A port-Hamiltonian approach to visual servo control of a pick and place system
Dirksz, Daniel A.; Scherpen, Jacquelien M.A.
2012-01-01
In this paper we take a port-Hamiltonian approach to address the problem of image-based visual servo control of a pick and place system. We realize a closed-loop system, including the nonlinear camera dynamics, which is port-Hamiltonian. Although the closed-loop system is nonlinear, the resulting
Optimal control of effective Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Verdeny Vilalta, Albert; Mintert, Florian [Freiburg Institute for Advanced Studies, Albert-Ludwigs University of Freiburg, Freiburg 79104 (Germany); Mueller, Cord A. [Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
2013-07-01
Periodically driven Hamiltonians can be approximately described by a time-independent effective Hamiltonian if the driving is sufficiently fast. There exist, however, many different drivings that result in the same effective Hamiltonian. Using optimal control techniques, we investigate which driving yields the best approximation to the dynamics induced by a desired effective Hamiltonian. The viability of our approach is proven for the simplest example of a driven three-level Lambda system, and shall ultimately help to improve the precision of quantum simulations.
A partial Hamiltonian approach for current value Hamiltonian systems
Naz, R.; Mahomed, F. M.; Chaudhry, Azam
2014-10-01
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
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.
Reyes Báez, Rodolfo; van der Schaft, Abraham; Jayawardhana, Bayu
2017-01-01
The problem of set-point regulation (stabilization) of mechanical port-Hamiltonian (pH) systems has been widely studied in the literature by means of energy-based methods. However, for motion control problems, where the reference signal is time-varying, it is not straightforward to design control
The Hamiltonian approach in classification and integrability of hydrodynamic chains
Pavlov, Maxim V.
2006-01-01
New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Energy Technology Data Exchange (ETDEWEB)
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.
Hamiltonian approach to the magnetostatic equilibrium problem
Energy Technology Data Exchange (ETDEWEB)
Tessarotto, M.; Zheng, Lin Jin [Universita di Trieste (Italy); Johnson, J.L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
1995-02-01
The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for non-symmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally, in a suitable subdomain, a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for general curvilinear coordinate systems. The properties of such Hamiltonian system are investigated. A representation of the magnetic field in terms of arbitrary general curvilinear coordinates is thus obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general non-symmetric toroidal equilibria, i.e., it is quasi-symmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasi-symmetric equilibria, which extends the Grad-Shafranov equation to fully three-dimensional configurations. As an application, the case is considered of quasi-helical equilibria, i.e., displaying a magnetic field magnitude depending on the poloidal ({chi}) and toroidal ({var_theta}) angles only in terms of {alpha}={chi}-N{theta} with N an arbitrary integer.
Betatron coupling: Merging Hamiltonian and matrix approaches
Directory of Open Access Journals (Sweden)
R. Calaga
2005-03-01
Full Text Available Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.
Covariant Hamiltonian tetrad approach to numerical relativity
Hamilton, Andrew J. S.
2017-12-01
A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, 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, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.
A Hamiltonian approach to stabilization of nonholonomic mechanical systems
Maschke, B.M.; Schaft, A.J. van der
1994-01-01
A simple procedure is provided to write the equations of motion of controlled mechanical systems with constraints as controlled Hamiltonian equations with respect to a "Poisson" bracket which does not necessarily satisfy the Jacobi-identity. Based on the Hamiltonian form a stabilization procedure is
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian ... TARUN KANTI GHOSH2. Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune 411 007, India; Department of Physics, Indian Institute of Technology, Kanpur 208 016, India ...
Using Hamiltonian control to desynchronize Kuramoto oscillators
Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo
2017-02-01
Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.
The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach
Likar, A.; Razpet, N.
2009-01-01
The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…
Adaptive control of port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.
2010-01-01
Adaptive control is an alternative approach for controlling systems which are sensitive to parameter uncertainty. With adaptive control it is possible to estimate parameter errors and to compensate for those errors. This can result in a better performance of the controlled system. Some techniques
Hamiltonian approach to second order gauge invariant cosmological perturbations
Domènech, Guillem; Sasaki, Misao
2018-01-01
In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Structure Preserving Adaptive Control of Port-Hamiltonian Systems
Dirksz, Daniel A.; Scherpen, Jacquelien M. A.
2012-01-01
In this technical note, an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation
Hamiltonian discretization of boundary control systems
Golo, Goran; Talasila, Viswanath; Schaft, Arjan van der; Maschke, Bernhard
2004-01-01
A fundamental problem in the simulation and control of complex physical systems containing distributed-parameter components concerns finite-dimensional approximation. Numerical methods for partial differential equations (PDEs) usually assume the boundary conditions to be given, while more often than
Hamiltonian discretization of boundary control systems
Golo, G.; Talasila, V.; van der Schaft, Arjan; Maschke, B.M.
A fundamental problem in the simulation and control of complex physical systems containing distributed-parameter components concerns finite-dimensional approximation. Numerical methods for partial differential equations (PDEs) usually assume the boundary conditions to be given, while more often than
Spacecraft Attitude Control in Hamiltonian Framework
DEFF Research Database (Denmark)
Wisniewski, Rafal
2000-01-01
is the sum of the gradient of the potential energy and the dissipative force. It is shown that this control law makes the system uniformly asymptotically stable to the desired reference point. Three problems were addressed in the paper: spacecraft stabilization in the inertial frame, libration damping...... with the use of electromagnetic coils and a slew maneuver with an additional objective of avoiding undesirable regions e.g. causing blindness of optical sensors...
H∞ control strategy for a class of switched Hamiltonian systems
Zhu, Huawei; Zhang, Zhisen; Zhao, Quanjun; Tu, Pu
2017-02-01
Using multiple Lyapunov function method, the H∞ control theory of switched Hamiltonian systems is discussed. The sufficient conditions in the form of linear matrix inequality (LMI) are presented to guarantee stability of switched Hamilton system. At the same time, an switching law based on switching dwell time is constructed. In order to prove the effectiveness of this conclusion, a numerical simulation example is given, in which the corresponding parameters are calculated by LMI.
SUSY approach to Pauli Hamiltonians with an axial symmetry
Energy Technology Data Exchange (ETDEWEB)
Ioffe, M V; Kuru, S; Negro, J; Nieto, L M [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2006-06-02
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second-order symmetries is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analysed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the associated matrix shape invariance. The relation between the intertwining operators and the second-order symmetries is established, and the full set of ladder operators that complete the dynamical algebra is constructed.
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...
Asymptotic freedom in the Hamiltonian approach to binding of color
Directory of Open Access Journals (Sweden)
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2017-03-01
We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians Hs and the (regularized) canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
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.
Port Hamiltonian Formulation of Infinite Dimensional Systems II. Boundary Control by Interconnection
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multi-variable case by
Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states.
Bonet-Luz, Esther; Tronci, Cesare
2016-05-01
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature.
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
Pang, Shengshi; Jordan, Andrew N.
2017-01-01
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.
Pang, Shengshi; Jordan, Andrew N
2017-03-09
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
Doria-Cerezo, A.; van der Heijden, L.; Scherpen, J. M. A.
2013-01-01
This paper presents the use of the memristor as a new element for designing passivity-based controllers. From the port-Hamiltonian description of the electrical circuits with memristors, a target dynamics is assigned to the matching equation proposed by the methodology known as Interconnection and
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...
Towards Ocean Grazer's Modular Power Take-Off System Modeling : A Port-Hamiltonian Approach
Barradas-Berglind, J. J.; Muñoz Arias, M.; Wei, Y.; Prins, W.A.; Vakis, A.I.; Jayawardhana, B.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
This paper presents a modular modeling framework for the Ocean Grazer's Power Take-Off (PTO) system, which operates as an array of point-absorber type devices connected to a hydraulic system. The modeling is based on the port-Hamiltonian (PH) framework that enables energy-based analysis and control
A Port-Hamiltonian Approach to Optimal Frequency Regulation in Power Grids
Stegink, Tjerk; De Persis, Claudio; van der Schaft, Arjan
2015-01-01
This paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. Two price-based controllers are proposed; the first one an internal-model-based controller and the second one based on a continuous gradient method for optimization. Both controllers can be implemented in a fully distributed fashion, with freedom in choosing a controller communication network. As a result, two real-time dynamic pricing models described by port- Hamiltonian systems are o...
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC
2012-12-15
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplica- tive approaches have been compared.
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta
2016-01-01
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...
Hamiltonian approach to QCD in Coulomb gauge: Gribov’s confinement scenario at work*
Directory of Open Access Journals (Sweden)
Reinhardt H.
2017-01-01
Full Text Available I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribov’s confinement scenario and the center vortex picture of confinement. I will then extend the Hamiltonian approach to QCD in Coulomb gauge to finite temperatures, first by the usual grand canonical ensemble and second by the compactification of a spatial dimension. I will present results for the pressure, energy density and interaction measure as well as for the Polyakov loop.
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
Dossetti-Romero, V.; Izrailev, F. M.; Krokhin, A. A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schrödinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance.
Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems
DEFF Research Database (Denmark)
Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle
2004-01-01
A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mob...
Regulation and input disturbance suppression for port-controlled Hamiltonian systems
Gentili, L.; Astolfi, A.; van der Schaft, Arjan; Gordillo, F.
2003-01-01
In this paper the output feedback regulation problem for port-controlled Hamiltonian systems (PCHS) is addressed. Following the nonlinear output regulation theory, the regulator which solves the problem is given by a parallel connection of two subcontrollers: an internal model unit and a regulator
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2011-01-01
Full Text Available We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u. We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.
Hamiltonian approach to QCD in Coulomb gauge at zero and finite temperature
Directory of Open Access Journals (Sweden)
Reinhardt H.
2017-01-01
Full Text Available I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector a vacuum wave functional is used which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170MeV and 198 MeV, respectively, are obtained.
A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model
Directory of Open Access Journals (Sweden)
Rodriguez-Alfaro Luis H.
2015-03-01
Full Text Available The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
An inversion-relaxation approach for sampling stationary points of spin model Hamiltonians
Hughes, Ciaran; Mehta, Dhagash; Wales, David J.
