Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.
2016-03-01
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.
Efficient fourth order symplectic integrators for near-harmonic separable Hamiltonian systems
Nielsen, Kristian Mads Egeris
2015-01-01
Efficient fourth order symplectic integrators are proposed for numerical integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric splitting coefficients with five to nine stages are obtained by higher order decomposition of the simple harmonic oscillator. The performance of the methods is evaluated for various Hamiltonian systems: Integration errors are compared to those of acclaimed integrators composed by S. Blanes et al. (2013), W. Kahan et al. (1999) and H. Yoshida (1990). Numerical tests indicate that the integrators obtained in this paper perform significantly better than previous integrators for common Hamiltonian systems.
A covariant Hamiltonian tetrad approach to numerical relativity
Hamilton, Andrew J S
2016-01-01
A Hamiltonian approach to the equations of general relativity is proposed in which the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 + 12 = 24 equations of motion and 6 identities, along with 10 constraint equations. By comparison, the ADM formalism has 12 equations of motion and 18 identities, while the BSSN formalism has 15 equations of motion and 15 identities. I conjecture that, by maximizing the number of "good" causal equations of motion and minimizing the number of "bad" acausal identities, the proposed approach may have improved properties of numerical stability.
Recent advances in the numerical solution of Hamiltonian partial differential equations
Barletti, Luigi; Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice
2016-10-01
In this paper, we study recent results in the numerical solution of Hamiltonian partial differential equations (PDEs), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional (which derives from a proper space semi-discretization), confers more robustness to the numerical solution of such problems.
Numerical Studies of Disordered Tight-Binding Hamiltonians
Scalettar, R. T.
2007-06-01
These are notes used for a set of lectures delivered at the Vietri summer school on Condensed Matter Physics in Fall 2006. They concern the general problem of the interplay of interactions and disorder in two dimensional electronic systems, as realized in the specific context of Quantum Monte Carlo simulations of the Anderson-Hubbard Hamiltonian. I wish to thank the organizers of this school for their hospitality during my visit, and their work in general in providing this educational opportunity for students over the years. It is a pleasure also to acknowledge the collaborators together with whom I have learned much of the physics and numerics presented in these notes: Zhaojun Bai, Andrew Baldwin, George Batrouni, Karim Bouadim, Wenbin Chen, Peter Denteneer, Fred Hébert, Norman Paris, Matt Schram, Nandini Trivedi, Martin Ulmke, Ichitaro Yamazaki and Gergely Zimanyi. This work was supported by the National Science Foundation (NSF-DMR-0312261 and NSF-ITR-0313390), and China Special Funds for Major State Basic Research Projects under contract 2005CB321700.
Simulating Hamiltonians in Quantum Networks Efficient Schemes and Complexity Bounds
Wocjan, P; Janzing, D; Beth, T; Wocjan, Pawel; Roetteler, Martin; Janzing, Dominik; Beth, Thomas
2001-01-01
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by applying sequences of appropriate local control sequences. Efficient schemes for decoupling and time reversal can be constructed from orthogonal arrays. Conditions on time optimal simulation are formulated in terms of spectral majorization of matrices characterizing the coupling parameters. Moreover, we consider a specific system of n harmonic oscillators with bilinear interaction. In this case, decoupling can efficiently be achieved using the combinatorial concept of difference schemes. For this type of interactions we present optimal schemes for inversion.
Harmonic bath averaged Hamiltonian: an efficient tool to capture quantum effects of large systems.
Yang, Yonggang; Liu, Xiaomeng; Meuwly, Markus; Xiao, Liantuan; Jia, Suotang
2012-11-26
Starting from a reaction path Hamiltonian, a suitably reduced harmonic bath averaged Hamiltonian is derived by averaging over all the normal mode coordinates. Generalization of the harmonic bath averaged Hamiltonian to any dimensions are performed and the feasibility to use a linear reaction path/surface are investigated and discussed. By use of a harmonic bath averaged Hamiltonian, the tunneling splitting and proton transfer dynamics of malonaldehyde is briefly discussed and shows that the harmonic bath averaged Hamiltonian is an efficient tool to capture quantum effects in larger systems.
A conservative numerical scheme for solving an autonomous Hamiltonian system
Petrov, A. G.; Uvarov, A. V.
2016-09-01
A new numerical scheme is proposed for solving Hamilton's equations that possesses the properties of symplecticity. Just as in all symplectic schemes known to date, in this scheme the conservation laws of momentum and angular momentum are satisfied exactly. A property that distinguishes this scheme from known schemes is proved: in the new scheme, the energy conservation law is satisfied for a system of linear oscillators. The new numerical scheme is implicit and has the third order of accuracy with respect to the integration step. An algorithm is presented by which the accuracy of the scheme can be increased up to the fifth and higher orders. Exact and numerical solutions to the two-body problem, calculated by known schemes and by the scheme proposed here, are compared.
Efficient variational diagonalization of fully many-body localized Hamiltonians
Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.
2016-07-01
We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.
Efficient unitary designs with nearly time-independent Hamiltonian dynamics
Nakata, Yoshifumi; Koashi, Masato; Winter, Andreas
2016-01-01
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic framework to investigate randomising time evolution in quantum many-body systems. The new constructions are based on recently proposed schemes of repeating random unitaires diagonal in mutually unbiased bases. We first show that, if a pair of the bases satisfies a certain condition, the process on one qudit approximately forms a unitary $t$-design after $O(t)$ repetitions. We then construct quantum circuits on $N$ qubits that achieve unitary $t$-designs for $t = o(N^{1/2})$ using $O(t N^2)$ gates, improving the previous result using $O(t^{10}N^2)$ gates in terms of $t$. Based on these results, we present a design Hamiltonian with periodically changing two-local spin-glass-type interactions, leading to fast and relatively natural realisations of unitary designs in complex many-bo...
Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants
Utsuno, Yutaka; Otsuka, Takaharu; Abe, Takashi
2012-01-01
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case where many matrix elements should be calculated, this computation can be transformed into a multiplication of dense matrices. It is demonstrated that the present method based on the matrix-matrix multiplication attains $\\sim$80\\% of the theoretical peak performance measured on systems equipped with modern microprocessors, a factor of 5-10 better than the normal method using indirectly indexed arrays to treat a sparse array. The reason for such different performances is discussed from the viewpoint of memory access.
闫庆友; 熊西文
2002-01-01
An efficient and stable structure preserving algorithm, which is a variant of the QR like (SR) algorithm due to Bunse-Gerstner and Mehrmann, is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix. In the algorithm two strategies are employed, one of which is called dis- unstabilization technique and the other is preprocessing technique. Together with them, a so-called ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm. It is shown that the new algorithm can overcome the instability and breakdown at low cost. Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.
A mollified numerical integrator of ring polymer Hamiltonian dynamics with constraints
Xiong, Yunfeng
2014-01-01
In this paper, a symplectic and time-reversible integrator is proposed of simulating the Hamiltonian dynamics with constraints in path integral molecular dynamics. The constraints are tackled by Matrix Inverted Linearized Constraint algorithm (MILC), while a slight modification is requested under normal mode representation, and the slow potential is mollified by Equilibrium method (Equilibrium MOLLY) to ameliorate the numerical resonance. It is demonstrated that the slow force impulse can be evaluated only at the centroid of beads, instead of being evaluated at the positions of each bead independently. Therefore, it not only allows longer time step but also reduces the complexity of computation. The numerical experiment is performed using SPC/E model in 298K with eight beads. Further discussion will involve the application of Equilibrium MOLLY in flexible bond model.
Tokmachev, A. M.; Robb, M. A.
The spin-Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics - valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge-transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin-Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step-by-step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin-Hamiltonian valence bond theory.
Lemesurier, Brenton
2013-09-01
The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as α-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth-order accurate energy-momentum conserving time discretization and with analytical explanation of the main numerical observations. Impulsive initial data associated with initial excitation of a single amide-I vibration by the energy released by ATP hydrolysis are used as well as the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long-wave approximation by the nonlinear Schrödinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schrödinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction of the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models.
Schwörer, Magnus; Breitenfeld, Benedikt; Tröster, Philipp; Bauer, Sebastian; Lorenzen, Konstantin; Tavan, Paul; Mathias, Gerald
2013-06-28
Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Dolfi, Michele, E-mail: dolfim@phys.ethz.ch; Troyer, Matthias, E-mail: troyer@phys.ethz.ch [ETH Zürich, Institute of Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
The Splitting Multisymplectic Numerical Methods for Hamiltonian Systems%哈密尔顿系统的分裂步多辛数值积分
孔令华
2015-01-01
For Hamiltonian systems,symplectic integrators or multisymplectic integrators are superior to tradi-tional numerica methods for Hamiltonian systems. However,most of them are implicit and engender a coupled nonlinear algebraic system at every time step. It leads to reduce the computational efficiency directly. Splitting multisymplectic integrator which combines multisymplectic integrators with splitting technique can offset this flaw. The framework of this numerical method will be briefly reviewed. Some numerical examples are shown to il-lustrate the application of the methods in physics.%对哈密尔顿系统而言，辛或多辛积分较传统的数值方法具有优越性。然而，此类数值格式大部分都是隐式的，从而在每一个时间步需要求解一个非线性的代数方程组，这将直接导致计算效率不高。在多辛积分中引进分裂步技巧，称之为分裂步多辛积分，可以弥补这一不足之处，这一数值方法的框架将在该文中简要地讨论，其中，数值例子给出了该方法在物理问题中的应用。
Jo, Sunhwan; Chipot, Christophe; Roux, Benoît
2015-05-12
The performance and accuracy of different simulation schemes for estimating the entropy inferred from free energy calculations are tested. The results obtained from replica-exchange molecular dynamics (REMD) simulations based on a simplified toy model are compared to exact numerically derived ones to assess accuracy and convergence. It is observed that the error in entropy estimation decreases by at least an order of magnitude and the quantities of interest converge much faster when the simulations are coupled via a temperature REMD algorithm and the trajectories from different temperatures are combined. Simulations with the infinite-swapping method and its variants show some improvement over the traditional nearest-neighbor REMD algorithms, but they are more computationally expensive. To test the methodologies further, the free energy profile for the reversible association of two methane molecules in explicit water was calculated and decomposed into its entropic and enthalpic contributions. Finally, a strategy based on umbrella sampling computations carried out via simultaneous temperature and Hamiltonian REMD simulations is shown to yield the most accurate entropy estimation. The entropy profile between the two methane molecules displays the characteristic signature of a hydrophobic interaction.
Dybeck, Eric C; Schieber, Natalie P; Shirts, Michael R
2016-08-09
We examine the free energies of three benzene polymorphs as a function of temperature in the point-charge OPLS-AA and GROMOS54A7 potentials as well as the polarizable AMOEBA09 potential. For this system, using a polarizable Hamiltonian instead of the cheaper point-charge potentials is shown to have a significantly smaller effect on the stability at 250 K than on the lattice energy at 0 K. The benzene I polymorph is found to be the most stable crystal structure in all three potentials examined and at all temperatures examined. For each potential, we report the free energies over a range of temperatures and discuss the added value of using full free energy methods over the minimized lattice energy to determine the relative crystal stability at finite temperatures. The free energies in the polarizable Hamiltonian are efficiently calculated using samples collected in a cheaper point-charge potential. The polarizable free energies are estimated from the point-charge trajectories using Boltzmann reweighting with MBAR. The high configuration-space overlap necessary for efficient Boltzmann reweighting is achieved by designing point-charge potentials with intramolecular parameters matching those in the expensive polarizable Hamiltonian. Finally, we compare the computational cost of this indirect reweighted free energy estimate to the cost of simulating directly in the expensive polarizable Hamiltonian.
Efficient numerical integrators for stochastic models
De Fabritiis, G; Español, P; Coveney, P V
2006-01-01
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.
LeMesurier, Brenton
2013-01-01
The phenomenon of coherent energetic pulse propagation in macromolecular chains such as $\\alpha$-helix protein is studied using the Davydov-Scott model, with both numerical studies using a new unconditionally stable fourth order accurate energy-momentum conserving time discretization, and with analysis based on ideas of center manifold theory. It is shown that for physically natural impulsive initial data, the coherent traveling pulses seen have a form related to the Airy function, but with rapid variation of phase along the chain. This can be explained in terms of a new continuum limit approximation by the third derivative nonlinear Schr\\"odinger equation, which differs from the previous continuum limit approximations related to the standard NLS equation. A theorem is given describing the construction of such conservative time discretizations for a large class of Hamiltonian systems.
Kaneko, Yuta
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-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.
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
Cieśliński, Jan L
2011-01-01
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete gradient schemes and integrators of arbitrary high order. In numerical experiments we compare our integrators with some other numerical schemes, including the standard discrete gradient method, the leap-frog scheme and a symplectic scheme of 4th order. We study the error accumulation for very long time and the conservation of the energy integral.
Efficient Numerical Evaluation of Feynman Integral
Li, Zhao; Yan, Qi-Shu; Zhao, Xiaoran
2016-01-01
Feynman loop integral is the key ingredient of high order radiation effect, which is responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing quasi-Monte Carlo method associated with the technique of CUDA/GPU. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in physical kinematic region can be evaluated in less than half minute with $\\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for the precise investigation on the high order effect in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with finite top quark mass.
LIU Zong-Liang; ZHAO Fang; LI Shao-Hua; ZHAO Mei-Shan; CHEN Chang-Yong
2008-01-01
This paper is concerned with the determination of a unique scaling parameter in complex scaling analysis and with accurate calculation of dynamics resonances. In the preceding paper we have presented a theoretical analysis and provided a formalism for dynamical resonance calculations. In this paper we present accurate numerical results for two non-trivial dynamical processes, namely, models of diatomie molecular predissoeiation and of barrier potential scattering for resonances. The results presented in this paper confirm our theoretical analysis, remove a theoretical ambiguity on determination of the complex scaling parameter, and provide an improved understanding for dynamical resonance calculations in rigged Hilbert space.
Efficient numerical evaluation of Feynman integrals
Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran
2016-03-01
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)
Yan, Jinliang; Zhang, Zhiyue
2016-04-01
Two energy-preserving schemes are proposed for the "good" Boussinesq (GBq) equation using the Hamiltonian Boundary Value and Fourier pseudospectral methods. The equation is discretized in space by Fourier pseudospectral method and in time by Hamiltonian Boundary Value methods (HBVMs). The outstanding advantages of the proposed schemes are that they can precisely conserve the global mass and energy, and provide highly accurate results. The single solitary wave, the interaction of two solitary waves and the birth of solitary waves are presented to validate the accuracy and conservation properties of the proposed schemes. In addition, we also compare our numerical results with other known studied methods in terms of numerical accuracy and conservation properties.
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
Power and thermal efficient numerical processing
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...
Equbal, Asif; Shankar, Ravi; Leskes, Michal; Vega, Shimon; Nielsen, Niels Chr.; Madhu, P. K.
2017-03-01
Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the 1H-1H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of 1H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme.
Efficient Numerical Inversion for Financial Simulations
Derflinger, Gerhard; Hörmann, Wolfgang; Leydold, Josef; Sak, Halis
2009-01-01
Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton interpolation and Gauss-Lobatto quadrature can be util...
Numerical aspects for efficient welding computational mechanics
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.
LI Wen-cheng; DENG Zi-chen; HUANG Yong-an
2006-01-01
Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method was proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the secondorder dynamic system was reformulated as the first-order system and the frame of reference was transfered by introducing new variables so that highly oscillatory behaviour inherits from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately designed for solving the above new form and some improved also were presented. Finally, numerical examples show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Botelho, Andre; Lin, Xi
2011-03-01
Two fully transferable physical parameters are incorporated into the historical Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene, one parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, free base porphyrin, polyaniline, and their oligomers of all lengths with an accuracy exceeding the time-dependent density functional theory. Additionally, its computational costs are four orders of magnitude or more lower than first-principles approaches.
Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling
Shin, S.; Reich, S.; Frank, J.E.
2011-01-01
We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of v
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 lik
Yachmenev, Andrey; Yurchenko, Sergei N
2015-07-07
We present a new numerical method to construct a rotational-vibrational Hamiltonian of a general polyatomic molecule in the Eckart frame as a power series expansion in terms of curvilinear internal coordinates. The expansion of the kinetic energy operator of an arbitrary order is obtained numerically using an automatic differentiation (AD) technique. The method is applicable to molecules of arbitrary size and structure and is flexible for choosing various types of internal coordinates. A new way of solving the Eckart-frame equations for curvilinear coordinates also based on the AD technique is presented. The resulting accuracy of the high-order expansion coefficients for the kinetic energy operator using our numerical technique is comparable to that obtained by symbolic differentiation, with the advantage of being faster and less demanding in memory. Examples for H2CO, NH3, PH3, and CH3Cl molecules demonstrate the advantages of the curvilinear internal coordinates and the Eckart molecular frame for accurate ro-vibrational calculations. Our results show that very high accuracy and quick convergence can be achieved even with moderate expansions if curvilinear coordinates are employed, which is important for applications involving large polyatomic molecules.
Yachmenev, Andrey; Yurchenko, Sergei N.
2015-07-01
We present a new numerical method to construct a rotational-vibrational Hamiltonian of a general polyatomic molecule in the Eckart frame as a power series expansion in terms of curvilinear internal coordinates. The expansion of the kinetic energy operator of an arbitrary order is obtained numerically using an automatic differentiation (AD) technique. The method is applicable to molecules of arbitrary size and structure and is flexible for choosing various types of internal coordinates. A new way of solving the Eckart-frame equations for curvilinear coordinates also based on the AD technique is presented. The resulting accuracy of the high-order expansion coefficients for the kinetic energy operator using our numerical technique is comparable to that obtained by symbolic differentiation, with the advantage of being faster and less demanding in memory. Examples for H2CO, NH3, PH3, and CH3Cl molecules demonstrate the advantages of the curvilinear internal coordinates and the Eckart molecular frame for accurate ro-vibrational calculations. Our results show that very high accuracy and quick convergence can be achieved even with moderate expansions if curvilinear coordinates are employed, which is important for applications involving large polyatomic molecules.
Numerical Processing Efficiency Improved in Experienced Mental Abacus Children
Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan
2013-01-01
Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
A Numerical and Experimental Study of Local Exhaust Capture Efficiency
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......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...
