01

    Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD

  16. Dissipative systems and Bateman's Hamiltonian

    International Nuclear Information System (INIS)

    Pedrosa, I.A.; Baseia, B.

    1983-01-01

    It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt

  17. Noncanonical Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Litteljohn, R.G.

    1986-01-01

    Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

  18. Instability in Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    A. Pumarino

    2005-11-01

    Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.

  19. An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators

    DEFF Research Database (Denmark)

    Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge

    2015-01-01

    A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally com...... to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 88%....

  20. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  1. Efficient numerical methods for fluid- and electrodynamics on massively parallel systems

    Energy Technology Data Exchange (ETDEWEB)

    Zudrop, Jens

    2016-07-01

    In the last decade, computer technology has evolved rapidly. Modern high performance computing systems offer a tremendous amount of computing power in the range of a few peta floating point operations per second. In contrast, numerical software development is much slower and most existing simulation codes cannot exploit the full computing power of these systems. Partially, this is due to the numerical methods themselves and partially it is related to bottlenecks within the parallelization concept and its data structures. The goal of the thesis is the development of numerical algorithms and corresponding data structures to remedy both kinds of parallelization bottlenecks. The approach is based on a co-design of the numerical schemes (including numerical analysis) and their realizations in algorithms and software. Various kinds of applications, from multicomponent flows (Lattice Boltzmann Method) to electrodynamics (Discontinuous Galerkin Method) to embedded geometries (Octree), are considered and efficiency of the developed approaches is demonstrated for large scale simulations.

  2. Recursive tridiagonalization of infinite dimensional Hamiltonians

    International Nuclear Information System (INIS)

    Haydock, R.; Oregon Univ., Eugene, OR

    1989-01-01

    Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

  3. Symplectic Geometric Algorithms for Hamiltonian Systems

    CERN Document Server

    Feng, Kang

    2010-01-01

    "Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development

  4. Hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms

  5. A dynamic optimization on economic energy efficiency in development: A numerical case of China

    International Nuclear Information System (INIS)

    Wang, Dong

    2014-01-01

    This paper is based on dynamic optimization methodology to investigate the economic energy efficiency issues in developing countries. The paper introduces some definitions about energy efficiency both in economics and physics, and establishes a quantitative way for measuring the economic energy efficiency. The linkage between economic energy efficiency, energy consumption and other macroeconomic variables is demonstrated primarily. Using the methodology of dynamic optimization, a maximum problem of economic energy efficiency over time, which is subjected to the extended Solow growth model and instantaneous investment rate, is modelled. In this model, the energy consumption is set as a control variable and the capital is regarded as a state variable. The analytic solutions can be derived and the diagrammatic analysis provides saddle-point equilibrium. A numerical simulation based on China is also presented; meanwhile, the optimal paths of investment and energy consumption can be drawn. The dynamic optimization encourages governments in developing countries to pursue higher economic energy efficiency by controlling the energy consumption and regulating the investment state as it can conserve energy without influencing the achievement of steady state in terms of Solow model. If that, a sustainable development will be achieved. - Highlights: • A new definition on economic energy efficiency is proposed mathematically. • A dynamic optimization modelling links economic energy efficiency with other macroeconomic variables in long run. • Economic energy efficiency is determined by capital stock level and energy consumption. • Energy saving is a key solution for improving economic energy efficiency

  6. Numerical quantification and minimization of perimeter losses in high-efficiency silicon solar cells

    Energy Technology Data Exchange (ETDEWEB)

    Altermatt, P.P.; Heiser, Gernot; Green, M.A. [New South Wales Univ., Kensington, NSW (Australia)

    1996-09-01

    This paper presents a quantitative analysis of perimeter losses in high-efficiency silicon solar cells. A new method of numerical modelling is used, which provides the means to simulate a full-sized solar cell, including its perimeter region. We analyse the reduction in efficiency due to perimeter losses as a function of the distance between the active cell area and the cut edge. It is shown how the optimum distance depends on whether the cells in the panel are shingled or not. The simulations also indicate that passivating the cut-face with a thermal oxide does not increase cell efficiency substantially. Therefore, doping schemes for the perimeter domain are suggested in order to increase efficiency levels above present standards. Finally, perimeter effects in cells that remain embedded in the wafer during the efficiency measurement are outlined. (author)

  7. Experimental and Numerical Simulations Predictions Comparison of Power and Efficiency in Hydraulic Turbine

    Directory of Open Access Journals (Sweden)

    Laura Castro

    2011-01-01

    Full Text Available On-site power and mass flow rate measurements were conducted in a hydroelectric power plant (Mexico. Mass flow rate was obtained using Gibson's water hammer-based method. A numerical counterpart was carried out by using the commercial CFD software, and flow simulations were performed to principal components of a hydraulic turbine: runner and draft tube. Inlet boundary conditions for the runner were obtained from a previous simulation conducted in the spiral case. The computed results at the runner's outlet were used to conduct the subsequent draft tube simulation. The numerical results from the runner's flow simulation provided data to compute the torque and the turbine's power. Power-versus-efficiency curves were built, and very good agreement was found between experimental and numerical data.

  8. Hamiltonian partial differential equations and applications

    CERN Document Server

    Nicholls, David; Sulem, Catherine

    2015-01-01

    This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

  9. Chromatic roots and hamiltonian paths

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2000-01-01

    We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...

  10. Real-time numerical simulation with high efficiency for an experimental reactor system

    International Nuclear Information System (INIS)

    Ding Shuling; Li Fu; Li Sifeng; Chu Xinyuan

    2006-01-01

    The paper presents a systematic and efficient method for numerical real-time simulation of an experimental reactor. The reactor models were built based on the physical characteristics of the experimental reactor, and several real-time simulation approaches were discussed and compared in the paper. How to implement the real-time reactor simulation system in Windows platform for the sake of hardware-in-loop experiment for the reactor power control system was discussed. (authors)

  11. Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

    Science.gov (United States)

    Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

    2018-02-01

    Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

  12. Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models

    International Nuclear Information System (INIS)

    Jošt, D; Škerlavaj, A; Lipej, A

    2012-01-01

    Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.

  13. Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models

    Science.gov (United States)

    Jošt, D.; Škerlavaj, A.; Lipej, A.

    2012-11-01

    Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.

  14. Redesign of the DFT/MRCI Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)

    2016-01-21

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

  15. A numerically efficient damping model for acoustic resonances in microfluidic cavities

    Energy Technology Data Exchange (ETDEWEB)

    Hahn, P., E-mail: hahnp@ethz.ch; Dual, J. [Institute of Mechanical Systems (IMES), Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, CH-8092 Zurich (Switzerland)

    2015-06-15

    Bulk acoustic wave devices are typically operated in a resonant state to achieve enhanced acoustic amplitudes and high acoustofluidic forces for the manipulation of microparticles. Among other loss mechanisms related to the structural parts of acoustofluidic devices, damping in the fluidic cavity is a crucial factor that limits the attainable acoustic amplitudes. In the analytical part of this study, we quantify all relevant loss mechanisms related to the fluid inside acoustofluidic micro-devices. Subsequently, a numerical analysis of the time-harmonic visco-acoustic and thermo-visco-acoustic equations is carried out to verify the analytical results for 2D and 3D examples. The damping results are fitted into the framework of classical linear acoustics to set up a numerically efficient device model. For this purpose, all damping effects are combined into an acoustofluidic loss factor. Since some components of the acoustofluidic loss factor depend on the acoustic mode shape in the fluid cavity, we propose a two-step simulation procedure. In the first step, the loss factors are deduced from the simulated mode shape. Subsequently, a second simulation is invoked, taking all losses into account. Owing to its computational efficiency, the presented numerical device model is of great relevance for the simulation of acoustofluidic particle manipulation by means of acoustic radiation forces or acoustic streaming. For the first time, accurate 3D simulations of realistic micro-devices for the quantitative prediction of pressure amplitudes and the related acoustofluidic forces become feasible.

  16. Numerical

    Directory of Open Access Journals (Sweden)

    M. Boumaza

    2015-07-01

    Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.

  17. A partial Hamiltonian approach for current value Hamiltonian systems

    Science.gov (United States)

    Naz, R.; Mahomed, F. M.; Chaudhry, Azam

    2014-10-01

    We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

  18. NLO renormalization in the Hamiltonian truncation

    Science.gov (United States)

    Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

    2017-09-01

    Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

  19. Numerical analysis of an entire ceramic kiln under actual operating conditions for the energy efficiency improvement.

    Science.gov (United States)

    Milani, Massimo; Montorsi, Luca; Stefani, Matteo; Saponelli, Roberto; Lizzano, Maurizio

    2017-12-01

    The paper focuses on the analysis of an industrial ceramic kiln in order to improve the energy efficiency and thus the fuel consumption and the corresponding carbon dioxide emissions. A lumped and distributed parameter model of the entire system is constructed to simulate the performance of the kiln under actual operating conditions. The model is able to predict accurately the temperature distribution along the different modules of the kiln and the operation of the many natural gas burners employed to provide the required thermal power. Furthermore, the temperature of the tiles is also simulated so that the quality of the final product can be addressed by the modelling. Numerical results are validated against experimental measurements carried out on a real ceramic kiln during regular production operations. The developed numerical model demonstrates to be an efficient tool for the investigation of different design solutions for the kiln's components. In addition, a number of control strategies for the system working conditions can be simulated and compared in order to define the best trade off in terms of fuel consumption and product quality. In particular, the paper analyzes the effect of a new burner type characterized by internal heat recovery capability aimed at improving the energy efficiency of the ceramic kiln. The fuel saving and the relating reduction of carbon dioxide emissions resulted in the order of 10% when compared to the standard burner. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls

    Directory of Open Access Journals (Sweden)

    Arun Arjunan

    2015-08-01

    Full Text Available Architects, designers, and engineers are making great efforts to design acoustically-efficient metal-framed walls, minimizing acoustic bridging. Therefore, efficient simulation models to predict the acoustic insulation complying with ISO 10140 are needed at a design stage. In order to achieve this, a numerical model consisting of two fluid-filled reverberation chambers, partitioned using a metal-framed wall, is to be simulated at one-third-octaves. This produces a large simulation model consisting of several millions of nodes and elements. Therefore, efficient meshing procedures are necessary to obtain better solution times and to effectively utilise computational resources. Such models should also demonstrate effective Fluid-Structure Interaction (FSI along with acoustic-fluid coupling to simulate a realistic scenario. In this contribution, the development of a finite element frequency-dependent mesh model that can characterize the sound insulation of metal-framed walls is presented. Preliminary results on the application of the proposed model to study the geometric contribution of stud frames on the overall acoustic performance of metal-framed walls are also presented. It is considered that the presented numerical model can be used to effectively visualize the noise behaviour of advanced materials and multi-material structures.

  1. Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

    Science.gov (United States)

    Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

    2012-07-02

    Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of

  2. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  3. A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

    International Nuclear Information System (INIS)

    Khotylev, V.A.; Hoogenboom, J.E.

    1996-01-01

    The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

  4. A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

    Energy Technology Data Exchange (ETDEWEB)

    Khotylev, V.A.; Hoogenboom, J.E. [Delft Univ. of Technology, Interfaculty Reactor Inst., Delft (Netherlands)

    1996-07-01

    The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

  5. Alternative Hamiltonian representation for gravity

    Energy Technology Data Exchange (ETDEWEB)

    Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)

    2007-11-15

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.

  6. Alternative Hamiltonian representation for gravity

    International Nuclear Information System (INIS)

    Rosas-RodrIguez, R

    2007-01-01

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity

  7. Numerical Simulations of Pillar Structured Solid State Thermal Neutron Detector Efficiency and Gamma Discrimination

    Energy Technology Data Exchange (ETDEWEB)

    Conway, A; Wang, T; Deo, N; Cheung, C; Nikolic, R

    2008-06-24

    This work reports numerical simulations of a novel three-dimensionally integrated, {sup 10}boron ({sup 10}B) and silicon p+, intrinsic, n+ (PIN) diode micropillar array for thermal neutron detection. The inter-digitated device structure has a high probability of interaction between the Si PIN pillars and the charged particles (alpha and {sup 7}Li) created from the neutron - {sup 10}B reaction. In this work, the effect of both the 3-D geometry (including pillar diameter, separation and height) and energy loss mechanisms are investigated via simulations to predict the neutron detection efficiency and gamma discrimination of this structure. The simulation results are demonstrated to compare well with the measurement results. This indicates that upon scaling the pillar height, a high efficiency thermal neutron detector is possible.

  8. Scattering theory for Stark Hamiltonians

    International Nuclear Information System (INIS)

    Jensen, Arne

    1994-01-01

    An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs

  9. A new perturbative treatment of pentadiagonal Hamiltonians

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian

  10. Numerical Research of Steam and Gas Plant Efficiency of Triple Cycle for Extreme North Regions

    Directory of Open Access Journals (Sweden)

    Galashov Nikolay

    2016-01-01

    Full Text Available The present work shows that temperature decrease of heat rejection in a cycle is necessary for energy efficiency of steam turbine plants. Minimum temperature of heat rejection at steam turbine plant work on water steam is 15°C. Steam turbine plant of triple cycle where lower cycle of steam turbine plant is organic Rankine cycle on low-boiling substance with heat rejection in air condenser, which safely allows rejecting heat at condensation temperatures below 0°C, has been offered. Mathematical model of steam and gas plant of triple cycle, which allows conducting complex researches with change of working body appearance and parameters defining thermodynamic efficiency of cycles, has been developed. On the basis of the model a program of parameters and index cycles design of steam and gas plants has been developed in a package of electron tables Excel. Numerical studies of models showed that energy efficiency of steam turbine plants of triple cycle strongly depend on low-boiling substance type in a lower cycle. Energy efficiency of steam and gas plants net 60% higher can be received for steam and gas plants on the basis of gas turbine plant NK-36ST on pentane and its condensation temperature below 0°C. It was stated that energy efficiency of steam and gas plants net linearly depends on condensation temperature of low-boiling substance type and temperature of gases leaving reco very boiler. Energy efficiency increases by 1% at 10% decrease of condensation temperature of pentane, and it increases by 0.88% at 15°C temperature decrease of gases leaving recovery boiler.

  11. Hamiltonian description of the ideal fluid

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1994-01-01

    Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems

  12. Kinetic Energy Losses and Efficiency of an Axial Turbine Stage in Numerical Modeling of Unsteady Flows

    Directory of Open Access Journals (Sweden)

    A. S. Laskin

    2015-01-01

    Full Text Available The article presents the results of numerical investigation of kinetic energy (KE loss and blading efficiency of the single-stage axial turbine under different operating conditions, characterized by the ratio u/C0. The calculations are performed by stationary (Stage method and nonstationary (Transient method methods using ANSYS CFX. The novelty of this work lies in the fact that the numerical simulation of steady and unsteady flows in a turbine stage is conducted, and the results are obtained to determine the loss of KE, both separately by the elements of the flow range and their total values, in the stage efficiency as well. The results obtained are compared with the calculated efficiency according to one-dimensional theory.To solve these problems was selected model of axial turbine stage with D/l = 13, blade profiles of rotor and stator of constant cross-section, similar to tested ones in inverted turbine when = 0.3. The degree of reactivity ρ = 0.27, the rotor speed was varied within the range 1000 ÷ 1800 rev/min.Results obtained allow us to draw the following conclusions:1. The level of averaged coefficients of total KE losses in the range of from 0.48 to 0.75 is from 18% to 21% when calculating by the Stage method and from 21% to 25% by the Transient one.2. The level of averaged coefficients of KE losses with the output speed of in the specified range is from 9% to 13%, and almost the same when in calculating by Stage and Transient methods.3. Levels of averaged coefficients of KE loss in blade tips (relative to the differential enthalpies per stage are changed in the range: from 4% to 3% (Stage and are stored to be equal to 5% (Transient; from 5% to 6% (Stage and from 6% to 8% (Transient.4. Coefficients of KE losses in blade tips GV and RB are higher in calculations of the model stage using the Transient method than the Stage one, respectively, by = 1.5 ÷ 2.5% and = 4 ÷ 5% of the absolute values. These are values to characterize the KE

  13. A Hamiltonian Monte–Carlo method for Bayesian inference of supermassive black hole binaries

    International Nuclear Information System (INIS)

    Porter, Edward K; Carré, Jérôme

    2014-01-01

    We investigate the use of a Hamiltonian Monte–Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte–Carlo (MCMC) methods, such as Metropolis–Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte–Carlo treats the inverse likelihood surface as a ‘gravitational potential’ and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. This method is not as widely used as other MCMC algorithms due to the necessity of calculating gradients of the log-likelihood, which for most applications results in a bottleneck that makes the algorithm computationally prohibitive. We circumvent this problem by using accepted initial phase-space trajectory points to analytically fit for each of the individual gradients. Eliminating the waveform generation needed for the numerical derivatives reduces the total number of required templates for a 10 6 iteration chain from ∼10 9 to ∼10 6 . The result is in an implementation of the Hamiltonian Monte–Carlo that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than a Hessian MCMC. (paper)

  14. A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

    KAUST Repository

    Bao, Weizhu; Marahrens, Daniel; Tang, Qinglin; Zhang, Yanzhi

    2013-01-01

    We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three

  15. Geometry and Hamiltonian mechanics on discrete spaces

    International Nuclear Information System (INIS)

    Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

    2004-01-01

    Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

  16. Horizontal circulation and jumps in Hamiltonian wave models

    NARCIS (Netherlands)

    Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno

    2013-01-01

    We are interested in the numerical modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian

  17. Energy preserving integration of bi-Hamiltonian partial differential equations

    NARCIS (Netherlands)

    Karasozen, B.; Simsek, G.

    2013-01-01

    The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the

  18. Numerical Analysis of Novel Back Surface Field for High Efficiency Ultrathin CdTe Solar Cells

    Directory of Open Access Journals (Sweden)

    M. A. Matin

    2013-01-01

    Full Text Available This paper numerically explores the possibility of high efficiency, ultrathin, and stable CdTe cells with different back surface field (BSF using well accepted simulator AMPS-1D (analysis of microelectronics and photonic structures. A modified structure of CdTe based PV cell SnO2/Zn2SnO4/CdS/CdTe/BSF/BC has been proposed over reference structure SnO2/Zn2SnO4/CdS/CdTe/Cu. Both higher bandgap materials like ZnTe and Cu2Te and low bandgap materials like As2Te3 and Sb2Te3 have been used as BSF to reduce minority carrier recombination loss at the back contact in ultra-thin CdTe cells. In this analysis the highest conversion efficiency of CdTe based PV cell without BSF has been found to be around 17% using CdTe absorber thickness of 5 μm. However, the proposed structures with different BSF have shown acceptable efficiencies with an ultra-thin CdTe absorber of only 0.6 μm. The proposed structure with As2Te3 BSF showed the highest conversion efficiency of 20.8% ( V,  mA/cm2, and . Moreover, the proposed structures have shown improved stability in most extents, as it was found that the cells have relatively lower negative temperature coefficient. However, the cell with ZnTe BSF has shown better overall stability than other proposed cells with temperature coefficient (TC of −0.3%/°C.