2014-05-01
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems.
The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics
Directory of Open Access Journals (Sweden)
Ming Xu
2013-01-01
Full Text Available A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively. The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilibrium to an elliptic one. With the poles assigned at any different positions on imaginary axis, the controlled Hamiltonian system is Lyapunov stable. The Floquet multiplier is employed to measure the stability of time-dependent Hamiltonian system, because the equilibrium of periodic system may be unstable even though the equilibrium is always elliptic. One type of periodic orbits is achieved by the resonant conditions of control gains, and another type is making judicious choice in the foundational motions with different frequencies. The control gains are selected from the viewpoint of both the local and global optimizations on fuel cost. This controller is applied to some astrodynamics to achieve some interesting conclusions, including stable lissajous orbits in solar sail’s three-body problem and degenerated two-body problem, quasiperiodic formation flying on a J2-perturbed mean circular orbit, and controlled frozen orbits for a spacecraft with a high area-to-mass ratio.
The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics
Ming Xu; Yan Wei; Shengli Liu
2013-01-01
A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively. The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilibrium to an elliptic one. With the poles assigned at any different positions on imaginary axis, the ...
Towards Ocean Grazer's Modular Power Take-Off System Modeling: A Port-Hamiltonian Approach
Barradas-Berglind, J. J.; Muñoz Arias, M.; Wei, Y; Prins, W.A.; Vakis, A. I.; Jayawardhana, B.
2017-01-01
This paper presents a modular modeling framework for the Ocean Grazer's Power Take-Off (PTO) system, which operates as an array of point-absorber type devices connected to a hydraulic system. The modeling is based on the port-Hamiltonian (PH) framework that enables energy-based analysis and control of the PTO system. Firstly, a modular model of a point-absorber hydraulic system, which represents the main building block of the PTO, is presented. The model consists of wave-mechanical and hydrau...
Directory of Open Access Journals (Sweden)
S. Sadeghzadeh
Full Text Available Abstract This paper implements the higher order Hamiltonian method to analyze an electrostatically actuated nonlinear micro beam-based micro electro mechanical oscillator. First, second and third approximate solutions are obtained, and the frequency responses of the system are compared with energy balance method solution and previously solved Variational Approach (VA and exact solution. After driving the equation of motion based on the Euler-Bernoulli beam theory, Galerkin method has been used to simplify the nonlinear equation of motion. Higher order Hamiltonian approach has been used to solve the problem and introduce a design strategy. Phase plane diagram of electrostatically actuated micro beam has plotted to show the stability of presented nonlinear system and natural frequencies are calculated to use for resonator design. According to the numerical results, the second approximate is more acceptable and results show that one could obtain a predesign strategy by prediction of effects of mechanical properties and electrical coefficients on the stability and free vibration of common electrostatically actuated micro beam.
Feedback Control of a Class of Nonholonomic Hamiltonian Systems
DEFF Research Database (Denmark)
Sørensen, Mathias Jesper
Feedback control of nonholonomic systems has always been problematic due to the nonholonomic constraints that limit the space of possible system velocities. This property is very basic, and Brockett proved that a nonholonomic system cannot be asymptotically stabilized by a time-invariant smooth...... turns out to be useful when stabilizing the nonholonomic system. If the system is properly actuated it is possible to asymptotically stabilize the primary part of the configuration coordinates via a passive energy shaping and damping injecting feedback. The feedback is smooth and time...... of the closed loop system some extensions are provided: integral action for asymptotic stabilization under the influence of disturbances, and an adaptive damping scheme ensuring that the robot travels at a predefined speed when tracking a path. Both of these extensions are defined in the framework...
Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.
Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao
2013-09-10
Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.
Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations
Aliyu, MDS
2011-01-01
A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter
Chou, Chia-Chun; Kouri, Donald J
2013-04-25
Supersymmetric quantum mechanics (SUSY-QM) is shown to provide a novel approach to the construction of the initial states for the imaginary time propagation method to determine the first and second excited state energies and wave functions for a two-dimensional system. In addition, we show that all calculations are carried out in sector one and none are performed with the tensor sector two Hamiltonian. Through our tensorial approach to multidimensional supersymmetric quantum mechanics, we utilize the correspondence between the eigenstates of the sector one and two Hamiltonians to construct appropriate initial sector one states from sector two states for the imaginary time propagation method. The imaginary time version of the time-dependent Schrödinger equation is integrated to obtain the first and second excited state energies and wave functions using the split operator method for a two-dimensional anharmonic oscillator system and a two-dimensional double well potential. The computational results indicate that we can obtain the first two excited state energies and wave functions even when a quantum system does not exhibit any symmetry. Moreover, instead of dealing with the increasing computational complexity resulting from computations in the tensor sector two Hamiltonian, this study presents a new supersymmetric approach to calculations of accurate excited state energies and wave functions by directly using the scalar sector one Hamiltonian.
Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems
Ortega, Romeo; Schaft, Arjan van der; Castaños, Fernando; Astolfi, Alessandro
2008-01-01
The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a
A Crystal Field Approach to Orbitally Degenerate SMMs: Beyond the Spin-Only Hamiltonian
Bhaskaran, Lakshmi; Marriott, Katie; Murrie, Mark; Hill, Stephen
Single-Molecule Magnets (SMMs) with large magnetization reversal barriers are promising candidates for high-density information storage. Recently, a large uniaxial magnetic anisotropy was observed for a mononuclear trigonal bipyramidal (TBP) [NiIICl3(Me-abco)2] SMM. High-field EPR studies analyzed on the basis of a spin-only Hamiltonian give ¦D¦>400 cm-1, which is close to the spin-orbit coupling parameter λ = 668 cm-1 for NiII, suggesting an orbitally degenerate ground state. The spin-only description is ineffective in this limit, necessitating the development of a model that includes the orbital moment. Here we describe a phenomenological approach that takes into account a full description of crystal field, electron-electron repulsion and spin-orbit coupling effects on the ground state of a NiII ion in a TBP coordination geometry. The model is in good agreement with the high-field EPR experiments, validating its use for spectroscopic studies of orbitally degenerate molecular nanomagnets. This work was supported by the NSF (DMR-1309463).
A novel approach of an absolute coding pattern based on Hamiltonian graph
Wang, Ya'nan; Wang, Huawei; Hao, Fusheng; Liu, Liqiang
2017-02-01
In this paper, a novel approach of an optical type absolute rotary encoder coding pattern is presented. The concept is based on the principle of the absolute encoder to find out a unique sequence that ensures an unambiguous shaft position of any angular. We design a single-ring and a n-by-2 matrix absolute encoder coding pattern by using the variations of Hamiltonian graph principle. 12 encoding bits is used in the single-ring by a linear array CCD to achieve an 1080-position cycle encoding. Besides, a 2-by-2 matrix is used as an unit in the 2-track disk to achieve a 16-bits encoding pattern by using an area array CCD sensor (as a sample). Finally, a higher resolution can be gained by an electronic subdivision of the signals. Compared with the conventional gray or binary code pattern (for a 2n resolution), this new pattern has a higher resolution (2n*n) with less coding tracks, which means the new pattern can lead to a smaller encoder, which is essential in the industrial production.
A geometric approach to the Lagrangian and Hamiltonian formalism of electrodynamics
Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A.; Eferina, E. G.; Velieva, T. R.
2017-04-01
In solving field problems, for example problems of electrodynamics, we commonly use the Lagrangian and Hamiltonian formalisms. Hamiltonian formalism of field theory has the advantage over the Lagrangian, which inherently contains a gauge condition. While the gauge condition is introduced ad hoc from some external reasons in the Lagrangian formalism. However, the use of the Hamiltonian formalism in the field theory is difficult due to the non-regularity of the field Lagrangian. We must use such variant of the Lagrangian and the Hamiltonian formalism, which would allow us to work with the field models, in particular, to solve the problem of electrodynamics. We suggest to use the modern differential geometry and the algebraic topology, in particular the theory of fiber bundles, as a mathematical apparatus. This apparatus leads to greater clarity in the understanding of mathematical structures, associated with physical and technical models. The usage the fiber bundles theory allows us to deepen and expand both the Lagrangian and the Hamiltonian formalism. We can detect a wide range of these formalisms. Also we can select the most appropriate formalism. Actually just using the fiber bundles formalism we can adequately solve the problems of the field theory, in particular the problems of electrodynamics.
Composition of Dirac structures and control of Port-Hamiltonian systems
van der Schaft, Arjan; Cervera, J.; Gilliam, D.S.; Rosenthal, J.
2002-01-01
Key feature of Dirac structures (as opposed to Poisson or symplectic structures) is the fact that the standard composition of two Dirac structures is again a Dirac structure. In particular this implies that any power-conserving interconnection of port-Hamiltonian systems is a port-Hamiltonian system
Hamiltonian approach to GR - Part 2: covariant theory of quantum gravity
Cremaschini, Claudio; Tessarotto, Massimo
2017-05-01
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant.
Hamiltonian approach to GR. Pt. 2. Covariant theory of quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio [Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics, Opava (Czech Republic)
2017-05-15
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. (orig.)
Hamiltonian approach to GR - Part 1: covariant theory of classical gravity
Cremaschini, Claudio
2016-01-01
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor $\\hat{g}(r)\\equiv \\left\\{ \\hat{g}_{\\mu \
Dirksz, D. A.; Scherpen, J. M. A.; Ortega, R.
2008-01-01
A dynamic extension for position feedback of port-Hamiltonian mechanical systems is studied. First we look at the consequences for the matching equations when applying Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Then we look at the possibilities of asymptotically
Energy Technology Data Exchange (ETDEWEB)
Wilson, David G.; Robinett, Rush D. III [Sandia National Laboratories, Albuquerque, NM (United States). Energy, Resources and Systems Analysis Center
2010-07-01
The swing equations for renewable generators connected to the grid are developed and a simple wind turbine with UPFC is used as an example. The swing equations for renewable generator are formulated as a natural Hamiltonian system with externally applied non-conservative forces. A two-step process referred to as Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) is used to analyze and design feedback controllers for the renewable generators system. This formulation extends previous results on the analytical verification of the Potential Energy Boundary Surface (PEBS) method to nonlinear control analysis and design and justifies the decomposition of the system into conservative and nonconservative systems to enable a two-step, serial analysis and design procedure. This paper presents the analysis and numerical simulation results for a nonlinear control design example that includes the One-Machine Infinite Bus (OMIB) system with a Unified Power Flow Control (UPEC) and applied to a simplified wind turbine generator. The needed power and energy storage/charging responses are also determined. (orig.)