Remarks on hamiltonian digraphs
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
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
Numerical study of particle capture efficiency in fibrous filter
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.
Numerical study of particle capture efficiency in fibrous filter
Fan, Jianhua; Lominé, Franck; Hellou, Mustapha
2017-06-01
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.
Efficient numerical solution to vacuum decay with many fields
Masoumi, Ali; Shlaer, Benjamin
2016-01-01
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 under 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.
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...
Yuan eYao
2015-05-01
Full Text Available This study examined whether long-term abacus-based mental calculation (AMC training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-hour/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a two-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG and event related potential (ERP recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC task or the physical size (PC task of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1 and later (N2 and LPC (late positive component time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children.
Yao, Yuan; Du, Fenglei; Wang, Chunjie; Liu, Yuqiu; Weng, Jian; Chen, Feiyan
2015-01-01
This study examined whether long-term abacus-based mental calculation (AMC) training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-h/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a 2-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG) and event related potential (ERP) recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC) (NC task) or the physical size (PC task) of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1) and later (N2 and LPC (late positive component) time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children.
An Efficient Numerical Approach for Nonlinear Fokker-Planck equations
Otten, Dustin; Vedula, Prakash
2009-03-01
Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.
Efficient numerical simulation of heat storage in subsurface georeservoirs
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
An accurate and efficient numerical framework for adaptive numerical weather prediction
Tumolo, G
2014-01-01
We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time discretization method and with a spatial discretization based on adaptive discontinuous finite elements. The resulting method has full second order accuracy in time and can employ polynomial bases of arbitrarily high degree in space, is unconditionally stable and can effectively adapt the number of degrees of freedom employed in each element, in order to balance accuracy and computational cost. The p-adaptivity approach employed does not require remeshing, therefore it is especially suitable for applications, such as numerical weather prediction, in which a large number of physical quantities are associated with a given mesh. Furthermore, although the proposed method can be implemented on arbitrary unstructured and nonconforming meshes, even its application on simple Cartesian...
Nagai, Yuki; Shinohara, Yasushi; Futamura, Yasunori; Sakurai, Tetsuya
2017-01-01
We propose the reduced-shifted conjugate-gradient (RSCG) method, which is numerically efficient to calculate a matrix element of a Green's function defined as a resolvent of a Hamiltonian operator, by solving linear equations with a desired accuracy. This method does not calculate solution vectors of linear equations but does directly calculate a matrix element of the resolvent. The matrix elements with different frequencies are simultaneously obtained. Thus, it is easy to calculate the exception value expressed as a Matsubara summation of these elements. To illustrate a power of our method, we choose a nano-structured superconducting system with a mean-field Bogoliubov-de Gennes (BdG) approach. This method allows us to treat with the system with the fabrication potential, where one cannot effectively use the kernel-polynomial-based method. We consider the d-wave nano-island superconductor by simultaneously solving the linear equations with a large number (˜50000) of Matsubara frequencies.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
RIOT: I/O-Efficient Numerical Computing without SQL
Zhang, Yi; Yang, Jun
2009-01-01
R is a numerical computing environment that is widely popular for statistical data analysis. Like many such environments, R performs poorly for large datasets whose sizes exceed that of physical memory. We present our vision of RIOT (R with I/O Transparency), a system that makes R programs I/O-efficient in a way transparent to the users. We describe our experience with RIOT-DB, an initial prototype that uses a relational database system as a backend. Despite the overhead and inadequacy of generic database systems in handling array data and numerical computation, RIOT-DB significantly outperforms R in many large-data scenarios, thanks to a suite of high-level, inter-operation optimizations that integrate seamlessly into R. While many techniques in RIOT are inspired by databases (and, for RIOT-DB, realized by a database system), RIOT users are insulated from anything database related. Compared with previous approaches that require users to learn new languages and rewrite their programs to interface with a datab...
Numerical calculation of particle collection efficiency in an electrostatic precipitator
Narendra Gajbhiye; V Eswaran; A K Saha; Anoop Kumar
2015-05-01
The present numerical study involves the finding of the collection efficiency of an electrostatic precipitator (ESP) using a finite volume (ANUPRAVAHA) solver for the Navier–Stokes and continuity equations, along with the Poisson’s equation for electric potential and current continuity. The particle movement is simulated using a Lagrangian approach to predict the trajectory of single particles in a fluid as the result of various forces acting on the particle. The ESP model consists of three wires and three collecting plates of combined length of L placed one after another. The calculations are carried out for a wire-to-plate spacing $H$ = 0.175 m, length of ESP $L$ = 2.210 m and wire-to-wire spacing of 0.725 m with radius of wire $R$wire = 10 mm and inlet air-particle velocity of 1.2 m/s. Different electrical potentials ($\\varphi$ = 15–30 kV) are applied to the three discharge electrodes wires. It is seen that the particle collection efficiency of the ESP increases with increasing particle diameter, electrical potential and plate length for a given inlet velocity.
Efficient numerical solution of excitation number conserving quantum systems
Zhang, Zheyong; Ding, Jianping; Wang, Hui-Tian
2017-08-01
A system composed of a harmonic oscillator coupled to a two-level atom is one of the quantum systems, which can be completely solved. Although this system is simple, it is never a easy work for the quantum calculations, especially when the system consists of many such simple constituent parts. In this paper, we present a programming method, by which the calculation tasks for the matrix representation of the Hamiltonian of system can be automatically fulfilled. Coupled-cavity array systems are used to demonstrate our programming method. Some quantum properties of these systems are also discussed.
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning
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
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
Robust preparation and manipulation of protected qubits using time--varying Hamiltonians
Coudreau, Thomas; Dubessy, Romain; Andreoli, Daria; Milman, Pérola
2011-01-01
We show that it is possible to initialize and manipulate in a deterministic manner protected qubits using time varying Hamiltonians. Taking advantage of the symmetries of the system, we predict the effect of the noise during the initialization and manipulation. These predictions are in good agreement with numerical simulations. Our study shows that the topological protection remains efficient under realistic experimental conditions.
吴颖; 罗亚军; 杨晓雪
2003-01-01
We present a novel formalism for energy eigenvalue problems when the corresponding Hamiltonians can be expressed as a function of an angular momentum. The problems are turned into finding operator polynomials by solving a c-number differential equation. Simple and efficient computer-aided analytical and numerical methods may be developed based on the formalism.
Efficient numerical integration of neutrino oscillations in matter
Casas, Fernando; D'Olivo, Juan Carlos
2016-01-01
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
Efficient numerical integration of neutrino oscillations in matter
Casas, F.; D'Olivo, J. C.; Oteo, J. A.
2016-12-01
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
Hamiltonian Algorithm Sound Synthesis
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.
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.
Simulating sparse Hamiltonians with star decompositions
Childs, Andrew M
2010-01-01
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts, this algorithm uses (d^2(d+log* N)||H||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||H||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
A separable shadow Hamiltonian hybrid Monte Carlo method.
Sweet, Christopher R; Hampton, Scott S; Skeel, Robert D; Izaguirre, Jesús A
2009-11-07
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc).
Efficient approximation of random fields for numerical applications
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.
Efficient numerical methods for entropy-linear programming problems
Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.
2016-04-01
Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Entanglement Concentration with Quantum Non Demolition Hamiltonians
Tatham, Richard
2011-01-01
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
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 ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
High-order Hamiltonian splitting for Vlasov-Poisson equations
Casas, Fernando; Faou, Erwan; Mehrenberger, Michel
2015-01-01
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions, we study the order conditions of such methods. It appears that these conditions are of Runge-Kutta-Nystr{\\"o}m type. In the one dimensional case, the order conditions can be further simplified, and efficient methods of order 6 with a reduced number of stages can be constructed. In the general case, high-order methods can also be constructed using explicit computations of commutators. Numerical results are performed and show the benefit of using high-order splitting schemes in that context. Complete and self-contained proofs of convergence results and rigorous error estimates are also given.
An efficient cuckoo search algorithm for numerical function optimization
Ong, Pauline; Zainuddin, Zarita
2013-04-01
Cuckoo search algorithm which reproduces the breeding strategy of the best known brood parasitic bird, the cuckoos has demonstrated its superiority in obtaining the global solution for numerical optimization problems. However, the involvement of fixed step approach in its exploration and exploitation behavior might slow down the search process considerably. In this regards, an improved cuckoo search algorithm with adaptive step size adjustment is introduced and its feasibility on a variety of benchmarks is validated. The obtained results show that the proposed scheme outperforms the standard cuckoo search algorithm in terms of convergence characteristic while preserving the fascinating features of the original method.
Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
He, Yang; Qin, Hong; Liu, Jian
2016-01-01
In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.
An Efficient Hidden Markov Model for Offline Handwritten Numeral Recognition
Saritha, B S
2010-01-01
Traditionally, the performance of ocr algorithms and systems is based on the recognition of isolated characters. When a system classifies an individual character, its output is typically a character label or a reject marker that corresponds to an unrecognized character. By comparing output labels with the correct labels, the number of correct recognition, substitution errors misrecognized characters, and rejects unrecognized characters are determined. Nowadays, although recognition of printed isolated characters is performed with high accuracy, recognition of handwritten characters still remains an open problem in the research arena. The ability to identify machine printed characters in an automated or a semi automated manner has obvious applications in numerous fields. Since creating an algorithm with a one hundred percent correct recognition rate is quite probably impossible in our world of noise and different font styles, it is important to design character recognition algorithms with these failures in min...
Efficient numerical diagonalization of hermitian 3x3 matrices
Kopp, J
2006-01-01
A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be very inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with a new, carefully designed analytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. This analytical algorithm outperforms the other algorithms by more than a factor of 2, but may be less accurate if the eigenvalues differ greatly in magnitude. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from http://www.mpi-hd.mpg.de/~jkopp/3x3/ .
Indirect quantum tomography of quadratic Hamiltonians
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.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices
Kopp, Joachim
A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
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.
An efficient numerical approach to electrostatic microelectromechanical system simulation
Li Pu
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.
Efficient planning and numerical analysis of industrial hemming processes
Burchitz, Igor; Fritsche, David; Grundmann, Göran; Hillmann, Matthias
2011-08-01
Hemming is a forming operation used in the automotive industry to join inner and outer components during the assembly of closures. These are typically opening parts of the body-in-white with additional requirements to their visual appearance. A suitable production concept of hemming operation which satisfies quality, capacity and cost requirements is determined during hemming planning activities. A digital tool to facilitate these activities and minimize the amount of trial and error iterations in try-out phase is presented in this paper. This tool can be used to define process plan, active tool surfaces and suitable process parameters for both die hemming and roll hemming operations. In case of early feasibility studies, when the die layout of the drawing operation is still not available, 3D part geometry is used directly to develop the concept of hemming process. Advanced validation studies, aimed at process optimization and controlling defects associated with hemming, can be based on complete simulation of all forming operations. Validation and analysis of developed concepts of hemming operation is done using the standard AutoForm-Incremental solver. Submesh strategy and special algorithm for contact description between inner and outer parts were implemented to ensure that accurate simulation results can be obtained within reasonable calculation time. Performance of the new software tool for hemming planning and accuracy of simulation results are demonstrated using several simple benchmarks and a real industrial part. It is shown that the new software tool can help to secure the efficient production launch by providing adequate support in try-out phase.
The NumPy array: a structure for efficient numerical computation
Van Der Walt, Stefan; Varoquaux, Gaël
2011-01-01
In the Python world, NumPy arrays are the standard representation for numerical data. Here, we show how these arrays enable efficient implementation of numerical computations in a high-level language. Overall, three techniques are applied to improve performance: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts. We first present the NumPy array structure, then show how to use it for efficient computation, and finally how to share array data with other libraries.
The NumPy array: a structure for efficient numerical computation
Van der Walt, Stefan; Colbert, S. Chris; Varoquaux, Gaël
2011-01-01
International audience; In the Python world, NumPy arrays are the standard representation for numerical data. Here, we show how these arrays enable efficient implementation of numerical computations in a high-level language. Overall, three techniques are applied to improve performance: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts. We first present the NumPy array structure, then show how to use it for efficient computation, and finally how to shar...
Huan, Ronghua; Zhu, Weiqiu [Zhejiang University, Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Hangzhou (China); Wu, Yongjun [East China University of Science and Technology, School of Information Science and Engineering, Shanghai (China)
2009-02-15
A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Ito stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang-bang control strategy. (orig.)
Numerical evaluation of acoustic power radiation and radiation efficiencies of baffled plates
Lemmen, R.L.C.; Panuszka, R.J.
1996-01-01
In this paper expressions are given for the numerical evaluation of radiation efficiencies and power radiation of baffled plates. The expressions can be used as a postprocessing tool in the Finite Element Method. Numerical results for simply supported plates are presented and compared with results o
An efficient numerical integral in three-dimensional electromagnetic field computations
Whetten, Frank L.; Liu, Kefeng; Balanis, Constantine A.
1990-01-01
An improved algorithm for efficiently computing a sinusoid and an exponential integral commonly encountered in method-of-moments solutions is presented. The new algorithm has been tested for accuracy and computer execution time against both numerical integration and other existing numerical algorithms, and has outperformed them. Typical execution time comparisons on several computers are given.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
D.C. Wan; G.W. Wei
2000-01-01
An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional NavierStokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has the potential of being extended to numerically solve much broader problems in fluid dynamics.
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Mesh-free Hamiltonian implementation of two dimensional Darwin model
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.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing
R. Company
2016-01-01
Full Text Available This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach.
Effective Hamiltonians for phosphorene and silicene
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.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature...
A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls
Arjunan, Arun; Wang, Chang; English, Martin; Stanford, Mark; Lister, Paul
2015-01-01
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 consi...
Xuehui Chen; Liancun Zheng; Xinxin Zhang
2006-01-01
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
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...
Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan
2017-03-01
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.
An efficient numerical model for hydrodynamic parameterization in 2D fractured dual-porosity media
Fahs, Hassane; Hayek, Mohamed; Fahs, Marwan; Younes, Anis
2014-01-01
This paper presents a robust and efficient numerical model for the parameterization of the hydrodynamic in fractured porous media. The developed model is based upon the refinement indicators algorithm for adaptive multi-scale parameterization. For each level of refinement, the Levenberg-Marquardt method is used to minimize the difference between the measured and predicted data that are obtained by solving the direct problem with the mixed finite element method. Sensitivities of state variables with respect to the parameters are calculated by the sensitivity method. The adjoint-state method is used to calculate the local gradients of the objective function necessary for the computation of the refinement indicators. Validity and efficiency of the proposed model are demonstrated by means of several numerical experiments. The developed numerical model provides encouraging results, even for noisy data and/or with a reduced number of measured heads.
Splitting K-symplectic methods for non-canonical separable Hamiltonian problems
Zhu, Beibei; Zhang, Ruili; Tang, Yifa; Tu, Xiongbiao; Zhao, Yue
2016-10-01
Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems; for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent.
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Collection Efficiency for Filters with Staggered Parallel Y and Triple Y Fibers: A Numerical Study
Huaning Zhu
2009-03-01
Full Text Available A numerical study is performed to determine the collection efficiency of filters composed of staggered parallel Y and triple Y fibers. By employing the Lattice Boltzmann method, the Navier–Stokes equations are solved for flow fields in a two-dimensional domain with periodic boundary conditions. Trajectories of particles with different diameters arranging from 0.02 μm to 5 μm are then computed by solving the particle motion equation hence obtaining the collection efficiency of single Y and triple Y fibers. The effects of fiber orientation, Brownian motion, particulate size and Reynolds number on the collection efficiency of these two types of fibers are also evaluated numerically.Y and triple Y fibers have low packing density and relatively large area to volume ratio, and the latter property helps enhance the Brownian diffusion collection mechanism for smaller particles. The large void zone of these fibers can accommodate more particles, which improves the particle loading capacity. It is also found out that the flow field and collection efficiency of triple Y fiber is less susceptible to different fiber orientations due to its geometric symmetry. The numerical results obtained in this work provide helpful information in designing high efficiency filters.
Numerical simulation of design for cylinder wall considering of scavenging efficiency
Sasaki, S.; Ezumi, T.; Satoh, K. [Dept. of Mechanical Eng., Shibaura Inst. of Tech., Tokyo (Japan)
2004-07-01
The transformation of the cylinder is examined and analyzed the pressure and the temperature by means of the numerical analysis under the change of the scavenging efficiency. The change of the scavenging efficiency makes the temperature and the pressure change. The combustion temperature of the 2-cycle internal combustion engine that a lot of fuels may burn in the cylinder when the scavenging efficiency goes up. According to the scavenging efficiency, the temperature and the pressure is getting high. So the cylinder is transformed under the high temperature and the high pressure. The authors simulated the change of the temperature and the pressure in the cylinder. When the cylinder is designed, the engineer must know the change of the state in the cylinder. Then the change of the scavenging efficiency was simulated and examined. At the same time, the NO gas generated. The authors examined the transformation of the cylinder and simulated the NO generation. (orig.)
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Numerical bifurcation of Hamiltonian relative periodic orbits
Wulff, Claudia; Schilder, Frank
2009-01-01
that the family of choreographies rotating around the $e^2$-axis bifurcates to the family of rotating choreographies that connects to the Lagrange relative equilibrium. Moreover, we compute several relative period-doubling bifurcations and a turning point of the family of planar rotating choreographies, which...... to symmetry-breaking/symmetry-increasing pitchfork bifurcations or to period-doubling/period-halving bifurcations. We apply our methods to the family of rotating choreographies which bifurcate from the famous figure eight solution of the three-body problem as angular momentum is varied. We find...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
Arbabi, Amir; Ball, Alexander J; Bagheri, Mahmood; Faraon, Andrei
2014-01-01
We report subwavelength-thick, polarization insensitive micro-lenses operating at telecom wavelength with focal spots as small as 0.57 wavelengths and measured focusing efficiency up to 82%. The lens design is based on high contrast transmitarrays that enable control of optical phase fronts with subwavelength spatial resolution. A rigorous method for ultra-thin lens design, and the trade-off between high efficiency and small spot size (or large numerical aperture) are discussed. The transmitarrays, composed of silicon nano-posts on glass, could be fabricated by high-throughput photo or nanoimprint lithography, thus enabling widespread adoption.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
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.
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
Improving Efficiency of CCS Numerical Simulations Through Use of Parallel Processing
Konopka K.