  19. A Robust and Efficient Numerical Method for RNA-Mediated Viral Dynamics

    Directory of Open Access Journals (Sweden)

    Vladimir Reinharz

    2017-10-01

    Full Text Available The multiscale model of hepatitis C virus (HCV dynamics, which includes intracellular viral RNA (vRNA replication, has been formulated in recent years in order to provide a new conceptual framework for understanding the mechanism of action of a variety of agents for the treatment of HCV. We present a robust and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, a Rosenbrock type method that is highly suited to solve this problem. We provide a Graphical User Interface that applies this method and is useful for simulating viral dynamics during treatment with anti-HCV agents that act against HCV on the molecular level.

  20. Numerical simulations on efficiency and measurement of capabilities of BGO detectors for high energy gamma ray

    CERN Document Server

    Wen Wan Xin

    2002-01-01

    The energy resolution and time resolution of two phi 75 x 100 BGO detectors for high energy gamma ray newly made were measured with sup 1 sup 3 sup 7 Cs and sup 6 sup 0 Co resources. The two characteristic gamma rays of high energy emitted from the thermal neutron capture of germanium in BGO crystal were used for the energy calibration of gamma spectra. The intrinsic photopeak efficiency, single escape probability and double escape probabilities of BGO detectors in photon energy range of 4-30 MeV are numerically calculated with GEANT code. The real count response and count ratio of the uniformly distributed incident photons in energy range of 0-30 MeV are also calculated. The distortion of gamma spectra caused by the photon energy loss extension to lower energy in detection medium is discussed

  1. An efficient numerical method for evolving microstructures with strong elastic inhomogeneity

    International Nuclear Information System (INIS)

    Jeong, Darae; Lee, Seunggyu; Kim, Junseok

    2015-01-01

    In this paper, we consider a fast and efficient numerical method for the modified Cahn–Hilliard equation with a logarithmic free energy for microstructure evolution. Even though it is physically more appropriate to use a logarithmic free energy, a quartic polynomial approximation is typically used for the logarithmic function due to a logarithmic singularity. In order to overcome the singularity problem, we regularize the logarithmic function and then apply an unconditionally stable scheme to the Cahn–Hilliard part in the model. We present computational results highlighting the different dynamic aspects from two different bulk free energy forms. We also demonstrate the robustness of the regularization of the logarithmic free energy, which implies the time-step restriction is based on accuracy and not stability. (paper)

  2. Numerical multistep methods for the efficient solution of quantum mechanics and related problems

    International Nuclear Information System (INIS)

    Anastassi, Z.A.; Simos, T.E.

    2009-01-01

    In this paper we present the recent development in the numerical integration of the Schroedinger equation and related systems of ordinary differential equations with oscillatory solutions, such as the N-body problem. We examine several types of multistep methods (explicit, implicit, predictor-corrector, hybrid) and several properties (P-stability, trigonometric fitting of various orders, phase fitting, high phase-lag order, algebraic order). We analyze the local truncation error and the stability of the methods. The error for the Schroedinger equation is also presented, which reveals the relation of the error to the energy. The efficiency of the methods is evaluated through the integration of five problems. Figures are presented and analyzed and some general conclusions are made. Code written in Maple is given for the development of all methods analyzed in this paper. Also the subroutines written in Matlab, that concern the integration of the methods, are presented.

  3. Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

    International Nuclear Information System (INIS)

    Havu, V.; Blum, V.; Havu, P.; Scheffler, M.

    2009-01-01

    We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.

  4. An efficient soil water balance model based on hybrid numerical and statistical methods

    Science.gov (United States)

    Mao, Wei; Yang, Jinzhong; Zhu, Yan; Ye, Ming; Liu, Zhao; Wu, Jingwei

    2018-04-01

    Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new

  5. Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

    KAUST Repository

    Frohne, Jörg

    2015-08-06

    © 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

  6. Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

    KAUST Repository

    Frohne, Jö rg; Heister, Timo; Bangerth, Wolfgang

    2015-01-01

    © 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

  7. An efficient numerical method for solving the Boltzmann equation in multidimensions

    Science.gov (United States)

    Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

    2018-01-01

    In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

  8. An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

    Science.gov (United States)

    Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

    2015-03-01

    We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

  9. First principles of Hamiltonian medicine.

    Science.gov (United States)

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-05-19

    We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

  10. Variational identities and Hamiltonian structures

    International Nuclear Information System (INIS)

    Ma Wenxiu

    2010-01-01

    This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

  11. Dynamical decoupling of unbounded Hamiltonians

    Science.gov (United States)

    Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

    2018-03-01

    We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

  12. Hamiltonian truncation approach to quenches in the Ising field theory

    Directory of Open Access Journals (Sweden)

    T. Rakovszky

    2016-10-01

    Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

  13. Experimental quantum Hamiltonian learning

    NARCIS (Netherlands)

    Wang, J.; Paesani, S.; Santagati, R.; Knauer, S.; Gentile, A.A.; Wiebe, N.; Petruzzella, M.; O’Brien, J.L.; Rarity, J.G.; Laing, A.; Thompson, M.G.

    2017-01-01

    The efficient characterization of quantum systems1, 2, 3, the verification of the operations of quantum devices4, 5, 6 and the validation of underpinning physical models7, 8, 9, are central challenges for quantum technologies10, 11, 12 and fundamental physics13, 14. The computational cost of such

  14. The intrinsic stochasticity of near-integrable Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu

    1989-09-01

    Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).

  15. Invariant metrics for Hamiltonian systems

    International Nuclear Information System (INIS)

    Rangarajan, G.; Dragt, A.J.; Neri, F.

    1991-05-01

    In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs

  16. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

    2015-11-14

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  17. An efficient numerical progressive diagonalization scheme for the quantum Rabi model revisited

    International Nuclear Information System (INIS)

    Pan, Feng; Bao, Lina; Dai, Lianrong; Draayer, Jerry P

    2017-01-01

    An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model. (paper)

  18. An Energy-Efficient Cluster-Based Vehicle Detection on Road Network Using Intention Numeration Method

    Directory of Open Access Journals (Sweden)

    Deepa Devasenapathy

    2015-01-01

    Full Text Available The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

  19. An energy-efficient cluster-based vehicle detection on road network using intention numeration method.

    Science.gov (United States)

    Devasenapathy, Deepa; Kannan, Kathiravan

    2015-01-01

    The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

  20. Semi-empirical γ-ray peak efficiency determination including self-absorption correction based on numerical integration

    International Nuclear Information System (INIS)

    Noguchi, M.; Takeda, K.; Higuchi, H.

    1981-01-01

    A method of γ-ray efficiency determination for extended (plane or bulk) samples based on numerical integration of point source efficiency is studied. The proposed method is widely applicable to samples of various shapes and materials. The geometrical factor in the peak efficiency can easily be corrected for by simply changing the integration region, and γ-ray self-absorption is also corrected by the absorption coefficients for the sample matrix. (author)

  1. Riemannian geometry of Hamiltonian chaos: hints for a general theory.

    Science.gov (United States)

    Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

    2008-10-01

    We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

  2. Derivation of Hamiltonians for accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Symon, K.R.

    1997-09-12

    In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

  3. Hamiltonian cycles in polyhedral maps

    Indian Academy of Sciences (India)

    We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...

  4. Maslov index for Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    Alessandro Portaluri

    2008-01-01

    Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.

  5. Hamiltonian formulation of the supermembrane

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Sezgin, E.; Tanii, Y.

    1987-06-01

    The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs

  6. Relativistic non-Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2010-01-01

    Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

  7. Deformation data modeling through numerical models: an efficient method for tracking magma transport

    Science.gov (United States)

    Charco, M.; Gonzalez, P. J.; Galán del Sastre, P.

    2017-12-01

    Nowadays, multivariate collected data and robust physical models at volcano observatories are becoming crucial for providing effective volcano monitoring. Nevertheless, the forecast of volcanic eruption is notoriously difficult. Wthin this frame one of the most promising methods to evaluate the volcano hazard is the use of surface ground deformation and in the last decades many developments in the field of deformation modeling has been achieved. In particular, numerical modeling allows realistic media features such as topography and crustal heterogeneities to be included, although it is still very time cosuming to solve the inverse problem for near-real time interpretations. Here, we present a method that can be efficiently used to estimate the location and evolution of magmatic sources base on real-time surface deformation data and Finite Element (FE) models. Generally, the search for the best-fitting magmatic (point) source(s) is conducted for an array of 3-D locations extending below a predefined volume region and the Green functions for all the array components have to be precomputed. We propose a FE model for the pre-computation of Green functions in a mechanically heterogeneous domain which eventually will lead to a better description of the status of the volcanic area. The number of Green functions is reduced here to the number of observational points by using their reciprocity relationship. We present and test this methodology with an optimization method base on a Genetic Algorithm. Following synthetic and sensitivity test to estimate the uncertainty of the model parameters, we apply the tool for magma tracking during 2007 Kilauea volcano intrusion and eruption. We show how data inversion with numerical models can speed up the source parameters estimations for a given volcano showing signs of unrest.

  8. Normal form for mirror machine Hamiltonians

    International Nuclear Information System (INIS)

    Dragt, A.J.; Finn, J.M.

    1979-01-01

    A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior

  9. Effective Hamiltonians for phosphorene and silicene

    International Nuclear Information System (INIS)

    Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M

    2015-01-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)

  10. Mathematical Modeling of Constrained Hamiltonian Systems

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    1995-01-01

    Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the

  11. Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

    Directory of Open Access Journals (Sweden)

    Tetsuya Misawa

    2010-01-01

    Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.

  12. The development of efficient numerical time-domain modeling methods for geophysical wave propagation

    Science.gov (United States)

    Zhu, Lieyuan

    This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The

  13. Numerical and experimental comparison of electromechanical properties and efficiency of HTS and ferromagnetic hysteresis motors

    International Nuclear Information System (INIS)

    Inacio, D; Inacio, S; Pina, J; Goncalves, A; Neves, M Ventim; Rodrigues, A Leao

    2008-01-01

    Hysteresis motors are very attractive in a wide range of fractional power applications, due to its torque-speed characteristics and simplicity of construction. This motor's performance is expected to improve when HTS rotors are used, and in fact, hysteresis motors have shown to be probably the most viable electrical machines using HTS materials. While these motors, either conventional or HTS, are both hysteresis motors, they base their operation on different physical phenomena: hysteretic behaviour in conventional ferromagnetic materials is due to the material's non-linear magnetic properties, while in HTS materials the hysteresis has an ohmic nature and is related with vortices' dynamics. In this paper, theoretical aspects of both conventional and HTS hysteresis motors are discussed, its operation principles are highlighted, and the characteristics of both motors are presented. The characteristics, obtained both by experimental tests and numerical simulation (made with commercial software), are compared, in order to evaluate not only the motor's electromechanical performances but also the overall systems efficiency, including cryogenics for the HTS device

  14. Geometric Hamiltonian structures and perturbation theory

    International Nuclear Information System (INIS)

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

  15. Notch filters for port-Hamiltonian systems

    NARCIS (Netherlands)

    Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.

    2012-01-01

    In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the

  16. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  17. The Hamiltonian of QED. Zero mode

    International Nuclear Information System (INIS)

    Zastavenko, L.G.

    1990-01-01

    We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs

  18. A progressive diagonalization scheme for the Rabi Hamiltonian

    International Nuclear Information System (INIS)

    Pan, Feng; Guan, Xin; Wang, Yin; Draayer, J P

    2010-01-01

    A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.

  19. An extended discrete gradient formula for oscillatory Hamiltonian systems

    International Nuclear Information System (INIS)

    Liu Kai; Shi Wei; Wu Xinyuan

    2013-01-01

    In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

  20. Non-stoquastic Hamiltonians in quantum annealing via geometric phases

    Science.gov (United States)

    Vinci, Walter; Lidar, Daniel A.

    2017-09-01

    We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

  1. Hamiltonian PDEs and Frobenius manifolds

    International Nuclear Information System (INIS)

    Dubrovin, Boris A

    2008-01-01

    In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

  2. Hamiltonian PDEs and Frobenius manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

    2008-12-31

    In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

  3. Weak KAM for commuting Hamiltonians

    International Nuclear Information System (INIS)

    Zavidovique, M

    2010-01-01

    For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)

  4. Hamiltonian dynamics of extended objects

    Science.gov (United States)

    Capovilla, R.; Guven, J.; Rojas, E.

    2004-12-01

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

  5. A Hamiltonian approach to Thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)

    2016-10-15

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

  6. Hamiltonian description of bubble dynamics

    International Nuclear Information System (INIS)

    Maksimov, A. O.

    2008-01-01

    The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.

  7. Hamiltonian dynamics of extended objects

    International Nuclear Information System (INIS)

    Capovilla, R; Guven, J; Rojas, E

    2004-01-01

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations

  8. Hamiltonian dynamics of extended objects

    Energy Technology Data Exchange (ETDEWEB)

    Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)

    2004-12-07

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.

  9. A Hamiltonian approach to Thermodynamics

    International Nuclear Information System (INIS)

    Baldiotti, M.C.; Fresneda, R.; Molina, C.

    2016-01-01

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

  10. On the domain of the Nelson Hamiltonian

    Science.gov (United States)

    Griesemer, M.; Wünsch, A.

    2018-04-01

    The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

  11. Hamiltonian systems in accelerator physics

    International Nuclear Information System (INIS)

    Laslett, L.J.

    1985-06-01

    General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs

  12. Contact symmetries and Hamiltonian thermodynamics

    International Nuclear Information System (INIS)

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-01-01

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production

  13. Generic Local Hamiltonians are Gapless

    Science.gov (United States)

    Movassagh, Ramis

    2017-12-01

    We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.

  14. Hamiltonian dynamics of preferential attachment

    International Nuclear Information System (INIS)

    Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri

    2016-01-01

    Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)

  15. Newton algorithm for Hamiltonian characterization in quantum control

    International Nuclear Information System (INIS)

    Ndong, M; Sugny, D; Salomon, J

    2014-01-01

    We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)

  16. Effective hamiltonian calculations using incomplete model spaces

    International Nuclear Information System (INIS)

    Koch, S.; Mukherjee, D.

    1987-01-01

    It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations

  17. Relativistic Many-Body Hamiltonian Approach to Mesons

    OpenAIRE

    Llanes-Estrada, Felipe J.; Cotanch, Stephen R.

    2001-01-01

    We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon app...

  18. A Numerical Study on the Improvement of Suction Performance and Hydraulic Efficiency for a Mixed-Flow Pump Impeller

    Directory of Open Access Journals (Sweden)

    Sung Kim

    2014-01-01

    Full Text Available This paper describes a numerical study on the improvement of suction performance and hydraulic efficiency of a mixed-flow pump by impellers. The design of these impellers was optimized using a commercial CFD (computational fluid dynamics code and DOE (design of experiments. The design variables of meridional plane and vane plane development were defined for impeller design. In DOE, variables of inlet part were selected as main design variables in meridional plane, and incidence angle was selected in vane plane development. The verification of the experiment sets that were generated by 2k factorial was done by numerical analysis. The objective functions were defined as the NPSHre (net positive suction head required, total efficiency, and total head of the impellers. The importance of the geometric design variables was analyzed using 2k factorial designs. The interaction between the NPSHre and total efficiency, according to the meridional plane and incidence angle, was discussed by analyzing the 2k factorial design results. The performance of optimally designed model was verified by experiments and numerical analysis and the reliability of the model was retained by comparison of numerical analysis and comparative analysis with the reference model.

  19. Coherent states for quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  20. Perturbation theory of effective Hamiltonians

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1975-01-01

    This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

  1. Integrable and nonintegrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Percival, I.

    1986-01-01

    Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications

  2. Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

    Energy Technology Data Exchange (ETDEWEB)

    Baskan, O.; Clercx, H. J. H [Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Speetjens, M. F. M. [Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Metcalfe, G. [Commonwealth Scientific and Industrial Research Organisation, Melbourne, Victoria 3190 (Australia); Swinburne University of Technology, Department of Mechanical Engineering, Hawthorn VIC 3122 (Australia)

    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.

  3. Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

    Science.gov (United States)

    Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

    2015-10-01

    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.

  4. Perspective: Quantum Hamiltonians for optical interactions

    Science.gov (United States)

    Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

    2018-01-01

    The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

  5. Generalized oscillator representations for Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Tyutin, I V; Voronov, B L

    2013-01-01

    This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

  6. General technique to produce isochronous Hamiltonians

    International Nuclear Information System (INIS)

    Calogero, F; Leyvraz, F

    2007-01-01

    We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra

  7. Collective Hamiltonians for dipole giant resonances

    International Nuclear Information System (INIS)

    Weiss, L.I.

    1991-07-01

    The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)

  8. Canonical transformations and hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

  9. Numerical simulation of quantum efficiency and surface recombination in HgCdTe IR photon-trapping structures

    Science.gov (United States)

    Schuster, Jonathan; Bellotti, Enrico

    2013-06-01

    We have investigated the quantum effiency in HgCdTe photovoltaic pixel arrays employing a photon-trapping structure realized with a periodic array of pillars intended to provide broadband operation. We have found that the quantum efficiency depends heavily on the passivation of the pillar surface. Pillars passivated with anodicoxide have a large fixed positive charge on the pillar surface. We use our three-dimensional numerical simulation model to study the effect of surface charge and surface recombination velocity on the exterior of the pillars. We then evaluate the quantum efficiency of this structure subject to different surface conditions. We have found that by themselves, the surface charge and surface recombination are detrimental to the quantum efficiency but the quantum efficiency is recovered when both phenomena are present. We will discuss the effects of these phenomena and the trade offs that exist between the two.

  10. On the efficient numerical solution of lattice systems with low-order couplings

    International Nuclear Information System (INIS)

    Ammon, A.; Genz, A.; Hartung, T.; Jansen, K.; Volmer, J.; Leoevey, H.

    2015-10-01

    We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.

  11. Numerical modelling of methane oxidation efficiency and coupled water-gas-heat reactive transfer in a sloping landfill cover.

    Science.gov (United States)

    Feng, S; Ng, C W W; Leung, A K; Liu, H W

    2017-10-01

    Microbial aerobic methane oxidation in unsaturated landfill cover involves coupled water, gas and heat reactive transfer. The coupled process is complex and its influence on methane oxidation efficiency is not clear, especially in steep covers where spatial variations of water, gas and heat are significant. In this study, two-dimensional finite element numerical simulations were carried out to evaluate the performance of unsaturated sloping cover. The numerical model was calibrated using a set of flume model test data, and was then subsequently used for parametric study. A new method that considers transient changes of methane concentration during the estimation of the methane oxidation efficiency was proposed and compared against existing methods. It was found that a steeper cover had a lower oxidation efficiency due to enhanced downslope water flow, during which desaturation of soil promoted gas transport and hence landfill gas emission. This effect was magnified as the cover angle and landfill gas generation rate at the bottom of the cover increased. Assuming the steady-state methane concentration in a cover would result in a non-conservative overestimation of oxidation efficiency, especially when a steep cover was subjected to rainfall infiltration. By considering the transient methane concentration, the newly-modified method can give a more accurate oxidation efficiency. Copyright © 2017. Published by Elsevier Ltd.