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
Directory of Open Access Journals (Sweden)
Shuanghe Yu
2013-01-01
Full Text Available Finite-time control scheme for speed regulation of permanent magnet synchronous motor (PMSM is investigated under the port-controlled Hamiltonian (PCH, terminal sliding mode (TSM, and fast TSM stabilization theories. The desired equilibrium is assigned to the PCH structure model of PMSM by maximum torque per ampere (MTPA principle, and the desired Hamiltonian function of state error is constructed in the form of fractional power structure as TSM and fast TSM, respectively. Finite-time TSM and fast TSM controllers are designed via interconnection and damping assignment passivity-based control (IDA-PBC methodology, respectively, and the finite-time stability of the desired equilibrium point is also achieved under the PCH framework. Simulation results validate the improved performance of the presented scheme.
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
N. N. Romanova
1998-01-01
Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum Electrodynamics
Jones, Billy D.
1997-10-01
Why is the study of the Lamb shift in hydrogen, which at the level of detail found in this paper was largely completed by Bethe in 1947, of any real interest today? While completing such a calculation using new techniques may be very interesting for formal and academic reasons, our primary motivation is to lay groundwork for precision bound-state calculations in QCD. The Lamb shift provides an excellent pedagogical tool for illustrating light-front Hamiltonian techniques, which are not widely known; but more importantly it presents three of the central dynamical and computational problems that we must face to make these techniques useful for solving QCD: How does a constituent picture emerge in a gauge field theory? How do bound-state energy scales emerge non-perturbatively? How does rotational symmetry emerge in a non-perturbative light-front calculation?
On the algebraic approach to the time-dependent quadratic Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Urdaneta, Ines; Palma, Alejandro [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico); Sandoval, Lourdes, E-mail: urdaneta@sirio.ifuap.buap.m [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)
2010-09-24
The unitary operator V(t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schroedinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano
2017-11-01
The quantization of systems with a position dependent mass (PDM) is studied. We present a method that starts with the study of the existence of Killing vector fields for the PDM geodesic motion (Lagrangian with a PDM kinetic term but without any potential) and the construction of the associated Noether momenta. Then the method considers, as the appropriate Hilbert space, the space of functions that are square integrable with respect to a measure related with the PDM and, after that, it establishes the quantization, not of the canonical momenta p, but of the Noether momenta P instead. The quantum Hamiltonian, that depends on the Noether momenta, is obtained as an Hermitian operator defined on the PDM Hilbert space. In the second part several systems with position-dependent mass, most of them related with nonlinear oscillators, are quantized by making use of the method proposed in the first part.
Implicit Hamiltonian Systems with Symmetry
Schaft, A.J. van der
1998-01-01
Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach
Implicit Hamiltonian systems with symmetry
van der Schaft, Arjan
1998-01-01
Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach
An Effective-Hamiltonian Approach to CH5+, Using Ideas from Atomic Spectroscopy
Hougen, Jon T.
2016-06-01
In this talk we present the first steps in the design of an effective Hamiltonian for the vibration-rotation energy levels of CH5+. Such a Hamiltonian would allow calculation of energy level patterns anywhere along the path travelled by a hypothetical CH5+ (or CD5+) molecule as it passes through various coupling cases, and might thus provide some hints for assigning the observed high-resolution spectra. The steps discussed here, which have not yet addressed computational problems, focus on mapping the vibration-rotation problem in CH5+ onto the five-electron problem in the boron atom, using ideas and mathematical machinery from Condon and Shortley's book on atomic spectroscopy. The mapping ideas are divided into: (i) a mapping of particles, (ii) a mapping of coordinates (i.e., mathematical degrees of freedom), and (iii) a mapping of quantum mechanical interaction terms. The various coupling cases along the path correspond conceptually to: (i) the analog of a free-rotor limit, where the H atoms see the central C atom but do not see each other, (ii) the low-barrier and high-barrier tunneling regimes, and (iii) the rigid-molecule limit, where the H atoms remain locked in some fixed molecular geometry. Since the mappings considered here often involve significant changes in mathematics, a number of interesting qualitative changes occur in the basic ideas when passing from B to CH5+, particularly in discussions of: (i) antisymmetrization and symmetrization ideas, (ii) n,l,ml,ms or n,l,j,mj quantum numbers, and (iii) Russell-Saunders computations and energy level patterns. Some of the mappings from B to CH5+ to be discussed are as follows. Particles: the atomic nucleus is replaced by the C atom, the electrons are replaced by protons, and the empty space between particles is replaced by an "electron soup." Coordinates: the radial coordinates of the electrons map onto the five local C-H stretching modes, the angular coordinates of the electrons map onto three rotational
Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach
Directory of Open Access Journals (Sweden)
Antoine Falaize
2016-09-01
Full Text Available We present a method that generates passive-guaranteed stable simulations of analog audio circuits from electronic schematics for real-time issues. On one hand, this method is based on a continuous-time power-balanced state-space representation structured into its energy-storing parts, dissipative parts, and external sources. On the other hand, a numerical scheme is especially designed to preserve this structure and the power balance. These state-space structures define the class of port-Hamiltonian systems. The derivation of this structured system associated with the electronic circuit is achieved by an automated analysis of the interconnection network combined with a dictionary of models for each elementary component. The numerical scheme is based on the combination of finite differences applied on the state (with respect to the time variable and on the total energy (with respect to the state. This combination provides a discrete-time version of the power balance. This set of algorithms is valid for both the linear and nonlinear case. Finally, three applications of increasing complexities are given: a diode clipper, a common-emitter bipolar-junction transistor amplifier, and a wah pedal. The results are compared to offline simulations obtained from a popular circuit simulator.
Hamiltonian approach to GR. Pt. 1. Covariant theory of classical gravity
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)
2017-05-15
A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor g(r) ≡ {g_μ_ν(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x ≡ {g,π} obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations. (orig.)
Mikulskis, Paulius; Genheden, Samuel; Wichmann, Karin; Ryde, Ulf
2012-05-05
We present a combination of semiempirical quantum-mechanical (SQM) calculations in the conductor-like screening model with the MM/GBSA (molecular-mechanics with generalized Born and surface-area solvation) method for ligand-binding affinity calculations. We test three SQM Hamiltonians, AM1, RM1, and PM6, as well as hydrogen-bond corrections and two different dispersion corrections. As test cases, we use the binding of seven biotin analogues to avidin, nine inhibitors to factor Xa, and nine phenol-derivatives to ferritin. The results vary somewhat for the three test cases, but a dispersion correction is mandatory to reproduce experimental estimates. On average, AM1 with the DH2 hydrogen-bond and dispersion corrections gives the best results, which are similar to those of standard MM/GBSA calculations for the same systems. The total time consumption is only 1.3-1.6 times larger than for MM/GBSA. Copyright © 2012 Wiley Periodicals, Inc.
Rosas-Ortiz, Oscar; Zelaya, Kevin
2018-01-01
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.
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
Port-Hamiltonian systems: an introductory survey
van der Schaft, 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
EXTENDED LUCAS TUBE: GRAF HAMILTONIAN BARU
Directory of Open Access Journals (Sweden)
Ernastuti .
2012-06-01
Full Text Available A Hamiltonian cycle in a connected graph G is defined as a closed walk that traverses every vertex of G exactly once, except the starting vertex at which the walk also terminates. If an edge from a Hamiltonian cycle is removed, it forms a path calleda Hamiltonian path. A graph G is called Hamiltonian if there is a Hamiltonian cyclein G. It is known that every hypercube graph is Hamiltonian. But when one or more vertices are removed from a hypercube graph, will it still be Hamiltonian? Some induced subgraphs of a hypercube graph such as the Fibonacci cube (FC, the extended Fibonaccicube (EFC, and the Lucas cube (LC have been introduced and their Hamiltonicities have been investigated. Research results showed that less than a third of FC graphs are Hamiltonian although all of them have Hamiltonian path. All EFC graphs are Hamiltonian and none of LC graphs is Hamiltonian although some still have Hamiltonian paths.This paper introduces another subgraph of a hypercube graph called the Extended Lucas Cube (ELC. The ELC is shown to be Hamiltonian by using the approach of k-Gray Code and Bipartition Property.
A Port-Hamiltonian Approach to Optimal Frequency Regulation in Power Grids
Stegink, Tjerk; Persis, Claudio De; Schaft, Arjan van der
2015-01-01
This paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. Two price-based controllers are proposed; the first one an internal-model-based controller and the second one based on a continuous gradient method for optimization. Both controllers can be
Indekeu, J O; Koga, K; Hooyberghs, H; Parry, A O
2013-08-01
We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.
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...
Hamiltonian systems with discontinuities
Tulczyjew, Wlodzimierz M.
2006-01-01
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation of a positive homogeneous Hamiltonian system by an outer oriented coisotropic submanifold of the phase space is proposed.
Chaos and correspondence in classical and quantum Hamiltonian ratchets: a Heisenberg approach.
Pelc, Jordan; Gong, Jiangbin; Brumer, Paul
2009-06-01
Previous work [Gong and Brumer, Phys. Rev. Lett. 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, although full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.
Charmonium spectrum and diffractive production in a light-front Hamiltonian approach
Chen, Guangyao; Li, Yang; Maris, Pieter; Tuchin, Kirill; Vary, James P.