2015-04-01
Full Text Available The study presents the findings of research concerning the possibilities for application of parallel processing in order to reduce the computing time of numerical simulations of the steel continuous casting process. The computing efficiency for a CCS model covering the mould and a strand fragment was analysed. The calculations were performed with the ProCAST software package using the finite element method. Two computing environments were used: the PL-Grid infrastructure and cloud computing platform.
Increasing numerical efficiency in coupled Eulerian-Lagrangian metal forming simulations
Hammelmüller, Franz; Zehetner, Christian
2015-01-01
The coupled Eulerian-Lagrangian formulation is an efficient tool for modelling and simulation of metal forming processes with large deformation. In many cases, thermo-mechanical coupling has to be considered. Usually the numerical effort is very high for such processes, and large simulation times are the consequence. In this paper, strategies for reducing the simulation time are investigated, based on the example of a hot forming process.
Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs
Tang, Wensheng; Sun, Yajuan; Cai, Wenjun
2017-02-01
In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.
Bifurcations and safe regions in open Hamiltonians
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models
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.
Robust H∞ Control of Hamiltonian System with Uncertainty
薛安成; 梅生伟; 胡伟; 周原
2003-01-01
This paper investigates the robust H∞ problem for a class of generalized forced Hamiltonian systems with uncertainties. The robust L2-gain was proved for the Hamiltonian with a sufficient condition for stable control of multimachine power systems expressed as a matrix algebraic inequality. A similar sufficient condition was then extended to the robust H∞ control of Hamiltonian systems to construct the state feedback H∞ control law. A numerical example is given to verify the validity of the proposed control scheme, which shows the effectiveness and promising application of the method.
Covariant Hamiltonian for the electromagnetic two-body problem
De Luca, Jayme
2005-09-01
We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.
A Hamiltonian Algorithm for Singular Optimal LQ Control Systems
Delgado-Tellez, M
2012-01-01
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the well-known Rabier-Rheinhboldt constraints algorithm used to solve differential-algebraic equations. Its geometrical content is exploited fully by implementing a Hamiltonian extension of it which is closer to Gotay-Nester presymplectic constraint algorithm used to solve singular Hamiltonian systems. Thus, given an optimal control problem whose optimal feedback is given in implicit form, a consistent set of equations is obtained describing the first order differential conditions of Pontryaguine's Maximum Principle. Such equations are shown to be Hamiltonian and the set of first class constraints corresponding to controls that are not determined, are obtained explicitly. The strength of the algorithm is shown by exhibiting a numerical implementation with partial feedback on the c...
Discrete-Time Models for Implicit Port-Hamiltonian Systems
Castaños, Fernando; Michalska, Hannah; Gromov, Dmitry; Hayward, Vincent
2015-01-01
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian sys...
Comparing Maps to Symplectic Integrators in a Galactic Type Hamiltonian
N. D. Caranicolas; N. J. Papadopoulos
2003-09-01
We obtain the - Poincare phase plane for a two dimensional, resonant, galactic type Hamiltonian using conventional numerical integration, a second order symplectic integrator and a map based on the averaged Hamiltonian. It is found that all three methods give good results, for small values of the perturbation parameter, while the symplectic integrator does a better job than the mapping, for large perturbations. The dynamical spectra are used to distinguish between regular and chaotic motion.
Li, Dongfang; Zhang, Jiwei
2016-10-01
Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.
Numerical Analysis of Microdischarge Oxygen Plasma and Prediction of Ozone Production Efficiency
Kawano, Satoyuki; Misaka, Takashi
In this research, numerical simulation of oxygen plasma produced by dielectric barrier discharge (DBD) is made as a basic research for the application of bioprocesses such as sterilization. Numerical simulation is based on an appropriate modeling of microdischarges including 9 kinds of species and 54 chemical reactions. Behavior of the oxygen plasma is analyzed by finite difference method in two-dimensional computational region. The detailed characteristics of filamentous discharge formed between parallel dielectric surfaces which cover the electrodes are investigated. The qualitative tendency of the discharge formation process agrees with the previous experimental observation. Ozone production efficiency (OPE) is obtained and compared with experimental results. Dependency of reduced electric field E/n on OPE is investigated by comparing the numerical results with previous experimental results by other researcher, where E/n is the ratio of electric field EE to number density n of neutral molecule in the gas. It is confirmed that the present numerical simulation has practically enough accuracy for the evaluation of the OPE to optimize the oxygen plasma sterilization devices.
Quantum control by means of hamiltonian structure manipulation.
Donovan, A; Beltrani, V; Rabitz, H
2011-04-28
A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited
A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls
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.
Milani, Massimo; Montorsi, Luca; Stefani, Matteo; Saponelli, Roberto; Lizzano, Maurizio
2017-04-05
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.
Vilas Carlos
2012-07-01
Full Text Available Abstract Background 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. Results 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. Conclusions 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
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, Tibor; Collura, Mario; Kormos, Márton; Takács, Gábor
2016-01-01
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 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...
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.
Quantum simulation of pairing Hamiltonians with nearest-neighbor-interacting qubits
Wang, Zhixin; Gu, Xiu; Wu, Lian-Ao; Liu, Yu-xi
2016-06-01
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators." Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.
Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
Tao, Molei
2016-01-01
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators, which are explicit, of any even order, symplectic in an extended phase space, and with pleasant long time properties. They are based on a mechanical restraint that binds two copies of phase space together. Using backward error analysis, KAM theory, and additional multiscale analysis, an error bound of $\\mathcal{O}(T\\delta^l \\omega)$ is established for integrable systems, where $T$, $\\delta$, $l$ and $\\omega$ are respectively the (long) simulation time, step size, integrator order, and some binding constant. For non-integrable systems with positive Lyapunov exponents, such an error bound is generally impossible, but satisfactory statistical behaviors were observed in a numerical experiment with a nonlinear Schr\\"{o}dinger equation.
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.
Numerical simulation of four-wave mixing efficiency and its induced relative intensity noise
Chen Wei; Meng Zhou; Zhou Hui-Juan; Luo Hong
2012-01-01
Four-wave mixing,as well as its induced intensity noise,is harmful to wavelength division multiplexing systems.The efficiency and the relative intensity noise of four-wave mixing are numerically simulated for the two-wave and the three-wave fiber transmissions.It is found that the efficiency decreases with the increase of both the frequency spacing and the fiber length,which can be explained using the quasi-phase-matching condition.Furthermore,the relative intensity noise decreases with the increase of frequency spacing,while it increases with the increase of fiber length,which is due to the considerable power loss of the pump light.This investigation presents a good reference for the practical application of wavelength division multiplexing systems.
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.
Hamiltonian partial differential equations and applications
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.
Deng, Jian; Sun, Liping; Teng, Lubao; Pan, Dingyi; Shao, Xueming
2016-09-01
We study numerically the propulsive wakes produced by a flapping foil. Both pure pitching and pure heaving motions are considered, respectively, at a fixed Reynolds number of Re = 1700. As the major innovation of this paper, we find an interesting coincidence that the efficiency maximum agrees well with the 2D-3D transition boundary, by plotting the contours of propulsive efficiency in the frequency-amplitude parametric space and comparing to the transition boundaries. Although there is a lack of direct 3D simulations, it is reasonable to conjecture that the propulsive efficiency increases with Strouhal number until the wake transits from a 2D state to a 3D state. By comparing between the pure pitching motion and the pure heaving motion, we find that the 2D-3D transition occurs earlier for the pure heaving foil than that of the pure pitching foil. Consequently, the efficiency for the pure heaving foil peaks more closely to the wake deflection boundary than that of the pure pitching foil. Furthermore, since we have drawn the maps on the same parametric space with the same Reynolds number, it is possible to make a direct comparison in the propulsive efficiency between a pure pitching foil and a pure heaving foil. We note that the maximum efficiency for a pure pitching foil is 15.6%, and that of a pure heaving foil is 17%, indicating that the pure heaving foil has a slightly better propulsive performance than that of the pure pitching foil for the currently studied Reynolds number.
Numerical Research of Steam and Gas Plant Efficiency of Triple Cycle for Extreme North Regions
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.
de La Bernardie, Jérôme; Bour, Olivier; de Dreuzy, Jean-Raynald; Guihéneuf, Nicolas; Chatton, Eliot; Labasque, Thierry; Le Borgne, Tanguy
2017-04-01
Geothermal energy is a renewable energy source particularly attractive due to associated low greenhouse gas emission rates. Crystalline rocks are in general considered of poor interest for geothermal applications at shallow depths (energy storage at these shallow depths is still remaining very challenging because of the low storativity of the medium. Within this framework, the purpose of this study is to test the possibility of efficient thermal energy storage in shallow fractured rocks. For doing so, several heat tracer tests have been carried on in a single well between two connected fractures. We completed this experimental work with numerical modeling of thermal transport in fractures embedded in an impermeable conductive matrix. The thermal tracer tests were achieved in a crystalline rock aquifer at the experimental site of Ploemeur (H+ observatory network). The experimental setup consists in injecting hot water in a fracture isolated by a double straddle packer in the borehole while pumping and monitoring the temperature in a fracture crossing the same borehole at greater elevation. Several tracer tests were achieved at different pumping and injection rates. This experimental set up allowed to estimate temperature breakthrough for different tracer test durations and hydraulic configurations from fully convergent to perfect dipole tracer tests. Thanks to those tests and numerical modeling of heat transport in fractures, we demonstrate that temperature recovery is highly dependent on flow rate and streamlines shape. Thus, thermal storage rate is inversely proportional to flow and is maximized in perfect dipole configuration. These thermal tracer tests and numerical modeling allow to define the most efficient configuration for optimizing shallow geothermal storage in fractured rock.
Chromatic roots and hamiltonian paths
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...
Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2002-01-01
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis
Zhu, Jinglong; Site, Luigi Delle
2016-01-01
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer/transition region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. \\blue{Such conditions show that molecular simulations in the current computational implementation require systems of large size and thus a Hamiltonian approach as the one proposed, at this stage, would not be practica...
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
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.
Assessment of Efficiency and Performance in Tsunami Numerical Modeling with GPU
Yalciner, Bora; Zaytsev, Andrey
2017-04-01
Non-linear shallow water equations (NSWE) are used to solve the propagation and coastal amplification of long waves and tsunamis. Leap Frog scheme of finite difference technique is one of the satisfactory numerical methods which is widely used in these problems. Tsunami numerical models are necessary for not only academic but also operational purposes which need faster and accurate solutions. Recent developments in information technology provide considerably faster numerical solutions in this respect and are becoming one of the crucial requirements. Tsunami numerical code NAMI DANCE uses finite difference numerical method to solve linear and non-linear forms of shallow water equations for long wave problems, specifically for tsunamis. In this study, the new code is structured for Graphical Processing Unit (GPU) using CUDA API. The new code is applied to different (analytical, experimental and field) benchmark problems of tsunamis for tests. One of those applications is 2011 Great East Japan tsunami which was instrumentally recorded on various types of gauges including tide and wave gauges and offshore GPS buoys cabled Ocean Bottom Pressure (OBP) gauges and DART buoys. The accuracy of the results are compared with the measurements and fairly well agreements are obtained. The efficiency and performance of the code is also compared with the version using multi-core Central Processing Unit (CPU). Dependence of simulation speed with GPU on linear or non-linear solutions is also investigated. One of the results is that the simulation speed is increased up to 75 times comparing to the process time in the computer using single 4/8 thread multi-core CPU. The results are presented with comparisons and discussions. Furthermore how multi-dimensional finite difference problems fits towards GPU architecture is also discussed. The research leading to this study has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No
Numerical Analysis of Novel Back Surface Field for High Efficiency Ultrathin CdTe Solar Cells
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.
Elias-Miro, Joan; Vitale, Lorenzo G.
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d >= 3.
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2017-05-01
We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.
Modesti, Davide
2016-01-01
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated with acoustic waves, in such a way to suppress, or at least mitigate the acoustic time step limitation. Together with replacement of the total energy equation with the entropy transport equation, this approach avoids the inversion of block-banded matrices involved in classical methods, which is replaced by less demanding inversion of standard banded matrices. The method is extended to deal with implicit integration of viscous terms and to multiple space dimensions through approximate factorization, and used as a building block of third-order Runge-Kutta time stepping scheme. Numerical experiments are carried out for isotropic turbulence, plane channel flow, and flow in a square duct. All available data support higher computational efficiency than existing methods, and saving ...
Numerical Analysis of Novel Back Surface Field for High Efficiency Ultrathin CdTe Solar Cells
Matin, M.A.; Tomal, M. U.; A. M. Robin; N. Amin
2013-01-01
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 ...
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
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
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.
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
2016-05-01
The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce an interpolation process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the interpolation process, for calculating topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.
Reinforcement learning for port-hamiltonian systems.
Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D
2015-05-01
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
On the Reaction Path Hamiltonian
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
Byrnes, Steven J; Aieta, Francesco; Capasso, Federico
2015-01-01
A metasurface lens (meta-lens) is a lens that bends light with an array of nanostructures on a flat surface, rather than by refraction. Macroscopic meta-lenses (mm- to cm-scale diameter) have been quite difficult to simulate and optimize, due to the large area, the lack of periodicity, and the billions of adjustable parameters. We describe a method for designing a large-area meta-lens that allows not only prediction of the efficiency and far-field, but also optimization of the shape and position of each individual nanostructure, with a computational cost that is almost independent of the lens size. Loosely speaking, the technique consists of designing a series of metasurface beam deflectors (blazed gratings), and then gluing them together. As a test of this framework, we design some high-numerical-aperture (NA=0.94) meta-lenses for visible light, based on TiO2 nano-pillars on a glass substrate. One of our designs is predicted to focus unpolarized 580nm light with 79% predicted efficiency; another focuses 580n...
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.
Jones, T W
2005-01-01
We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The efficiency of the scheme derives from its use of coarse-grained finite momentum volumes. This approach has enabled us, using $\\sim 10 - 20$ momentum bins spanning nine orders of magnitude in momentum, to carry out simulations that agree well with results from simulations of modified shocks carried out with our conventional finite difference scheme requiring more than an order of magnitude more momentum points. The coarse-grained, CGMV scheme reduces execution times by a factor approximately half the ratio of momentum bins used in the two methods. Depending on the momentum dependence of the diffusion, additional economies in required spatial and time resolution can be utilized in the CGMV scheme, as well. These allow a computational speed-up of at least an order of magnitude i...
Numerical investigation of the thrust efficiency of a laser propelled vehicle
mulroy jr
1990-08-01
The flow situation for a thruster propelled by ablated gas which is energized by a laser pulse is numerically simulated. The flow is axisymmetric and nonsteady, and is assumed to be inviscid due to its high Reynolds number. The high pressure expansion of the laser heated gas generates thrust as it pushes against the vehicle. Gas expansion lateral to the thrust vector causes performance to decrease. The vehicle geometry and the laser pulse characteristics determine the degree to which the flow is one dimensional. As the thruster's parameters are varied, its impulse is calculated and compared to the limiting impulse of a one-dimensional system, and thus the thrust efficiency is computed. Lateral expansion losses computed by simulating the flow of the expanding gas time-accurately on a computer are far less than losses predicted using the method of characteristics, which is the best alternate means of computation. Flows which exhibit a substantial amount of lateral expansion can still yield an expansion efficiency which exceeds 70%. This finding has significant implications on the eventual design of flight hardware. Steger and Warming's flux split numerics for the Euler equations are modified for blast simulations into near vacuum ambient conditions. At the interface between the near vacuum ambient and the wave front, the solution is first order accurate but sufficiently robust to handle pressure ratios exceeding one million and density ratios exceeding 10,000 between the thrust gas and the ambient gas. Elsewhere the solution is second order accurate. The majority of the calculations performed assume an ideal gas equation of state with {gamma} = 1.2. The propellant Lithium Hydride has shown excellent promise in the laboratory, yielding I{sub sp} = 800-1000 sec. Equilibrium and kinetic modeling of LiH is undertaken, with a variable {gamma} of from 1.25 to 1.66 resulting from the kinetic assumptions of ionization equilibrium and frozen chemistry. These
Dyson--Schwinger Approach to Hamiltonian QCD
Campagnari, Davide R; Huber, Markus Q; Vastag, Peter; Ebadati, Ehsan
2016-01-01
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
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...
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Hamiltonian Structure of PI Hierarchy
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Alternative Hamiltonian representation for gravity
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.
Study on the stability of switched dissipative Hamiltonian systems
ZHU Liying; WANG Yuzhen
2006-01-01
The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.
The rovibrational Hamiltonian for ammonia-like molecules.
Makarewicz, Jan; Skalozub, Alexander
2002-03-01
A new exact quantum mechanical rovibrational Hamiltonian operator for ammonia-like molecules is derived. The Hamiltonian is constructed in a molecular system of axes, such that its z' axis makes a trisection of the pyramidal angle formed by three bond vectors with the vertex on the central atom. The introduced set of the internal rovibrational coordinates is adapted to facilitate a convenient description of the inversion motion. These internal coordinates and the molecular axis system have a remarkable property, namely, the internal vibrational angular momentum of the molecule equals zero. This property significantly reduces the Coriolis coupling and simplifies the form of the Hamiltonian. The correctness of this Hamiltonian is proved by a numerical procedure. The orthogonal Radau vectors allowing us to define a similar molecular axis system and the internal coordinates are considered. The Hamiltonian for the Radau parameterization takes a form simple enough to carry out effectively variational calculations of the molecular rovibrational states. Under the appropriate choice of the variational basis functions, the Hamiltonian matrix elements are fully factorizable and do not have any singularities. A convenient method of symmetrization of the basis functions is proposed.
Adaptive molecular resolution approach in Hamiltonian form: An asymptotic analysis
Zhu, Jinglong; Klein, Rupert; Delle Site, Luigi
2016-10-01
Adaptive molecular resolution approaches in molecular dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer (transition) region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined, and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size, and thus a Hamiltonian approach such as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes.
Reverse engineering of a Hamiltonian by designing the evolution operators.
Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie
2016-07-22
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments.
Hamiltonian analysis of interacting fluids
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
Li, Zheng; Wang, Hong; Yang, Danping
2017-10-01
We present a space-time fractional Allen-Cahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space-time fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.
Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E
2016-08-09
Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system.
Hamiltonian description of the ideal fluid
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.