  12. Investigation of Schottky-Barrier carbon nanotube field-effect transistor by an efficient semi-classical numerical modeling

    International Nuclear Information System (INIS)

    Chen Changxin; Zhang Wei; Zhao Bo; Zhang Yafei

    2009-01-01

    An efficient semi-classical numerical modeling approach has been developed to simulate the coaxial Schottky-barrier carbon nanotube field-effect transistor (SB-CNTFET). In the modeling, the electrostatic potential of the CNT is obtained by self-consistently solving the analytic expression of CNT carrier distribution and the cylindrical Poisson equation, which significantly enhances the computational efficiency and simultaneously present a result in good agreement to that obtained from the non-equilibrium Green's function (NEGF) formalism based on the first principle. With this method, the effects of the CNT diameter, power supply voltage, thickness and dielectric constant of gate insulator on the device performance are investigated.

  13. Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

    International Nuclear Information System (INIS)

    Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

    1984-01-01

    Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

  14. Efficient algorithms for finding optimal binary features in numeric and nominal labeled data

    NARCIS (Netherlands)

    Mampaey, Michael; Nijssen, Siegfried; Feelders, Adrianus; Konijn, Rob; Knobbe, Arno

    2013-01-01

    An important subproblem in supervised tasks such as decision tree induction and subgroup discovery is finding an interesting binary feature (such as a node split or a subgroup refinement) based on a numeric or nominal attribute, with respect to some discrete or continuous target variable. Often one

  15. An efficient numerical target strength prediction model: Validation against analysis solutions

    NARCIS (Netherlands)

    Fillinger, L.; Nijhof, M.J.J.; Jong, C.A.F. de

    2014-01-01

    A decade ago, TNO developed RASP (Rapid Acoustic Signature Prediction), a numerical model for the prediction of the target strength of immersed underwater objects. The model is based on Kirchhoff diffraction theory. It is currently being improved to model refraction, angle dependent reflection and

  16. An optimized efficient dual junction InGaN/CIGS solar cell: A numerical simulation

    Science.gov (United States)

    Farhadi, Bita; Naseri, Mosayeb

    2016-08-01

    The photovoltaic performance of an efficient double junction InGaN/CIGS solar cell including a CdS antireflector top cover layer is studied using Silvaco ATLAS software. In this study, to gain a desired structure, the different design parameters, including the CIGS various band gaps, the doping concentration and the thickness of CdS layer are optimized. The simulation indicates that under current matching condition, an optimum efficiency of 40.42% is achieved.

  17. Numerical modeling of positive streamer in air in nonuniform fields: Efficiency of radicals production

    International Nuclear Information System (INIS)

    Kulikovsky, A.A.

    2001-01-01

    The efficiency of streamer corona depends on a number of factors such as geometry of electrodes, voltage pulse parameters, gas pressure etc. In a past 5 years a two-dimensional models of streamer in nonuniform fields in air have been developed. These models allow to simulate streamer dynamics and generation of species and to investigate the influence of external parameters on species production. In this work the influence of Laplacian field on efficiency of radicals generation is investigated

  18. An efficient approach for computing the geometrical optics field reflected from a numerically specified surface

    Science.gov (United States)

    Mittra, R.; Rushdi, A.

    1979-01-01

    An approach for computing the geometrical optic fields reflected from a numerically specified surface is presented. The approach includes the step of deriving a specular point and begins with computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Then, a cluster of three adjacent rays are chosen to define a 'mean ray' and the divergence factor associated with this mean ray. Finally, the ampilitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.

  19. An efficient approach to the numerical solution of rate-independent problems with nonconvex energies

    Czech Academy of Sciences Publication Activity Database

    Bartels, S.; Kružík, Martin

    2011-01-01

    Roč. 9, č. 3 (2011), s. 1275-1300 ISSN 1540-3459 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : numerical solution * nonconvexity Subject RIV: BA - General Mathematics Impact factor: 2.009, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf

  20. Hamiltonian analysis of Plebanski theory

    International Nuclear Information System (INIS)

    Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph

    2004-01-01

    We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity

  1. A phenomenological Hamiltonian for the Lotka-Volterra problem

    International Nuclear Information System (INIS)

    Georgian, T.; Findley, G.L.

    1996-01-01

    We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x 1 ,x 2 ) for the Lotka-Volterra problem, which leads to the rate equations x 1 =ax 1 -bx 1 x 2 , x 2 =-cx 2 +bx 1 x 2 , with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y 1 = x 1 and y 2 = x 2 ] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton's equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed

  2. Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

    International Nuclear Information System (INIS)

    Hoover, W.G.

    1980-01-01

    Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

  3. Tsallis thermostatistics for finite systems: a Hamiltonian approach

    Science.gov (United States)

    Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.

    2003-05-01

    The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.

  4. Optimal protocols for Hamiltonian and Schrödinger dynamics

    International Nuclear Information System (INIS)

    Schmiedl, Tim; Dieterich, Eckhard; Dieterich, Peter-Simon; Seifert, Udo

    2009-01-01

    For systems in an externally controllable time dependent potential, the optimal protocol minimizes the mean work spent in a finite time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations for the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space

  5. Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

    African Journals Online (AJOL)

    Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

  6. A Direct Method of Hamiltonian Structure

    International Nuclear Information System (INIS)

    Li Qi; Chen Dengyuan; Su Shuhua

    2011-01-01

    A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)

  7. Port Hamiltonian modeling of Power Networks

    NARCIS (Netherlands)

    van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R

    2012-01-01

    In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all

  8. Hamiltonian representation of divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-11-01

    Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields

  9. Hamiltonian structure of linearly extended Virasoro algebra

    International Nuclear Information System (INIS)

    Arakelyan, T.A.; Savvidi, G.K.

    1991-01-01

    The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order

  10. Momentum and hamiltonian in complex action theory

    DEFF Research Database (Denmark)

    Nagao, Keiichi; Nielsen, Holger Frits Bech

    2012-01-01

    $-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...

  11. A parcel formulation for Hamiltonian layer models

    NARCIS (Netherlands)

    Bokhove, Onno; Oliver, M.

    Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of

  12. On Distributed Port-Hamiltonian Process Systems

    NARCIS (Netherlands)

    Lopezlena, Ricardo; Scherpen, Jacquelien M.A.

    2004-01-01

    In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the

  13. Relativistic magnetohydrodynamics as a Hamiltonian system

    International Nuclear Information System (INIS)

    Holm, D.D.; Kupershmidt, A.

    1985-01-01

    The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr

  14. Hamiltonian Cycles on Random Eulerian Triangulations

    DEFF Research Database (Denmark)

    Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard

    1998-01-01

    . Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...

  15. Almost periodic Hamiltonians: an algebraic approach

    International Nuclear Information System (INIS)

    Bellissard, J.

    1981-07-01

    We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians

  16. A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

    KAUST Repository

    Bao, Weizhu

    2013-01-01

    We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.Copyright © by SIAM.

  17. Numerical Design of Megawatt Gyrotron with 120 GHz Frequency and 50% Efficiency for Plasma Fusion Application

    Science.gov (United States)

    Kumar, Nitin; Singh, Udaybir; Kumar, Anil; Bhattacharya, Ranajoy; Singh, T. P.; Sinha, A. K.

    2013-02-01

    The design of 120 GHz, 1 MW gyrotron for plasma fusion application is presented in this paper. The mode selection is carried out considering the aim of minimum mode competition, minimum cavity wall heating, etc. On the basis of the selected operating mode, the interaction cavity design and beam-wave interaction computation are carried out by using the PIC code. The design of triode type Magnetron Injection Gun (MIG) is also presented. Trajectory code EGUN, synthesis code MIGSYN and data analysis code MIGANS are used in the MIG designing. Further, the design of MIG is also validated by using the another trajectory code TRAK. The design results of beam dumping system (collector) and RF window are also presented. Depressed collector is designed to enhance the overall tube efficiency. The design study confirms >1 MW output power with tube efficiency around 50% (with collector efficiency).

  18. Numerical modelling of high efficiency InAs/GaAs intermediate band solar cell

    Science.gov (United States)

    Imran, Ali; Jiang, Jianliang; Eric, Debora; Yousaf, Muhammad

    2018-01-01

    Quantum Dots (QDs) intermediate band solar cells (IBSC) are the most attractive candidates for the next generation of photovoltaic applications. In this paper, theoretical model of InAs/GaAs device has been proposed, where we have calculated the effect of variation in the thickness of intrinsic and IB layer on the efficiency of the solar cell using detailed balance theory. IB energies has been optimized for different IB layers thickness. Maximum efficiency 46.6% is calculated for IB material under maximum optical concentration.

  19. Hamiltonian reductions in plasma physics about intrinsic gyrokinetic

    International Nuclear Information System (INIS)

    Guillebon de Resnes, L. de

    2013-01-01

    Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including

  20. Numerical Analysis of Neutral Entrainment Effect on Field-Reversed Configuration Thruster Efficiency

    Science.gov (United States)

    2014-12-01

    Δx < ζλe in order to avoid the finite grid instability. Here, ωpe is the electron plasma frequency, and λe is the electron Debye length . In an...Celeste3D results in highly efficient simulations based on ion length and timescales (and not electron scales as explicit methods do) while retaining

  1. Numerical Investigation of Effect of Parameters on Hovering Efficiency of an Annular Lift Fan Aircraft

    OpenAIRE

    Yun Jiang; Bo Zhang

    2016-01-01

    The effects of various parameters on the hovering performance of an annular lift fan aircraft are investigated by using numerical scheme. The pitch angle, thickness, aspect ratio (chord length), number of blades, and radius of duct inlet lip are explored to optimize the figure of merit. The annular lift fan is also compared with a conventional circular lift fan of the same features with the same disc loading and similar geometry. The simulation results show that the pitch angle of 27°, the th...

  2. Seven-Spot Ladybird Optimization: A Novel and Efficient Metaheuristic Algorithm for Numerical Optimization

    Directory of Open Access Journals (Sweden)

    Peng Wang

    2013-01-01

    Full Text Available This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO. The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions.

  3. Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces

    KAUST Repository

    Kou, Jisheng

    2015-08-01

    Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.

  4. Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

    Energy Technology Data Exchange (ETDEWEB)

    Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)

    2014-05-01

    This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

  5. Experimental and numerical investigations of heat transfer and thermal efficiency of an infrared gas stove

    Science.gov (United States)

    Charoenlerdchanya, A.; Rattanadecho, P.; Keangin, P.

    2018-01-01

    An infrared gas stove is a low-pressure gas stove type and it has higher thermal efficiency than the other domestic cooking stoves. This study considers the computationally determine water and air temperature distributions, water and air velocity distributions and thermal efficiency of the infrared gas stove. The goal of this work is to investigate the effect of various pot diameters i.e. 220 mm, 240 mm and 260 mm on the water and air temperature distributions, water and air velocity distributions and thermal efficiency of the infrared gas stove. The time-dependent heat transfer equation involving diffusion and convection coupled with the time-dependent fluid dynamic equation is implemented and is solved by using the finite element method (FEM). The computer simulation study is validated with an experimental study, which is use standard experiment by LPG test for low-pressure gas stove in households (TIS No. 2312-2549). The findings revealed that the water and air temperature distributions increase with greater heating time, which varies with the three different pot diameters (220 mm, 240 mm and 260 mm). Similarly, the greater heating time, the water and air velocity distributions increase that vary by pot diameters (220, 240 and 260 mm). The maximum water temperature in the case of pot diameter of 220 mm is higher than the maximum water velocity in the case of pot diameters of 240 mm and 260 mm, respectively. However, the maximum air temperature in the case of pot diameter of 260 mm is higher than the maximum water velocity in the case of pot diameters of 240 mm and 220 mm, respectively. The obtained results may provide a basis for improving the energy efficiency of infrared gas stoves and other equipment, including helping to reduce energy consumption.

  6. Estimation of the drift eliminator efficiency using numerical and experimental methods

    Directory of Open Access Journals (Sweden)

    Stodůlka Jiří

    2016-01-01

    Full Text Available The purpose of the drift eliminators is to prevent water from escaping in significant amounts the cooling tower. They are designed to catch the droplets dragged by the tower draft and the efficiency given by the shape of the eliminator is the main evaluation criteria. The ability to eliminate the escaping water droplets is studied using CFD and using the experimental IPI method.

  7. FASTREACT – An efficient numerical framework for the solution of reactive transport problems

    International Nuclear Information System (INIS)

    Trinchero, Paolo; Molinero, Jorge; Román-Ross, Gabriela; Berglund, Sten; Selroos, Jan-Olof

    2014-01-01

    Highlights: • We present a tool for the efficient solution of reactive transport problems. • The tool is used to simulate radionuclide transport in a two-dimensional medium. • The results are successfully compared with those obtained using an Eulerian approach. • A large-scale application example is also solved. • The results show that the proposed tool can efficiently solve large-scale models. - Abstract: In the framework of safety assessment studies for geological disposal, large scale reactive transport models are powerful inter-disciplinary tools aiming at supporting regulatory decision making as well as providing input to repository engineering activities. Important aspects of these kinds of models are their often very large temporal and spatial modelling scales and the need to integrate different non-linear processes (e.g., mineral dissolution and precipitation, adsorption and desorption, microbial reactions and redox transformations). It turns out that these types of models may be computationally highly demanding. In this work, we present a Lagrangian-based framework, denoted as FASTREACT, that aims at solving multi-component-reactive transport problems with a computationally efficient approach allowing complex modelling problems to be solved in large spatial and temporal scales. The tool has been applied to simulate radionuclide migration in a synthetic heterogeneous transmissivity field and the results have been successfully compared with those obtained using a standard Eulerian approach. Finally, the same geochemical model has been coupled to an ensemble of realistic three-dimensional transport pathways to simulate the migration of a set of radionuclides from a hypothetical repository for spent nuclear fuel to the surface. The results of this modelling exercise, which includes key processes such as the exchange of mass between the conductive fractures and the matrix, show that FASTREACT can efficiently solve large-scale reactive transport models

  8. Numerical study of hydrodynamic behavior and conversion efficiency of a two-buoy wave energy converter

    Science.gov (United States)

    Yang, Cen; Zhang, Yong-liang

    2018-04-01

    In this paper we propose a two-buoy wave energy converter composed of a heaving semi-submerged cylindrical buoy, a fixed submerged cylindrical buoy and a power take-off (PTO) system, and investigate the effect of the fixed submerged buoy on the hydrodynamics of the heaving semi-submerged buoy based on the three-dimensional potential theory. And the dynamic response of the semi-submerged buoy and the wave energy conversion efficiency of the converter are analyzed. The difference of the hydrodynamics and the wave energy conversion efficiency of a semi-submerged buoy converter with and without a fixed submerged buoy is discussed. It is revealed that the influence of the fixed submerged buoy on the exciting wave force, the added mass, the radiation damping coefficient and the wave energy conversion efficiency can be significant with a considerable variation, depending on the vertical distance between the heaving semi-submerged buoy and the fixed submerged buoy, the diameter ratio of the fixed submerged buoy to the heaving semi-submerged buoy and the water depth.

  9. Interface COMSOL-PHREEQC (iCP), an efficient numerical framework for the solution of coupled multiphysics and geochemistry

    Science.gov (United States)

    Nardi, Albert; Idiart, Andrés; Trinchero, Paolo; de Vries, Luis Manuel; Molinero, Jorge

    2014-08-01

    This paper presents the development, verification and application of an efficient interface, denoted as iCP, which couples two standalone simulation programs: the general purpose Finite Element framework COMSOL Multiphysics® and the geochemical simulator PHREEQC. The main goal of the interface is to maximize the synergies between the aforementioned codes, providing a numerical platform that can efficiently simulate a wide number of multiphysics problems coupled with geochemistry. iCP is written in Java and uses the IPhreeqc C++ dynamic library and the COMSOL Java-API. Given the large computational requirements of the aforementioned coupled models, special emphasis has been placed on numerical robustness and efficiency. To this end, the geochemical reactions are solved in parallel by balancing the computational load over multiple threads. First, a benchmark exercise is used to test the reliability of iCP regarding flow and reactive transport. Then, a large scale thermo-hydro-chemical (THC) problem is solved to show the code capabilities. The results of the verification exercise are successfully compared with those obtained using PHREEQC and the application case demonstrates the scalability of a large scale model, at least up to 32 threads.

  10. A numerical study of the effects of design parameters on the acoustics noise of a high efficiency propeller

    Science.gov (United States)

    Yang, Liu; Huang, Jun; Yi, Mingxu; Zhang, Chaopu; Xiao, Qian

    2017-11-01

    A numerical study of a high efficiency propeller in the aerodynamic noise generation is carried out. Based on RANS, three-dimensional numerical simulation is performed to obtain the aerodynamic performance of the propeller. The result of the aerodynamic analysis is given as input of the acoustic calculation. The sound is calculated using the Farassat 1A, which is derived from Ffowcs Williams-Hawkings equation, and compared with the data of wind tunnel. The propeller is modified for noise reduction by changing its geometrical parameters such as diameter, chord width and pitch angle. The trend of variation between aerodynamic analysis data and acoustic calculation result are compared and discussed for different modification tasks. Meaningful conclusions are drawn on the noise reduction of propeller.

  11. An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery

    Directory of Open Access Journals (Sweden)

    Michal Beneš

    2018-01-01

    Full Text Available We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.

  12. Numerical Investigation of Effect of Parameters on Hovering Efficiency of an Annular Lift Fan Aircraft

    Directory of Open Access Journals (Sweden)

    Yun Jiang

    2016-10-01

    Full Text Available The effects of various parameters on the hovering performance of an annular lift fan aircraft are investigated by using numerical scheme. The pitch angle, thickness, aspect ratio (chord length, number of blades, and radius of duct inlet lip are explored to optimize the figure of merit. The annular lift fan is also compared with a conventional circular lift fan of the same features with the same disc loading and similar geometry. The simulation results show that the pitch angle of 27°, the thickness of 4% chord length, the aspect ratio of 3.5~4.0, 32 blades, and the radius of inlet lip of 4.7% generate the maximum figure of merit of 0.733. The optimized configuration can be used for further studies of the annular lift fan aircraft.

  13. An integrated DEA PCA numerical taxonomy approach for energy efficiency assessment and consumption optimization in energy intensive manufacturing sectors

    International Nuclear Information System (INIS)

    Azadeh, A.; Amalnick, M.S.; Ghaderi, S.F.; Asadzadeh, S.M.