2017-08-01
We study exclusive charmonium production in diffractive deep inelastic scattering and ultra-peripheral heavy-ion collisions within the dipole picture. The mass spectrum and light-front wavefunctions of charmonium are obtained from the basis light-front quantization approach, using the one-gluon exchange interaction plus a confining potential inspired by light-front holography. We apply these light-front wavefunctions to exclusive charmonium production. The resulting cross sections are in reasonable agreement with electron-proton collision data at HERA and ultra-peripheral nucleus collision measurements at RHIC and LHC. The charmonium cross-section has model dependence on the dipole model. We observe that the cross-section ratio of excited states to the ground state has a weaker dependence than the cross-section itself. We suggest that measurements of excited states of heavy quarkonium production in future electron-ion collision experiments will impose rigorous constraints on heavy quarkonium light-front wave-functions, thus improving our understanding of meson structure, which eventually will help us develop a precise description of the gluon distribution function in the small-x regime.
Gelin, M F; Kosov, D S
2008-07-01
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations or measurements performed on nonequilibrium systems.
Adaptive tracking control of fully actuated port-Hamiltonian mechanical systems
Dirksz, D.A.; Scherpen, J.M.A.
2010-01-01
In the presence of parameter uncertainty tracking control can result in significant tracking errors. To overcome this problem adaptive control is applied, which estimates and compensates for the errors of the uncertain parameters. A new adaptive tracking control scheme is presented for standard
Energy-Shaping of Port-Controlled Hamiltonian Systems by Interconnection
Ortega, Romeo; Schaft, Arjan van der; Maschke, Bernhard; Escobar, Gerardo
1999-01-01
Passivity-based control (PBC) has shown to be very powerful to design robust controllers for physical systems described by Euler-Lagrange (EL) equations of motion. The application of PBC in regulation problems of mechanical systems yields controllers that have a clear physical interpretation in
Energy Technology Data Exchange (ETDEWEB)
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Bravetti, Alessandro; Cruz, Hans; Tapias, Diego
2016-01-01
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.
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.
Port-Hamiltonian and power-based integral control of a manipulator system
Dirksz, Daniel; Scherpen, Jacquelien M.A.
2011-01-01
In industrial applications integral control is often used in controllers to counteract the effects of disturbances and other uncertainties. The integral action compensates for steady-state errors caused by such uncertainties. However, for nonlinear systems, when adding an integrator in the classical
The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics
National Research Council Canada - National Science Library
Xu, Ming; Wei, Yan; Liu, Shengli
2013-01-01
A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively...
Maxwell's equations instantaneous Hamiltonian
Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A.; Eferina, E. G.; Velieva, T. R.; Zaryadov, I. S.
2017-04-01
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 field theories. In the case of irregular Lagrangian the Dirac-Bergman 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 instantaneous (symplectic) Hamiltonian formalism.
Directory of Open Access Journals (Sweden)
E.R. Bittner
2016-03-01
Full Text Available We present here a formally exact model for electronic transitions between an initial (donor and final (acceptor states linked by an intermediate (bridge state. Our model incorporates a common set of vibrational modes that are coupled to the donor, bridge, and acceptor states and serves as a dissipative bath that destroys quantum coherence between the donor and acceptor. Taking the memory time of the bath as a free parameter, we calculate transition rates for a heuristic 3-state/2 mode Hamiltonian system parameterized to represent the energetics and couplings in a typical organic photovoltaic system. Our results indicate that if the memory time of the bath is of the order of 10-100 fs, a two-state kinetic (i.e., incoherent hopping model will grossly underestimate overall transition rate.
DEFF Research Database (Denmark)
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...
Tadyszak, Krzysztof; Rudowicz, Czesław; Ohta, Hitoshi; Sakurai, Takahiro
2017-10-01
The spin Hamiltonian (SH) parameters experimentally determined by EMR (EPR) may be corroborated or otherwise using various theoretical modeling approaches. To this end semiempirical modeling is carried out for high-spin (S=2) manganese (III) 3d 4 ions in complex of tetraphenylporphyrinato manganese (III) chloride (MnTPPCl). This modeling utilizes the microscopic spin Hamiltonians (MSH) approach developed for the 3d 4 and 3d 6 ions with spin S=2 at orthorhombic and tetragonal symmetry sites in crystals, which exhibit an orbital singlet ground state. Calculations of the zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors (g || =g z , g ⊥ =g x =g y ) are carried out for wide ranges of values of the microscopic parameters using the MSH/VBA package. This enables to examine the dependence of the theoretically determined ZFS parameters b k q (in the Stevens notation) and the Zeeman factors g i on the spin-orbit (λ), spin-spin (ρ) coupling constant, and the ligand-field energy levels (Δ i ) within the 5 D multiplet. The results are presented in suitable tables and graphs. The values of λ, ρ, and Δ i best describing Mn(III) ions in MnTPPCl are determined by matching the theoretical second-rank ZFSP b 2 0 (D) parameter and the experimental one. The fourth-rank ZFS parameters (b 4 0 , b 4 4 ) and the ρ (spin-spin)-related contributions, which have been omitted in previous studies, are considered for the first time here and are found important. Semiempirical modeling results are compared with those obtained recently by the density functional theory (DFT) and/or ab initio methods. Copyright © 2017 Elsevier Inc. All rights reserved.
Miskovic, O; Miskovic, Olivera; Zanelli, Jorge
2003-01-01
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable. However, Dirac's treatment can be slightly modified to obtain, in some cases, a Hamiltonian description completely equivalent to the Lagrangian one. A recipe to deal with the different cases is provided, along with a few pedagogical examples.
Mananga, Eugene Stephane; Hu, Bingwen
2016-11-03
The importance of the average Hamiltonian theory and its antecedent the Magnus expansion are discussed. The investigation of its convergence in different situations is very important. In this paper, we introduced a well-established approach to minimize the zeroth-order average Hamiltonian for modified composite pulse sequence in quadrupolar spectroscopy of spin-1. We designed two modified composite pulse sequences constructed by modifying the timing sequence in the original composite pulse sequences.17 We tested various configurations of times associated with the free evolution of the spin system in the modified composite pulses. We found that by decreasing the time delays between the pulses associated with the free evolution of spin system, the line shapes become increasingly better until we obtained the new modified composite pulses showing improvement of the signal compared to the original composite pulse sequences.17 This promising work is expected to play an important role not only for recording high resolution spectra of amino acids, pharmaceutical samples, and peptides but also for probing structural and dynamic information in biomolecules. The generality of the present theoretical scheme points to potential applications in solid-state NMR, to problems in chemical physics, quantum mechanics and theoretical developments, chemistry, and physical chemistry, and in interdisciplinary research areas whenever they include spin dynamics approach.
Non-Hamiltonian commutators in quantum mechanics.
Sergi, Alessandro
2005-12-01
The symplectic structure of quantum commutators is first unveiled and then exploited to describe generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a particular realization of such a bracket. In light of previous work, this paper explains a unified approach to classical and quantum-classical non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian commutators, it is shown how to define thermodynamic constraints in quantum-classical systems. In particular, quantum-classical Nosé-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nosé-Hoover chains and Nosé-Andersen (constant-pressure, constant-temperature) dynamics are also given. Perspectives of the formalism are discussed.
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.
2018-01-01
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Remarks on hamiltonian digraphs
DEFF Research Database (Denmark)
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 ...
Hamiltonian paths on Platonic graphs
Directory of Open Access Journals (Sweden)
Brian Hopkins
2004-07-01
Full Text Available We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.
Energy Technology Data Exchange (ETDEWEB)
Albert, Christopher G.; Heyn, Martin F.; Kapper, Gernot; Kernbichler, Winfried; Martitsch, Andreas F. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Kasilov, Sergei V. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology,” ul. Akademicheskaya 1, 61108 Kharkov (Ukraine)
2016-08-15
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.
An electromechanical Ising Hamiltonian.
Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi
2016-06-01
Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.
Quantum Hamiltonian Complexity
Gharibian, Sevag; Huang, Yichen; Landau, Zeph; Shin, Seung Woo
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...
HAMILTONIAN INCLUSIONS WITH CONVEX DISSIPATION WITH A VIEW TOWARDS APPLICATIONS
Directory of Open Access Journals (Sweden)
Marius Buliga
2010-01-01
Full Text Available We propose a generalization of Hamiltonian mechanics, as a Hamiltonian inclusion with convex dissipation function. We obtain a dynamical version of the approach of Mielke to quasistatic rate-independent processes. Then we show that a class of models of dynamical brittle damage can be formulated in this setting.
Hamiltonian approach for explosive percolation.
Moreira, A A; Oliveira, E A; Reis, S D S; Herrmann, H J; Andrade, J S
2010-04-01
We present a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by D. Achlioptas [Science 323, 1453 (2009)]. We show that the following two ingredients are sufficient for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on treelike graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the presented mechanism can be viewed as a generalization of standard percolation that discloses a family of models with potential application in growth and fragmentation processes of real network systems.
Distributed port-Hamiltonian formulation of infinite dimensional systems
Macchelli, Alessandro; Macchelli, A.; van der Schaft, Arjan; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and
Distributed Port-Hamiltonian Formulation of Innite Dimensional Systems
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and
Globally superintegrable Hamiltonian systems
Kurov, A. V.; Sardanashvily, G. A.
2017-06-01
The generalization of the Mishchenko-Fomenko theorem for symplectic superintegrable systems to the case of an arbitrary, not necessarily compact, invariant submanifold allows giving a global description of a superintegrable Hamiltonian system, which can be split into several nonequivalent globally superintegrable systems on nonoverlapping open submanifolds of the symplectic phase manifold having both compact and noncompact invariant submanifolds. A typical example of such a composition of globally superintegrable systems is motion in a centrally symmetric field, in particular, the two-dimensional Kepler problem.
Zezyulin, Dmitry A.; Konotop, Vladimir V.
2018-01-01
We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose–Einstein condensates in nonlinear lattices are discussed.
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
Subasi, Yigit; Jarzynski, Christopher
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 two-body interactions only. 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. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l 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. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.
Memristive port-Hamiltonian Systems
Jeltsema, Dimitri; Schaft, Arjan J. van der
2010-01-01
The port-Hamiltonian modelling framework is extended to a class of systems containing memristive elements and phenomena. First, the concept of memristance is generalised to the same generic level as the port-Hamiltonian framework. Second, the underlying Dirac structure is augmented with a memristive
HAMILTONIAN FORMALISM ON CHARACTERISTIC SURFACES.