Shun Zou
2015-02-01
Full Text Available An efficient IBLF-dts scheme is proposed to integrate the bounce-back LBM and FVM scheme to solve the Navier-Stokes equations and the constitutive equation, respectively, for the simulation of viscoelastic fluid flows. In order to improve the efficiency, the bounce-back boundary treatment for LBM is introduced in to improve the grid mapping of LBM and FVM, and the two processes are also decoupled in different time scales according to the relaxation time of polymer and the time scale of solvent Newtonian effect. Critical numerical simulations have been carried out to validate the integrated scheme in various benchmark flows at vanishingly low Reynolds number with open source CFD toolkits. The results show that the numerical solution with IBLF-dts scheme agrees well with the exact solution and the numerical solution with FVM PISO scheme and the efficiency and scalability could be remarkably improved under equivalent configurations.
Hamiltonian vortices and reconnection in a magnetized plasma
Kuvshinov, B. N.; Lakhin, V. P.; Pegoraro, F.; Schep, T. J.
1998-01-01
Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and exten
Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian
Cuerno, R
1993-01-01
The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic $R$ matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.
Horizontal circulation and jumps in Hamiltonian wave models
Gagarina, E.; Vegt, van der J.; Bokhove, O.
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 dyn
Numerical calculation of radiation protective clothing efficiency by using Monte Carlo method
Моргунов, Владимир Викторович; Диденко, Наталья Викторовна; Трищ, Роман Михайлович
2016-01-01
The article presents the results of numerical experiments on modeling of absorption of gamma-radiation with/without using the proposed radiation-protective suit and radiation-shielding material (lead glass in the form of microspheres). The proposed method numerical experiments leads to the reduction of human, time and financial resources. When conducting numerical experiments we used the software package GEANT4. When conducting numerical experiments, we used a phantom of the human body (total...
Hamiltonian truncation approach to quenches in the Ising field theory
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.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.
2016-10-01
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.
Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul
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.
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.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.
Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A
2007-02-01
Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.
Effective Hamiltonian for a microwave billiard with attached waveguide.
Stöckmann, H-J; Persson, E; Kim, Y-H; Barth, M; Kuhl, U; Rotter, I
2002-06-01
In a recent work the resonance widths in a microwave billiard with attached waveguide were studied in dependence on the coupling strength [E. Persson et al., Phys. Rev. Lett. 85, 2478 (2000)], and resonance trapping was experimentally found. In the present paper an effective Hamiltonian is derived that depends exclusively on billiard and waveguide geometry. Its eigenvalues give the poles of the scattering matrix provided that the system and environment are defined adequately. Further, we present the results of resonance trapping measurements where, in addition to our previous work, the position of the slit aperture within the waveguide was varied. Numerical simulations with the derived Hamiltonian qualitatively reproduce the experimental data.
Efficient Numerical Modeling of Slow-Slip and Quasi-Dynamic Earthquake Ruptures
Bradley, A. M.; Segall, P.
2010-12-01
the nonlinear equations. For efficiency, we group fault cells by physical properties, perform only one sparse LU factorization per group, and efficiently update the LU factorization at each solve, yielding a method that is linear in the number of diffusion profile nodes. We parallelize the nonlinear solves to work on a shared-memory system using OpenMP. We approximate the elasticity matrix relating slip and stress by a hierarchical low-rank representation to speed up matrix-vector products. This presentation will describe our software and numerical methods, and simulation results that highlight our software's capabilities.
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
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, 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 preferential attachment. 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 preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
First principles of Hamiltonian medicine.
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.
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians
Patel, Apoorva; Priyadarsini, Anjani
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
Enumerating Hamiltonian Cycles in a Planar Graph Using Combinatorial Cycle Bases
Retno MAHARESI
2016-04-01
Full Text Available Cycle bases belong to a k-connected simple graph used both for listing and enumerating Hamiltonian cycles contained in a planar graph. Planar cycle bases have a weighted induced graph whose weight values limited to 1. Hence making it was possible used in the Hamiltonian cycle enumeration procedures efficiently. In this paper a Hamiltonian cycle enumeration scheme is obtained through two stages. First, i cycles out of m bases cycles are determined using an appropriate constructed constraint. Secondly, to search all Hamiltonian cycles which are formed by the combination of i bases cycles obtained in the first stage efficiently. This efficiency achieved through a generation a class of objects as the representation of i cycle combinations among m bases cycles. The experiment conducted based on the proposed algorithm successfully generated and enumerated all the Hamiltonian cycles contained in a well-known example of planar graph.
Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms
Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei
2016-01-01
In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).
Itoh, Satoru G; Okumura, Hisashi
2013-11-05
We propose the Hamiltonian replica-permutation method (RPM) (or multidimensional RPM) for molecular dynamics and Monte Carlo simulations, in which parameters in the Hamiltonian are permuted among more than two replicas with the Suwa-Todo algorithm. We apply the Coulomb RPM, which is one of realization of the Hamiltonian RPM, to an alanine dipeptide and to two amyloid-β(29-42) molecules. The Hamiltonian RPM realizes more efficient sampling than the Hamiltonian replica-exchange method. We illustrate the protein misfolding funnel of amyloid-β(29-42) and reveal its dimerization pathways.
Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung
2015-01-01
and basis vectors for use according to the target system. The proposed model reduction scheme is applied to the numerical simulation of the simple mass-damping-spring system and the acoustic metamaterial systems (i.e., acoustic lens and acoustic cloaking device) for the first time. Through these numerical...
ANALYSIS OF LIMIT CYCLES TO A PERTURBED INTEGRABLE NON-HAMILTONIAN SYSTEM
无
2012-01-01
Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian system.The study reveals that the system has 3 limit cycles.By the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are determined.The study also indicates that each ...
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Maslov index for Hamiltonian systems
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.
Dynamical stability of Hamiltonian systems
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Derivation of Hamiltonians for accelerators
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.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
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.
Phase equilibria in polymer blend thin films: a Hamiltonian approach.
Souche, M; Clarke, N
2009-12-28
We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.
Dual partitioning for effective Hamiltonians to avoid intruders
Ten-no, Seiichiro
2015-01-01
We present a new Hamiltonian partitioning which converges an arbitrary number of states of interest in the effective Hamiltonian to the full configuration interaction limits simultaneously. This feature is quite useful for the recently developed model space quantum Monte Carlo. A dual partitioning (DP) technique is introduced to avoid the intruder state problem present in the previous eigenvalue independent partitioning of Coope. The new approach is computationally efficient and applicable to general excited states involving conical intersections. We present a preliminary application of the method to model systems to investigate the performance.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Constructing Dense Graphs with Unique Hamiltonian Cycles
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…
Geometric Hamiltonian structures and perturbation theory
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.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
Hamiltonian structure of propagation equations for ultrashort optical pulses
Amiranashvili, Sh.; Demircan, A.
2010-07-01
A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation for the electric field is transformed into a first-order propagation equation for a suitably defined complex electric field. The Hamiltonian formulation is then introduced in terms of normal variables, i.e., classical complex fields referring to the quantum creation and annihilation operators. The derived z-propagated Hamiltonian accounts for forward and backward waves, arbitrary medium dispersion, and four-wave mixing processes. As a simple application we obtain integrals of motion for the pulse propagation. The integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse. Furthermore, pulses in the form of stationary nonlinear waves are considered. They yield extremal values of the momentum flux for a given energy flux. Simplified propagation equations are obtained by reduction of the Hamiltonian. In particular, the complex electric field reduces to an analytic signal for the unidirectional propagation. Solutions of the full bidirectional model are numerically compared to the predictions of the simplified equation for the analytic signal and to the so-called forward Maxwell equation. The numerics is effectively tested by examining the conservation laws.
Nonperturbative light-front Hamiltonian methods
Hiller, J R
2016-01-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, $\\phi^4$ theory, ordinary Yukawa theory, supersymmetric Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations...
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Hamiltonian description of composite fermions: Magnetoexciton dispersions
Murthy, Ganpathy
1999-11-01
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in fractional quantum hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the ν=13, 25, and 37 gapped fractions, and find approximate agreement with numerical results. I also analyze the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 25 and 37, and it is shown that the spin-polarized 25 state, in contrast to the spin-polarized 13 state, cannot be described as a simple quantum ferromagnet.
Nonperturbative light-front Hamiltonian methods
Hiller, J. R.
2016-09-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
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.
Sørensen, Dan Nørtoft; Sørensen, Jens Nørkær
2000-01-01
A numerically efficient mathematical model for the aerodynamics of rotor-only axial fans has been developed. The model is based on a blade-elementprinciple whereby the rotor is divided into a number of annular streamtubes. For each of these streamtubes relations for velocity, pressure, and radial......A numerically efficient mathematical model for the aerodynamics of rotor-only axial fans has been developed. The model is based on a blade-elementprinciple whereby the rotor is divided into a number of annular streamtubes. For each of these streamtubes relations for velocity, pressure......, and radialposition are derived from the incompressible conservation laws for mass, tangential momentum, and energy. The resulting system of equations isnonlinear and, due to mass conservation and pressure equilibrium far downstream of the rotor, strongly coupled. The equations are solved using the...
Numerical Investigation on Mixing Efficiency and Exponential Fluid Stretching in Chaotic Mixing
王林翔; 陈鹰; 范毓润; 路甬祥
2000-01-01
The stretching and folding of fluid element during chaotic mixing field is studied using numerical method. The chaotic mixing process is caused by periodic secondary flow in a twisted curved pipe. Using the nonlinear discrete velocity field as the dynamical system, the present study connects the fluid particle's stretching along its trajectory in one period to a linearized time-varying variational equation. After numerical approximation of the variational equation, fluid stretching is calculated on the whole cross section. The stretching distribution shows an exponential fluid stretching and folding, which indicates an excellent mixing performance.
On the efficient numerical solution of lattice systems with low-order couplings
Ammon, A; Hartung, T; Jansen, K; Leövey, H; Volmer, J
2015-01-01
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.
On the efficient numerical solution of lattice systems with low-order couplings
Ammon, A.; Genz, A.; Hartung, T.; Jansen, K.; Leövey, H.; Volmer, J.
2016-01-01
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.
On the efficient numerical solution of lattice systems with low-order couplings
Ammon, A. [OAKLABS GmbH, Hennigsdorf (Germany); Genz, A. [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, T. [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, K.; Volmer, J. [DESY Zeuthen (Germany). NIC; Leoevey, H. [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2015-10-15
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.
Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems
Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger [Institut für Experimentelle Physik II, Universität Leipzig, Linnéstr. 5, 04103 Leipzig (Germany)
2015-12-07
We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.
(Anti-Hermitian Generalized (Anti-Hamiltonian Solution to a System of Matrix Equations
Juan Yu
2014-01-01
Full Text Available We mainly solve three problems. Firstly, by the decomposition of the (anti-Hermitian generalized (anti-Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-Hermitian generalized (anti-Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution minX∈K∥X^-X∥ is obtained, where K is the (anti-Hermitian generalized (anti-Hamiltonian solution set of the above system and X^ is the given matrix. Thirdly, the least squares (anti-Hermitian generalized (anti-Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-Hermitian generalized (anti-Hamiltonian solution and the corresponding numerical examples are presented.
张素英; 邓子辰
2004-01-01
For the constrained generalized Hamiltonian system with dissipation, by introducing Lagrange multiplier and using projection technique, the Lie group integration method was presented, which can preserve the inherent structure of dynamic system and the constraint-invariant. Firstly, the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system, then Lie group integration algorithm for the non-constraint generalized Hamiltonian system was discussed, finally the projection method for generalized Hamiltonian system with constraint was given. It is found that the constraint invariant is ensured by projection technique, and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A presented numerical example shows the effectiveness of the method.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Numerical Simulation of the Discharge Efficiency in Five-electrode AC PDP
何锋; 李永东; 刘纯亮; 孙鉴
2004-01-01
A new type of AC PDP (alternating current plasma display panel) cell with a fiveelectrode structure is developed to improve the luminous efficiency of AC PDP. The discharge efficiency of this new cell structure is investigated by a 2D fluid simulation. Continuity equations and flux density equations for charged particles and excited atoms, energy balance equation for electrons are included in the model. The discharge gas is He+5%Xe. The reactions of ionization,excitation, recombination, and radiation are taken into account. The vacuum ultraviolet radiation efficiency of the five-electrode cell structure is about 20% higher than that of a conventional three-electrode cell structure.
An efficient numerical target strength prediction model: Validation against analysis solutions
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 t
Efficient numerical solution of steady free-surface Navier-Stokes flow
Brummelen, E.H. van; Raven, H.C.; Koren, B.
2001-01-01
Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic cond
Efficient algorithms for finding optimal binary features in numeric and nominal labeled data
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
Hamiltonian dynamics of extended objects
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.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
On Hamiltonian formulation of cosmologies
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
A Hamiltonian approach to Thermodynamics
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.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang
2014-07-17
Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Haoliang Huang
2016-01-01
Full Text Available In this research, self-healing due to further hydration of unhydrated cement particles is taken as an example for investigating the effects of capsules on the self-healing efficiency and mechanical properties of cementitious materials. The efficiency of supply of water by using capsules as a function of capsule dosages and sizes was determined numerically. By knowing the amount of water supplied via capsules, the efficiency of self-healing due to further hydration of unhydrated cement was quantified. In addition, the impact of capsules on mechanical properties was investigated numerically. The amount of released water increases with the dosage of capsules at different slops as the size of capsules varies. Concerning the best efficiency of self-healing, the optimizing size of capsules is 6.5 mm for capsule dosages of 3%, 5%, and 7%, respectively. Both elastic modulus and tensile strength of cementitious materials decrease with the increase of capsule. The decreasing tendency of tensile strength is larger than that of elastic modulus. However, it was found that the increase of positive effect (the capacity of inducing self-healing of capsules is larger than that of negative effects (decreasing mechanical properties when the dosage of capsules increases.
New efficient optimizing techniques for Kalman filters and numerical weather prediction models
Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis
2016-06-01
The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.
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.
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.
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.
Numerical simulation of effective efficiency of a discrete multi V-pattern rib solar air channel
Kumar, Anil; Saini, R. P.; Saini, J. S.
2016-10-01
The use of artificial roughness in the form of repeated ribs has been found to be an efficient method of improving the heat transfer to fluid flowing in the channel. In this study, performance of solar air channel as a function of discrete multi V-pattern rib shapes has been investigated. The e/D was varied from 0.022 to 0.043, Gd/Lv was varied from 0.24 to 0.80, g/e was varied from 0.5 to 1.5, α was varied from 30° to 75°, P/e was varied from 6.0 to 12.0 and W/w was varied from 1.0 to 10.0. A methodology has been developed for the prediction of effective efficiency. Based on the values of effective efficiency, an optimization has been carried out to determine the set of data of roughness shapes parameters that correspond to better effective efficiency for given values of operating parameters of the air channel. Design plots have been represent to depict the data of individual roughness shapes parameters that characterize the optimum condition as a function of performance parameter and intensity of radiation. It was observed that the maximum values of effective efficiency for e/D of 0.043, Gd/Lv of 0.69, g/e of 1.0, α of 60°, P/e of 8.0 and W/w of 6.0. Discrete multi v-rib shape has been found to be better thermohydraulic performance (effective efficiency) as comparison to other rib shapes solar air channels.
张桂菊; 鄂加强; 左青松; 龚金科; 左威; 袁文华
2015-01-01
Taking wall-flow diesel particulate filter(DPF) as the research objective and separately assuming its filtering wall to be composed of numerous spherical or cylindrical elements, two different mathematical models of steady filtration for wall-flow diesel particulate filter were developed and verified by experiments as well as numerically solved. Furthermore, the effects of the macroand micro-structural parameters of filtering wall and exhaust-flow characteristic parameters on trapping efficiency were also analyzed and researched. The results show that: 1) The two developed mathematical models are consistent with the prediction of variation of particulate size; the influence of various factors on the steady trapping efficiency is exactly the same. Compared to model 2, model 1 is more suitable for describing the steady filtration process of wall-flow diesel particulate filter; 2)The major influencing factors on steady trapping efficiency of wall-flow diesel particulate filter are the macro-and micro-structural parameters of filtering wall; and the secondary influencing factors are the exhaust-flow characteristic parameters and macro-structural parameters of filter; 3)The steady trapping efficiency will be improved by increasing filter body volume, pore density as well as wall thickness and by decreasing exhaust-flow, but effects will be weakened when particulate size exceeds a certain critical value; 4) The steady trapping efficiency will be significantly improved by increasing exhaust-flow temperature and filtering wall thickness, but effects will be also weakened when particulate size exceeds a certain critical value; 5) The steady trapping efficiency will approximately linearly increase with reducing porosity, micropore aperture and pore width.
Chaos and Exponentially Localized Eigenstates in Smooth Hamiltonian Systems
Santhanam, M S; Lakshminarayan, A
1998-01-01
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase space structure around the scarring orbit; indicating sharp localization when the orbit undergoes a pitchfork bifurcation and loses stability.
Numerical analysis of transmission efficiency for parabolic optical fiber nano-probe.
Zhu, Wei; Shi, Tielin; Tang, Zirong; Gong, Bo; Liao, Guanglan; Liu, Shiyuan
2013-11-18
Theoretical calculations are performed for the transmission efficiencies of parabolic nano-probes with different shapes, based on the finite element method. It shows that the transmittance will fluctuate dramatically with the variation of either wavelength or probe shape, and the efficiency could be rather high even at long wavelengths. Subsequently, we thoroughly investigate this phenomenon and find that these fluctuations are due to the joint effect of light propagating modes and surface plasmon polaritons modes. It indicates that high transmittance can be achieved with the selection of appropriate wavelength and probe structure.
Computational studies of competing phases in model Hamiltonians
Jiang, Mi
superfluid phase. Finally, a newly developed numerical scheme for solving Langevin equations, which eliminates step-size error, is tested in the two-dimensional (2D) classical XY model and proven to be efficient to obtain the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. We further used the method to study the 2D antiferromagnetic Heisenberg model with an external magnetic field, which belongs to the same universality class as the 2D XY model due to the antiferromagnetic coupling. The BKT-type transition temperature vs magnetic field Tc( B) is obtained. The organization of this dissertation is as follows: In Chap. 1 we introduce the model Hamiltonians studied throughout the dissertation and their basic properties. Chap. 2 illustrates various methodologies utilized. Chap. 3-5 discuss the applications of determinant Quantum Monte Carlo (DQMC) in three different physical problems, which are based on Phys. Rev. B 86, 195117 (2012) and Phys. Rev. B 87, 165101 (2013) respectively. Chap. 6 focuses on the interplay between s-wave superconductivity and spin-dependent disorder via the Bogoliubov-de Gennes mean field theory and is based on New J. Phys. 15, 023023 (2013) and Phys. Rev. B 85, 134506 (2012). Chap. 7 is devoted to the test of a newly developed Langevin scheme and its applications in two-dimensional classical XY model and antiferromagnetic Heisenberg model.