    2007-01-01

    This paper introduces an integrated approach based on data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT) for total energy efficiency assessment and optimization in energy intensive manufacturing sectors. Total energy efficiency assessment and optimization of the proposed approach considers structural indicators in addition conventional consumption and manufacturing sector output indicators. The validity of the DEA model is verified and validated by PCA and NT through Spearman correlation experiment. Moreover, the proposed approach uses the measure-specific super-efficiency DEA model for sensitivity analysis to determine the critical energy carriers. Four energy intensive manufacturing sectors are discussed in this paper: iron and steel, pulp and paper, petroleum refining and cement manufacturing sectors. To show superiority and applicability, the proposed approach has been applied to refinery sub-sectors of some OECD (Organization for Economic Cooperation and Development) countries. This study has several unique features which are: (1) a total approach which considers structural indicators in addition to conventional energy efficiency indicators; (2) a verification and validation mechanism for DEA by PCA and NT and (3) utilization of DEA for total energy efficiency assessment and consumption optimization of energy intensive manufacturing sectors

  14. Optimization Of The Efficiency Of A Pre And Post Apodized Piaa Coronagraph Using A Numerical Propagator.

    Science.gov (United States)

    Carlotti, Alexis; Pueyo, L.; Kasdin, N. J.

    2011-01-01

    Using a numerical propagator based on the Huygens integral, we study the apodization profiles (and PSFs) provided by a set of two PIAA mirrors that follow a square geometry. This choice is made as deformable mirrors could potentially be used as pupil mappers. A pre-apodizer and a post-apodizer are needed to improve the contrast and relax the manufacturing constraints of the mirrors. The stroke, minimum radius of curvature and diameter of the mirrors altogether with the parameters that define the pre and post apodizers’ properties are connected to the performances of the coronagraph in term of contrast, throughput and inner working angle. Characterizing these relations allows us to invert some of them. For example, we are able to set a specific value for the final throughput and to find out, for a particular mirror's diameter and stroke, the distance between the mirrors as well as the characteristics of the pre and post apodizers that need to be used. Contrast maps are given as functions of the stroke, the diameter, the radius of curvature and the throughput. All these numerical tools help us to understand the trade-offs that exist behind the design of a PIAA system. There is a direct relation between the diameter, stroke, maximum radius of curvature of the mirrors and the strength of the post-apodizer. Increasing the diameter improves the contrast but asks for a higher stroke and bigger distance. For a given set of mirrors, a better contrast can then be obtained by strengthening the pre and post apodizers at the expense of the throughput and the inner working angle. The post-apodizer could either be a transmittive, continuous apodizer or a binary apodizer. The latter case is explored and optimized binary apodizers are found for several PIAA cases. This work is supported by a NASA APRA grant.

  15. Numerical analysis on thermal characteristics and ice melting efficiency for microwave deicing vehicle

    Science.gov (United States)

    Wang, Can; Yang, Bo; Tan, Gangfeng; Guo, Xuexun; Zhou, Li; Xiong, Shengguang

    2016-05-01

    In the high latitudes, the icy patches on the road are frequently generated and have a wide distribution, which are difficult to remove and obviously affect the normal usage of the highways, bridges and airport runways. Physical deicing, such as microwave (MW) deicing, help the ice melt completely through heating mode and then the ice layer can be swept away. Though it is no pollution and no damage to the ground, the low efficiency hinders the development of MW deicing vehicle equipped without sufficient speed. In this work, the standard evaluation of deicing is put forward firstly. The intensive MW deicing is simplified to ice melting process characterized by one-dimensional slab with uniform volumetric energy generation, which results in phase transformation and interface motion between ice and water. The heating process is split into the superposition of three parts — non-heterogeneous heating for ground without phase change, heat transfer with phase change and the heat convection between top surface of ice layer and flow air. Based on the transient heat conduction theory, a mathematical model, combining electromagnetic and two-phase thermal conduction, is proposed in this work, which is able to reveal the relationship between the deicing efficiency and ambient conditions, as well as energy generation and material parameters. Using finite difference time-domain, this comprehensive model is developed to solve the moving boundary heat transfer problem in a one-dimensional structured gird. As a result, the stimulation shows the longitudinal temperature distributions in all circumstances and quantitative validation is obtained by comparing simulated temperature distributions under different conditions. In view of the best economy and fast deicing, these analytic solutions referring to the complex influence factors of deicing efficiency demonstrate the optimal matching for the new deicing design.

  16. Numerical assessment of efficiency and control stability of an HTS synchronous motor

    Energy Technology Data Exchange (ETDEWEB)

    Xian Wei; Yuan Weijia; Coombs, T A, E-mail: wx210@cam.ac.u [Electronic, Power and Energy Conversion Group, Engineering Department, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 0FA (United Kingdom)

    2010-06-01

    A high temperature superconducting (HTS) permanent magnet synchronous motor (PMSM) is designed and developed in Cambridge University. It is expected to become cost competitive with the conventional PMSM owing to its high efficiency, high power density, high torque density, etc. The structure and parameters of HTS PMSM are detailed. Both AC losses by transport current and applied filed in stator armature winding of HTS PMSM are also analyzed. Computed and simulated results of the characteristics of the HTS PMSM and conventional PMSM are compared. The improvement on stability of direct torque control (DTC) on the HTS PMSM is estimated, and proved by simulation on Matlab/Simulink.

  17. Numerically robust and efficient nonlocal electron transport in 2D DRACO simulations

    Science.gov (United States)

    Cao, Duc; Chenhall, Jeff; Moses, Greg; Delettrez, Jacques; Collins, Tim

    2013-10-01

    An improved implicit algorithm based on Schurtz, Nicolai and Busquet (SNB) algorithm for nonlocal electron transport is presented. Validation with direct drive shock timing experiments and verification with the Goncharov nonlocal model in 1D LILAC simulations demonstrate the viability of this efficient algorithm for producing 2D lagrangian radiation hydrodynamics direct drive simulations. Additionally, simulations provide strong incentive to further modify key parameters within the SNB theory, namely the ``mean free path.'' An example 2D polar drive simulation to study 2D effects of the nonlocal flux as well as mean free path modifications will also be presented. This research was supported by the University of Rochester Laboratory for Laser Energetics.

  18. Tailored high-resolution numerical weather forecasts for energy efficient predictive building control

    Science.gov (United States)

    Stauch, V. J.; Gwerder, M.; Gyalistras, D.; Oldewurtel, F.; Schubiger, F.; Steiner, P.

    2010-09-01

    The high proportion of the total primary energy consumption by buildings has increased the public interest in the optimisation of buildings' operation and is also driving the development of novel control approaches for the indoor climate. In this context, the use of weather forecasts presents an interesting and - thanks to advances in information and predictive control technologies and the continuous improvement of numerical weather prediction (NWP) models - an increasingly attractive option for improved building control. Within the research project OptiControl (www.opticontrol.ethz.ch) predictive control strategies for a wide range of buildings, heating, ventilation and air conditioning (HVAC) systems, and representative locations in Europe are being investigated with the aid of newly developed modelling and simulation tools. Grid point predictions for radiation, temperature and humidity of the high-resolution limited area NWP model COSMO-7 (see www.cosmo-model.org) and local measurements are used as disturbances and inputs into the building system. The control task considered consists in minimizing energy consumption whilst maintaining occupant comfort. In this presentation, we use the simulation-based OptiControl methodology to investigate the impact of COSMO-7 forecasts on the performance of predictive building control and the resulting energy savings. For this, we have selected building cases that were shown to benefit from a prediction horizon of up to 3 days and therefore, are particularly suitable for the use of numerical weather forecasts. We show that the controller performance is sensitive to the quality of the weather predictions, most importantly of the incident radiation on differently oriented façades. However, radiation is characterised by a high temporal and spatial variability in part caused by small scale and fast changing cloud formation and dissolution processes being only partially represented in the COSMO-7 grid point predictions. On the

  19. An efficient and general numerical method to compute steady uniform vortices

    Science.gov (United States)

    Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.

    2011-07-01

    Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.

  20. Single-particle dynamics - Hamiltonian formulation

    International Nuclear Information System (INIS)

    Montague, B.W.

    1977-01-01

    In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)

  1. Incomplete Dirac reduction of constrained Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Chandre, C., E-mail: chandre@cpt.univ-mrs.fr

    2015-10-15

    First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

  2. Quantum entangling power of adiabatically connected Hamiltonians

    International Nuclear Information System (INIS)

    Hamma, Alioscia; Zanardi, Paolo

    2004-01-01

    The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied

  3. Quantum Hamiltonian Physics with Supercomputers

    International Nuclear Information System (INIS)

    Vary, James P.

    2014-01-01

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed

  4. Quantum Hamiltonian Physics with Supercomputers

    Energy Technology Data Exchange (ETDEWEB)

    Vary, James P.

    2014-06-15

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

  5. Recombination efficiency of molecular hydrogen on interstellar grains - II: A numerical study

    International Nuclear Information System (INIS)

    Chakrabarti, S.K.; Ankan, Das; Kinsuk, Acharyya; Sonali, Chakrabarti

    2006-05-01

    Knowledge of the recombination time on the grain surfaces has been a major obstacle in deciding the production rate of molecular hydrogen and other molecules in the interstellar medium. We present a numerical study to compute this time for molecular hydrogen for various cloud and grain parameters. We also find the time dependence, particularly when a grain is freshly injected into the system. Apart from the fact that the recombination times seem to be functions of the grain parameters such as the activation barrier energy, temperature etc., our result also shows the dependence on the number of sites in the grain S and the effective accretion rate per site a s of atomic hydrogen. To put simply the average time that a pair of atomic hydrogens will take to produce one molecular hydrogen depends on how heavily the grain is already populated by atomic and molecular hydrogens and how fast the hopping and desorption times are. We show that if we write the average recombination time as T r ∼ S α /A H , where, A H is the hopping rate, then α could be much greater than 1 for all astrophysically relevant accretion rates. Thus the average formation rate of H 2 is also dependent on the grain parameters, temperature and the accretion rate. We believe that our results will affect the overall rate of the formation of complex molecules such as methanol which requires successive hydrogenation on the grain surfaces in the interstellar medium. (author)

  6. An efficient numerical technique for solving navier-stokes equations for rotating flows

    International Nuclear Information System (INIS)

    Haroon, T.; Shah, T.M.

    2000-01-01

    This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

  7. Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank

    DEFF Research Database (Denmark)

    Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2013-01-01

    A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau...... method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...... wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes....

  8. A numerical investigation on the efficiency of range extending systems using Advanced Vehicle Simulator

    Science.gov (United States)

    Varnhagen, Scott; Same, Adam; Remillard, Jesse; Park, Jae Wan

    2011-03-01

    Series plug-in hybrid electric vehicles of varying engine configuration and battery capacity are modeled using Advanced Vehicle Simulator (ADVISOR). The performance of these vehicles is analyzed on the bases of energy consumption and greenhouse gas emissions on the tank-to-wheel and well-to-wheel paths. Both city and highway driving conditions are considered during the simulation. When simulated on the well-to-wheel path, it is shown that the range extender with a Wankel rotary engine consumes less energy and emits fewer greenhouse gases compared to the other systems with reciprocating engines during many driving cycles. The rotary engine has a higher power-to-weight ratio and lower noise, vibration and harshness compared to conventional reciprocating engines, although performs less efficiently. The benefits of a Wankel engine make it an attractive option for use as a range extender in a plug-in hybrid electric vehicle.

  9. Numerical simulation and analysis of fuzzy PID and PSD control methodologies as dynamic energy efficiency measures

    International Nuclear Information System (INIS)

    Ardehali, M.M.; Saboori, M.; Teshnelab, M.

    2004-01-01

    Energy efficiency enhancement is achieved by utilizing control algorithms that reduce overshoots and undershoots as well as unnecessary fluctuations in the amount of energy input to energy consuming systems during transient operation periods. It is hypothesized that application of control methodologies with characteristics that change with time and according to the system dynamics, identified as dynamic energy efficiency measures (DEEM), achieves the desired enhancement. The objective of this study is to simulate and analyze the effects of fuzzy logic based tuning of proportional integral derivative (F-PID) and proportional sum derivative (F-PSD) controllers for a heating and cooling energy system while accounting for the dynamics of the major system components. The procedure to achieve the objective includes utilization of fuzzy logic rules to determine the PID and PSD controllers gain coefficients so that the control laws for regulating the heat exchangers heating or cooling energy inputs are determined in each time step of the operation period. The performances of the F-PID and F-PSD controllers are measured by means of two cost functions that are based on quadratic forms of the energy input and deviation from a set point temperature. It is found that application of the F-PID control algorithm, as a DEEM, results in lower costs for energy input and deviation from a set point temperature by 24% and 17% as compared to a PID and 13% and 8% as compared to a PSD, respectively. It is also shown that the F-PSD performance is better than that of the F-PID controller

  10. Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

    Science.gov (United States)

    Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

    2017-09-01

    The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite

  11. A Fast Numerical Method for Max-Convolution and the Application to Efficient Max-Product Inference in Bayesian Networks.

    Science.gov (United States)

    Serang, Oliver

    2015-08-01

    Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.

  12. Jacobi fields of completely integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.

    2003-01-01

    We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion

  13. Quantum Hamiltonian reduction in superspace formalism

    International Nuclear Information System (INIS)

    Madsen, J.O.; Ragoucy, E.

    1994-02-01

    Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

  14. Integrable Hamiltonian systems and spectral theory

    CERN Document Server

    Moser, J

    1981-01-01

    Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.

  15. Spectral properties of almost-periodic Hamiltonians

    International Nuclear Information System (INIS)

    Lima, R.

    1983-12-01

    We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr

  16. Air parcels and air particles: Hamiltonian dynamics

    NARCIS (Netherlands)

    Bokhove, Onno; Lynch, Peter

    We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations

  17. Discrete Hamiltonian evolution and quantum gravity

    International Nuclear Information System (INIS)

    Husain, Viqar; Winkler, Oliver

    2004-01-01

    We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

  18. Classical mechanics Hamiltonian and Lagrangian formalism

    CERN Document Server

    Deriglazov, Alexei

    2016-01-01

    This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.

  19. Hamiltonian cycle problem and Markov chains

    CERN Document Server

    Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T

    2014-01-01

    This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.

  20. Variable Delay in port-Hamiltonian Telemanipulation

    NARCIS (Netherlands)

    Secchi, C; Stramigioli, Stefano; Fantuzzi, C.

    2006-01-01

    In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.

  1. Laboratory Experiment and Numerical Analysis of a New Type of Solar Tower Efficiently Generating a Thermal Updraft

    Directory of Open Access Journals (Sweden)

    Yuji Ohya

    2016-12-01

    Full Text Available A new type of solar tower was developed through laboratory experiments and numerical analyses. The solar tower mainly consists of three components. The transparent collector area is an aboveground glass roof, with increasing height toward the center. Attached to the center of the inside of the collector is a vertical tower within which a wind turbine is mounted at the lower entry to the tower. When solar radiation heats the ground through the glass roof, ascending warm air is guided to the center and into the tower. A solar tower that can generate electricity using a simple structure that enables easy and less costly maintenance has considerable advantages. However, conversion efficiency from sunshine energy to mechanical turbine energy is very low. Aiming to improve this efficiency, the research project developed a diffuser-type tower instead of a cylindrical tower, and investigated a suitable diffuser shape for practical use. After changing the tower height and diffuser open angle, with a temperature difference between the ambient air aloft and within the collector, various diffuser tower shapes were tested by laboratory experiments and numerical analyses. As a result, it was found that a diffuser tower with a semi-open angle of 4° is an optimal shape, producing the fastest updraft at each temperature difference in both the laboratory experiments and numerical analyses. The relationships between thermal updraft speed and temperature difference and/or tower height were confirmed. It was found that the thermal updraft velocity is proportional to the square root of the tower height and/or temperature difference.

  2. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

    Science.gov (United States)

    Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

    2010-10-01

    Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

  3. On local Hamiltonians and dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)

    2006-11-15

    We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.

  4. Generalized Hubbard Hamiltonian: renormalization group approach

    International Nuclear Information System (INIS)

    Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

    1991-01-01

    We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

  5. On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

    Science.gov (United States)

    Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

    2015-01-01

    We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

  6. 3D-radiative transfer in terrestrial atmosphere: An efficient parallel numerical procedure

    Science.gov (United States)

    Bass, L. P.; Germogenova, T. A.; Nikolaeva, O. V.; Kokhanovsky, A. A.; Kuznetsov, V. S.

    2003-04-01

    Light propagation and scattering in terrestrial atmosphere is usually studied in the framework of the 1D radiative transfer theory [1]. However, in reality particles (e.g., ice crystals, solid and liquid aerosols, cloud droplets) are randomly distributed in 3D space. In particular, their concentrations vary both in vertical and horizontal directions. Therefore, 3D effects influence modern cloud and aerosol retrieval procedures, which are currently based on the 1D radiative transfer theory. It should be pointed out that the standard radiative transfer equation allows to study these more complex situations as well [2]. In recent year the parallel version of the 2D and 3D RADUGA code has been developed. This version is successfully used in gammas and neutrons transport problems [3]. Applications of this code to radiative transfer in atmosphere problems are contained in [4]. Possibilities of code RADUGA are presented in [5]. The RADUGA code system is an universal solver of radiative transfer problems for complicated models, including 2D and 3D aerosol and cloud fields with arbitrary scattering anisotropy, light absorption, inhomogeneous underlying surface and topography. Both delta type and distributed light sources can be accounted for in the framework of the algorithm developed. The accurate numerical procedure is based on the new discrete ordinate SWDD scheme [6]. The algorithm is specifically designed for parallel supercomputers. The version RADUGA 5.1(P) can run on MBC1000M [7] (768 processors with 10 Gb of hard disc memory for each processor). The peak productivity is equal 1 Tfl. Corresponding scalar version RADUGA 5.1 is working on PC. As a first example of application of the algorithm developed, we have studied the shadowing effects of clouds on neighboring cloudless atmosphere, depending on the cloud optical thickness, surface albedo, and illumination conditions. This is of importance for modern satellite aerosol retrieval algorithms development. [1] Sobolev

  7. Jet formation and equatorial superrotation in Jupiter's atmosphere: Numerical modelling using a new efficient parallel code

    Science.gov (United States)

    Rivier, Leonard Gilles

    Using an efficient parallel code solving the primitive equations of atmospheric dynamics, the jet structure of a Jupiter like atmosphere is modeled. In the first part of this thesis, a parallel spectral code solving both the shallow water equations and the multi-level primitive equations of atmospheric dynamics is built. The implementation of this code called BOB is done so that it runs effectively on an inexpensive cluster of workstations. A one dimensional decomposition and transposition method insuring load balancing among processes is used. The Legendre transform is cache-blocked. A "compute on the fly" of the Legendre polynomials used in the spectral method produces a lower memory footprint and enables high resolution runs on relatively small memory machines. Performance studies are done using a cluster of workstations located at the National Center for Atmospheric Research (NCAR). BOB performances are compared to the parallel benchmark code PSTSWM and the dynamical core of NCAR's CCM3.6.6. In both cases, the comparison favors BOB. In the second part of this thesis, the primitive equation version of the code described in part I is used to study the formation of organized zonal jets and equatorial superrotation in a planetary atmosphere where the parameters are chosen to best model the upper atmosphere of Jupiter. Two levels are used in the vertical and only large scale forcing is present. The model is forced towards a baroclinically unstable flow, so that eddies are generated by baroclinic instability. We consider several types of forcing, acting on either the temperature or the momentum field. We show that only under very specific parametric conditions, zonally elongated structures form and persist resembling the jet structure observed near the cloud level top (1 bar) on Jupiter. We also study the effect of an equatorial heat source, meant to be a crude representation of the effect of the deep convective planetary interior onto the outer atmospheric layer. We

  8. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

    Science.gov (United States)

    Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

    2018-03-01

    We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

  9. Numerically Simulated Impact of Gas Prandtl Number and Flow Model on Efficiency of the Machine-less Energetic Separation Device

    Directory of Open Access Journals (Sweden)

    K. S. Egorov

    2015-01-01

    Full Text Available The presented paper regards the influence of one of similarity criteria – the Prandtl number of gas (Pr - on the efficiency of the machine-less energetic separation device (Leontiev pipe, using numerical modeling in ANSYS software. This device, equally as Rank-Hilsch and Hartman-Schprenger pipes, is designed to separate one gas flow into two flows with different temperatures. One flow (supersonic streams out of the pipe with a temperature higher than initial and the other (subsonic flows out with a temperature lower than initial. This direction of energetic separation is true if the Prandtl number is less than 1 that corresponds to gases.The Prandtl number affects the efficiency of running Leontiev pipe indirectly both through a temperature difference on which a temperature recovery factor has an impact and through a thermal conductivity coefficient that shows the impact of heat transfer intensity between gas and solid wall.The Prandtl number range in the course of research was from 0.1 to 0.7. The Prandtl number value equal to 0.7 corresponds to the air or pure gases (for example, inert argon gas. The Prandtl number equal to 0.2 corresponds to the mixtures of inert gases such as helium-xenon.The numerical modeling completed for the supersonic flow with Mach number 2.0 shows that efficiency of the machine-less energetic separation device has been increased approximately 2 times with the Prandtl number decreasing from 0.7 to 0.2. Moreover, for the counter-flow scheme this effect is a little higher due to its larger heat efficiency in comparison with the straight-flow one.Also, the research shows that the main problem for the further increase of the Leontiev pipe efficiency is a small value of thermal conductivity coefficient, which requires an intensification of the heat exchange, especially in the supersonic flow. It can be obtained, for example, by using a system of oblique shock waves in the supersonic channel.