The problem of the construction of a Hamiltonian formalism suitable for propagation of a field off characteristic or null surfaces is considered. In...is developed on characteristic surfaces. A Hamiltonian for gravitation (general relativity) is constructed, first on null surfaces described only by
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Valence band effective Hamiltonians in nitride semiconductors
Punya, Atchara; Schwertfager, Nucharee; Lambrecht, Walter
2012-02-01
Valence band effective Hamiltonians are useful to determine the electronic states of shallow impurities, quantum wells, quantum wires and quantum dots within the effective mass approximation. Although significant experimental and theoretical work has been performed, basic parameters such as the Rashba Sheka Pikus (RSP) Hamiltonian parameters are still uncertain. In this work, the electronic band structures of AlN, GaN and InN, all in the wurtzite crystal structure, as well as the RSP Hamiltonian parameters are determined by using the QSGW approximation in a FP-LMTO implementation. The corrections offered by this approach beyond the LDA are important to obtain the splittings and effective masses accurately. The present GW implementation, which allows for a real space representation of the self-energy, enables us to interpolate exactly to a fine k-mesh and hence to obtain accurate effective masses. We find the crystal field splitting in GaN (12 meV) in much closer agreement with experiment than previous work and obtain a negative SO coupling for InN. Moreover, we have generalized the method of invariants to crystals with orthorombic symmetry, such as ZnSiN2 ZnGeN2, ZnSnN2 and CdGeN2 and determined the corresponding Hamiltonian parameters.
Hamiltonian gadgets with reduced resource requirements
Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre
2015-01-01
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k -body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a Y Y interaction term using Hamiltonians containing only {X ,Z ,X X ,Z Z } terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.
Hamiltonian methods in the theory of solitons
Faddeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
Subasi, Yigit; Jarzynski, Christopher
2016-01-01
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 two-body interactions only. 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...
Hamiltonian Structure of PI Hierarchy
Directory of Open Access Journals (Sweden)
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.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
Dipendu Maity
2017-08-24
contractible separating Hamiltonian cycles; proper graphs in polyhedral maps. Mathematics Subject Classification. 57M20, 57N05, 05C38. 1. Introduction and definitions. By a topological graph we mean a representation of a graph in ...
Applications of Noether conservation theorem to Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr
2016-09-15
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.
Construction of alternative Hamiltonian structures for field equations
Energy Technology Data Exchange (ETDEWEB)
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Hamiltonian analysis of interacting fluids
Energy Technology Data Exchange (ETDEWEB)
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.)
Non-Hamiltonian equilibrium statistical mechanics.
Sergi, Alessandro
2003-02-01
In this paper the equilibrium statistical mechanics of non-Hamiltonian systems is formulated introducing an algebraic bracket. The latter defines non-Hamiltonian equations of motion in classical phase space according to the approach introduced in Phys. Rev. E 64, 056125 (2001). The Jacobi identity is no longer satisfied by the generalized bracket and as a result the algebra of phase space functions is not time translation invariant. The presence of a nonzero phase space compressibility spoils also the time-reversal invariance of the dynamics. The general Liouville equation is rederived and the properties of statistical averages are accounted for. The features of time correlation functions and linear response theory are also discussed.
Hamiltonian description of the ideal fluid
Energy Technology Data Exchange (ETDEWEB)
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.
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...
Effective Hamiltonian of strained graphene
Linnik, T. L.
2012-05-01
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.
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.
Hamiltonians defined by biorthogonal sets
Bagarello, Fabio; Bellomonte, Giorgia
2017-04-01
In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of G -quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible.
Quantum gates by inverse engineering of a Hamiltonian
Santos, Alan C.
2018-01-01
Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.
Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology
Directory of Open Access Journals (Sweden)
Pinaki Patra
2014-01-01
Full Text Available The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense Lagrangian. We have used this method for the Regge-Teitelboim (RT minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.
Action-minimizing methods in Hamiltonian dynamics
Sorrentino, Alfonso
2015-01-01
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Integrable Hamiltonian systems with swallowtails
Efstathiou, K.; Sugny, D.
2010-01-01
We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint
Maslov index for Hamiltonian systems
Directory of Open Access Journals (Sweden)
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...
On Hamiltonian formulation of cosmologies
Indian Academy of Sciences (India)
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. Keywords. Hamiltonian formulation; some cosmologies. PACS No. 98.80. Hw. It has been shown by Novelloet al [1,2] that it is possible to study perturbations in the ...
Hamiltonian formulation of the supermembrane
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1988-01-01
The hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with
Mathematical Modeling of Constrained Hamiltonian Systems
Schaft, A.J. van der; Maschke, B.M.
1995-01-01
Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the
Simplifying quantum double Hamiltonians using perturbative gadgets
Koenig, Robert
2009-01-01
Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered p...
Noether's first theorem in Hamiltonian mechanics
Sardanashvily, G.
2015-01-01
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase space. This facts enable one to apply Noether's first theorem both to Lagrangian and Hamiltonian mechanics. By virtue of Noether's first theorem, any symmetry defines a symmetry current which is an integral of motion in Lagrangian and Hamiltonian mechanics. The ...
Notch filters for port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.
2012-01-01
In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the
Discrete port Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Clemente Gallardo, J.J.; van der Schaft, Arjan; Horacek, P; Simandl, M; Zitek, P
2005-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
Tronko, Natalia
2015-01-01
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Lastly, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.
Wormhole Hamiltonian Monte Carlo.
Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak
2014-07-31
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.
Hamiltonian dynamics of extended objects
Energy Technology Data Exchange (ETDEWEB)
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
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.
Generic Local Hamiltonians are Gapless
Movassagh, Ramis
2017-12-01
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.
Lagrangian and Hamiltonian formulation of classical electrodynamics without potentials
Vollick, Dan N.
2017-10-01
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials A^{μ} are taken as the dynamical variables. In this paper I take the electric field \\overrightarrow{E} and the magnetic field \\overrightarrow{B} as the dynamical variables. I find a Lagrangian that gives the dynamical Maxwell equations and include the constraint equations by using Lagrange multipliers. In passing to the Hamiltonian one finds that the canonical momenta \\overrightarrow{Π}E and \\overrightarrow{Π}B are constrained giving 6 second class constraints at each point in space. Gauss's law and \\overrightarrow{\
Hamiltonian and Godunov structures of the Grad hierarchy.
Grmela, Miroslav; Hong, Liu; Jou, David; Lebon, Georgy; Pavelka, Michal
2017-03-01
The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures.
Lanting, Trevor; King, Andrew D.; Evert, Bram; Hoskinson, Emile
2017-10-01
Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground-state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states.
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Newer approaches to malaria control.
Damodaran, Se; Pradhan, Prita; Pradhan, Suresh Chandra
2011-07-01
Malaria is the third leading cause of death due to infectious diseases affecting around 243 million people, causing 863,000 deaths each year, and is a major public health problem. Most of the malarial deaths occur in children below 5 years and is a major contributor of under-five mortality. As a result of environmental and climatic changes, there is a change in vector population and distribution, leading to resurgence of malaria at numerous foci. Resistance to antimalarials is a major challenge to malaria control and there are new drug developments, new approaches to treatment strategies, combination therapy to overcome resistance and progress in vaccine development. Now, artemisinin-based combination therapy is the first-line therapy as the malarial parasite has developed resistance to other antimalarials. Reports of artemisinin resistance are appearing and identification of new drug targets gains utmost importance. As there is a shift from malaria control to malaria eradication, more research is focused on malaria vaccine development. A malaria vaccine, RTS,S, is in phase III of development and may become the first successful one. Due to resistance to insecticides and lack of environmental sanitation, the conventional methods of vector control are turning out to be futile. To overcome this, novel strategies like sterile insect technique and transgenic mosquitoes are pursued for effective vector control. As a result of the global organizations stepping up their efforts with continued research, eradication of malaria can turn out to be a reality.
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted P T symmetry in ...
Hamiltonian theory of stochastic acceleration.
Makhnovskii, Yurii A; Pollak, Eli
2006-04-01
Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle's momentum and coordinate. Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling. Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this paper does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in time without bound.
Subthreshold dynamics of a single neuron from a Hamiltonian perspective.
Wilson, M T; Steyn-Ross, D A
2008-12-01
We use Hamilton's equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton's equations. The conjugate momenta are found to be linear combinations of the noise input to the system. We use this approach to consider theoretically and computationally the most likely manner in which such a modeled neuron approaches a firing event. We find that the firing of a neuron is a result of a drop in inhibition, due to a temporary increase in negative bias of the mean noise input to the inhibitory control equation. Moreover, we demonstrate through theory and simulation that, on average, the bias in the noise increases in an exponential manner on the approach to an action potential. In the Hamiltonian description, an action potential can therefore be considered a result of the exponential growth of the conjugate momenta variables pulling the system away from its equilibrium state, into a nonlinear regime.
Conservation Laws and Symmetries for Hamiltonian Systems with Inputs
Schaft, A.J. van der
1984-01-01
After a brief introduction to Hamiltonian Systems with external forces (inputs) we define symmetries and conservations laws for such systems, and prove a generalization of Soether's theorem. Finally we show how this theory can be applied to the solution of optimal control problems.
Elements of (super-)Hamiltonian Formalism
Nersessian, Armen
2005-01-01
In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard texbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction illustrating it by the examples related to Hopf maps. Then we briefly discuss the supergeneralisation(s) of the Hamiltonian formalism and present some simple models of supersymmetric mechanics on K\\"ahler manifolds.
Hamiltonian closures in fluid models for plasmas
Tassi, Emanuele
2017-11-01
This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; Oliver, M.
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; 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
Momentum and hamiltonian in complex action theory
DEFF Research Database (Denmark)
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
Energy Technology Data Exchange (ETDEWEB)
Shikakhwa, M.S., E-mail: mohammad@metu.edu.tr [Department of Physics, The University of Jordan, Amman 11942 (Jordan); Middle East Technical University Northern Cyprus Campus, Kalkanlı, Güzelyurt, via Mersin 10 (Turkey); Chair, N. [Department of Physics, The University of Jordan, Amman 11942 (Jordan)
2016-08-19
The Schrödinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin–orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases, the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schrödinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived. - Highlights: • New physical approach to confine particles to curved surfaces. • Confinement of a particle in a magnetic field to a surface is gauge-independent. • Spin one-half particle with SO coupling confined to a surface.