Numerical Analysis of Neutral Entrainment Effect on Field-Reversed Configuration Thruster Efficiency
2014-12-01
efficiently accelerated by the electromagnetic field. On the contrary, the electron impact ionization, being a highly endothermic reaction, takes away...The authors used, in part, the Extreme Science and Engineering Discovery Environment, which is supported by National Science Foundation grant number
The dynamical feature of transition of a Hamiltonian system to a dissipative system
Zhang Guang-Cai; Zhang Hong-Jun
2004-01-01
The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formationof attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.
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.
Numerical Investigation on Mixing Efficiency and Exponential Fluid Stretching in Chaotic Mixing
无
2000-01-01
The stretching and folding of fluid element during chaotic mixing field isstudied using numerical method. The chaotic mixing process is caused byperiodicsecondary flow in a twisted curved pipe. Using the nonlinear discrete velocity field as thedynamical system, the present study connects the fluid particle's stretching along itstrajectory in one period to a linearized time-varying variational equation. After numericalapproximation of the variational equation, fluid stretching is calculated on the whole crosssection. The stretching distribution shows an exponential fluid stretching and folding,which indicates an excellent mixing performance.
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.
Botello-Smith, Wesley M.; Luo, Ray
2016-01-01
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
Saumier, Louis-Philippe; Khouider, Boualem
2010-01-01
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method relies on a numerical resolution of the corresponding Monge-Amp\\`ere equation. We use an existing Newton-like algorithm that we generalize to the case of a non uniform final density. The main idea consists of designing an iterative scheme where the fully nonlinear equation is approximated by a non-constant coefficient linear elliptic PDE that we discretize and solve at each iteration, in two different ways: a second order finite difference scheme and a fast Fourier transform (FFT) method. The FFT method, made possible thanks to a preconditioning step based on the coefficient-averaged equation, results in an overall O(P log P)-operations algorithm, where P is the number of discretization points. In particular, we use fourth order finite differences to approximate the action of the densities on the solution iterates, which result in more a...
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
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.
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.
Numerical simulation: Toward the design of high-efficiency planar perovskite solar cells
Liu, Feng; Zhu, Jun, E-mail: zhujzhu@gmail.com, E-mail: sydai@ipp.ac.cn; Wei, Junfeng; Li, Yi; Lv, Mei [Key Laboratory of Novel Thin Film Solar Cells, Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Yang, Shangfeng [Hefei National Laboratory for Physical Sciences at Microscale, Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026 (China); Zhang, Bing; Yao, Jianxi [State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206 (China); Dai, Songyuan, E-mail: zhujzhu@gmail.com, E-mail: sydai@ipp.ac.cn [Key Laboratory of Novel Thin Film Solar Cells, Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206 (China)
2014-06-23
Organo-metal halide perovskite solar cells based on planar architecture have been reported to achieve remarkably high power conversion efficiency (PCE, >16%), rendering them highly competitive to the conventional silicon based solar cells. A thorough understanding of the role of each component in solar cells and their effects as a whole is still required for further improvement in PCE. In this work, the planar heterojunction-based perovskite solar cells were simulated with the program AMPS (analysis of microelectronic and photonic structures)-1D. Simulation results revealed a great dependence of PCE on the thickness and defect density of the perovskite layer. Meanwhile, parameters including the work function of the back contact as well as the hole mobility and acceptor density in hole transport materials were identified to significantly influence the performance of the device. Strikingly, an efficiency over 20% was obtained under the moderate simulation conditions.
Mazzi, Giacomo; Samaey, Giovanni
2012-01-01
In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations, ranging from heterogeneous catalysis to electrochemical or (membrane) biological processes, to cite a few. We analyzed in this context different techniques within the framework of an important multiscale approach known as the equation free method (EFM), which "bridges the multiscale gap" by building microscopic configurations using macroscopic-level information only. We hereby considered two simple reactive processes on a one-dimensional lattice, the simplicity of which allowed for an in-depth understanding of the parameters controlling the efficiency of this approach. We demonstrate in particular that it is not enough to base the EFM on the time evolution of the average concentrations of particles on the lattice, but that the time evolution of clusters of particles has to be in...
黄海燕; 姚秀美; 朱海燕; 陈亚江
2016-01-01
Based on the Hamilton principle,a numerical algorithm associated with Lagrange multiplier method for the classical motion path problem is proposed. Different from traditional variational method,the present algorithm transforms the classical motion path problem into the conditional extremum problem with respect to the motion equation. By utilizing this algorithm,numerical solutions to motion path problems in one-dimensional gravitation potential and one-dimensional elastic potential are obtained and compared with the corresponding analytical results,respectively. Such two examples can be used as practical and interesting teaching cases for the relevant curriculums,e.g. Mechanics in college physics,Hamilton principle in theoretical mechanics and numerical calculation in computational mathematics. These examples are helpful for students to understand the Hamilton principle more deeply,and improve the ability of applying the knowledge in the fields of physics,mathematics, and computer science.%基于哈密顿原理，提出经典运动路径问题的拉格朗日乘数数值算法。与传统的变分方法不同，该算法将经典运动路径问题改写为关于路径方程的条件极值问题。利用该算法得到了一维重力势中的运动路径和一维弹性势中的运动路径的数值解，并与各自的解析解作了比较分析。这2个例子可以作为大学物理力学、理论力学哈密顿原理以及计算数学数值计算等相关课程内容实用教学案例，其有助于学生更深刻地理解哈密顿原理，提高综合应用物理、数学、计算机科学等知识的能力。
Monte Carlo Hamiltonian: Linear Potentials
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films
Elrod, Harold G.
1989-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution.
Numerical tests of efficiency of the retrospective time integration scheme in the self-memory model
GU Xiangqian; YOU Xingtian; ZHU He; CAO Hongxing
2004-01-01
A set of numerical tests was carried out to compare the retrospective time integral scheme in a self-memory model,whose dynamic kernel is the barotropical quasi-geostrophic model, with the ordinary centered difference scheme in the barotropical quasigeostrophic model. The Rossby-Haurwitz wave function was taken as the initial fields for both schemes. The results show that in comparison with the ordinary centered difference scheme, the retrospective time integral scheme reduces by 2 orders of magnitude the forecast error, and the forecast error increases very little with lengthening of the time-step. Therefore, the retrospective time integral scheme has advantages of improving the forecast accuracy, extending the predictable duration and reducing the computation amount.
Mehrling, T.J., E-mail: timon.mehrling@desy.de [Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg (Germany); Robson, R.E. [Centre for Quantum Dynamics, School of Natural Sciences, Griffith University, Brisbane (Australia); Erbe, J-H.; Osterhoff, J. [Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg (Germany)
2016-09-01
This paper introduces a semi-analytic numerical approach (SANA) for the rapid computation of the transverse emittance of beams with finite energy spread in plasma wakefield accelerators in the blowout regime. The SANA method is used to model the beam emittance evolution when injected into and extracted from realistic plasma profiles. Results are compared to particle-in-cell simulations, establishing the accuracy and efficiency of the procedure. In addition, it is demonstrated that the tapering of vacuum-to-plasma and plasma-to-vacuum transitions is a viable method for the mitigation of emittance growth of beams during their injection and extraction from and into plasma cells.
A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle
Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin
1989-01-01
A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.
Coherent site-directed transport in complex molecular networks: an effective Hamiltonian approach.
Weissman, Shira; Peskin, Uri
2010-03-21
Defining the conditions for coherent site-directed transport from an electron donor to a specific acceptor through tunneling barriers in a network of multiple donor/acceptors sites is an important step toward controlling electronic processes in molecular networks. The required analysis is most challenging since the entire network in essentially involved in coherent transport. In this work we introduce an efficient approach for formulating an effective donor/acceptor coupling in terms of the entire network parameters. The approach is based on implementation of Feshbach projection operators to map the entire network Hamiltonian onto a subspace defined by two specific donor and acceptor sites. This nonperturbative approach enables to define regimes of network parameters in which the effective donor-acceptor coupling is optimal. This is demonstrated numerically for simple models of molecular networks.
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.
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Hamiltonian cosmology in bigravity and massive gravity
Soloviev, Vladimir O
2015-01-01
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María; Głazek, Stanisław D.
2016-07-01
We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.
Kihm, J.; Park, S.; Kim, J.; SNU CO2 GEO-SEQ TEAM
2011-12-01
A series of integrated injection well and geologic formation numerical simulations was performed to evaluate the injection efficiency of carbon dioxide using a multiphase thermo-hydrological numerical model. The numerical simulation results show that groundwater flow, carbon dioxide flow, and heat transport in both injection well and sandstone formation can be simultaneously analyzed, and thus the injection efficiency (i.e., injection rate and injectivity) of carbon dioxide can be quantitatively evaluated using the integrated injection well and geologic formation numerical simulation scheme. The injection rate and injectivity of carbon dioxide increase rapidly during the early period of time (about 10 days) and then increase slightly up to about 2.07 kg/s (equivalent to 0.065 Mton/year) and about 2.84 × 10-7 kg/s/Pa, respectively, until 10 years for the base case. The sensitivity test results show that the injection pressure and temperature of carbon dioxide at the wellhead have significant impacts on its injection rate and injectivity. The vertical profile of the fluid pressure in the injection well becomes almost a hydrostatical equilibrium state within 1 month for all the cases. The vertical profile of the fluid temperature in the injection well becomes a monotonously increasing profile with the depth due to isenthalpic or adiabatic compression within 6 months for all the cases. The injection rate of carbon dioxide increases linearly with the fluid pressure difference between the well bottom and the sandstone formation far from the injection well. In contrast, the injectivity of carbon dioxide varies unsystematically with the fluid pressure difference. On the other hand, the reciprocal of the kinematic viscosity of carbon dioxide at the well bottom has an excellent linear relationship with the injectivity of carbon dioxide. It indicates that the above-mentioned variation of the injectivity of carbon dioxide can be corrected using this linear relationship. The
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
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
A numerically efficient technique of regional gravity field modeling using Radial Basis Functions
Shahbazi, Anahita; Safari, Abdolreza; Foroughi, Ismael; Tenzer, Robert
2016-02-01
Radial Basis Functions (RBFs) have been extensively used in regional gravity and (quasi)geoid modeling. Reliable models require the choice of an optimal number of RBFs and of their parameters. The RBF parameters are typically optimized using a regularization algorithm. Therefore, the determination of the number of RBFs is the most challenging task in the modeling procedure. For this purpose, we design a data processing scheme to optimize the number of RBFs and their parameters simultaneously. Using this scheme, the gravimetric quasi-geoid model can be validated without requiring additional information on the quasi-geoidal geometry obtained from GPS/leveling data. Furthermore, the Levenberg-Marquardt algorithm, used for regularization, is modified to enhance its numerical performance. We demonstrate that these modifications guarantee the convergence of the solution to the global minimum while substantially decreasing the number of iterations. The proposed methodology is evaluated using synthetic gravity data and compared with existing methods for validating the RBF parameterization of the gravity field.
Experimental and numerical analysis of unsteady behaviour of high efficiency mixed-flow pump
Sedlář Milan
2014-03-01
Full Text Available This work deals with the experimental and numerical investigation of cavitating and noncavitating flow inside a mixed-flow pump and its influence on performance curves of this pump. The experimental research has been carried out in the closed horizontal loop with the main tank capacity of 35 m3. The loop is equipped with both the compressor and the vacuum pump capable of creating different pressure levels while maintaining constant volume flow rate. Pump investigated in this project has been equipped with transparent windows, which enabled the visualization of flow and cavitation phenomena for a wide range of flow conditions. A comprehensive CFD analysis of tested pump has been done both in the cavitating and noncavitating regimes. The ANSYS CFX commercial CFD package has been used to solve URANS equations together with the Rayleigh-Plesset model and the SST-SAS turbulence model. Both the experimental research and the CFD analysis have provided a good illustration of the flow structures inside the pump and their dynamics for a wide range of flow rates and NPSH values. Flow and cavitation instabilities have been detected at suboptimal flow rates which correspond to increased values of noise and vibrations. The calculated results agree well with the measurements.
Experimental and numerical analysis of unsteady behaviour of high efficiency mixed-flow pump
Sedlář, Milan; Komárek, Martin; Vyroubal, Michal; Doubrava, Vít; Varchola, Michal; Hlbočan, Peter
2014-03-01
This work deals with the experimental and numerical investigation of cavitating and noncavitating flow inside a mixed-flow pump and its influence on performance curves of this pump. The experimental research has been carried out in the closed horizontal loop with the main tank capacity of 35 m3. The loop is equipped with both the compressor and the vacuum pump capable of creating different pressure levels while maintaining constant volume flow rate. Pump investigated in this project has been equipped with transparent windows, which enabled the visualization of flow and cavitation phenomena for a wide range of flow conditions. A comprehensive CFD analysis of tested pump has been done both in the cavitating and noncavitating regimes. The ANSYS CFX commercial CFD package has been used to solve URANS equations together with the Rayleigh-Plesset model and the SST-SAS turbulence model. Both the experimental research and the CFD analysis have provided a good illustration of the flow structures inside the pump and their dynamics for a wide range of flow rates and NPSH values. Flow and cavitation instabilities have been detected at suboptimal flow rates which correspond to increased values of noise and vibrations. The calculated results agree well with the measurements.
ZHANG Kai; LIN Jianzhong; LI Huijun
2006-01-01
The mixing of samples in heterogeneous microchannels with a periodically stepwise surface potential was analyzed numerically using the control volume method. The equations describing the wall potential and external potential were solved first to get the distribution of wall potential and external potential, respectively, then the momentum equation was solved to get the developed flow field.Finally, the mass transport equation was solved to get the concentration field. The simulation results show that the distribution of samples at the inlet of the microchannel determines its theoretical value of concentration, therefore, the pattern of the distribution of samples at the inlet and its corresponding velocity can be changed to get the desirable concentration of solute. The heterogeneous wall potential almost has no effect on the mixing of samples in two-inlet microfluidic devices. For three-inlet microfluidic devices, the comprehensive ability of transportation and mixing has an optimization when the ratio of periodic length of wall potential to the height of the microchannel is about 4.88.The above conclusions are helpful to the optimization of the design of microfluidic devices.
Miliordos, Evangelos; Xantheas, Sotiris S
2013-08-15
We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilson's GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N - 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. In all cases the frequencies based on internal coordinates differ on average by coordinates.
Liu, Yuxiang; Barnett, Alex H.
2016-11-01
We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution operator using separation into P azimuthal modes via the FFT, the method of fundamental solutions (with N proxy points lying on a curve), and dense direct least-squares solves; the effort is O (N3 P) with a small constant. Periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global Helmholtz basis expansion to represent the distant contributions, and enforcing quasiperiodicity and radiation conditions on the unit cell walls. Eliminating the auxiliary coefficients, and preconditioning with the one-obstacle solution operator, leaves a well-conditioned square linear system that is solved iteratively. The solution time per incident wave is then O (NP) at fixed frequency. Our scheme avoids singular quadratures, periodic Green's functions, and lattice sums, and its convergence rate is unaffected by resonances within obstacles. We include numerical examples such as scattering from a grating of period 13 λ × 13 λ comprising highly-resonant sound-hard "cups" each needing NP = 64800 surface unknowns, to 10-digit accuracy, in half an hour on a desktop.
Benini, Ernesto; Biollo, Roberto; Ponza, Rita [Department of Mechanical Engineering - University of Padova, Via Venezia, 1 - 35131 Padova (Italy)
2011-03-15
Several passive and active techniques were studied and developed by compressor designers with the aim of improving the aerodynamic behavior of compressor blades by reducing, or even eliminating, flow separation. Fluidic-based methods, in particular, have been investigated for a long time, including both steady and unsteady suction, blowing and oscillating jets. Recently, synthetic jets (zero mass flux) have been proposed as a promising solution to reduce low-momentum fluid regions inside turbomachines. Synthetic jets, with the characteristics of zero net mass flux and non-zero momentum flux, do not require a complex system of pumps and pipes. They could be very efficient because at the suction part of the cycle the low-momentum fluid is sucked into the device, whereas in the blowing part a high-momentum jet accelerates it. To the authors' knowledge, the use of synthetic jets has never been experimented in transonic compressor rotors, where this technique could be helpful (i) to reduce the thickness and instability of blade suction side boundary layer after the interaction with the shock, and (ii) to delay the arising of the low-momentum region which can take place from the shock-tip clearance vortex interaction at low flow operating conditions, a flow feature which is considered harmful to rotor stability. Therefore, synthetic jets could be helpful to improve both efficiency and stall margin in transonic compressor rotors. In this paper, an accurate and validated CFD model is used to simulate the aerodynamic behavior of a transonic compressor rotor with and without synthetic jets. Four technical solutions were evaluated, different for jet position and velocity, and one was investigated in detail. (author)
张素英
2012-01-01
Numerical methods of nonlinear Hamiltonian systems are constructed in the interaction picture of quantum mechanics. Firstly the original system is transformed to interaction picture of quantum mechanics. This reduces the problem to a system of ordinary differential equations in time. Subsequently,the modified system is integrated in time and then transformed back to the initial representation of the state vector. Varies discrete schemes can be obtained based on different integration methods. The methods in this paper can also be used to solve multi-component Bose-Einstein condensate problem.%文章在量子力学的相互作用绘景中给出了非线性哈密顿系统离散格式的构造方法.首先将原非线性哈密顿问题变换至相互作用绘景,导出一个含时的常微分方程系统,离散该常微分方程并变换回原系统的态矢即可得到原问题的离散格式.基于不同的常微分方程数值方法,可得到原系统不同的离散格式.该方法还可以有效地求解多组分的Bose-Einstein凝聚态物理问题.
Gaudreault, Stéphane; Pudykiewicz, Janusz A.