  10. Numerical study of geometric parameters effecting temperature and thermal efficiency in a premix multi-hole flat flame burner

    International Nuclear Information System (INIS)

    Saberi Moghaddam, Mohammad Hossein; Saei Moghaddam, Mojtaba; Khorramdel, Mohammad

    2017-01-01

    This paper investigates the geometric parameters related to thermal efficiency and pollution emission of a multi-hole flat flame burner. Recent experimental studies indicate that such burners are significantly influenced by both the use of distribution mesh and the size of the diameter of the main and retention holes. The present study numerically simulated methane-air premixed combustion using a two-step mechanism and constant mass diffusivity for all species. The results indicate that the addition of distribution mesh leads to uniform flow and maximum temperature that will reduce NOx emissions. An increase in the diameter of the main holes increased the mass flow which increased the temperature, thermal efficiency and NOx emissions. The size of the retention holes should be considered to decrease the total flow velocity and bring the flame closer to the burner surface, although a diameter change did not considerably improve temperature and thermal efficiency. Ultimately, under temperature and pollutant emission constraints, the optimum diameters of the main and retention holes were determined to be 5 and 1.25 mm, respectively. - Highlights: • Using distribution mesh led to uniform flow and reduced Nox pollutant by 53%. • 93% of total heat transfer occurred by radiation method in multi-hole burner. • Employing retention hole caused the flame become closer to the burner surface.

  11. pH variation and influence in an autotrophic nitrogen removing biofilm system using an efficient numerical solution strategy

    DEFF Research Database (Denmark)

    Vangsgaard, Anna Katrine; Mauricio Iglesias, Miguel; Valverde Perez, Borja

    2013-01-01

    A pH simulator consisting of an efficient numerical solver of a system of nine nonlinear equations was constructed and implemented in the modeling software MATLAB. The pH simulator was integrated in a granular biofilm model and used to simulate the pH profiles within granules performing...... the nitritation-anammox process for a range of operating points. The simulation results showed that pH profiles were consistently increasing with increasing depth into the granule, since the proton producing aerobic ammonium oxidizers (AOB) were located close to the granule surface.Despite this pH profile, more...... NH3 was available for AOB than for anaerobic ammonium oxidizers (AnAOB), located in the center of the granules. However, operating at a higher oxygen loading resulted in steeper changes in pH over the depth of the granule and caused the NH3 concentration profile to increase from the granule surface...

  12. Numerical dataset for analyzing the performance of a highly efficient ultrathin film CdTe solar cell

    Directory of Open Access Journals (Sweden)

    Rucksana Safa Sultana

    2017-06-01

    Full Text Available The article comprises numerical data of distinct semiconductor materials applied in the sketch of a CdTe absorber based ultrathin film solar cell. Additionally, the contact layer parametric values of the cell have been described also. Therefore, the simulation has been conducted with data related to the hetero-structured (n-ZnO/n-CdS/p-CdTe/p-ZnTe semiconductor device and a J–V characteristics curve was obtained. The operating conditions have also been recorded. Afterward, the solar cell performance parameters such as open circuit voltage (Voc, short circuit current density (Jsc, fill factor (FF, and efficiency (η have been investigated and compared with reference cell.

  13. Discrete port-Hamiltonian systems

    NARCIS (Netherlands)

    Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

    2006-01-01

    Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

  14. An IBM-3 hamiltonian from a multi-j-shell model

    International Nuclear Information System (INIS)

    Evans, J.A.; Elliott, J.P.; Lac, V.S.; Long, G.L.

    1995-01-01

    The number and isospin dependence of the hamiltonian in the isospin invariant form (IBM-3) of the boson model is deduced from a seniority mapping onto a shell-model system of several shells. The numerical results are compared with earlier work for a single j-shell. (orig.)

  15. Hamiltonian Monte Carlo study of (1+1)-dimensional models with restricted supersymmetry on the lattice

    International Nuclear Information System (INIS)

    Ranft, J.; Schiller, A.

    1984-01-01

    Lattice versions with restricted suppersymmetry of simple (1+1)-dimensional supersymmetric models are numerically studied using a local hamiltonian Monte Carlo method. The pattern of supersymmetry breaking closely follows the expectations of Bartels and Bronzan obtain in an alternative lattice formulation. (orig.)

  16. A microscopic derivation of the dependence of the IBM3 hamiltonian on the boson number and isospin

    International Nuclear Information System (INIS)

    Evans, J.A.; Long, G.L.P.; Elliott, J.P.

    1993-01-01

    The number and isospin dependence of the hamiltonian in the isospin invariant form (IBM3) of the boson model has been deduced from a seniority mapping into a single j-shell, making use of shell-model formulae recently obtained from vector coherent state theory. Numerical results are given for a specific shell-model example and the qualitative behaviour of the different parameters in the hamiltonian is discussed. (orig.)

  17. Microscopic determination of leading terms of the interaction Hamiltonian between sd- and g-parts in the sdg IBM

    International Nuclear Information System (INIS)

    Zhang Zhanjun; Liu Yong; Sang Jianping

    1995-01-01

    Starting from one of the microscopic sdg interacting boson approximations, the leading terms in the interaction Hamiltonian are discussed by using numerical investigations. Comparisons of both the calculated levels and the overlap of wave functions between the exact results and the approximations are made to find out negligible part in the Hamiltonian. The results show that the leading terms given may provide a way to simplify the complex calculations

  18. Gravitational surface Hamiltonian and entropy quantization

    Directory of Open Access Journals (Sweden)

    Ashish Bakshi

    2017-02-01

    Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

  19. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1982-01-01

    A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

  20. Hamiltonian boundary term and quasilocal energy flux

    International Nuclear Information System (INIS)

    Chen, C.-M.; Nester, James M.; Tung, R.-S.

    2005-01-01

    The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant

  1. Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

    Science.gov (United States)

    LeMesurier, Brenton

    2012-01-01

    A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

  2. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  3. Hamiltonian dynamics for complex food webs

    Science.gov (United States)

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

  4. Convergence to equilibrium under a random Hamiltonian

    Science.gov (United States)

    Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

    2012-09-01

    We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

  5. Ostrogradski Hamiltonian approach for geodetic brane gravity

    International Nuclear Information System (INIS)

    Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

    2010-01-01

    We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.

  6. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

    Directory of Open Access Journals (Sweden)

    F. F. Ngwane

    2017-01-01

    Full Text Available In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs, including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs. Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.

  7. Molecular dynamics with deterministic and stochastic numerical methods

    CERN Document Server

    Leimkuhler, Ben

    2015-01-01

    This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

  8. Computing the real-time Green's Functions of large Hamiltonian matrices

    OpenAIRE

    Iitaka, Toshiaki

    1998-01-01

    A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method...

  9. Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

    Science.gov (United States)

    Minesaki, Yukitaka

    2018-04-01

    We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

  10. A modified chaos-based communication scheme using Hamiltonian forms and observer

    International Nuclear Information System (INIS)

    Lopez-Mancilla, D; Cruz-Hernandez, C; Posadas-Castillo, C

    2005-01-01

    In this work, a modified chaos-based communication scheme is presented. In particular, we use the modified scheme proposed by Lopez-Mancilla and Cruz-Hernandez (2005), that improves the basic scheme for chaotic masking using a single transmission channel proposed by Cuomo and coworkers (1993). It is extended for a special class of Generalized Hamiltonian systems. Substantial differences that significantly affect the reception quality of the sent message, with or without considering noise effect in the transmission channel are given. We use two Hamiltonian Lorenz systems unidirectionally coupled, the first like a master/transmitter system and the other like a slave/receiver system in order to illustrate with numerical simulations the effectiveness of the modified scheme, using chaos synchronization with Hamiltonian forms and observer

  11. A modified chaos-based communication scheme using Hamiltonian forms and observer

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Mancilla, D [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103, Carretera Tijuana-Ensenada, 22860, Ensenada, B.C. (Mexico); Cruz-Hernandez, C [Telematics Direction, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107 Carretera Tijuana-Ensenada, 22860 Ensenada, B.C. (Mexico); Posadas-Castillo, C [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103, Carretera Tijuana-Ensenada, 22860, Ensenada, B.C. (Mexico); Faculty of Engineering Mechanic and Electrical (FIME), Nuevo Leon Autonomous University (UANL), Pedro de alba s/n Cd. Universitaria San Nicolas de los Garza N.L. (Mexico)

    2005-01-01

    In this work, a modified chaos-based communication scheme is presented. In particular, we use the modified scheme proposed by Lopez-Mancilla and Cruz-Hernandez (2005), that improves the basic scheme for chaotic masking using a single transmission channel proposed by Cuomo and coworkers (1993). It is extended for a special class of Generalized Hamiltonian systems. Substantial differences that significantly affect the reception quality of the sent message, with or without considering noise effect in the transmission channel are given. We use two Hamiltonian Lorenz systems unidirectionally coupled, the first like a master/transmitter system and the other like a slave/receiver system in order to illustrate with numerical simulations the effectiveness of the modified scheme, using chaos synchronization with Hamiltonian forms and observer.

  12. Effective Hamiltonian for ΔS=1 weak nonleptonic decays in the six-quark model

    International Nuclear Information System (INIS)

    Gilman, F.J.; Wise, M.B.

    1979-01-01

    Strong-interaction corrections to the nonleptonic weak-interaction Hamiltonian are calculated in the leading-logarithmic approximation using quantum chromodynamics. Starting with a six-quark theory, the W boson, t quark, b quark, and c quark are successively considered as ''heavy'' and the effective Hamiltonian is calculated. The resulting effective Hamiltonian for strangeness-changing nonleptonic decays involves u, d, and s quarks and has possible CP-violating pieces both in the usual (V-A) x (V-A) terms and in induced, ''penguin''-type terms. Numerically, the CP-violating compared to CP-conserving parts of the latter terms are close to results calculated on the basis of the lowest-order ''penguin'' diagram

  13. pH variation and influence in an autotrophic nitrogen removing biofilm system using an efficient numerical solution strategy.

    Science.gov (United States)

    Vangsgaard, Anna Katrine; Mauricio-Iglesias, Miguel; Valverde-Pérez, Borja; Gernaey, Krist V; Sin, Gürkan

    2013-01-01

    A pH simulator consisting of an efficient numerical solver of a system of nine nonlinear equations was constructed and implemented in the modeling software MATLAB. The pH simulator was integrated in a granular biofilm model and used to simulate the pH profiles within granules performing the nitritation-anammox process for a range of operating points. The simulation results showed that pH profiles were consistently increasing with increasing depth into the granule, since the proton-producing aerobic ammonium-oxidizing bacteria (AOB) were located close to the granule surface. Despite this pH profile, more NH3 was available for AOB than for anaerobic ammonium oxidizers, located in the center of the granules. However, operating at a higher oxygen loading resulted in steeper changes in pH over the depth of the granule and caused the NH3 concentration profile to increase from the granule surface towards the center. The initial value of the background charge and influent bicarbonate concentration were found to greatly influence the simulation result and should be accurately measured. Since the change in pH over the depth of the biofilm was relatively small, the activity potential of the microbial groups affected by the pH did not change more than 5% over the depth of the granules.

  14. Adaptive control of port-Hamiltonian systems

    NARCIS (Netherlands)

    Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András

    2010-01-01

    In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for

  15. Iterated Hamiltonian type systems and applications

    Science.gov (United States)

    Tiba, Dan

    2018-04-01

    We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

  16. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    2000-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we

  17. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    1999-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we

  18. Hamiltonian evolutions of twisted polygons in RPn

    International Nuclear Information System (INIS)

    Beffa, Gloria Marì; Wang, Jing Ping

    2013-01-01

    In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)

  19. Discrete variable representation for singular Hamiltonians

    DEFF Research Database (Denmark)

    Schneider, B. I.; Nygaard, Nicolai

    2004-01-01

    We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...

  20. The hamiltonian structures of the KP hierarchy

    International Nuclear Information System (INIS)

    Das, A.; Panda, S.; Huang Wenjui

    1991-01-01

    We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)

  1. Hamiltonian structure for rescaled integrable Lorenz systems

    International Nuclear Information System (INIS)

    Haas, F.; Goedert, J.

    1993-01-01

    It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)

  2. Singularities of Poisson structures and Hamiltonian bifurcations

    NARCIS (Netherlands)

    Meer, van der J.C.

    2010-01-01

    Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom

  3. Transparency in port-Hamiltonian based telemanipulation

    NARCIS (Netherlands)

    Secchi, C; Stramigioli, Stefano; Fantuzzi, C.

    2005-01-01

    After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian based teleoperators. Furthermore we provide a transparency analysis of

  4. Transparency in Port-Hamiltonian-Based Telemanipulation

    NARCIS (Netherlands)

    Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare

    After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of

  5. Equivalence of Lagrangian and Hamiltonian BRST quantizations

    International Nuclear Information System (INIS)

    Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

    1992-01-01

    Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme

  6. Hamiltonian formulation of anomaly free chiral bosons

    International Nuclear Information System (INIS)

    Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.

    1988-01-01

    Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt

  7. Hamiltonian structure of gravitational field theory

    International Nuclear Information System (INIS)

    Rayski, J.

    1992-01-01

    Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations

  8. Port-Hamiltonian Systems on Open Graphs

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    2010-01-01

    In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

  9. Gauge theories of infinite dimensional Hamiltonian superalgebras

    International Nuclear Information System (INIS)

    Sezgin, E.

    1989-05-01

    Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs

  10. The Hamiltonian structures of the KP hierarchy

    International Nuclear Information System (INIS)

    Das, A.; Panda, S.; Huang Wenjui

    1991-08-01

    We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs

  11. Quasi exact solution of the Rabi Hamiltonian

    CERN Document Server

    Koç, R; Tuetuencueler, H

    2002-01-01

    A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

  12. Edge-disjoint Hamiltonian cycles in hypertournaments

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2006-01-01

    We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...

  13. Numerical analysis of the efficiency of earth to air heat exchange systems in cold and hot-arid climates

    International Nuclear Information System (INIS)

    Fazlikhani, Faezeh; Goudarzi, Hossein; Solgi, Ebrahim

    2017-01-01

    Highlights: • A numerical model is developed to evaluate performance of earth to air heat exchanger. • The cooling/heating potential of earth to air heat exchanger is investigated in hot-dry and cold climates. • The more performance of earth to air heat exchanger in hot-dry climates compared to cold climates. • The high efficiency of earth to air heat exchanger for pre-heating in both hot-dry and cold climates. - Abstract: In order to examine and compare the efficiency of earth to air heat exchanger (EAHE) systems in hot-arid (Yazd) and cold (Hamadan) climates in Iran a steady state model was developed to evaluate the impact of various parameters including inlet air temperatures, pipe lengths and ground temperatures on the cooling and heating potential of EAHEs in both climates. The results demonstrated the ability of the system to not only improve the average temperature and decrease the temperature fluctuation of the outlet air temperature of EAHE, but also to trigger considerable energy saving. It was found that in both climates, the system is highly utilized for pre-heating, and its usage is unfeasible in certain periods throughout the year. In winter, EAHEs have the potential of increasing the air temperature in the range of 0.2–11.2 °C and 0.1–17.2 °C for Yazd and Hamadan, respectively. However, in summer, the system decreases the air temperature for the aforementioned cities in the range of 1.3–11.4 °C and 5.7–11.1 °C, respectively. The system ascertains to be more efficient in the hot-arid climate of Yazd, where it can be used on 294 days of the year, leading to 50.1–63.6% energy saving, when compared to the cold climate of Hamadan, where it can be used on 225 days of the year resulting in a reduction of energy consumption by 24.5–47.9%.

  14. Hamiltonian constraint in polymer parametrized field theory

    International Nuclear Information System (INIS)

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-01

    Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

  15. Effective low-energy Hamiltonians for interacting nanostructures

    Science.gov (United States)

    Kinza, Michael; Ortloff, Jutta; Honerkamp, Carsten

    2010-10-01

    We present a functional renormalization group (fRG) treatment of trigonal graphene nanodisks and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodisks, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications [M. Ezawa, Eur. Phys. J. B 67, 543 (2009)10.1140/epjb/e2009-00041-7]. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodisks the degeneracy of the one-particle-states with zero energy turns out to be protected against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisk. We also discuss a second class of nanostructures, bow-tie-shaped systems, where the zero-energy states are not protected.

  16. The group of Hamiltonian automorphisms of a star product

    OpenAIRE

    La Fuente-Gravy, Laurent

    2015-01-01

    We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  17. QCD string with quarks. 2. Light cone Hamiltonian

    International Nuclear Information System (INIS)

    Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.

    1994-01-01

    The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom

  18. Experimental and numerical investigation of the aperture size effect on the efficient solar energy harvesting for solar thermochemical applications

    International Nuclear Information System (INIS)

    Sarwar, J.; Georgakis, G.; Kouloulias, K.; Kakosimos, K.E.