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 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.
DEFF Research Database (Denmark)
Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu
2012-01-01
the minimax stochastic optimal control strategy based on the stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by the minimax dynamical programming equation with the constraints of disturbance bounds and MR damper dynamics. Finally...... strategy, which is also compared with the clipped linear-quadratic-Gaussian control strategy to show the advantages....
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara
2016-01-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a mode...
Xie, Yu; Jiang, Shengshi; Zheng, Jie; Lan, Zhenggang
2017-12-21
Photoinduced excited-state electron and energy transfer processes are crucial in biological photoharvesting systems and organic photovoltaic devices. We discuss the construction of a diabatic vibronic Hamiltonian for the proper treatment of these processes involving the projection approach acting on both electronic wave functions and vibrational modes. In the electronic part, the wave function projection approach is used to construct the diabatic Hamiltonian in which both local excited states and charge-transfer states are included on the same footing. For the vibrational degrees of freedom, the vibronic couplings in the diabatic Hamiltonian are obtained in the basis of the pseudonormal modes localized on each monomer site by applying delocalized-to-localized mode projection. This systematic approach allows us to construct the vibronic diabatic Hamiltonian in molecular aggregates.
Contamination Control: a systems approach
Donck, J.C.J. van der
2010-01-01
Contamination influences a wide variety of industrial processes. For complex systems, contamination control, the collective effort to control contamination to such a level that it guarantees or even improves process or product functionality, offers a way for finding workable solutions. Central in
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Energy Technology Data Exchange (ETDEWEB)
Khodel, V.A.; Saperstein, E.E.; Zverev, M.V.
1987-04-13
Different effects of the mass operator energy dependence are discussed. They are calculated within the framework of the Hartree-Fock (HF) method with effective forces as RPA corrections to the HF ground state. In the quasiparticle Lagrange method (QLM) they arise naturally and are taken into account in the self-consistent procedure itself. Approaches with the quasiparticle lagrangian and quasiparticle hamiltonian are compared. It is shown that the QLM can also be formulated with the help of the hamiltonian, but a simple lagrangian corresponds to a very complicated hamiltonian. Arguments in favour of the simple lagrangian are presented.
Quantum adiabatic protocols using emergent local Hamiltonians.
Modak, Ranjan; Vidmar, Lev; Rigol, Marcos
2017-10-01
We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial band-insulating states, and how to adiabatically transfer systems from linear and harmonic traps into box traps. Our protocols consist of two stages. The first one involves a free expansion followed by a quench to an emergent local Hamiltonian. In the second stage, the emergent local Hamiltonian is "turned off" quasistatically. For the adiabatic transfer from a harmonic trap, we consider both zero- and nonzero-temperature initial states.
Improved Sufficient Conditions for Hamiltonian Properties
Directory of Open Access Journals (Sweden)
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.
Quantum Hamiltonian Physics with Supercomputers
Energy Technology Data Exchange (ETDEWEB)
Vary, James P.
2014-06-15
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.
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.
Current approaches to myopia control.
Leo, Seo Wei
2017-05-01
Myopia is a global problem, being particularly prevalent in the urban areas of east and southeast Asia. In addition to the direct economic and social burdens, associated ocular complications may lead to substantial vision loss. With prevalence of myopia above 80% and high myopia over 20%, it is crucial to control myopia. The aim of this review to is provide an update on the interventions to slow the onset of myopia and retard its progression. The epidemic of myopia is characterized by increasingly early onset, combined with high myopia progression rates. There are two pathways for myopia control: firstly to slow the onset of myopia and secondly to reduce or prevent progression. Increased time outdoors can reduce the onset of myopia. Atropine 0.01% dose offers an appropriate risk-benefit ratio, with no clinically significant visual side effects balanced against a significant 50% reduction in myopia progression. Orthokeratology contact lenses can slow axial length elongation, but infective keratitis is a risk. Peripheral defocussing lenses may both have a role in slowing myopic progression in a subset of children and further help our understanding of the physiologic control of ocular growth. Myopia control can be achieved by slowing the onset of myopia, which now appears to be possible through increasing time outdoors and slowing the progression of myopia with interventions like atropine and orthokeratology.
The Design of Large Geothermally Powered Air-Conditioning Systems Using an Optimal Control Approach
Horowitz, F. G.; O'Bryan, L.
2010-12-01
The direct use of geothermal energy from Hot Sedimentary Aquifer (HSA) systems for large scale air-conditioning projects involves many tradeoffs. Aspects contributing towards making design decisions for such systems include: the inadequately known permeability and thermal distributions underground; the combinatorial complexity of selecting pumping and chiller systems to match the underground conditions to the air-conditioning requirements; the future price variations of the electricity market; any uncertainties in future Carbon pricing; and the applicable discount rate for evaluating the financial worth of the project. Expanding upon the previous work of Horowitz and Hornby (2007), we take an optimal control approach to the design of such systems. By building a model of the HSA system, the drilling process, the pumping process, and the chilling operations, along with a specified objective function, we can write a Hamiltonian for the system. Using the standard techniques of optimal control, we use gradients of the Hamiltonian to find the optimal design for any given set of permeabilities, thermal distributions, and the other engineering and financial parameters. By using this approach, optimal system designs could potentially evolve in response to the actual conditions encountered during drilling. Because the granularity of some current models is so coarse, we will be able to compare our optimal control approach to an exhaustive search of parameter space. We will present examples from the conditions appropriate for the Perth Basin of Western Australia, where the WA Geothermal Centre of Excellence is involved with two large air-conditioning projects using geothermal water from deep aquifers at 75 to 95 degrees C.
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.
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.
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.
Supersymmetric analysis of a spin Hamiltonian model
Energy Technology Data Exchange (ETDEWEB)
Demircioglu, B. [Saraykoey Nuclear Research and Training Center, Saraykoey /Ankara (Turkey); Bilge Ocak, S. [Saraykoey Nuclear Research and Training Center, Saraykoey/Ankara (Turkey)]. E-mail: semamuzo@yahoo.com; Kuru, S. [Department of Physics, Ankara University, Faculty of Science, 06100 Tandogan/Ankara (Turkey)
2006-04-17
The intertwining method has been applied to the effective potential of the spin Hamiltonian H=-{gamma}S{sub z}{sup 2}-BS{sub x}. The supersymmetric partner potentials, some of which are singular, are obtained by using low-lying states of this potential. Applying the intertwining method successively, hierarchy of effective potentials has been established. Supersymmetric partner of the transformed spin Hamiltonian's effective potential has also been constructed.
An application of Hamiltonian neurodynamics using Pontryagin's Maximum (Minimum) Principle.
Koshizen, T; Fulcher, J
1995-12-01
Classical optimal control methods, notably Pontryagin's Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagations (SBP) on the XOR problem.
STRUCTURAL APPROACH TO THE CONTROLLING
Directory of Open Access Journals (Sweden)
LOREDANA CIURLĂU
2016-10-01
Full Text Available Economic concentration has led to the emergence of large enterprises and complex that by the activities or the environment of their operation because of an activity of decentralization. The enterprise is cut in centers of responsibility which enjoys a autonomy more or less widely. The management control will be able to meet the needs of coordination of these organizations decentralised, orienting the "actors" within the meaning of the desired by the manager through the evaluation of the results obtained. The success of an enterprise requires a continuous adapting it to the environment or and competitiveness is transformed into a economic criterion by excellence.
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Hamiltonian Dynamics of Doubly-Foliable Space-Times
Directory of Open Access Journals (Sweden)
Cecília Gergely
2018-01-01
Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.
Extended hamiltonian formalism and Lorentz-violating lagrangians
Colladay, Don
2017-09-01
A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
Electronic Structure Calculations and the Ising Hamiltonian.
Xia, Rongxin; Bian, Teng; Kais, Sabre
2017-11-20
Obtaining exact solutions to the Schrödinger equation for atoms, molecules, and extended systems continues to be a "Holy Grail" problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new devices is, "Can these machines be used to perform electronic structure calculations?" Within this work, we review the general procedure used by these devices and prove that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. Additionally, we provide simulation results of the transformed Ising Hamiltonian for H2 , He2 , HeH+, and LiH molecules, which match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. This is an early step in developing generalized methods on such devices for chemical physics.
Trojan dynamics well approximated by a new Hamiltonian normal form
Páez, Rocío Isabel; Locatelli, Ugo
2015-10-01
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Non-Hamiltonian perturbation theory for deformable fast rotators
Varadi, F.; Moore, W. B.
2005-05-01
Deformable fast rotators, such as the Earth and Mars, change both their rotational states (spin axis direction) and shapes due to external forces and internal material motions. The standard approach to rigid-body dynamics is Hamiltonian perturbation theory in canonical action-angle (Andoyer) variables which incorporate the moments of inertia form the outset. Dealing with deformations is usually based on linear perturbation theory around rigid-body reference solutions which yields transfer functions from the rigid to the deformable case. We present the elements of a general, non-Hamiltonian perturbation theory in non-canonical variables based on Lie series. First, we present general results on non-Hamiltonian perturbation theory and averaging, such as a coordinate-free formula for the solution of the homological equation of the Lie series in the case of perturbed periodic orbits. In general, the averaged system does not fully Lie-commute with the unperturbed system and the reduction of the averaged system to the orbit space of unperturbed system has to allow for drift along the unperturbed orbits. In the case of a fast rotator, we start with rotation around the spin axis as the unperturbed system. The orientation of the body is represented as a rotation matrix and we derive the appropriate Lie bracket. After averaging over the rotation period, we reduce the system by eliminating the phase variable associated with pure rotation around the spin axis. The reduced system is expressed in terms of the spin axis in both inertial and body frames. We compare our results to those of traditional Hamiltonian theories and numerical simulations. This work is supported by NSF Planetary Astronomy.