2016-10-01
The exponential propagation methods were applied in the past for accurate integration of the shallow water equations on the sphere. Despite obvious advantages related to the exact solution of the linear part of the system, their use for the solution of practical problems in geophysics has been limited because efficiency of the traditional algorithm for evaluating the exponential of Jacobian matrix is inadequate. In order to circumvent this limitation, we modify the existing scheme by using the Incomplete Orthogonalization Method instead of the Arnoldi iteration. We also propose a simple strategy to determine the initial size of the Krylov space using information from previous time instants. This strategy is ideally suited for the integration of fluid equations where the structure of the system Jacobian does not change rapidly between the subsequent time steps. A series of standard numerical tests performed with the shallow water model on a geodesic icosahedral grid shows that the new scheme achieves efficiency comparable to the semi-implicit methods. This fact, combined with the accuracy and the mass conservation of the exponential propagation scheme, makes the presented method a good candidate for solving many practical problems, including numerical weather prediction.
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
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.
Kihm, J.; Kim, J.
2010-12-01
A series of numerical simulations using a multiphase thermo-hydrological numerical model is performed to analyze groundwater flow, carbon dioxide flow, and heat transport due to geologic storage of carbon dioxide in a geologic storage formation (sandstone aquifer) and to evaluate impacts of its saturated (i.e., porosity and intrinsic permeability) and unsaturated (i.e., residual water saturation, residual gas saturation, gas-entry pressure, and van Genuchten’s exponent) hydrological properties on the injection efficiency of carbon dioxide. The numerical simulation results show that the hydrological properties of the storage formation have significant effects on the injection efficiency of carbon dioxide. Under a constant injection pressure of carbon dioxide, the injection rate and injectivity of carbon dioxide increase rapidly during the early period of carbon dioxide injection (about 2 weeks) and then increases monotonously until the end of carbon dioxide injection. The injection rate and injectivity of carbon dioxide are most sensitive to variations in the intrinsic permeability and van Genuchten’s exponent of the storage formation. They increase significantly as the intrinsic permeability and van Genuchten’s exponent of the storage formation increase, whereas they decrease slightly as the porosity and the residual gas saturation of the storage formation increase. However, they are most insensitive to variations in the residual water saturation and the gas-entry pressure of the storage formation. These results indicate that the injection efficiency of carbon dioxide is significantly dependent on the relative permeability, which is a function of the unsaturated hydrological properties (i.e., residual water saturation, residual gas saturation, gas-entry pressure, and van Genuchten’s exponent) of the storage formation, as well as its saturated hydrological properties (i.e., porosity and intrinsic permeability) in different degrees. Therefore it may be
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.
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.
Sibaev, M; Crittenden, D L
2016-06-01
In this paper, we outline a general, scalable, and black-box approach for calculating high-order strongly coupled force fields in rectilinear normal mode coordinates, based upon constructing low order expansions in curvilinear coordinates with naturally limited mode-mode coupling, and then transforming between coordinate sets analytically. The optimal balance between accuracy and efficiency is achieved by transforming from 3 mode representation quartic force fields in curvilinear normal mode coordinates to 4 mode representation sextic force fields in rectilinear normal modes. Using this reduced mode-representation strategy introduces an error of only 1 cm(-1) in fundamental frequencies, on average, across a sizable test set of molecules. We demonstrate that if it is feasible to generate an initial semi-quartic force field in curvilinear normal mode coordinates from ab initio data, then the subsequent coordinate transformation procedure will be relatively fast with modest memory demands. This procedure facilitates solving the nuclear vibrational problem, as all required integrals can be evaluated analytically. Our coordinate transformation code is implemented within the extensible PyPES library program package, at http://sourceforge.net/projects/pypes-lib-ext/.
Solving the Hamiltonian constraint for 1+log trumpets
Dietrich, Tim
2013-01-01
The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point. When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention. The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data. We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and 1+log-trumpet type. Additionally, we describe a method to solve the Hamiltonian constraint for two 1+log trumpets for a given extrinsic curvature with non-vanishing trace. We investigate properties of this constructed initial data during binary black hole evolutions and find that the initial gauge dynamics is reduced.
Local temperatures and local terms in modular Hamiltonians
Arias, Raul; Casini, Horacio; Huerta, Marina
2016-01-01
We show there are analogues to the Unruh temperature that can be defined for any quantum field theory and region of the space. These local temperatures are defined using relative entropy with localized excitations. We show important restrictions arise from relative entropy inequalities and causal propagation between Cauchy surfaces. These suggest a large amount of universality for local temperatures, specially the ones affecting null directions. For regions with any number of intervals in two space-time dimensions the local temperatures might arise from a term in the modular Hamiltonian proportional to the stress tensor. We argue this term might be universal, with a coefficient that is the same for any theory, and check analytically and numerically this is the case for free massive scalar and Dirac fields. In dimensions $d\\ge 3$ the local terms in the modular Hamiltonian producing these local temperatures cannot be formed exclusively from the stress tensor. For a free scalar field we classify the structure of...
Tsallis thermostatistics for finite systems: a Hamiltonian approach
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.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2002-01-01
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 applications for the $u, d, s$ and $c$ quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing $H$: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin an...
When a local Hamiltonian must be frustration-free.
Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich
2016-06-07
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Matin, M.A. [Department of Electrical, Electronic and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Department of Electrical and Electronics Engineering, Chittagong University of Engineering and Technology (CUET), Chittagong (Bangladesh); Mannir Aliyu, M.; Quadery, Abrar H. [Department of Electrical, Electronic and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Amin, Nowshad [Department of Electrical, Electronic and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Center of Excellence for Research in Engineering Materials (CEREM), College of Engineering, King Saud University, Riyadh 11421 (Saudi Arabia)
2010-09-15
Cadmium telluride (CdTe) thin film solar cell has long been recognized as a leading photovoltaic candidate for its high efficiency and low cost. A numerical simulation has been performed using AMPS-1D simulator to explore the possibility of higher efficiency and stable CdS/CdTe cell among several cell structures with indium tin oxide (ITO) and cadmium stannate (Cd{sub 2}SnO{sub 4}) as front contact material, tin oxide (SnO{sub 2}), zinc oxide (ZnO) and zinc stannate (Zn{sub 2}SnO{sub 4}) as buffer layer, and silver (Ag) or antimony telluride (Sb{sub 2}Te{sub 3}) with molybdenum (Mo) or zinc telluride (ZnTe) with aluminium (Al) as back contact material. The cell structure ITO/i-ZnO/CdS/CdS{sub x}Te{sub 1-x}/CdTe/Ag has shown the best conversion efficiency of 16.9% (Voc=0.9 V, Jsc=26.35 mA/cm{sup 2}, FF=0.783). This analysis has shown that ITO as front contact material, ZnO as buffer layer and ZnTe or Sb{sub 2}Te{sub 3} back surface reflector (BSR) are suitable material system for high efficiency (>15%) and stable CdS/CdTe cells. The cell normalized efficiency linearly decreased at a temperature gradient of -0.25%/ C for ZnTe based cells, and at -0.40%/ C for other cells. (author)
Implicit variational principle for contact Hamiltonian systems
Wang, Kaizhi; Wang, Lin; Yan, Jun
2017-02-01
We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
A parcel formulation for Hamiltonian layer models
Bokhove, O.; Oliver, M.
2009-01-01
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 Hamilton
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS
QI Zhao-hui(齐朝晖); Alexander P. Seyranian
2002-01-01
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Normal Form for Families of Hamiltonian Systems
Zhi Guo WANG
2007-01-01
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d+1. And some dynamical consequences are obtained.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
Momentum and hamiltonian in complex action theory
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...
Square conservation systems and Hamiltonian systems
王斌; 曾庆存; 季仲贞
1995-01-01
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
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.
A Hamiltonian approach to Thermodynamics
Baldiotti, M C; 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 ontop 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.
Effective Hamiltonians for Complexes of Unstable Particles
Urbanowski, K
2014-01-01
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \\rightarrow \\infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\\rightarrow \\infty$.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Souza, M.R.A. [Universidade Federal da Paraiba (UFPB), Joao Pessoa, PB (Brazil). Lab. de Energia Solar]. E-mail: marciosouza@ct.ufpb.br; Lima, J.A. [Universidade Federal do Rio Grande do Norte (UFRN), Natal, RN (Brazil). Dept. de Engenharia Mecanica]. E-mail: jalima@dem.ufrn.br
2008-07-01
With the exponential growth of market of natural gas for automotive refueling use, several researches have been developed for a better use of that technology. One of those arrivals consists of the application of microporous materials (adsorbents) inside the reservoirs that store the referred fuel. The adsorption benefits in the storage of the natural gas, for vehicles use, is many advantages on the storage viewpoint, principally respecting moderated pressure value necessary to storage an amount of gas approximately equivalent that one obtained only by compression. Therefore, there is stress reduction on the reservoir wall during adsorption storage process. Although, some problems relatives to adsorbed natural gas (ANG) employ has been described in specialized literature. Among everyone arguments contrary to adoption of this alternative, the most critical is the reservoir efficiency loss due to thermal effects, characteristics of the gas flow in porous media. Several studies has been developed objecting to minimize the temperature either rise or drop, observed in the charge and discharge gas process, respectively, once such variations is decisive factors to not provisioning of all storage capacity into ANG tanks. In present study is proposed a comparison between the boarded methodology (experimental or numerical) in literature, where in the first, the discharge rate flow is considered constant, and a second methodology (present work), apply a numerical approaching of discharge process interspaced by periods of no rate flow, proportioning a thermal equilibrium in the porous media and hence improvement in the adsorption system efficiency. Such pauses in the discharge process simulate the utilization, day by day, of a reservoir into a popular automotive vehicle. (author)
Raskutti, Sudhir; Ostriker, Eve C.; Skinner, M. Aaron
2016-10-01
Radiation feedback from stellar clusters is expected to play a key role in setting the rate and efficiency of star formation in giant molecular clouds. To investigate how radiation forces influence realistic turbulent systems, we have conducted a series of numerical simulations employing the Hyperion radiation hydrodynamics solver, considering the regime that is optically thick to ultraviolet and optically thin to infrared radiation. Our model clouds cover initial surface densities between Σ cl,0∼ 10--300 M⊙ pc-2, with varying initial turbulence. We follow them through turbulent, self-gravitating collapse, star cluster formation, and cloud dispersal by stellar radiation. All our models display a log-normal distribution of gas surface density Σ for an initial virial parameter αvir,0=2, the log-normal standard deviation is σln Σ =1-1.5 and the star formation rate coefficient ɛff,ρ=0.3-0.5, both of which are sensitive to turbulence but not radiation feedback. The net star formation efficiency (SFE) ɛfinal increases with Σcl,0 and decreases with α vir,0. We interpret these results via a simple conceptual framework, whereby steady star formation increases the radiation force, such that local gas patches at successively higher Σ become unbound. Based on this formalism (with fixed σln Σ), we provide an analytic upper bound on ɛfinal, which is in good agreement with our numerical results. The final SFE depends on the distribution of Eddington ratios in the cloud and is strongly increased by the turbulent compression of gas.
Comparative index and Sturmian theory for linear Hamiltonian systems
Šepitka, Peter; Šimon Hilscher, Roman
2017-01-01
The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory.
Unconstrained Hamiltonian formulation of low energy QCD
Pavel Hans-Peter
2014-04-01
Full Text Available Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case. The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons, and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate
BACKWARD ERROR ANALYSIS OF SYMPLECTIC INTEGRATORS FOR LINEAR SEPARABLE HAMILTONIAN SYSTEMS
Peter G(o)rtz
2002-01-01
Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge Kutta, and Runge-Kutta-Nystrom methods applied to the simple Hamiltonian system p = -vq, q = κp are studied. Some new results in connection with P-stability are pre sented. The main part is focused on backward error analysis. The numerical solution produced by a symplectic method with an appropriate stepsize is the exact solution of a perturbed Hamiltonian system at discrete points. This system is studied in detail and new results are derived. Numerical examples are presented.
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Exact decoupling of the Dirac Hamiltonian. III. Molecular properties.
Wolf, Alexander; Reiher, Markus
2006-02-14
Recent advances in the theory of the infinite-order Douglas-Kroll-Hess (DKH) transformation of the Dirac Hamiltonian require a fresh and unified view on the calculation of atomic and molecular properties. It is carefully investigated how the four-component Dirac Hamiltonian in the presence of arbitrary electric and magnetic potentials is decoupled to two-component form. In order to cover the whole range of electromagnetic properties on the same footing, a consistent description within the DKH theory is presented. Subtle distinctions are needed between errors arising from any finite-order DKH scheme and effects due to oversimplified and thus approximate decoupling strategies for the Dirac operator, which will, though being numerically negligible in most cases, still be visible in the infinite-order limit of the two-component treatment. Special focus is given to the issue, whether the unitary DKH transformations to be applied to the Dirac Hamiltonian should depend on the property under investigation or not. It is explicitly shown that up to third order in the external potential the transformed property operator is independent of the chosen parametrization of the unitary transformations of the generalized DKH scheme. Since the standard DKH protocol covers the transformation of one-electron integrals only, the presentation is developed for one-electron properties for the sake of brevity. Nevertheless, all findings for the calculation of one-electron properties within a two-component framework presented here also hold for two-electron properties as well.
Hamiltonian Dynamics of Several Rigid Bodies Interacting with Point Vortices
Weißmann, Steffen
2014-04-01
We derive the dynamics of several rigid bodies of arbitrary shape in a two-dimensional inviscid and incompressible fluid, whose vorticity is given by point vortices. We adopt the idea of Vankerschaver et al. (J. Geom. Mech. 1(2): 223-226, 2009) to derive the Hamiltonian formulation via symplectic reduction from a canonical Hamiltonian system. The reduced system is described by a noncanonical symplectic form, which has previously been derived for a single circular disk using heavy differential-geometric machinery in an infinite-dimensional setting. In contrast, our derivation makes use of the fact that the dynamics of the fluid, and thus the point vortex dynamics, is determined from first principles. Using this knowledge we can directly determine the dynamics on the reduced, finite-dimensional phase space, using only classical mechanics. Furthermore, our approach easily handles several bodies of arbitrary shape. From the Hamiltonian description we derive a Lagrangian formulation, which enables the system for variational time integrators. We briefly describe how to implement such a numerical scheme and simulate different configurations for validation.
Scintilla, Leonardo Daniele; Tricarico, Luigi
2013-02-01
In this paper, energy aspects related to the efficiency of laser welding process using a 2 kW Nd:YAG laser were investigated and reported. AZ31B magnesium alloy sheets 3.3 mm thick were butt-welded without filler using Helium and Argon as shielding gases. A three-dimensional and semi-stationary finite element model was developed to evaluate the effect of laser power and welding speed on the absorption coefficient, the melting and welding efficiencies. The modeled volumetric heat source took into account a scale factor, and the shape factors given by the attenuation of the beam within the workpiece and the beam intensity distribution. The numerical model was calibrated using experimental data on the basis of morphological parameters of the weld bead. Results revealed a good correspondence between experiment and simulation analysis of the energy aspects of welding. Considering results of mechanical characterization of butt joints previously obtained, the optimization of welding condition in terms of mechanical properties and energy parameters was performed. The best condition is represented by the lower laser power and higher welding speed that corresponds to the lower heat input given to the joint.
Etienne, Zachariah; Ruchlin, Ian; Baumgarte, Thomas
2017-01-01
Short-inspiral black hole binary (BHB) mergers are perhaps the most extensively studied LIGO source candidate by numerical relativity (NR), so it was extremely fortuitous that LIGO's first detections of gravitational waves (GWs) were from precisely these systems. In a sense, these discoveries represent coming-of-age for our field, but NR's current position is a precarious one. LIGO data analysis depends on NR-based GW catalogs built upon only one NR code and remain largely unvalidated by independent NR codes. More worryingly, LIGO may soon detect GWs from a double neutron star (DNS) binary, and there currently exist no NR codes capable of generating DNS GWs with small, convergent phase errors over large numbers of orbits in-band. We introduce SENR, a Super-Efficient, open-development NR code aimed at addressing these critical shortcomings. Building upon recent breakthroughs in reference metric-based simulations, SENR employs dynamical coordinate systems to increase the efficiency of moving-puncture BHB and DNS GW modeling by 100x. Excitingly, SENR has the potential to afford high-end gamers the opportunity to join us in source modeling, potentially increasing throughput of GW generation by an enormous factor. We present an overview of the SENR code and its development.
Varado, N.; Braud, I.; Ross, P. J.
2003-04-01
5; but was generally less than 10%. The study also showed that the Lai and Katul (2000) model formulation was not adapted for sandy soils. Twice less water than the Li model could be extracted on sandy soils. The comparison of the two root modules with the initial version of SiSPAT shows that the Lai model was unable to extract as water as the initial SiSPAT or the Li model, even when changing the sensitive parameters. As a conclusion the new numerical method coupled with the Li et al. (2001) model provides an efficient and accurate solution for inclusion of a physically-based infiltration-evapotranspiration module into larger scale watershed models.
Lectures on Hamiltonian Dynamics : Theory and Applications
Benettin, Giancarlo; Kuksin, Sergei
2005-01-01
This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
EXISTENCE OF HAMILTONIAN κ-FACTOR
CAI Maocheng; FANG Qizhi; LI Yanjun
2004-01-01
A Hamiltonian k-factor is a k-factor containing a Hamiltonian cycle. An n/2-critical graph G is a simple graph of order n which satisfies δ(G) ≥ n/2 and δ(G - e) ＜ n/2for any edge e ∈ E(G). Let κ≥ 2 be an integer and G be an n/2-critical graph of even order n ≥ 8κ - 14. It is shown in this paper that for any given Hamiltonian cycle Cexcept that G - C consists of two components of odd orders when κ is odd, G has a k-factor containing C.
Orthogonal separable Hamiltonian systems on T2
无
2007-01-01
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way.
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
Yuqian GUO; Daizhan CHENG
2006-01-01
In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
On a general Heisenberg exchange effective Hamiltonian
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
Algebraic Hamiltonian for Vibrational Spectra of Stibine
HOU Xi-Wen
2004-01-01
@@ An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan,is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Dicycle Cover of Hamiltonian Oriented Graphs
Khalid A. Alsatami
2016-01-01
Full Text Available A dicycle cover of a digraph D is a family F of dicycles of D such that each arc of D lies in at least one dicycle in F. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.