    2015-01-01

    Highlights: • Experimental results on thermal analysis of a solar cavity for variable apertures. • Development of an optical model for energy transfer from light source to the cavity. • Development of a coupled ray tracing and heat transfer model for the cavity. • Validation of both the models with experimental measurements. • Use of the models to study new cases like the efficiency of the variable apertures. - Abstract: In this paper, experimental and numerical work have been undertaken to investigate the steady state temperatures throughout the day of a cylindrical solar receiver when using fixed and variable size apertures. A high flux solar simulator, consisting of a 7 kW xenon short arc lamp, is employed as a light source. The sunlight intensity variations at early morning (06:30), morning (07:15) and noon (12:00) time of a reference day are imitated by changing the input current to the lamp. Experiments have been performed with different aperture diameters across selected irradiance levels to imitate sunlight variations. An optical model is developed to simulate incident flux distribution and the output is compared with the experimental measurements for validation. A finite volume algorithm is developed, based on a coupled Monte Carlo heat transfer model, to calculate the steady state temperatures in the receiver. Experimental and numerical temperatures are compared and an excellent agreement with an average temperature difference of ±0.2%, is observed. The optimum aperture size varies with the change in irradiance intensity and therefore the time of day. Simulations for a 30 kW light source show that the daily steady state temperature differential for fixed apertures of 8–10 cm is 170–190 K. Variable apertures reduce power consumption by half when compared to fixed apertures. Variable apertures maintain steady state temperatures of 1000 K, 1100 K and 1200 K by consuming 26.8 kW day, 33.2 kW day and 26.9 kW day, respectively

  19. Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors

    International Nuclear Information System (INIS)

    Wang, C.-x.

    2006-01-01

    A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

  20. On integrable Hamiltonians for higher spin XXZ chain

    International Nuclear Information System (INIS)

    Bytsko, Andrei G.

    2003-01-01

    Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain

  1. Effective Hamiltonians in quantum physics: resonances and geometric phase

    International Nuclear Information System (INIS)

    Rau, A R P; Uskov, D

    2006-01-01

    Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian

  2. Hamiltonian flow over saddles for exploring molecular phase space structures

    Science.gov (United States)

    Farantos, Stavros C.

    2018-03-01

    Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

  3. Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

    Science.gov (United States)

    Baaquie, Belal E

    2009-10-01

    Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

  4. Coherent states of systems with quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

    2015-06-15

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  5. Coherent states of systems with quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

    2015-01-01

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  6. Effective Hamiltonian for high Tc Cu oxides

    International Nuclear Information System (INIS)

    Fukuyama, H.; Matsukawa, H.

    1989-01-01

    Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived

  7. Partial quantization of Lagrangian-Hamiltonian systems

    International Nuclear Information System (INIS)

    Amaral, C.M. do; Soares Filho, P.C.

    1979-05-01

    A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt

  8. Quadratic hamiltonians and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

    1981-01-01

    For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

  9. Hamiltonian mechanics and divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1986-08-01

    The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space

  10. Quantum mechanical Hamiltonian models of discrete processes

    International Nuclear Information System (INIS)

    Benioff, P.

    1981-01-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement

  11. Boundary Hamiltonian Theory for Gapped Topological Orders

    Science.gov (United States)

    Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

    2017-06-01

    We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

  12. Hamiltonian reduction of Kac-Moody algebras

    International Nuclear Information System (INIS)

    Kimura, Kazuhiro

    1991-01-01

    Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)

  13. Phase transitions in the Hubbard Hamiltonian

    International Nuclear Information System (INIS)

    Chaves, C.M.; Lederer, P.; Gomes, A.A.

    1977-05-01

    Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

  14. A diagrammatic construction of formal E-independent model hamiltonian

    International Nuclear Information System (INIS)

    Kvasnicka, V.

    1977-01-01

    A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

  15. Boson mapping and the microscopic collective nuclear Hamiltonian

    International Nuclear Information System (INIS)

    Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.

    1990-01-01

    Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs

  16. Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

    International Nuclear Information System (INIS)

    Doveil, F.; Ruzzon, A.; Elskens, Y.

    2010-01-01

    Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step.This contribution reviews: presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm.The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation.A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of

  17. Hamiltonian theory of guiding-center motion

    International Nuclear Information System (INIS)

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion

  18. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1982-01-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  19. Dynamical invariants for variable quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Suslov, Sergei K

    2010-01-01

    We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

  20. The Effective Hamiltonian in the Scalar Electrodynamics

    CERN Document Server

    Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K

    2002-01-01

    On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.

  1. Quantization of non-Hamiltonian physical systems

    International Nuclear Information System (INIS)

    Bolivar, A.O.

    1998-09-01

    We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)

  2. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1981-12-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  3. Symplectic topology of integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Nguyen Tien Zung.

    1993-08-01

    We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs

  4. Hamiltonian description and quantization of dissipative systems

    Science.gov (United States)

    Enz, Charles P.

    1994-09-01

    Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

  5. Hamiltonian theory of guiding-center motion

    Energy Technology Data Exchange (ETDEWEB)

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

  6. Hamiltonian description of the ideal fluid

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1998-01-01

    The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society

  7. Large-scale stochasticity in Hamiltonian systems

    International Nuclear Information System (INIS)

    Escande, D.F.

    1982-01-01

    Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)

  8. An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths

    Science.gov (United States)

    Zhang, H.-m.; Chen, X.-f.; Chang, S.

    - It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.

  9. On the generating function of Poincare plots defining one dimensional perturbed Hamiltonian systems

    International Nuclear Information System (INIS)

    Montvai, A.

    1989-01-01

    A simple numerical method has been devised, for deriving the generating function of an arbitrary, one dimensional Hamiltonian system represented by its Poincare plot. In this case, the plot to be numerically processed is an area preserving transformation of a two-dimensional surface onto itself. Although the method in its present form is capable of treating only this case, there are no principal restrictions excluding the analysis of systems with higher dimensionality as well. As an example, the generating function of the motion of alpha particles in a nonsymmetric, toroidal magnetic field is derived and studied numerically. (orig.)

  10. Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Cobb, J.W.

    1995-02-01

    There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

  11. High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)

    2014-05-01

    While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

  12. High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

    International Nuclear Information System (INIS)

    Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.

    2014-01-01

    While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

  13. Dynamically Adapted Mesh Construction for the Efficient Numerical Solution of a Singular Perturbed Reaction-diffusion-advection Equation

    Directory of Open Access Journals (Sweden)

    Dmitry V. Lukyanenko

    2017-01-01

    Full Text Available This  work develops  a theory  of the  asymptotic-numerical investigation of the  moving fronts  in reaction-diffusion-advection models.  By considering  the  numerical  solution  of the  singularly perturbed Burgers’s  equation  we discuss a method  of dynamically  adapted mesh  construction that is able to significantly  improve  the  numerical  solution  of this  type of equations.  For  the  construction we use a priori information that is based  on the  asymptotic analysis  of the  problem.  In  particular, we take  into account the information about  the speed of the transition layer, its width  and structure. Our algorithms  are able to reduce significantly complexity and enhance stability of the numerical  calculations in comparison  with classical approaches for solving this class of problems.  The numerical  experiment is presented to demonstrate the effectiveness of the proposed  method.The article  is published  in the authors’  wording. 

  14. Quantum Hamiltonian reduction and conformal field theories

    International Nuclear Information System (INIS)

    Bershadsky, M.

    1991-01-01

    It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity

  15. An efficient approach to numerical study of the coupled-BBM system with B-spline collocation method

    Directory of Open Access Journals (Sweden)

    khalid ali

    2016-11-01

    Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

  16. Classical effective Hamiltonians, Wigner functions, and the sign problem

    International Nuclear Information System (INIS)

    Samson, J.H.

    1995-01-01

    In the functional-integral technique an auxiliary field, coupled to appropriate operators such as spins, linearizes the interaction term in a quantum many-body system. The partition function is then averaged over this time-dependent stochastic field. Quantum Monte Carlo methods evaluate this integral numerically, but suffer from the sign (or phase) problem: the integrand may not be positive definite (or not real). It is shown that, in certain cases that include the many-band Hubbard model and the Heisenberg model, the sign problem is inevitable on fundamental grounds. Here, Monte Carlo simulations generate a distribution of incompatible operators---a Wigner function---from which expectation values and correlation functions are to be calculated; in general no positive-definite distribution of this form exists. The distribution of time-averaged auxiliary fields is the convolution of this operator distribution with a Gaussian of variance proportional to temperature, and is interpreted as a Boltzmann distribution exp(-βV eff ) in classical configuration space. At high temperatures and large degeneracies this classical effective Hamiltonian V eff tends to the static approximation as a classical limit. In the low-temperature limit the field distribution becomes a Wigner function, the sign problem occurs, and V eff is complex. Interpretations of the distributions, and a criterion for their positivity, are discussed. The theory is illustrated by an exact evaluation of the Wigner function for spin s and the effective classical Hamiltonian for the spin-1/2 van der Waals model. The field distribution can be negative here, more noticeably if the number of spins is odd

  17. Periodic trajectories for a two-dimensional nonintegrable Hamiltonian

    International Nuclear Information System (INIS)

    Baranger, M.; Davies, K.T.R.

    1987-01-01

    A numerical study is made of the classical periodic trajectories for the two-dimensional nonintegrable Hamiltonian H = 1/2(p 2 /sub x/+p 2 /sub y/)+(y-1/2x 2 ) 2 +0.05 x 2 . In addition to x--y pictures of the trajectories, E--tau (energy--period) plots of the periodic families are presented. Efforts have been ade to include all trajectories with short periods and all simple branchings of these trajectories. The monodromy matrix has been calculated in all cases, and from it the stability properties are derived. The topology of the E--tau plot has been explored, with the following results. One family may have several stable regions. The plot is not completely connected; there are islands. The plot is not a tree; there are cycles. There are isochronous branchings, period-doublings, and period-multiplyings of higher orders, and examples of each of these are presented. There is often more than one branch issuing from a branch point. Some general empirical rules are inferred. In particular, the existence of isochronous branching is seen to be a consequence of the symmetry of the Hamiltonian. All these results agree with the general classification of possible branchings derived in Ref. [10]. (M. A. M. de Aguiar, C. P. Malta, M. Baranger, and K. T. R. Davies, in preparation). Finally, some nonperiodic trajectories are calculated to illustrate the fact that stable periodic trajectories lie in ''regular'' regions of phase space, while unstable ones lie in ''chaotic'' regions

  18. Does a Single Eigenstate Encode the Full Hamiltonian?

    Science.gov (United States)

    Garrison, James R.; Grover, Tarun

    2018-04-01

    The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

  19. Integrable Time-Dependent Quantum Hamiltonians

    Science.gov (United States)

    Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

    2018-05-01

    We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

  20. Discrete variable representation for singular Hamiltonians

    DEFF Research Database (Denmark)

    Schneider, B. I.; Nygaard, Nicolai

    2004-01-01

    We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

  1. Resonant driving of a nonlinear Hamiltonian system

    International Nuclear Information System (INIS)

    Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

    2013-01-01

    As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

  2. Nonabelian N=2 superstrings: Hamiltonian structure

    International Nuclear Information System (INIS)

    Isaev, A.P.; Ivanov, E.A.

    1991-04-01

    We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs

  3. Effective Hamiltonians for phosphorene and silicene

    DEFF Research Database (Denmark)

    Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.

    2015-01-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...

  4. Hamiltonian Description of Convective-cell Generation

    International Nuclear Information System (INIS)

    Krommes, J.A.; Kolesnikov, R.A.

    2004-01-01

    The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted

  5. Eigenfunctions of quadratic hamiltonians in Wigner representation

    International Nuclear Information System (INIS)

    Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

    1984-01-01

    Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

  6. Action-minimizing methods in Hamiltonian dynamics

    CERN Document Server

    Sorrentino, Alfonso

    2015-01-01

    John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a

  7. A numerical study into the effects of elongated capsules on the healing efficiency of liquid-based systems

    NARCIS (Netherlands)

    Mookhoek, S.D.; Fischer, H.R.; Zwaag, S. van der

    2009-01-01

    In this numerical study the release of healing agent for liquid-based self-healing systems for elongated microcapsules is studied and compared with that for the usual spherical capsules. It is shown that a high aspect ratio and a proper spatial orientation of the elongated capsules have a positive

  8. Emergence of Landauer transport from quantum dynamics: A model Hamiltonian approach.

    Science.gov (United States)

    Pal, Partha Pratim; Ramakrishna, S; Seideman, Tamar

    2018-04-14

    The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.

  9. Effective hamiltonian within the microscopic unitary nuclear model

    International Nuclear Information System (INIS)

    Avramenko, V.I.; Blokhin, A.L.

    1989-01-01

    Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs

  10. A Hamiltonian functional for the linearized Einstein vacuum field equations

    International Nuclear Information System (INIS)

    Rosas-RodrIguez, R

    2005-01-01

    By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

  11. Introduction to thermodynamics of spin models in the Hamiltonian limit

    Energy Technology Data Exchange (ETDEWEB)

    Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)

    2006-01-01

    A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.

  12. Hamiltonian structure of the Lotka-Volterra equations

    Science.gov (United States)

    Nutku, Y.

    1990-03-01

    The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

  13. Hamiltonian structures of some non-linear evolution equations

    International Nuclear Information System (INIS)

    Tu, G.Z.

    1983-06-01

    The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

  14. Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics

    International Nuclear Information System (INIS)

    Hoover, W.G.; Evans, D.J.; Hickman, R.B.; Ladd, A.J.C.; Ashurst, W.T.; Moran, B.

    1980-01-01

    A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced ''long-time tails.''

  15. Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

    Science.gov (United States)

    Temme, Kristan

    2017-03-01

    We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

  16. Nonextensive formalism and continuous Hamiltonian systems

    International Nuclear Information System (INIS)

    Boon, Jean Pierre; Lutsko, James F.

    2011-01-01

    A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.

  17. Hamiltonian Anomalies from Extended Field Theories

    Science.gov (United States)

    Monnier, Samuel

    2015-09-01

    We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

  18. Phase space eigenfunctions of multidimensional quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man'ko, V.I.

    1986-01-01

    We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

  19. Numerical studies of various Néel-VBS transitions in SU(N) anti-ferromagnets

    Science.gov (United States)

    Kaul, Ribhu K.; Block, Matthew S.

    2015-09-01

    In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(105) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions - a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the “designer” Hamiltonians.

  20. Numerical studies of various Néel-VBS transitions in SU(N) anti-ferromagnets

    International Nuclear Information System (INIS)

    Kaul, Ribhu K; Block, Matthew S

    2015-01-01

    In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(10 5 ) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions - a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the “designer” Hamiltonians. (paper)

  1. Diffeomorphism invariance in the Hamiltonian formulation of General Relativity

    International Nuclear Information System (INIS)

    Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.

    2008-01-01

    It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity

  2. Matchings Extend to Hamiltonian Cycles in 5-Cube

    Directory of Open Access Journals (Sweden)

    Wang Fan

    2018-02-01

    Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.

  3. Squeezed states from a quantum deformed oscillator Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

    2016-03-11

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

  4. A Hamiltonian approach to model and analyse networks of ...

    Indian Academy of Sciences (India)

    2015-09-24

    Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.

  5. The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

    Energy Technology Data Exchange (ETDEWEB)

    Mei, Lijie, E-mail: bxhanm@126.com; Wu, Xinyuan, E-mail: xywu@nju.edu.cn

    2016-10-15

    In general, extended Runge–Kutta–Nyström (ERKN) methods are more effective than traditional Runge–Kutta–Nyström (RKN) methods in dealing with oscillatory Hamiltonian systems. However, the theoretical analysis for ERKN methods, such as the order conditions, the symplectic conditions and the symmetric conditions, becomes much more complicated than that for RKN methods. Therefore, it is a bottleneck to construct high-order ERKN methods efficiently. In this paper, we first establish the ERKN group Ω for ERKN methods and the RKN group G for RKN methods, respectively. We then rigorously show that ERKN methods are a natural extension of RKN methods, that is, there exists an epimorphism η of the ERKN group Ω onto the RKN group G. This epimorphism gives a global insight into the structure of the ERKN group by the analysis of its kernel and the corresponding RKN group G. Meanwhile, we establish a particular mapping φ of G into Ω so that each image element is an ideal representative element of the congruence class in Ω. Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity. From the epimorphism η together with its section φ, we may gain knowledge about the structure of the ERKN group Ω via the RKN group G. In light of the theoretical analysis of this paper, we obtain high-order structure-preserving ERKN methods in an effective way for solving oscillatory Hamiltonian systems. Numerical experiments are carried out and the results are very promising, which strongly support our theoretical analysis presented in this paper.

  6. Luminescence and efficiency optimization of InGaN/GaN core-shell nanowire LEDs by numerical modelling

    Science.gov (United States)

    Römer, Friedhard; Deppner, Marcus; Andreev, Zhelio; Kölper, Christopher; Sabathil, Matthias; Strassburg, Martin; Ledig, Johannes; Li, Shunfeng; Waag, Andreas; Witzigmann, Bernd

    2012-02-01

    We present a computational study on the anisotropic luminescence and the efficiency of a core-shell type nanowire LED based on GaN with InGaN active quantum wells. The physical simulator used for analyzing this device integrates a multidimensional drift-diffusion transport solver and a k . p Schrödinger problem solver for quantization effects and luminescence. The solution of both problems is coupled to achieve self-consistency. Using this solver we investigate the effect of dimensions, design of quantum wells, and current injection on the efficiency and luminescence of the core-shell nanowire LED. The anisotropy of the luminescence and re-absorption is analyzed with respect to the external efficiency of the LED. From the results we derive strategies for design optimization.

  7. A Numerical Study on Mass Transfer and Methanol Conversion Efficiency According to Porosity and Temperature Change of Curved Channel Methanol-Steam Reformer

    International Nuclear Information System (INIS)

    Seong, Hong Seok; Lee, Chung Ho; Suh, Jeong Se

    2016-01-01

    Micro methanol-steam reformer for fuel cell can effectively produce hydrogen as reforming response to steam takes place in low temperature (less than 250℃). This study conducted numerical research on this reformer. First, study set wall temperature of the reformer at 100, 140, 180 and 220℃ while methanol conversion efficiency was set in 0, 0.072, 3.83 and 46.51% respectively. Then, porosity of catalyst was set in 0.1, 0.35, 0.6 and 0.85 and although there was no significant difference in methanol conversion efficiency, values of pressure drop were 4645.97, 59.50, 5.12 and 0.45 kPa respectively. This study verified that methanol-steam reformer rarely responds under the temperature of 180℃ and porosity does not have much effect on methanol conversion efficiency if the fluid flowing through reformer lowers activation energy by sufficiently contacting reformer.