Stability, bifurcation, and control of Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Marsden, J.E. (California Univ., Berkeley, CA (United States). Dept. of Mathematics); Ratiu, T.S. (California Univ., Santa Cruz, CA (United States). Dept. of Mathematics)
1993-01-01
Work is being done on dissipation-induced instabilities, gyroscopic stabilization and its destruction by a small damping for both finite dimensional and certain infinite dimensional systems (such as rotating rods, strings), nonabelian and abelian cases, Euler-Lagrange-Poincare equations, the Routhian having a form of a Lagrangian with a gyroscopic term, Euler-Lagrange equations, etc.
Stability, bifurcation, and control of Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Marsden, J.E. [California Univ., Berkeley, CA (United States). Dept. of Mathematics; Ratiu, T.S. [California Univ., Santa Cruz, CA (United States). Dept. of Mathematics
1993-04-01
Work is being done on dissipation-induced instabilities, gyroscopic stabilization and its destruction by a small damping for both finite dimensional and certain infinite dimensional systems (such as rotating rods, strings), nonabelian and abelian cases, Euler-Lagrange-Poincare equations, the Routhian having a form of a Lagrangian with a gyroscopic term, Euler-Lagrange equations, etc.
Fuzzy Approach to Statistical Control Charts
Directory of Open Access Journals (Sweden)
Shahryar Sorooshian
2013-01-01
Full Text Available After investigating the advantages and disadvantages of current methods of statistical process control, it becomes important to overcome the disadvantages and then use the advantages to improve a method for monitoring a process with categorical observations. An approach which considers uncertainty and vagueness is tried for this study; and for this purpose, fuzzy set theory is inevitable to use. So, a new approach based on fuzzy set theory is introduced in this research for monitoring attribute quality characteristics. This approach is then compared with the current related approach to see the difference in performance.
Gravitational surface Hamiltonian and entropy quantization
Directory of Open Access Journals (Sweden)
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Integrability Of Non-KAM Hamiltonians
Salat, A.
1984-09-01
The integrability of Hamiltonians of the type H(P1, P2, Q1, Q2) = ? Pi ·Gi (Q1, Q2), Gi 2 π-periodic in Q1, Q2, is investigated numerically and analytically. With Gi = ωi + Fi (Q1, Q2) and = H0 = ? ωi + Pi, the unperturbed frequencies ωi = ∂H0/∂Pi, are independent of the momenta, and KAM theory cannot be applied. Surface of section plots and Fourier analysis of orbits reveal that "most" Hamiltonians are integrable. Possibly non-integrable Hamiltonians do not show "island plus ergodic region" structure but sequences which tend towards infinity. No theory is available to distinguish completely the classes of integrable and non-integrable functions Gi(Q1,Q2). In such a theory the problem of "small denominators" would play an essential role just as in KAM theory.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Samanta, Saurav
2016-01-01
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.
Gravitational surface Hamiltonian and entropy quantization
Energy Technology Data Exchange (ETDEWEB)
Bakshi, Ashish, E-mail: ashishbakshi@outlook.com [Indian Statistical Institute, 203 B.T. Road, Kolkata-700108 (India); Majhi, Bibhas Ranjan, E-mail: bibhas.majhi@iitg.ernet.in [Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam (India); Samanta, Saurav, E-mail: srvsmnt@gmail.com [Narasinha Dutt College, 129, Belilious Road, Howrah-711101 (India)
2017-02-10
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.
Polynomial entropies for Bott nondegenerate Hamiltonian systems
Labrousse, Clémence; Marco, Jean-Pierre
2012-01-01
In this paper, we study the entropy of a Hamiltonian flow in restriction to an enregy level where it admits a first integral which is nondegenerate in the Bott sense. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies. We prove that, under conditions on the critical level of the Bott first integral and dynamical conditions on the hamiltonian function, the weak polynomial entropy belongs to {0,1} and the polyno...
Systems Approach to Arms Control Verification
Energy Technology Data Exchange (ETDEWEB)
Allen, K; Neimeyer, I; Listner, C; Stein, G; Chen, C; Dreicer, M
2015-05-15
Using the decades of experience of developing concepts and technologies for verifying bilateral and multilateral arms control agreements, a broad conceptual systems approach is being developed that takes into account varying levels of information and risk. The IAEA has already demonstrated the applicability of a systems approach by implementing safeguards at the State level, with acquisition path analysis as the key element. In order to test whether such an approach could also be implemented for arms control verification, an exercise was conducted in November 2014 at the JRC ITU Ispra. Based on the scenario of a hypothetical treaty between two model nuclear weapons states aimed at capping their nuclear arsenals at existing levels, the goal of this exercise was to explore how to use acquisition path analysis in an arms control context. Our contribution will present the scenario, objectives and results of this exercise, and attempt to define future workshops aimed at further developing verification measures that will deter or detect treaty violations.
Fuzzy Approach to Statistical Control Charts
Shahryar Sorooshian
2013-01-01
After investigating the advantages and disadvantages of current methods of statistical process control, it becomes important to overcome the disadvantages and then use the advantages to improve a method for monitoring a process with categorical observations. An approach which considers uncertainty and vagueness is tried for this study; and for this purpose, fuzzy set theory is inevitable to use. So, a new approach based on fuzzy set theory is introduced in this research for monitoring attribu...
Numerical bifurcation of Hamiltonian relative periodic orbits
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2009-01-01
Relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and the motion of rigid bodies. RPOs are solutions which are periodic orbits of the symmetry-reduced system. In this paper we analyze certain symmetry...
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
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
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,
The HELP inequality for Hamiltonian systems
Directory of Open Access Journals (Sweden)
Evans WD
1999-01-01
Full Text Available We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994 but without the Hilbert space setting which he uses.
Predictive Approaches to Control of Complex Systems
Karer, Gorazd
2013-01-01
A predictive control algorithm uses a model of the controlled system to predict the system behavior for various input scenarios and determines the most appropriate inputs accordingly. Predictive controllers are suitable for a wide range of systems; therefore, their advantages are especially evident when dealing with relatively complex systems, such as nonlinear, constrained, hybrid, multivariate systems etc. However, designing a predictive control strategy for a complex system is generally a difficult task, because all relevant dynamical phenomena have to be considered. Establishing a suitable model of the system is an essential part of predictive control design. Classic modeling and identification approaches based on linear-systems theory are generally inappropriate for complex systems; hence, models that are able to appropriately consider complex dynamical properties have to be employed in a predictive control algorithm. This book first introduces some modeling frameworks, which can encompass the most frequ...
[The hierarchy of approaches to tobacco control
Squier, Ch
2001-01-01
Tobacco represents the single most preventable cause of disease and death in the world today. Of 260 million male deaths in the developed world between 1950 and 2000, it is estimated that 50 million will be due to smoking. In the oral and craniofacial region tobacco use has been associated with the occurrence of cleft palate, periodontal disease and tooth loss, and a variety of soft tissue lesions including oral cancer. For example, smoking is estimated to account for 92% of cancers of the lip, oral cavity and pharynx. Few studies have examined relative efficiency of the many different approaches to tobacco control but, in general, legislative approaches such as increasing tobacco taxes and prohibiting advertising are most effective and those based on printed educational materials and cessation groups, the least effective. In all cases, advice or intervention by health care professionals ranked among the most effective non-legislative approaches to control. A very wide range of professionally-based interventions have been described, including pharmacologic interventions, behavioral approaches and group counseling. The dental profession has a unique opportunity to influence tobacco use by their patients. Its use is almost always immediately evident to the dentist or dental assistant in terms of odor, staining, poor oral hygiene or obvious oral disease. There is also a tendency for the length of personal contact with the dentist to be greater than with a physician. Guidelines are now available that provide the dental professional with advice on the best approaches to tobacco control with their patients.
The Behavioural Approach to Systems and Control
Willems, Jan C.
1996-01-01
The purpose of this paper is to provide an informal introduction to the behavioural approach to systems and control. We start with some historical observations. Then we turn to the modelling of dynamical systems and argue that interconnected systems lead to models involving both manifest and latent
A Modular Approach to Redundant Robot Control
Energy Technology Data Exchange (ETDEWEB)
Anderson, R.J.
1997-12-01
This paper describes a modular approach for computing redundant robot kinematics. First some conventional redundant control methods are presented and shown to be `passive control laws`, i.e. they can be represented by a network consisting of passive elements. These networks are then put into modular form by applying scattering operator techniques. Additional subnetwork modules can then be added to further shape the motion. Modules for obstacle detection, joint limit avoidance, proximity sensing, and for imposing nonlinear velocity constraints are presented. The resulting redundant robot control system is modular, flexible and robust.
Controllable Load Management Approaches in Smart Grids
Directory of Open Access Journals (Sweden)
Jingshuang Shen
2015-10-01
Full Text Available With rapid smart grid technology development, the customer can actively participate in demand-side management (DSM with the mutual information communication between the distributor operation company and the smart devices in real-time. Controllable load management not only has the advantage of peak shaving, load balance, frequency regulation, and voltage stability, but is also effective at providing fast balancing services to the renewable energy grid in the distributed power system. The load management faces an enormous challenge as the customer has a large number of both small residential loads and dispersed renewable sources. In this paper, various controllable load management approaches are discussed. The traditional controllable load approaches such as the end users’ controllable appliances, storage battery, Vehicle-to-Grid (V2G, and heat storage are reviewed. The “broad controllable loads” management, such as the microgrid, Virtual Power Plant (VPP, and the load aggregator are also presented. Furthermore, the load characteristics, control strategies, and control effectiveness are analyzed.
Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems
Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.
2012-02-01
Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.
On Hamiltonian cycles of power graphs of abelian groups
Mukherjee, Himadri
2015-01-01
In this article we discuss the question of presence of Hamiltonian cycle in the un-directed power graph of a group. In the process we develop weighted Hamiltonian cycle concept and prove a few general results regarding the Hamiltonian question.
Effective Floquet Hamiltonian for spin = 1 in magic angle spinning ...
Indian Academy of Sciences (India)
Contact transformation is an operator transformation method in time-independent perturbation theory which is used successfully in molecular spectroscopy to obtain an effective Hamiltonian. Floquet theory is used to transform the periodic time-dependent Hamiltonian, to a time-independent Floquet Hamiltonian. In this ...