Improved Sufficient Conditions for Hamiltonian Properties
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Cai, Xin; Liu, Jinsong; Wang, Shenglie
2009-02-16
This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.
Law, Sean M; Ahlstrom, Logan S; Panahi, Afra; Brooks, Charles L
2014-10-02
Molecular recognition by intrinsically disordered proteins (IDPs) plays a central role in many critical cellular processes. Toward achieving detailed mechanistic understanding of IDP-target interactions, here we employ the "Hamiltonian mapping" methodology, which is rooted in the weighted histogram analysis method (WHAM), for the fast and efficient calibration of structure-based models in studies of IDPs. By performing reference simulations on a given Hamiltonian, we illustrate for two model IDPs how this method can extrapolate thermodynamic behavior under a range of modified Hamiltonians, in this case representing changes in the binding affinity (Kd) of the system. Given sufficient conformational sampling in a single trajectory, Hamiltonian mapping accurately reproduces Kd values from direct simulation. This method may be generally applied to systems beyond IDPs in force field optimization and in describing changes in thermodynamic behavior as a function of external conditions for connection with experiment.
Nandi, Debottam; Shankaranarayanan, S.
2016-10-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Polynomial approximation of Poincare maps for Hamiltonian system
Froeschle, Claude; Petit, Jean-Marc
1992-01-01
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Formulation of quantized Hamiltonian dynamics in terms of natural variables.
Akimov, Alexey V; Prezhdo, Oleg V
2012-12-14
We present a formulation of quantized Hamiltonian dynamics (QHD) using variables that arise naturally from the Heisenberg equation of motion. The QHD equations are obtained and solved either directly in terms of these generalized variables, or by employing a wavefunction ansatz. The approach avoids a Taylor expansion and other approximations to the potential, leading to more stable dynamics and a higher precision of the calculated quantities. The proposed formulation is also amenable to for analytic and numerical implementations, thus facilitating its use in molecular dynamics simulation.
Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
Kapela, Tomasz; Simó, Carles
2017-03-01
We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of application for systems with two and three degrees of freedom. The first example verifies the existence of tiny elliptic islands inside large chaotic domains for a quartic potential. In the 3-body problem we prove the KAM stability of the well-known figure eight orbit and two selected orbits of the so called family of rotating eights. Some additional theoretical and numerical information is also given for the dynamics of both examples.
Hamiltonian system for orthotropic plate bending based on analogy theory
无
2001-01-01
Based on analogy between plane elasticity and plate bending as well as variational principles of mixed energy, Hamiltonian system is further led to orthotropic plate bending problems in this paper. Thus many effective methods of mathematical physics such as separation of variables and eigenfunction expansion can be employed in orthotropic plate bending problems as they are used in plane elasticity. Analytical solutions of rectangular plate are presented directly, which expands the range of analytical solutions. There is an essential distinction between this method and traditional semi-inverse method. Numerical results of orthotropic plate with two lateral sides fixed are included to demonstrate the effectiveness and accuracy of this method.
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
2015-06-01
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) equation or its fourth-order analogue P. 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.
Effective stability for generalized Hamiltonian systems
CONG; Fuzhong; LI; Yong
2004-01-01
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
Spinor-Like Hamiltonian for Maxwellian Optics
Kulyabov D.S.
2016-01-01
Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.
Integrable Hamiltonian systems and spectral theory
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.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi; Nielsen, Holger Bech
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Classical mechanics Hamiltonian and Lagrangian formalism
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.
Jacobi fields of completely integrable Hamiltonian systems
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G
2003-03-31
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.
Polysymplectic Hamiltonian formalism and some quantum outcomes
Giachetta, G; Sardanashvily, G
2004-01-01
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\\beta$-function coincides with the one obtained in an earlier calculation using a different generator.
Hamiltonian cycle problem and Markov chains
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.
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems
Fu Jingli
2008-01-01
Full Text Available This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multistage scheme of order 2 which its order of accuracy is 2n. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.
Hamiltonian formulation of guiding center motion
Stern, D. P.
1971-01-01
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
On Hamiltonians Generating Optimal-Speed Evolutions
2008-01-01
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality ...
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel; Wocjan, Pawel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in th...
Minimal realizations of supersymmetry for matrix Hamiltonians
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Hamiltonian Dynamics at Spatial Infinity.
Alexander, Matthew
We employ a projective construction of spatial infinity in four-dimensional spacetimes which are asymptotically flat. In this construction, points of the spatial boundary of the spacetime manifold are identified with congruences of asymptotically parallel spacelike curves that are asymptotically geodesic. It is shown that for this type of construction spatial infinity is represented by a three-dimensional timelike hyperboloid, and that this follows as a consequence of the vacuum Einstein equations. We then construct tensor fields which are defined at spatial infinity, and which embody the information carried by the gravitational field regarding the total mass, linear, and angular momentum of the spacetime. It is shown that these tensor fields must satisfy a set of second order partial differential field equations at spatial infinity. The asymptotic symmetry group implied by the projective construction is examined, and is identified with the Spi group. The field equations satisfied by the tensor fields at spatial infinity can be derived from an action principle, however this action does not appear to be related in any obvious way to the Hilbert-Einstein action of general relativity. Under mappings generated by the Spi group our Lagrangian is left form -invariant, and the corresponding Noether-conserved quantities are examined. It is found that for spacetimes which are stationary or axisymmetric, these conserved quantities are not the limits of the conserved quantities associated with the infinitesimal four-dimensional coordinate transformations. It is shown that using the tensor fields at spatial infinity one can define a set of canonical variables. Further, we show that the "time" derivatives of the configuration variables can be expressed in terms of some of the momentum densities; the remaining momentum densities are constrained. Finally, we construct the Hamiltonian, and examine the transformations generated by it.
When a local Hamiltonian must be frustration-free
Sattath, Or; Morampudi, Siddhardh C.; Laumann, Chris R.; Moessner, Roderich
2016-06-01
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Raskutti, Sudhir; Skinner, M Aaron
2016-01-01
Radiation feedback from stellar clusters is expected to play a key role in setting the rate and efficiency of star formation in giant molecular clouds (GMCs). To investigate how radiation forces influence realistic turbulent systems, we have conducted a series of numerical simulations employing the {\\it Hyperion} radiation hydrodynamics solver, considering the regime that is optically thick to ultraviolet (UV) and optically thin to infrared (IR) radiation. Our model clouds cover initial surface densities between $\\Sigma_{\\rm cl,0} \\sim 10-300~M_{\\odot}~{\\rm pc^{-2}}$, with varying initial turbulence. We follow them through turbulent, self-gravitating collapse, formation of star clusters, and cloud dispersal by stellar radiation. All our models display a lognormal distribution of gas surface density $\\Sigma$; for an initial virial parameter $\\alpha_{\\rm vir,0} = 2$, the lognormal standard deviation is $\\sigma_{\\rm ln \\Sigma} = 1-1.5$ and the star formation rate coefficient $\\varepsilon_{\\rm ff,\\bar\\rho} = 0.3-...
Arth, G.; Taferner, M.; Bernhard, C.; Michelic, S.
2016-07-01
Cooling strategies in continuous casting of steel can vary from rapid cooling to slow cooling, mainly controlled by adjusting the amount of water sprayed onto the surface of the product. Inadequate adjustment however can lead to local surface undercooling or reheating, leading to surface and inner defects. This paper focuses on cooling efficiency of Air-Mist nozzles on casted steel and the experimental and numerical prediction of surface temperature distributions over the product width. The first part explains the determination of heat transfer coefficients (HTC) on laboratory scale, using a so called nozzle measuring stand (NMS). Based on measured water distributions and determined HTC's for air-mist nozzles using the NMS, surface temperatures are calculated by a transient 2D-model on a simple steel plate, explained in the second part of this paper. Simulations are carried out varying water impact density and spray water distribution, consequently influencing the local HTC distribution over the plate width. Furthermore, these results will be interpreted with regard to their consequence for surface and internal quality of the cast product. The results reveal the difficulty of correct adjustment of the amount of sprayed water, concurrent influencing water distribution and thus changing HTC distribution and surface temperature.
Cruel, Magali; Bensidhoum, Morad; Nouguier-Lehon, Cécile; Dessombz, Olivier; Becquart, Pierre; Petite, Hervé; Hoc, Thierry
2015-09-01
Controlling the mechanical environment in bioreactors represents a key element in the reactors' optimization. Positive effects of fluid flow in three-dimensional bioreactors have been observed, but local stresses at cell scale remain unknown. These effects led to the development of numerical tools to assess the micromechanical environment of cells in bioreactors. Recently, new possible scaffold geometry has emerged: granular packings. In the present study, the primary goal was to compare the efficiency of such a scaffold to the other ones from literature in terms of wall shear stress levels and distributions. To that aim, three different types of granular packings were generated through discrete element method, and computational fluid dynamics was used to simulate the flow within these packings. Shear stress levels and distributions were determined. A linear relationship between shear stress and inlet velocity was observed, and its slope was similar to published data. The distributions of normalized stress were independent of the inlet velocity and were highly comparable to those of widely used porous scaffolds. Granular packings present similar features to more classical porous scaffolds and have the advantage of being easy to manipulate and seed. The methods of this work are generalizable to the study of other granular packing configurations.
Molecular dynamics with deterministic and stochastic numerical methods
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...
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
Modification of logarithmic Hamiltonians and application of explicit symplectic-like integrators
Li, Dan; Wu, Xin
2017-08-01
We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or function) to both the kinetic energy and the force function. Explicit symplectic algorithms are available when the logarithmic Hamiltonian has two separable parts of coordinates and momenta. However, they are not if the logarithmic Hamiltonian is inseparable. Fortunately, they are still efficient by manipulating the logarithmic Hamiltonian as a new separable Hamiltonian in an extended phase space. In fact, they belong to symplectic-like integrators. The choice of mixing maps affects the performance of the considered symplectic-like integrators. It is shown that two maps about sequent permutations of coordinates and momenta are inferior to a map with mid-point permutations in some cases. The choice of the constant (or function) added also exerts some influence on the performance of the algorithms. As a result, with the help of the mid-point permutations and a suitable choice for the constant (or function) included, the logarithmic Hamiltonian methods bring an increase in accuracy compared to the non-logarithmic ones, particularly for highly eccentric orbits.
Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method
Dubinkina, S.; Frank, J.E.
2009-01-01
We conduct long simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The observed results a
Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method
Dubinkina, S.; Frank, J.E.
2010-01-01
We conduct long-time simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field of the discretization. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experime
无
2011-01-01
Using qualitative analysis, we study perturbed Hamiltonian systems with different n-th order polynomial as perturbation terms. By numerical simulation, we show that these perturbed systems have the same distribution of limit cycles. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.
Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method
S. Dubinkina; J. Frank
2010-01-01
We conduct long-time simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field of the discretization. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experime
Scattering matrix of arbitrary tight-binding Hamiltonians
Ramírez, C.; Medina-Amayo, L. A.
2017-03-01
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
Hamiltonian Description of Multi-fluid Streaming
Valls, C.; de La Llave, R.; Morrison, P. J.
2001-10-01
The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.
An intuitive Hamiltonian for quantum search
Fenner, S A
2000-01-01
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can ...
Hamiltonian replica exchange molecular dynamics using soft-core interactions.
Hritz, Jozef; Oostenbrink, Chris
2008-04-14
To overcome the problem of insufficient conformational sampling within biomolecular simulations, we have developed a novel Hamiltonian replica exchange molecular dynamics (H-REMD) scheme that uses soft-core interactions between those parts of the system that contribute most to high energy barriers. The advantage of this approach over other H-REMD schemes is the possibility to use a relatively small number of replicas with locally larger differences between the individual Hamiltonians. Because soft-core potentials are almost the same as regular ones at longer distances, most of the interactions between atoms of perturbed parts will only be slightly changed. Rather, the strong repulsion between atoms that are close in space, which in many cases results in high energy barriers, is weakened within higher replicas of our proposed scheme. In addition to the soft-core interactions, we proposed to include multiple replicas using the same Hamiltonian/level of softness. We have tested the new protocol on the GTP and 8-Br-GTP molecules, which are known to have high energy barriers between the anti and syn conformation of the base with respect to the sugar moiety. During two 25 ns MD simulations of both systems the transition from the more stable to the less stable (but still experimentally observed) conformation is not seen at all. Also temperature REMD over 50 replicas for 1 ns did not show any transition at room temperature. On the other hand, more than 20 of such transitions are observed in H-REMD using six replicas (at three different Hamiltonians) during 6.8 ns per replica for GTP and 12 replicas (at six different Hamiltonians) during 8.7 ns per replica for 8-Br-GTP. The large increase in sampling efficiency was obtained from an optimized H-REMD scheme involving soft-core potentials, with multiple simulations using the same level of softness. The optimization of the scheme was performed by fast mimicking [J. Hritz and C. Oostenbrink, J. Chem. Phys. 127, 204104 (2007)].
Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian
Eduardo Mattei
2013-11-01
Full Text Available We introduce a Hamiltonian for two interacting su(2 spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight. Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable p+ip pairing Hamiltonian.
Hamiltonian dynamics of the two-dimensional lattice {phi}{sup 4} model
Caiani, Lando [Scuola Internazionale Superiore di Studi Avanzati (SISSA/ISAS), Trieste (Italy); Casetti, Lapo [Istituto Nazionale di Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Florence (Italy)
1998-04-17
The Hamiltonian dynamics of the classical {phi}{sup 4} model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics. (author)
Equivalent Hamiltonians with additional discrete states
Chinn, C.R. (Physics Department, Lawrence Livermore National Laboratory, Livermore, CA (USA)); Thaler, R.M. (Los Alamos National Laboratory, Los Alamos, NM (USA) Department of Physics, Case Western Reserve University, Cleveland, OH (USA))
1991-01-01
Given a particular Hamiltonian {ital H}, we present a method to generate a new Hamiltonian {ital {tilde H}}, which has the same discrete energy eigenvalues and the same continuum phase shifts as {ital H}, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian {ital h}{sub 1}, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Equivalent Hamiltonians with additional discrete states
Chinn, C. R.; Thaler, R. M.
1991-01-01
Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Hamiltonian Dynamics of Cosmological Quintessence Models
Ivanov, Rossen I
2016-01-01
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any pos...
Gravitational surface Hamiltonian and entropy quantization
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.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
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.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
Nowshad Amin; Matin, M.A.; Aliyu, M. M.; M. A. Alghoul; Karim, M. R.; K. Sopian
2010-01-01
Polycrystalline CdTe shows greater promises for the development of cost-effective, efficient, and reliable thin film solar cells. Results of numerical analysis using AMPS-1D simulator in exploring the possibility of ultrathin, high efficiency, and stable CdS/CdTe cells are presented. The conventional baseline case structure of CdS/CdTe cell has been explored with reduced CdTe absorber and CdS window layer thickness, where 1 μm thin CdTe and 50 nm CdS layers showed reasonable efficiencies over...
Application of the SCC method to the multi-O(4) model: The collective Hamiltonian
GU JianZhong; KOBAYASI Masato
2009-01-01
The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate (SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov (TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the spherical and deformed cases.Numerical simulations indicate that the low-lying states of the collective Hamiltonian and the transition amplitudes among them mimic fairly well those obtained by exactly diagonalizing the Hamiltonian of the multi-O(4) model.The numerical results for the deformed case imply that the "optimized RPA boundary condition" is also valid for the well-known η*,η expansion around the unstable HB point of the multi-O(4) model.All these illuminate the power of the SCC method.
Application of the SCC method to the multi-O(4) model:The collective Hamiltonian
KOBAYASI; Masato
2009-01-01
The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the spherical and deformed cases.Numerical simulations indicate that the low-lying states of the collective Hamiltonian and the transition amplitudes among them mimic fairly well those obtained by exactly diagonalizing the Hamiltonian of the multi-O(4) model.The numerical results for the deformed case imply that the "optimized RPA boundary condition" is also valid for the well-known η*,η expansion around the unstable HB point of the multi-O(4) model.All these illuminate the power of the SCC method.
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Hamiltonian Dynamics of Protein Filament Formation.
Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J
2016-01-22
We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
Hamiltonian dynamics for complex food webs.
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.
Hamiltonian adaptive resolution simulation for molecular liquids.
Potestio, Raffaello; Fritsch, Sebastian; Español, Pep; Delgado-Buscalioni, Rafael; Kremer, Kurt; Everaers, Ralf; Donadio, Davide
2013-03-08
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.
Stability of Frustration-Free Hamiltonians
Michalakis, Spyridon
2011-01-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al., on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Hamiltonian theory of guiding-center motion
Cary, John R.; Brizard, Alain J. [Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States) and Tech-X Corporation, Boulder, Colorado 80303 (United States); Department of Chemistry and Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States)
2009-04-15
Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem (hence invariants follow from symmetries), and they preserve the Poincare invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields--something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time
Hamiltonian dynamics of the parametrized electromagnetic field
G., J Fernando Barbero; Villaseñor, Eduardo J S
2015-01-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Hamiltonian dynamics of the parametrized electromagnetic field
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2016-06-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Convergence to equilibrium under a random Hamiltonian.
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.
Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems
2014-10-13
representing the Hamiltonian of the many body system . Such a flexibility is made possible by using the discontinuous Galerkin method to approximate the... Hamiltonian matrix elements with proper constructions of numerical DG fluxes at the finite element interfaces. [3] Computation of electrostatics...Multi-physics Numerical Methods For Modeling Transport in Mesoscopic Systems (a proposal submitted to Numerical Analysis Program, Mathematical
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
Description of Atom-Field Interaction via Quantized Caldirola-Kanai Hamiltonian
Daneshmand, Roohollah; Tavassoly, Mohammad Kazem
2017-01-01
In this paper we outline an approach to the study of atom-field interacting systems, where the Hamiltonian of the field is simply inspired from the quantized Caldirola-Kanai Hamiltonian. As a simple physical realization of the model, the interaction between a two-level atom with such a single-mode field is studied. The explicit form of the atom-field entangled state associated with the considered system is analytically deduced and the dynamics of a few of its physical properties is numerically evaluated. To achieve the latter purposes, the temporal behavior of the degree of entanglement, atomic population inversion as well as sub-Poissonian statistics and quadrature squeezing of the field are evaluated. Moreover, the effects of the intensity of initial field and the damping parameter within the Caldirola-Kanai Hamiltonian on the above-mentioned criteria are investigated. As is shown, by adjusting the latter evolved parameters one can appropriately tune the discussed physical quantities.