  8. A Numerical Study on Mass Transfer and Methanol Conversion Efficiency According to Porosity and Temperature Change of Curved Channel Methanol-Steam Reformer

    Energy Technology Data Exchange (ETDEWEB)

    Seong, Hong Seok; Lee, Chung Ho; Suh, Jeong Se [Gyeongsang Nat’l Univ., Jinju (Korea, Republic of)

    2016-11-15

    Micro methanol-steam reformer for fuel cell can effectively produce hydrogen as reforming response to steam takes place in low temperature (less than 250℃). This study conducted numerical research on this reformer. First, study set wall temperature of the reformer at 100, 140, 180 and 220℃ while methanol conversion efficiency was set in 0, 0.072, 3.83 and 46.51% respectively. Then, porosity of catalyst was set in 0.1, 0.35, 0.6 and 0.85 and although there was no significant difference in methanol conversion efficiency, values of pressure drop were 4645.97, 59.50, 5.12 and 0.45 kPa respectively. This study verified that methanol-steam reformer rarely responds under the temperature of 180℃ and porosity does not have much effect on methanol conversion efficiency if the fluid flowing through reformer lowers activation energy by sufficiently contacting reformer.

  9. Hamiltonian study of improved U(1) lattice gauge theory in three dimensions

    International Nuclear Information System (INIS)

    Loan, Mushtaq; Hamer, Chris

    2004-01-01

    A comprehensive analysis of the Symanzik improved anisotropic three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made. Monte Carlo techniques are used to obtain numerical results for the static potential, ratio of the renormalized and bare anisotropies, the string tension, lowest glueball masses and the mass ratio. Evidence that rotational symmetry is established more accurately for the Symanzik improved anisotropic action is presented. The discretization errors in the static potential and the renormalization of the bare anisotropy are found to be only a few percent compared to errors of about 20-25 % for the unimproved gauge action. Evidence of scaling in the string tension, antisymmetric mass gap and the mass ratio is observed in the weak coupling region and the behavior is tested against analytic and numerical results obtained in various other Hamiltonian studies of the theory. We find that more accurate determination of the scaling coefficients of the string tension and the antisymmetric mass gap has been achieved, and the agreement with various other Hamiltonian studies of the theory is excellent. The improved action is found to give faster convergence to the continuum limit. Very clear evidence is obtained that in the continuum limit the glueball ratio M S /M A approaches exactly 2, as expected in a theory of free, massive bosons

  10. Geometric solitons of Hamiltonian flows on manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-12-15

    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  11. Hamiltonian indices and rational spectral densities

    Science.gov (United States)

    Byrnes, C. I.; Duncan, T. E.

    1980-01-01

    Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

  12. Betatron coupling: Merging Hamiltonian and matrix approaches

    Directory of Open Access Journals (Sweden)

    R. Calaga

    2005-03-01

    Full Text Available Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.

  13. A Hamiltonian five-field gyrofluid model

    Energy Technology Data Exchange (ETDEWEB)

    Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)

    2015-11-15

    A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

  14. Hamiltonian circuited simulations in reactor physics

    International Nuclear Information System (INIS)

    Rio Hirowati Shariffudin

    2002-01-01

    In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)

  15. Hamiltonian inclusive fitness: a fitter fitness concept.

    Science.gov (United States)

    Costa, James T

    2013-01-01

    In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.

  16. Renormalized semiclassical quantization for rescalable Hamiltonians

    International Nuclear Information System (INIS)

    Takahashi, Satoshi; Takatsuka, Kazuo

    2004-01-01

    A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum

  17. Spectral bounds for the PT-breaking Hamiltonian p2 + x4 + iax

    International Nuclear Information System (INIS)

    Handy, C R; Wang Xiaoqian

    2003-01-01

    The non-Hermitian Hamiltonian p 2 + x 4 + iax, which spontaneously breaks PT-symmetry, and the subject of a recent study by Bender et al (2001 J. Phys. A: Math. Gen. 34 L31), is amenable to a positivity representation, facilitating the generation of converging bounds to the complex-eigenenergies of the PT-breaking states. This system is much easier (i.e. fewer variational parameters) than the previously studied case of the Hamiltonian p 2 + ix 3 + iax (2001 Handy J. Phys. A: Math. Gen. 34 5065, Handy et al 2001 J. Phys. A: Math. Gen. 34 5593), as first proposed by Delabaere and Trinh (2000 J. Phys. A: Math. Gen. 33 8771), enabling the generation of low order algebraic spectral bounds (i.e. Re(E) > 81/4 (Im(E)/a) 4 + O(a 2 )), in addition to high order, numerically generated, converging bounds to the discrete states. We examine both approaches here

  18. Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators

    International Nuclear Information System (INIS)

    Sabarathinam, S.; Thamilmaran, K.

    2015-01-01

    Highlights: •We have examined transient chaos in globally coupled oscillators. •We analyze transient chaos using new techniques. •We give experimental confirmation of transient chaos. -- Abstract: In this work, transient chaos in a ring and globally coupled system of nearly conservative Hamiltonian Duffing oscillators is reported. The networks are formed by coupling of three, four and six Duffing oscillators. The nearly conservative Hamiltonian nature of the coupled system is proved by stability analysis. The transient phenomenon is confirmed through various numerical investigations such as recurrence analysis, 0–1 test and Finite Time Lyapunov Exponents. Further, the effect of damping and the average transient lifetime of three, four and six coupled schemes for randomly generated initial conditions have been analyzed. The experimental confirmation of transient chaos in an illustrative system of three ringly coupled Duffing oscillators is also presented

  19. Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

    Science.gov (United States)

    Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

    2018-04-01

    Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

  20. Non-self-adjoint hamiltonians defined by Riesz bases

    Energy Technology Data Exchange (ETDEWEB)

    Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)

    2014-03-15

    We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.

  1. The Group of Hamiltonian Automorphisms of a Star Product

    Energy Technology Data Exchange (ETDEWEB)

    La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)

    2016-09-15

    We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  2. Hamiltonian formulation for the Martin-Taylor model

    International Nuclear Information System (INIS)

    Vasconcelos, D.B.; Viana, R.L.

    1993-01-01

    Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)

  3. Formulation of Hamiltonian mechanics with even and odd Poisson brackets

    International Nuclear Information System (INIS)

    Khudaverdyan, O.M.; Nersesyan, A.P.

    1987-01-01

    A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs

  4. Effective Hamiltonian within the microscopic unitary nuclear model

    International Nuclear Information System (INIS)

    Filippov, G.F.; Blokhin, A.L.

    1989-01-01

    A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs

  5. Classical and quantum mechanics of complex Hamiltonian systems ...

    Indian Academy of Sciences (India)

    Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.

  6. Local Hamiltonians for maximally multipartite-entangled states

    Science.gov (United States)

    Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

    2010-10-01

    We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

  7. Local Hamiltonians for maximally multipartite-entangled states

    International Nuclear Information System (INIS)

    Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

    2010-01-01

    We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

  8. Modelling chaotic Hamiltonian systems as a Markov Chain ...

    African Journals Online (AJOL)

    The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

  9. On the physical applications of hyper-Hamiltonian dynamics

    International Nuclear Information System (INIS)

    Gaeta, Giuseppe; Rodriguez, Miguel A

    2008-01-01

    An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin

  10. The Group of Hamiltonian Automorphisms of a Star Product

    International Nuclear Information System (INIS)

    La Fuente-Gravy, Laurent

    2016-01-01

    We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  11. Hamiltonian reduction of SU(2) Yang-Mills field theory

    International Nuclear Information System (INIS)

    Khvedelidze, A.M.; Pavel, H.-P.

    1998-01-01

    The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2

  12. An effective Hamiltonian approach to quantum random walk

    Indian Academy of Sciences (India)

    2017-02-09

    Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...

  13. Model reduction of port-Hamiltonian systems as structured systems

    NARCIS (Netherlands)

    Polyuga, R.V.; Schaft, van der A.J.

    2010-01-01

    The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.

  14. Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling

    NARCIS (Netherlands)

    Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio

    2004-01-01

    In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.

  15. Port-Hamiltonian approaches to motion generation for mechanical systems

    NARCIS (Netherlands)

    Sakai, Satoru; Stramigioli, Stefano

    This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system

  16. Structure preserving port-Hamiltonian model reduction of electrical circuits

    NARCIS (Netherlands)

    Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.

    2011-01-01

    This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the

  17. Residual gauge invariance of Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Ryang, S.; Saito, T.; Shigemoto, K.

    1984-01-01

    The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

  18. Effects of radiation transport on mass ablation rate and conversion efficiency in numerical simulations of inertial confinement fusion

    International Nuclear Information System (INIS)

    Gupta, N.K.

    2002-01-01

    The effects of radiation transport on hydrodynamic parameters of laser produced plasmas are studied. LTE and non-LTE atomic models are used to calculate multi group opacities and emissivities. Screened hydrogenic atom model is used to calculate the energy levels. The population densities of neutral to fully ionized ions are obtained by solving the steady state rate equations. Radiation transport is treated in multi-group diffusion or Sn method. A comparison is made between 1 and 100 group radiation transport and LTE and non-LTE models. For aluminium, multi group radiation transport leads to much higher mass ablation as compared to the 1 group and no radiation transport cases. This in turn leads to higher ablation pressures. However, for gold gray approximation gives higher mass ablation as compared to multi group simulations. LTE conversion efficiency of laser light into x-rays is more than the non-LTE estimates. For LTE as well as non-LTE cases, the one group approximation over-predicts the conversion efficiency Multi group non-LTE simulations predict that the conversion efficiency increases with laser intensity up to a maximum and then it decreases. (author)

  19. Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

    Science.gov (United States)

    Bui-Thanh, T.; Girolami, M.

    2014-11-01

    We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint

  20. A generalized AKNS hierarchy and its bi-Hamiltonian structures

    International Nuclear Information System (INIS)

    Xia Tiecheng; You Fucai; Chen Dengyuan

    2005-01-01

    First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator

  1. Local modular Hamiltonians from the quantum null energy condition

    Science.gov (United States)

    Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

    2018-03-01

    The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

  2. Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

    Energy Technology Data Exchange (ETDEWEB)

    Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

    2010-05-15

    In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

  3. Sdg interacting boson hamiltonian in the seniority scheme

    Energy Technology Data Exchange (ETDEWEB)

    Yoshinaga, N.

    1989-03-06

    The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

  4. sdg Interacting boson hamiltonian in the seniority scheme

    Science.gov (United States)

    Yoshinaga, N.

    1989-03-01

    The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

  5. Frustration-free Hamiltonians supporting Majorana zero edge modes

    International Nuclear Information System (INIS)

    Jevtic, Sania; Barnett, Ryan

    2017-01-01

    A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)

  6. Frustration-free Hamiltonians supporting Majorana zero edge modes

    Science.gov (United States)

    Jevtic, Sania; Barnett, Ryan

    2017-10-01

    A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.

  7. Improving eco-sustainable characteristics and energy efficiency of evaporative fluid cooler via experimental and numerical study

    Directory of Open Access Journals (Sweden)

    Rašković Predrag O.

    2008-01-01

    Full Text Available This paper presents an on-going research project that aims to identify possibilities for wider use of evaporative cooling in process industry, especially the use of evaporative fluid cooler units. Experimental study is performed on small scale evaporative fluid cooler, while the correlation based model has been carried out to explore the detailed heat and mass transfer processes inside this unit. Numerical integration of mathematical model is executed by new approach, based on differential, collocation Simpson method. Proposed models have been verified by comparing the computed results with those obtained by the experimental measurements. The results of research will enable the creation of more comprehensive simulation software, with wider range of operating and construction parameters.

  8. Hamiltonian analysis of fast wave current drive in tokamak plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Becoulet, A; Fraboulet, D; Giruzzi, G; Moreau, D; Saoutic, B [Association Euratom-CEA, Centre d` Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Chinardet, J [CISI Ingenierie, Centre d` Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France)

    1993-12-01

    The Hamiltonian formalism is used to analyze the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron phase space trajectories is derived, and together with extrinsic de-correlation processes, assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full-wave resolution of the Maxwell-Vlasov set of equations provides the exact pattern of the wave fields in a complete tokamak geometry, for a realistic antenna spectrum. The local quasilinear diffusion tensor is derived from the wave fields, and is used for a computation of the driven current and deposited power profiles, the current drive efficiency, including possible non-linear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, as well as results concerning combination of FWCD with other non inductive current drive methods. An analytical expression for the current drive efficiency is given in the high single-pass absorption regimes. (authors). 20 figs., 1 tab., 26 refs.

  9. Hamiltonian analysis of fast wave current drive in tokamak plasmas

    International Nuclear Information System (INIS)

    Becoulet, A.; Fraboulet, D.; Giruzzi, G.; Moreau, D.; Saoutic, B.

    1993-12-01

    The Hamiltonian formalism is used to analyze the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron phase space trajectories is derived, and together with extrinsic de-correlation processes, assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full-wave resolution of the Maxwell-Vlasov set of equations provides the exact pattern of the wave fields in a complete tokamak geometry, for a realistic antenna spectrum. The local quasilinear diffusion tensor is derived from the wave fields, and is used for a computation of the driven current and deposited power profiles, the current drive efficiency, including possible non-linear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, as well as results concerning combination of FWCD with other non inductive current drive methods. An analytical expression for the current drive efficiency is given in the high single-pass absorption regimes. (authors). 20 figs., 1 tab., 26 refs

  10. An efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor

    International Nuclear Information System (INIS)

    Larroche, O.

    2007-01-01

    A locally split-step explicit (LSSE) algorithm was developed for efficiently solving a multi-dimensional advection-diffusion type equation involving a highly inhomogeneous and highly anisotropic diffusion tensor, which makes the problem very ill-conditioned for standard implicit methods involving the iterative solution of large linear systems. The need for such an optimized algorithm arises, in particular, in the frame of thermonuclear fusion applications, for the purpose of simulating fast charged-particle slowing-down with an ion Fokker-Planck code. The LSSE algorithm is presented in this paper along with the results of a model slowing-down problem to which it has been applied

  11. Energy efficiency vs. performance of the numerical solution of PDEs: An application study on a low-power ARM-based cluster

    Science.gov (United States)

    Göddeke, Dominik; Komatitsch, Dimitri; Geveler, Markus; Ribbrock, Dirk; Rajovic, Nikola; Puzovic, Nikola; Ramirez, Alex

    2013-03-01

    Power consumption and energy efficiency are becoming critical aspects in the design and operation of large scale HPC facilities, and it is unanimously recognised that future exascale supercomputers will be strongly constrained by their power requirements. At current electricity costs, operating an HPC system over its lifetime can already be on par with the initial deployment cost. These power consumption constraints, and the benefits a more energy-efficient HPC platform may have on other societal areas, have motivated the HPC research community to investigate the use of energy-efficient technologies originally developed for the embedded and especially mobile markets. However, lower power does not always mean lower energy consumption, since execution time often also increases. In order to achieve competitive performance, applications then need to efficiently exploit a larger number of processors. In this article, we discuss how applications can efficiently exploit this new class of low-power architectures to achieve competitive performance. We evaluate if they can benefit from the increased energy efficiency that the architecture is supposed to achieve. The applications that we consider cover three different classes of numerical solution methods for partial differential equations, namely a low-order finite element multigrid solver for huge sparse linear systems of equations, a Lattice-Boltzmann code for fluid simulation, and a high-order spectral element method for acoustic or seismic wave propagation modelling. We evaluate weak and strong scalability on a cluster of 96 ARM Cortex-A9 dual-core processors and demonstrate that the ARM-based cluster can be more efficient in terms of energy to solution when executing the three applications compared to an x86-based reference machine.

  12. Riemannian theory of Hamiltonian chaos and Lyapunov exponents

    Science.gov (United States)

    Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

    1996-12-01

    A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

  13. Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

    Science.gov (United States)

    Risser, Steven Michael

    This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

  14. Numerical Analysis of Efficiency Enhancement in Plasmonic Thin-Film Solar Cells by Using the SILVACO TCAD Simulator

    International Nuclear Information System (INIS)

    Kim Un-Chol; Jiang Xiao-Qing

    2012-01-01

    A physical model for simulating plasmonic solar cells (SCs) using the SILVACO TCAD simulator is established and the effects of some factors on the efficiency enhancement of the amorphous silicon thin film SCs are simulated. Through this simulation, it is demonstrated that our method can successfully simulate the optical and electrical properties of plasmonic solar cells without the overestimation of the characteristics and without the neglect of parameter change in the device operation process. It is shown that not only the size and kind of metal nanoparticles but also other factors, such as the surrounding medium, the distance from the bottom of particles to the device surface, and the light incident angle, play important roles in the optical and electrical properties of plasmonic SCs. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

  15. Calibration of a single hexagonal NaI(Tl) detector using a new numerical method based on the efficiency transfer method

    Energy Technology Data Exchange (ETDEWEB)

    Abbas, Mahmoud I., E-mail: mabbas@physicist.net [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Badawi, M.S. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Ruskov, I.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); El-Khatib, A.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Grozdanov, D.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); Thabet, A.A. [Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria (Egypt); Kopatch, Yu.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Gouda, M.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Skoy, V.R. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)

    2015-01-21

    Gamma-ray detector systems are important instruments in a broad range of science and new setup are continually developing. The most recent step in the evolution of detectors for nuclear spectroscopy is the construction of large arrays of detectors of different forms (for example, conical, pentagonal, hexagonal, etc.) and sizes, where the performance and the efficiency can be increased. In this work, a new direct numerical method (NAM), in an integral form and based on the efficiency transfer (ET) method, is used to calculate the full-energy peak efficiency of a single hexagonal NaI(Tl) detector. The algorithms and the calculations of the effective solid angle ratios for a point (isotropic irradiating) gamma-source situated coaxially at different distances from the detector front-end surface, taking into account the attenuation of the gamma-rays in the detector's material, end-cap and the other materials in-between the gamma-source and the detector, are considered as the core of this (ET) method. The calculated full-energy peak efficiency values by the (NAM) are found to be in a good agreement with the measured experimental data.

  16. Multi-hump potentials for efficient wave absorption in the numerical solution of the time-dependent Schrödinger equation

    Science.gov (United States)

    Silaev, A. A.; Romanov, A. A.; Vvedenskii, N. V.

    2018-03-01

    In the numerical solution of the time-dependent Schrödinger equation by grid methods, an important problem is the reflection and wrap-around of the wave packets at the grid boundaries. Non-optimal absorption of the wave function leads to possible large artifacts in the results of numerical simulations. We propose a new method for the construction of the complex absorbing potentials for wave suppression at the grid boundaries. The method is based on the use of the multi-hump imaginary potential which contains a sequence of smooth and symmetric humps whose widths and amplitudes are optimized for wave absorption in different spectral intervals. We show that this can ensure a high efficiency of absorption in a wide range of de Broglie wavelengths, which includes wavelengths comparable to the width of the absorbing layer. Therefore, this method can be used for high-precision simulations of various phenomena where strong spreading of the wave function takes place, including the phenomena accompanying the interaction of strong fields with atoms and molecules. The efficiency of the proposed method is demonstrated in the calculation of the spectrum of high-order harmonics generated during the interaction of hydrogen atoms with an intense infrared laser pulse.