An Introduction to Control of Chaos for Quasi-Integrable Hamiltonian Systems
Silva, Vilarbo da
2013-01-01
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of perturbation that breaks the integrability of the system. The value of the critical perturbation responsible for this transition is a key element in the control of chaos . In this paper, we explore a procedure for the control in quasi-integrable Hamiltonian systems via canonical map. Initially, we present the basic tools for this study: Hamiltonian map, linearization of the map and Chirikov criterion. Subsequently, we investigated the behavior of a wave-particle interaction front perturbation. Finally, we confront with a numerical analytical approach (iteration of the map) results, showing a good agreement.
An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian
Dyall, Kenneth G.
1994-01-01
The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
Soliton equations and Hamiltonian systems
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
Lattice effects on Laughlin wave functions and parent Hamiltonians
Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.
2016-12-01
We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.
Efficient Numerical Modeling of 3D, Half-Space, Slow-Slip and Quasi-Dynamic Earthquake Ruptures
Bradley, A. M.; Segall, P.
2011-12-01
tolerance on the approximation to parameters of the compression algorithms (Bradley [submitted]) improves the compression efficiency for the third-order 1/r3 singularity with elastic Green's functions, relative to the standard method, by factors of two to five---importantly, while still providing the same straightforward error bound on the approximation. The compression (and so, roughly, the speedup) factor for a problem in which the fault is discretized by 156 ± 402 rectangles and the tolerance on the relative error is 10-5 is just over 75. We will describe our numerical methods and present preliminary simulation results.
On the exactness of effective Floquet Hamiltonians employed in solid-state NMR spectroscopy
Garg, Rajat; Ramachandran, Ramesh
2017-05-01
Development of theoretical models based on analytic theory has remained an active pursuit in molecular spectroscopy for its utility both in the design of experiments as well as in the interpretation of spectroscopic data. In particular, the role of "Effective Hamiltonians" in the evolution of theoretical frameworks is well known across all forms of spectroscopy. Nevertheless, a constant revalidation of the approximations employed in the theoretical frameworks is necessitated by the constant improvements on the experimental front in addition to the complexity posed by the systems under study. Here in this article, we confine our discussion to the derivation of effective Floquet Hamiltonians based on the contact transformation procedure. While the importance of the effective Floquet Hamiltonians in the qualitative description of NMR experiments has been realized in simpler cases, its extension in quantifying spectral data deserves a cautious approach. With this objective, the validity of the approximations employed in the derivation of the effective Floquet Hamiltonians is re-examined through a comparison with exact numerical methods under differing experimental conditions. The limitations arising from the existing analytic methods are outlined along with remedial measures for improving the accuracy of the derived effective Floquet Hamiltonians.
I.P. van Staveren (Irene)
2009-01-01
textabstractThe dominant economic theory, neoclassical economics, employs a single economic evaluative criterion: efficiency. Moreover, it assigns this criterion a very specific meaning. Other – heterodox – schools of thought in economics tend to use more open concepts of efficiency, related to comm
Quantum Hamiltonian daemons: Unitary analogs of combustion engines
Thesing, Eike P.; Gilz, Lukas; Anglin, James R.
2017-07-01
Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.
Szalay, Viktor
2015-05-07
A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Hamiltonian Approach to the Gribov Problem
Heinzl, T
1996-01-01
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
Edge-disjoint Hamiltonian cycles in hypertournaments
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...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Linear Hamiltonian Behaviors and Bilinear Differential Forms
Rapisarda, P.; Trentelman, H.L.
2004-01-01
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study
Discrete variable representation for singular Hamiltonians
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...
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Hamiltonian analysis of BHT massive gravity
Blagojević, M
2010-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\\Lambda_0/m^2\
Hamiltonian and self-adjoint control systems
Schaft, A. van der; Crouch, P.E.
1987-01-01
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoin
Hamiltonian constants for several new entire solutions
2008-01-01
Using the Hamiltonian identities and the corresponding Hamilto- nian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
2008-01-01
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 p
Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation
Mane, S R
2016-01-01
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi
2011-01-01
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view. In arXiv:1104.3381[quant-ph], introducing a philosophy to keep the analyticity in parameter variables of FPI and defining a modified set of complex conjugate, hermitian conjugates and bras, we have extended $| q >$ and $| p >$ to complex $q$ and $p$ so that we can deal with a complex coordinate $q$ and a complex momentum $p$. After reviewing them briefly, we describe in terms of the newly introduced devices the time development of a $\\xi$-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 to the momentum again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have t...
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems, electromec
The Maslov indices of Hamiltonian periodic orbits
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approa
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved and a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced. Numerical tests against an experimental rotational band of HF are provided.
He, Lewei; Wang, Wen-Ge
2014-02-01
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.
STOCHASTIC HOPF BIFURCATION IN QUASI-INTEGRABLE-HAMILTONIAN SYSTEMS
GAN Chunbiao
2004-01-01
A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system's energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrableHamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system's parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions.
Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures
Roberto Zivieri
2012-01-01
Full Text Available Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
A phenomenological Hamiltonian for the Lotka-Volterra problem
Georgian, T. [Corps of Engineers, Omaha, NE (United States); Findley, G.L. [Northeast Louisiana Univ., Monroe, LA (United States)
1996-12-31
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{sub 1},x{sub 2}) for the Lotka-Volterra problem, which leads to the rate equations x{sub 1}=ax{sub 1}-bx{sub 1}x{sub 2}, x{sub 2}=-cx{sub 2}+bx{sub 1}x{sub 2}, with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y{sub 1} = x{sub 1} and y{sub 2} = x{sub 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.
Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions
Bonnaillie-Noel, V [IRMAR, ENS Cachan Bretagne, Univ. Rennes 1, CNRS, UEB, av Robert Schuman, 35 170 Bruz (France); Helffer, B [Laboratoire de Mathematiques, Bat. 425, Univ Paris-Sud and CNRS, 91 405 Orsay Cedex (France); Hoffmann-Ostenhof, T [International Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, A-090 Wien (Austria)], E-mail: Virginie.Bonnaillie@bretagne.ens-cachan.fr, E-mail: Bernard.Helffer@math.u-psud.fr, E-mail: thoffman@esi.ac.at
2009-05-08
The spectral analysis of Aharonov-Bohm Hamiltonians with flux 1/2 leads surprisingly to a new insight on some questions of isospectrality appearing for example in Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (J. Phys. A: Math. Gen. 39 2073-82) and of minimal partitions (Helffer et al 2009 Ann. Inst. H. Poincare Anal. Non Lineaire 26 101-38). We will illustrate this point of view by discussing the question of spectral minimal 3-partitions for the rectangle. It has been observed in Helffer et al (2009 Ann. Inst. H. Poincare Anal. Non Lineaire 26 101-38) that the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles. We will describe a possible mechanism of transition for increasing a/b between these nodal minimal 3-partitions and non-nodal minimal 3-partitions at the value {radical}3/8 and discuss the existence of symmetric candidates for giving minimal 3-partitions when {radical}3/8Numerical analysis leads very naturally to nice questions of isospectrality which are solved by the introduction of Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle.
Effective Hamiltonian for surface states of topological insulator nanotubes
Siu, Zhuo Bin; Tan, Seng Ghee; Jalil, Mansoor B. A.
2017-04-01
In this work we derive an effective Hamiltonian for the surface states of a hollow topological insulator (TI) nanotube with finite width walls. Unlike a solid TI cylinder, a TI nanotube possesses both an inner as well as outer surface on which the states localized at each surface are coupled together. The curvature along the circumference of the nanotube leads to a spatial variation of the spin orbit interaction field experienced by the charge carriers as well as an asymmetry between the inner and outer surfaces of the nanotube. Both of these features result in terms in the effective Hamiltonian for a TI nanotube absent in that of a flat TI thin film of the same thickness. We calculate the numerical values of the parameters for a Bi2Se3 nanotube as a function of the inner and outer radius, and show that the differing relative magnitudes between the parameters result in qualitatively differing behaviour for the eigenstates of tubes of different dimensions.
Khatami, F.; Weide, van der E.T.A.; Hoeijmakers, H.W.M.
2015-01-01
In this paper a numerical simulation of unsteady sheet cavitation is presented as it occurs on an NACA-0015 hydrofoil. The computational approach is based on the Euler equations for unsteady compressible flow, using an equilibrium cavitation model of Schnerr, Schmidt, and Saurel. It was found that f
Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory
Casolari, Andrea
2013-01-01
In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian character of the ray tracing equations is investigated analytically and numerically in order to deduce the physical properties of the wave propagating without absorption in the confined plasma. The consequences of the Hamiltonian character of the equations on the travelling wave, in particular, on the evolution of the parallel wavenumber along the propagation path have been accounted and the chaotic diffusion of the timeaveraged parallel wave-number towards higher values has been evaluated. Numerical analysis by means of a Runge-Kutta based algorithm implemented in a ray tracing code supplies the analytical considerations. A numerical tool based on the symplectic integration of the ray trajectories has been developed.
Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory
Casolari, A. [Università di Pisa, Pisa (Italy); Cardinali, A. [Associazione Euratom-ENEA sulla Fusione, C.P. 65 - I-00044 - Frascati, Rome (Italy)
2014-02-12
In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian character of the ray tracing equations is investigated analytically and numerically in order to deduce the physical properties of the wave propagating without absorption in the confined plasma. The consequences of the Hamiltonian character of the equations on the travelling wave, in particular, on the evolution of the parallel wavenumber along the propagation path have been accounted and the chaotic diffusion of the timeaveraged parallel wave-number towards higher values has been evaluated. Numerical analysis by means of a Runge-Kutta based algorithm implemented in a ray tracing code supplies the analytical considerations. A numerical tool based on the symplectic integration of the ray trajectories has been developed.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
GUO Fu-Kui; ZHANG Yu-Feng
2006-01-01
The Hamiltonian structure of the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratic-form identity.
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
Chimera: A hybrid approach to numerical loop quantum cosmology
Diener, Peter; Singh, Parampreet
2013-01-01
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosi...
Bayne, Mike; Chakraborty, Arindam
2013-01-01
A resolution of identity approach to explicitly correlated congruent transformed Hamiltonian (CTH) is presented. One of the principle challenges associated with the congruent transformation of the many-electron Hamiltonian is the generation of three, four, five, and six particle operators. Successful application of the congruent transformation requires efficient implementation of the many-particle operators. In this work, we present the resolution of identity congruent transformed Hamiltonian (RI-CTH) method to handle many-particle operators. The resolution of identity was used to project the explicitly correlated operator in a N-particle finite basis to avoid explicit computation of the many-particle operators. Single-particle states were obtained by performing Hartee-Fock calculations, which were then used for construction of many-particle states. The limitation of the finite nature of the resolution of identity was addressed by developing partial infinite order (PIOS) diagrammatic summation technique. In t...
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Berche, B; Berche, Bertrand; Lopez, Alexander
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.
Ivančič, Matic; Naglič, Peter; Likar, Boštjan; Pernuš, Franjo; Bürmen, Miran
2017-02-01
For a given experimental setting, the measured spatially resolved reflectance rapidly drops with decreasing numerical aperture of the detection scheme. Consequently, for detection schemes with small numerical apertures, the computational time of MC simulations required to obtain adequate signal-to-noise ratio of the spatially resolved reflectance can become very long. We mitigate the issue by virtually increasing the numerical aperture of the detection scheme in MC simulations and devise a criterion for robust estimation of its maximum value. By using the proposed methodology, we show that the acceptance angle of a selected imaging system can be virtually increased from 3 to 11 while preserving a low relative error of the simulated spatially resolved reflectance over a wide range of tissue-like optical properties. As a result, a more than eightfold improvement in the computation time is attained.
Fridlind, Ann; Seifert, Axel; Ackerman, Andrew; Jensen, Eric
2004-01-01
Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.
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.
Matrix product states for Hamiltonian lattice gauge theories
Buyens, Boye; Haegeman, Jutho; Verstraete, Frank
2014-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Cluster Monte Carlo methods for the FePt Hamiltonian
Lyberatos, A.; Parker, G. J.
2016-02-01
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.
Searching for integrable Hamiltonian systems with Platonic symmetries
Rastelli, Giovanni
2010-01-01
In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try here to find the simplest possible expressions for this kind of dynamical systems. Even in the simplest cases it is not easy to prove their integrability by direct computation of the first integrals, therefore, we make use of numerical methods to provide evidences of integrability; namely, by analyzing their Poincar\\'e sections (surface sections). In this way we find three systems with platonic symmetries, one for each class of equivalent Platonic polyhedra: tetrahedral, exahedral-octahedral, dodecahedral-icosahedral, showing evidences of integrability. The proof of integrability and the construction of the first integrals are left for further works. As an outline of the possible developments if the integrability of these systems will be proved, we show how to build from th...
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, L; Pettini, M; Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-01-01
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.
Schoups, G.H.W.; Vrugt, J.A.; Fenicia, F.; Van de Giesen, N.C.
2010-01-01
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 e
Lou, X M; Hassebrook, L G; Lhamon, M E; Li, J
1997-01-01
We introduce a new method for determining the number of straight lines, line angles, offsets, widths, and discontinuities in complicated images. In this method, line angles are obtained by searching the peaks of a hybrid discrete Fourier and bilinear transformed line angle spectrum. Numerical advantages and performance are demonstrated.
Schoups, G.; Vrugt, J.A.; Fenicia, F.; van de Giesen, N.C.
2010-01-01
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 e
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
求解振荡哈密顿系统的相拟合辛PRK方法%PHASE-FITTED SYMPLECTIC PRK METHODS FOR OSCILLATORY HAMILTONIAN SYSTEMS
陈朝霞; 石磊; 游雄
2012-01-01
研究求解可分哈密顿系统的相拟合辛PRK(FSPRK)方法.给出了修正PRK方法的代数阶条件、辛条件及相拟合与振幅拟合条件.构造了一个2级2阶和一个3级3阶FSPRK方法.对经典力学和量子力学的几个著名问题实验的数值结果证明,新的三阶方法在保持哈密顿能量与计算效率方面优于文献中的一些高效方法.%Phase-fitted symplectic PRK (FSPRK) methods for separable Hamiltonian systems are investigated.Algebraic order conditions,symplecticity conditions and phase-fitting and amplification-fitting conditions for modified PRK methods are presented.A two-stage FSPRK method of order two and a three-stage FSPRK method of order three are constructed.The numerical results of experiments on several famous testing problems in classical and quantum mechanics show that the new method of order three is superior to some highly efficient integrators in the literature in preserving the Hamiltonian energy and in efficiency.
Interest rates in quantum finance: the Wilson expansion and Hamiltonian.
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.
Ghosh, Esha; Rangan, C Pandu
2011-01-01
Hamiltonicity is an important property in parallel and distributed computation. Existence of Hamiltonian cycle allows efficient emulation of distributed algorithms on a network wherever such algorithm exists for linear-array and ring, and can ensure deadlock freedom in some routing algorithms in hierarchical interconnection networks. Hamiltonicity can also be used for construction of independent spanning tree and leads to designing fault tolerant protocols. Optical Transpose Interconnection Systems or OTIS (also referred to as two-level swapped network) is a widely studied interconnection network topology which is popular due to high degree of scalability, regularity, modularity and package ability. Surprisingly, to our knowledge, only one strong result is known regarding Hamiltonicity of OTIS - showing that OTIS graph built of Hamiltonian base graphs are Hamiltonian. In this work we consider Hamiltonicity of OTIS networks, built on Non-Hamiltonian base and answer some important questions. First, we prove tha...
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
蔡茂诚; 方奇志; 李延军
2003-01-01
A Hamiltonian [k, k + 1]-factor is a [k, k + 1]-factor containing a Hamiltonian cycle. A simple graph G of order n is n/2-critical if δ(G) ≥ n/2 but δ(G - e) ＜ n/2 for any edge e ∈ E(G). Let k ≥ 2 be an integer and G be an n/2-critical graph with n ≥ 4k - 6 and n ≥ 7. In this paper it is proved that for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. This result is an improvement on some recent results about the existence of Hamiltonian [k, k + 1]-factor.%本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性.Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\\e)＜n/2(对任意的e∈E(G)),则称G为n/2-临界图.设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子.该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Hamiltonian Approach To Dp-Brane Noncommutativity
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
Hamiltonian approach to hybrid plasma models
Tronci, Cesare
2010-01-01
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.
ON THE ELUSIVENESS OF HAMILTONIAN PROPERTY
高随祥
2001-01-01
Decision tree complexity is an important measure of computational complexity. A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set. Let P be a graph property on n vertices, if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case, then it is said that the decision tree complexity of P is k. If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case, then P is said to be elusive. Karp conjectured that every nontrivial monotone graph property is elusive. This paper concerns the elusiveness of Hamiltonian property. It is proved that if n=p+1, pq or pq+1, (where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
A Hamiltonian Formulation of Topological Gravity
Waelbroeck, Henri
2009-01-01
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.
Quantum Hamiltonian complexity and the detectability lemma
Aharonov, Dorit; Landau, Zeph; Vazirani, Umesh
2010-01-01
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint satisfaction (such as SAT), with the additional ingredient of multi-particle entanglement. This additional ingredient of course makes generalizations of celebrated theorems such as the PCP theorem from classical to the quantum domain highly non-trivial; it also raises entirely new questions such as bounds on entanglement and correlations in ground states, and in particular area laws. We propose a simple combinatorial tool that helps to handle such questions: it is a simplified, yet more general version of the detectability lemma introduced by us in the more restricted context on quantum gap amplification a year ago. Here, we argue that this lemma is applicable in much more general contexts. We use it to provide a simplified and more combinatorial proof of Hastings' 1D area law...
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.
Hamiltonian hierarchy and the Hulthen potential
Gönül, B
2000-01-01
We deal with the Hamiltonian hierarchy problem of the Hulth\\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulth\\'{e}n potential which gives satisfactory values for the non-zero angular momentum states.
Hamiltonian theory of guiding-center motion
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.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Monte Carlo Hamiltonian:Inverse Potential
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Spectral analysis of tridiagonal Fibonacci Hamiltonians
Yessen, William
2011-01-01
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.