  17. Multicast backup reprovisioning problem for Hamiltonian cycle-based protection on WDM networks

    Science.gov (United States)

    Din, Der-Rong; Huang, Jen-Shen

    2014-03-01

    As networks grow in size and complexity, the chance and the impact of failures increase dramatically. The pre-allocated backup resources cannot provide 100% protection guarantee when continuous failures occur in a network. In this paper, the multicast backup re-provisioning problem (MBRP) for Hamiltonian cycle (HC)-based protection on WDM networks for the link-failure case is studied. We focus on how to recover the protecting capabilities of Hamiltonian cycle against the subsequent link-failures on WDM networks for multicast transmissions, after recovering the multicast trees affected by the previous link-failure. Since this problem is a hard problem, an algorithm, which consists of several heuristics and a genetic algorithm (GA), is proposed to solve it. The simulation results of the proposed method are also given. Experimental results indicate that the proposed algorithm can solve this problem efficiently.

  18. A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

    KAUST Repository

    Saavedra, Sebastian

    2012-07-01

    The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.

  19. New Hamiltonian constraint operator for loop quantum gravity

    Directory of Open Access Journals (Sweden)

    Jinsong Yang

    2015-12-01

    Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  20. Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

    2011-12-01

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  1. Homotopical Dynamics IV: Hopf invariants and hamiltonian flows

    OpenAIRE

    Cornea, Octavian

    2001-01-01

    In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...

  2. New Hamiltonian constraint operator for loop quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

    2015-12-17

    A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  3. Remarks on Hamiltonian structures in G2-geometry

    International Nuclear Information System (INIS)

    Cho, Hyunjoo; Salur, Sema; Todd, A. J.

    2013-01-01

    In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

  4. Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

    2006-01-01

    We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out

  5. The Hamiltonian structure of general relativistic perfect fluids

    International Nuclear Information System (INIS)

    Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.

    1985-01-01

    We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)

  6. Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

    CERN Document Server

    Jacob, Birgit

    2012-01-01

    This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir

  7. Toric codes and quantum doubles from two-body Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)

    2011-05-15

    We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.

  8. Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

    2011-12-23

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  9. Relativistic and separable classical hamiltonian particle dynamics

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1981-01-01

    We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light

  10. Atomizing industrial gas-liquid flows – Development of an efficient hybrid VOF-LPT numerical framework

    International Nuclear Information System (INIS)

    Ström, Henrik; Sasic, Srdjan; Holm-Christensen, Olav; Shah, Louise Jivan

    2016-01-01

    Highlights: • Modelling of turbulent atomizing gas-liquid flows in real industrial devices. • A combined VOF-LPT framework with statistical coupling. • Regions of separated and dispersed multiphase flow treated simultaneously. • Statistical model based on a limited amount of highly resolved VOF data. - Abstract: Atomizing gas-liquid flows are used in industrial applications where high interphase heat and mass transfer rates and good mixing are of primary importance. Today, there is no single mathematical framework available to predict the entire liquid breakup process at an acceptable computational cost for a typical problem of industrial size. In this work, we develop a volume-of-fluid (VOF) framework that is combined with Lagrangian particle tracking (LPT) to take advantage of the respective strengths of these two approaches. The two frameworks are coupled via a statistical model that enables a transition from the VOF to the LPT formulation using input data about the primary breakup process obtained from detailed VOF simulations in dedicated switching zones. LPT-to-VOF transitions are handled directly by analyzing the proximity of LPT parcels to larger VOF structures. The combined framework is specifically designed to accommodate situations where atomization occurs in several locations simultaneously and when separated and dispersed turbulent gas-liquid flows co-exist in the same industrial unit. The procedure in which the statistical model is derived is presented and discussed, its performance is verified and the computational efficiency of the combined VOF-LPT model is assessed. Finally, the application of the coupled framework to the simulation of an industrial gas-liquid mixer with four separate atomization regions is presented.

  11. Equivalent Hermitian Hamiltonian for the non-Hermitian -x4 potential

    International Nuclear Information System (INIS)

    Jones, H.F.; Mateo, J.

    2006-01-01

    The potential V(x)=-x 4 , which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integrable systems, was subsequently constructed for the general class of potentials -(ix) N . For such Hamiltonians the natural PT metric is not positive definite, but a dynamically-defined positive-definite metric can be defined, depending on an operator Q. Further, with the help of this operator an equivalent Hermitian Hamiltonian h can be constructed. This programme has been carried out exactly for a few soluble models, and the first few terms of a perturbative expansion have been found for the potential m 2 x 2 +igx 3 . However, until now, the -x 4 potential has proved intractable. In the present paper we give explicit, closed form expressions for Q and h, which are made possible by a particular parametrization of the contour in the complex plane on which the problem is defined. This constitutes an explicit proof of the reality of the spectrum. The resulting equivalent Hamiltonian has a potential with a positive quartic term together with a linear term

  12. An inversion-relaxation approach for sampling stationary points of spin model Hamiltonians

    International Nuclear Information System (INIS)

    Hughes, Ciaran; Mehta, Dhagash; Wales, David J.

    2014-01-01

    Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems

  13. g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...

    Indian Academy of Sciences (India)

    Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.

  14. Integrable Hamiltonian systems and interactions through quadratic constraints

    International Nuclear Information System (INIS)

    Pohlmeyer, K.

    1975-08-01

    Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

  15. Towards practical characterization of quantum systems with quantum Hamiltonian learning

    NARCIS (Netherlands)

    Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.

    2017-01-01

    Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.

  16. On the quantization of sectorially Hamiltonian dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)

    2009-10-15

    We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.

  17. On the quantization of sectorially Hamiltonian dissipative systems

    International Nuclear Information System (INIS)

    Castagnino, M.; Gadella, M.; Lara, L.P.

    2009-01-01

    We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.

  18. Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

    Directory of Open Access Journals (Sweden)

    Krzysztof Andrzejewski

    2014-12-01

    Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

  19. Experimental Hamiltonian identification for controlled two-level systems

    International Nuclear Information System (INIS)

    Schirmer, S.G.; Kolli, A.; Oi, D.K.L.

    2004-01-01

    We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable

  20. A local inverse spectral theorem for Hamiltonian systems

    International Nuclear Information System (INIS)

    Langer, Matthias; Woracek, Harald

    2011-01-01

    We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients

  1. Hamiltonian Approach to 2+1 Dimensional Gravity

    Science.gov (United States)

    Cantini, L.; Menotti, P.; Seminara, D.

    2002-12-01

    It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

  2. Time and a physical Hamiltonian for quantum gravity.

    Science.gov (United States)

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-06

    We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

  3. A hierarchy of Liouville integrable discrete Hamiltonian equations

    Energy Technology Data Exchange (ETDEWEB)

    Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

    2008-05-12

    Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

  4. On the topological entropy of an optical Hamiltonian flow

    OpenAIRE

    Niche, Cesar J.

    2000-01-01

    In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.

  5. SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS

    OpenAIRE

    Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.

    2006-01-01

    In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.

  6. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

    International Nuclear Information System (INIS)

    Morrison, P.J.; Greene, J.M.

    1980-04-01

    A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables

  7. Families of superintegrable Hamiltonians constructed from exceptional polynomials

    International Nuclear Information System (INIS)

    Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc

    2012-01-01

    We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)

  8. Construction of alternative Hamiltonian structures for field equations

    Energy Technology Data Exchange (ETDEWEB)

    Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

    2001-08-10

    We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

  9. Orbits and variational principles for conservative Hamiltonian systems

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1989-01-01

    It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)

  10. ON HAMILTONIAN FORMULATIONS AND CONSERVATION LAWS FOR PLATE THEORIES OF VEKUA-AMOSOV TYPE

    Directory of Open Access Journals (Sweden)

    Sergey I. Zhavoronok

    2017-12-01

    Full Text Available Some variants of the generalized Hamiltonian formulation of the plate theory of I. N. Vekua – A. A. Amosov type are presented. The infinite dimensional formulation with one evolution variable, or an “instantaneous” formalism, as well as the de Donder – Weyl one are considered, and their application to the numerical simulation of shell and plate dynamics is briefly discussed. The main conservation laws are formulated for the general plate theory of Nth order, and the possible motion integrals are introduced

  11. Generalizing the classical fixed-centres problem in a non-Hamiltonian way

    International Nuclear Information System (INIS)

    Albouy, A; Stuchi, T J

    2004-01-01

    The problem of two gravitational (or Coulombian) fixed centres is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. We introduce some straightforward generalizations of the problem that still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations showing the main features of their dynamics. In the domain of bounded orbits the behaviour of these a priori non-Hamiltonian systems is very similar to the behaviour of usual near-integrable systems

  12. Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

    International Nuclear Information System (INIS)

    Sergeevich, Alexandr; Bartlett, Stephen D.; Chandran, Anushya; Combes, Joshua; Wiseman, Howard M.

    2011-01-01

    We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean-square error (MSE) that decreases at best as a power law ∼N -2 in the number of measurements N. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to exp(-0.3N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.

  13. Oscillator representations for self-adjoint Calogero Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

    2011-10-21

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  14. Oscillator representations for self-adjoint Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Gitman, D M; Tyutin, I V; Voronov, B L

    2011-01-01

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  15. Hamiltonian quantum simulation with bounded-strength controls

    International Nuclear Information System (INIS)

    Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza

    2014-01-01

    We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)

  16. Numerical study on the damage efficiency of half-premade fragmented PELE%半预制破片PELE弹丸效能的数值分析

    Institute of Scientific and Technical Information of China (English)

    张洪成; 尹建平; 王志军

    2013-01-01

    为研究壳体刻槽长度和深度对半预制破片PELE弹丸效能的影响,对5种不同刻槽长度和不同深度的PELE弹丸侵彻4340钢质靶板的过程进行数值分析.结果表明:半预制破片PELE弹丸比普通PELE弹丸的后效毁伤性能有显著提高;不同刻槽长度的半预制破片PELE弹丸,随刻槽长度的增加,形成破片的最大径向速度变化较小,破片数量减少,形成破片的大小、质量逐渐增加,动能增大,毁伤性能增强;随着刻槽深度的增加,形成破片的最大径向速度显著增加,破片数量增多,但破片的大小、质量逐渐减小,动能减小,毁伤性能降低.%Numerical simulations of five different kinds of PELE penetrating 4340 steel by LS-DYNA were carried out to study the influence of V-shaped cavity length and depth on the damage efficiency of half-premade fragmented PELE projectile. The results indicate that the damage efficiency of half-premade fragmented PELE is apparently improved compared with normal PELE; for different length of V-shaped cavity, the amount of fragments decreases and the size of fragments increases as the length increases, and the damage efficiency is therefore enhanced; as to different depth of V-shaped cavity, the amount of fragments increases and the size of fragments reduces as the depth increases, and the damage efficiency is weakened.

  17. Numerical investigation of the efficiency of emission reduction and heat extraction in a sedimentary geothermal reservoir: a case study of the Daming geothermal field in China.

    Science.gov (United States)

    Guo, Xuyang; Song, Hongqing; Killough, John; Du, Li; Sun, Pengguang

    2018-02-01

    The utilization of geothermal energy is clean and has great potential worldwide, and it is important to utilize geothermal energy in a sustainable manner. Mathematical modeling studies of geothermal reservoirs are important as they evaluate and quantify the complex multi-physical effects in geothermal reservoirs. However, previous modeling efforts lack the study focusing on the emission reduction efficiency and the deformation at geothermal wellbores caused by geothermal water extraction/circulation. Emission efficiency is rather relevant in geothermal projects introduced in areas characterized by elevated air pollution where the utilization of geothermal energy is as an alternative to burning fossil fuels. Deformation at geothermal wellbores is also relevant as significant deformation caused by water extraction can lead to geothermal wellbore instability and can consequently decrease the effectiveness of the heat extraction process in geothermal wells. In this study, the efficiency of emission reduction and heat extraction in a sedimentary geothermal reservoir in Daming County, China, are numerically investigated based on a coupled multi-physical model. Relationships between the efficiency of emission reduction and heat extraction, deformation at geothermal well locations, and geothermal field parameters including well spacing, heat production rate, re-injection temperature, rock stiffness, and geothermal well placement patterns are analyzed. Results show that, although large heat production rates and low re-injection temperatures can lead to decreased heat production in the last 8 years of heat extraction, they still improve the overall heat production capacity and emission reduction capacity. Also, the emission reduction capacity is positively correlated with the heat production capacity. Deformation at geothermal wellbore locations is alleviated by smaller well spacing, lower heat production rates, and smaller numbers of injectors in the well pattern, and by

  18. A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

    OpenAIRE

    Naz, Rehana

    2018-01-01

    Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.

  19. Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

    International Nuclear Information System (INIS)

    Tassi, E

    2014-01-01

    We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems

  20. Discrete port-Hamiltonian systems : mixed interconnections

    NARCIS (Netherlands)

    Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der

    2005-01-01

    Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

  1. Stochasticity and transport in Hamiltonian systems

    International Nuclear Information System (INIS)

    MacKay, R.S.; Meiss, J.D.; Percival, I.C.

    1984-01-01

    The theory of transport in nonlinear dynamics is developed in terms of ''leaky'' barriers which remain when invariant tori are destroyed. A critical exponent for transport times across destroyed tori is obtained which explains numerical results of Chirikov. The combined effects of many destroyed tori lead to power-law decay of correlations observed in many computations. (author)

  2. Geometry and Hamiltonian mechanics on discrete spaces

    NARCIS (Netherlands)

    Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

    2004-01-01

    Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to

  3. Geometry and Hamiltonian mechanics on discrete spaces

    NARCIS (Netherlands)

    Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan

    2004-01-01

    Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to

  4. The renormalized Hamiltonian truncation method in the large E{sub T} expansion

    Energy Technology Data Exchange (ETDEWEB)

    Elias-Miró, J. [SISSA and INFN, I-34136 Trieste (Italy); Montull, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); Riembau, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); DESY, Notkestrasse 85, 22607 Hamburg (Germany)

    2016-04-22

    Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in refs. http://dx.doi.org/10.1103/PhysRevD.91.085011; http://dx.doi.org/10.1103/PhysRevD.93.065014; http://dx.doi.org/10.1103/PhysRevD.91.025005. The method is general but as an example we calculate the exact g{sup 2} and some of the g{sup 3} contributions for the ϕ{sup 4} theory in two dimensions. The coefficients of the local expansion calculated in ref. http://dx.doi.org/10.1103/PhysRevD.91.085011 are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.

  5. Multivector field formulation of Hamiltonian field theories: equations and symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)

    1999-12-03

    We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)

  6. Effective Hamiltonian for protected edge states in graphene

    International Nuclear Information System (INIS)

    Winkler, R.; Deshpande, H.

    2017-01-01

    Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.

  7. Cluster expansion for ground states of local Hamiltonians

    Directory of Open Access Journals (Sweden)

    Alvise Bastianello

    2016-08-01

    Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

  8. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  9. Hamiltonian approach to second order gauge invariant cosmological perturbations

    Science.gov (United States)

    Domènech, Guillem; Sasaki, Misao

    2018-01-01

    In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

  10. Intertwined Hamiltonians in two-dimensional curved spaces

    International Nuclear Information System (INIS)

    Aghababaei Samani, Keivan; Zarei, Mina

    2005-01-01

    The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle

  11. NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications

    CERN Document Server

    2008-01-01

    Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...

  12. Lie transforms and their use in Hamiltonian perturbation theory

    International Nuclear Information System (INIS)

    Cary, J.R.

    1978-06-01

    A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here

  13. EMR-related problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians

    Directory of Open Access Journals (Sweden)

    Rudowicz Czesław

    2015-07-01

    Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.

  14. Numerical model for predicting thermodynamic cycle and thermal efficiency of a beta-type Stirling engine with rhombic-drive mechanism

    Energy Technology Data Exchange (ETDEWEB)

    Cheng, Chin-Hsiang; Yu, Ying-Ju [Department of Aeronautics and Astronautics, National Cheng Kung University, No. 1, Ta-Shieh Road, Tainan 70101, Taiwan (China)

    2010-11-15

    This study is aimed at development of a numerical model for a beta-type Stirling engine with rhombic-drive mechanism. By taking into account the non-isothermal effects, the effectiveness of the regenerative channel, and the thermal resistance of the heating head, the energy equations for the control volumes in the expansion chamber, the compression chamber, and the regenerative channel can be derived and solved. Meanwhile, a fully developed flow velocity profile in the regenerative channel, in terms of the reciprocating velocity of the displacer and the instantaneous pressure difference between the expansion and the compression chambers, is derived for calculation of the mass flow rate through the regenerative channel. In this manner, the internal irreversibility caused by pressure difference in the two chambers and the viscous shear effects due to the motion of the reciprocating displacer on the fluid flow in the regenerative channel gap are included. Periodic variation of pressures, volumes, temperatures, masses, and heat transfers in the expansion and the compression chambers are predicted. A parametric study of the dependence of the power output and thermal efficiency on the geometrical and physical parameters, involving regenerative gap, distance between two gears, offset distance from the crank to the center of gear, and the heat source temperature, has been performed. (author)

  15. Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

    International Nuclear Information System (INIS)

    Martins, Caroline G L; De Carvalho, R Egydio; Marcus, F A; Caldas, I L

    2011-01-01

    A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

  16. Some sufficient conditions for Hamiltonian property in terms of ...

    Indian Academy of Sciences (India)

    [1, D], or Wf (G) ≥ f (1). 2 n2 + [f(2) − 3. 2 f(1)]n − 2[f(2) − f(1)] for a monotonically decreasing function f(x) on x ∈ [1, D], then G is Hamiltonian, unless G ∼= K∗ n or K2∨3K1. Proof. Assume that G is not a Hamiltonian graph with degree sequence (d1,d2,...,dn), where d1 ≤ d2 ≤ ··· ≤ dn and n ≥ 3. By Lemma 1, there is a ...

  17. Painlevé IV Hamiltonian systems and coherent states

    International Nuclear Information System (INIS)

    Bermudez, D; Contreras-Astorga, A; Fernández C, D J

    2015-01-01

    Schrödinger Hamiltonians with third-order differential ladder operators are linked to the Painlevé IV equation. Some of these appear from applying SUSY QM to the harmonic oscillator. Departing from them, we will build coherent states as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as displaced extremal states using linearized ladder operators. To each Hamiltonian corresponds two families of coherent states for fixed ladder operators: one in the infinite dimension subspace associated with the oscillator spectrum and another in the finite dimension one generated by the eigenstates created by SUSY QM. (paper)

  18. Noether symmetries and integrability in time-dependent Hamiltonian mechanics

    Directory of Open Access Journals (Sweden)

    Jovanović Božidar

    2016-01-01

    Full Text Available We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.

  19. Topological color codes and two-body quantum lattice Hamiltonians

    Science.gov (United States)

    Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.

    2010-02-01

    Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the

  20. Necessary conditions for super-integrability of Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: maria.przybylska@astri.uni.torun.pl; Yoshida, Haruo [National Astronomical Observatory, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo (Japan)], E-mail: h.yoshida@nao.ac.jp

    2008-08-18

    We formulate a general theorem which gives a necessary condition for the maximal super-integrability of a Hamiltonian system. This condition is expressed in terms of properties of the differential Galois group of the variational equations along a particular solution of the considered system. An application of this general theorem to natural Hamiltonian systems of n degrees of freedom with a homogeneous potential gives easily computable and effective necessary conditions for the super-integrability. To illustrate an application of the formulated theorems, we investigate: three known families of integrable potentials, and the three body problem on a line.