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Operator approach to linear control systems
Cheremensky, A
1996-01-01
Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......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.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
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 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.
Hamiltonian deformations of Gabor frames: First steps.
de Gosson, Maurice A
2015-03-01
Gabor frames can advantageously be redefined using the Heisenberg-Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed - as the title suggests - as the very first steps towards a general deformation theory for Gabor frames.
Hamiltonian theory of guiding-center motion
Energy Technology Data Exchange (ETDEWEB)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
The Effective Hamiltonian in the Scalar Electrodynamics
Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K
2002-01-01
On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.
Edge-disjoint Hamiltonian cycles in hypertournaments
DEFF Research Database (Denmark)
Thomassen, Carsten
2006-01-01
We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only i......) 2005 Wiley Periodicals, Inc....
Hamiltonian gyrokinetic Vlasov-Maxwell system
Burby, J. W.; Brizard, A. J.; Morrison, P. J.; Qin, H.
2015-09-01
A new formulation of electromagnetic gyrokinetics that possesses Hamiltonian form is constructed. The new formulation replaces Poisson-like equations by hyperbolic equations for the electromagnetic field with the speed of light slowed to that of the gyrokinetic vacuum, thereby significantly reducing computational cost. An energy principle is derived using the field-theoretic noncanonical Poisson bracket formulation of the theory. The energy principle is used to prove stability of the thermal equilibrium state in a uniform background magnetic field.
Diffusion in a weakly random Hamiltonian flow
Komorowski, T.; Ryzhik, L.
2005-01-01
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves...
Alternative approaches to control--quo vadit?
Jackson, Frank; Miller, Jim
2006-07-31
The increasing prevalence of anthelmintic resistance has provided a spur for research into 'alternative/novel' approaches to the control of helminthoses that are intended to reduce our reliance upon using chemoprophylaxis. The different approaches either target the parasite population in the host or on pasture, but the goal of all of them is to restrict host parasite contact to levels which minimise the impact of helminths on host welfare and/or performance. Infrapopulation regulation can be achieved through methods that enhance immunity such as optimised nutrition (immunonutrition), genetic selection and vaccination, or by an 'anthelmintic' route using bioactive forages, copper oxide wire particles, or use of targeted selective treatment strategies such as FAMACHA, which reduce the selection pressure for the development of resistance by maintaining a population in refugia. Suprapopulation control can be achieved through grazing management, or by using predacious fungi such as Duddingtonia flagrans. All of these approaches have been developed beyond the proof of concept stage and some are capable of being employed currently. However, some still require knowledge transfer, or commercialisation before they can be tested and widely applied in the field. All of the different approaches present unique challenges to the researchers engaged in developing them, and in comparison to simple prescriptive anthelmintic treatments, their use appears complex and requires some expertise on behalf of the advisor and/or end user. At present, most of our data are derived from trials using single approaches, but it is apparent that we need to move towards integrating some of these technologies which again represents a further challenge to the extension/advisory services. Progress in establishing different approaches requires not only the funding to support their scientific development but also to support the development of computer based models which can be used to highlight
Optimal Hamiltonian Simulation by Quantum Signal Processing.
Low, Guang Hao; Chuang, Isaac L
2017-01-06
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error ε is O[td∥H[over ^]∥_{max}+log(1/ε)/loglog(1/ε)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Continuum balances from extended Hamiltonian dynamics.
Giusteri, Giulio G; Podio-Guidugli, Paolo; Fried, Eliot
2017-06-14
The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach. We here propose a physically consistent application of the Irving-Kirkwood-Noll procedure to the extended Hamiltonian systems of material points. Our procedure produces balance equations at the continuum level featuring non-standard terms because the presence of auxiliary degrees of freedom gives rise to additional fluxes and sources that influence the thermodynamic and transport properties of the continuum model. Being aware of the additional contributions may prove crucial when designing multiscale computational schemes in which information is exchanged between the atomistic and continuum levels.
Hamiltonian mechanics limits microscopic engines
Anglin, James; Gilz, Lukas; Thesing, Eike
2015-05-01
We propose a definition of fully microscopic engines (micro-engines) in terms of pure mechanics, without reference to thermodynamics, equilibrium, or cycles imposed by external control, and without invoking ergodic theory. This definition is pragmatically based on the observation that what makes engines useful is energy transport across a large ratio of dynamical time scales. We then prove that classical and quantum mechanics set non-trivial limits-of different kinds-on how much of the energy that a micro-engine extracts from its fuel can be converted into work. Our results are not merely formal; they imply manageable design constraints on micro-engines. They also suggest the novel possibility that thermodynamics does not emerge from mechanics in macroscopic regimes, but rather represents the macroscopic limit of a generalized theory, valid on all scales, which governs the important phenomenon of energy transport across large time scale ratios. We propose experimental realizations of the dynamical mechanisms we identify, with trapped ions and in Bose-Einstein condensates (``motorized bright solitons'').
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.
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Directory of Open Access Journals (Sweden)
Vladimir S. Gerdjikov
2006-02-01
Full Text Available The construction of a family of real Hamiltonian forms (RHF for the special class of affine 1+1-dimensional Toda field theories (ATFT is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.
A unified theoretical framework for mapping models for the multi-state Hamiltonian.
Liu, Jian
2016-11-28
We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model.
Comparison of Routable Control System Security Approaches
Energy Technology Data Exchange (ETDEWEB)
Edgar, Thomas W.; Hadley, Mark D.; Carroll, Thomas E.; Manz, David O.; Winn, Jennifer D.
2011-06-01
This document is an supplement to the 'Secure and Efficient Routable Control Systems.' It addressed security in routable control system communication. The control system environment that monitors and manages the power grid historically has utilized serial communication mechanisms. Leased-line serial communication environments operating at 1200 to 9600 baud rates are common. However, recent trends show that communication media such as fiber, optical carrier 3 (OC-3) speeds, mesh-based high-speed wireless, and the Internet are becoming the media of choice. In addition, a dichotomy has developed between the electrical transmission and distribution environments, with more modern communication infrastructures deployed by transmission utilities. The preceding diagram represents a typical control system. The Communication Links cloud supports all of the communication mechanisms a utility might deploy between the control center and devices in the field. Current methodologies used for security implementations are primarily led by single vendors or standards bodies. However, these entities tend to focus on individual protocols. The result is an environment that contains a mixture of security solutions that may only address some communication protocols at an increasing operational burden for the utility. A single approach is needed that meets operational requirements, is simple to operate, and provides the necessary level of security for all control system communication. The solution should be application independent (e.g., Distributed Network Protocol/Internet Protocol [DNP/IP], International Electrotechnical Commission [IEC] C37.118, Object Linking and Embedding for Process Control [OPC], etc.) and focus on the transport layer. In an ideal setting, a well-designed suite of standards for control system communication will be used for vendor implementation and compliance testing. An expected outcome of this effort is an international standard.
The solution of the Schroedinger equation for complex Hamiltonian systems in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Chand, Fakir [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Singh, Ram Mehar [Department of Physics, Haryana College of Technology and Management, Kaithal-136 027, Haryana (India); Kumar, Narender [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Mishra, S C [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India)
2007-08-17
We investigate the ground state solutions of the Schroedinger equation for complex (non-Hermitian) Hamiltonian systems in two dimensions within the framework of an extended complex phase-space approach. The eigenvalues and eigenfunctions of some two-dimensional complex potentials are found.
Controlling vibrational cooling with zero-width resonances: An adiabatic Floquet approach
Leclerc, Arnaud; Viennot, David; Jolicard, Georges; Lefebvre, Roland; Atabek, Osman
2016-10-01
In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected zero-width resonances (ZWRs) with, in principle, infinite lifetimes. Their potential to induce basic quenching mechanisms has recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A 87, 031403(R) (2013), 10.1103/PhysRevA.87.031403]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelope-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage of its continuous transport on the corresponding ZWR all along the pulse duration. As compared with previous control scenarios that actually suffered from nonadiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps us to find and interpret a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, turns out to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, which has the potential to be transposed to other diatomics, is Na2 prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.
Transgenic approaches to western corn rootworm control.
Narva, Kenneth E; Siegfried, Blair D; Storer, Nicholas P
2013-01-01
The western corn rootworm, Diabrotica virgifera virgifera LeConte (Coleoptera: Chrysomelidae) is a significant corn pest throughout the United States corn belt. Rootworm larvae feed on corn roots causing yield losses and control expenditures that are estimated to exceed US$1 billion annually. Traditional management practices to control rootworms such as chemical insecticides or crop rotation have suffered reduced effectiveness due to the development of physiological and behavioral resistance. Transgenic maize expressing insecticidal proteins are very successful in protecting against rootworm damage and preserving corn yield potential. However, the high rate of grower adoption and early reliance on hybrids expressing a single mode of action and low-dose traits threatens the durability of commercialized transgenic rootworm technology for rootworm control. A summary of current transgenic approaches for rootworm control and the corresponding insect resistance management practices is included. An overview of potential new modes of action based on insecticidal proteins, and especially RNAi targeting mRNA coding for essential insect proteins is provided.
Approaches to Learning to Control Dynamic Uncertainty
Directory of Open Access Journals (Sweden)
Magda Osman
2015-10-01
Full Text Available In dynamic environments, when faced with a choice of which learning strategy to adopt, do people choose to mostly explore (maximizing their long term gains or exploit (maximizing their short term gains? More to the point, how does this choice of learning strategy influence one’s later ability to control the environment? In the present study, we explore whether people’s self-reported learning strategies and levels of arousal (i.e., surprise, stress correspond to performance measures of controlling a Highly Uncertain or Moderately Uncertain dynamic environment. Generally, self-reports suggest a preference for exploring the environment to begin with. After which, those in the Highly Uncertain environment generally indicated they exploited more than those in the Moderately Uncertain environment; this difference did not impact on performance on later tests of people’s ability to control the dynamic environment. Levels of arousal were also differentially associated with the uncertainty of the environment. Going beyond behavioral data, our model of dynamic decision-making revealed that, in actual fact, there was no difference in exploitation levels between those in the highly uncertain or moderately uncertain environments, but there were differences based on sensitivity to negative reinforcement. We consider the implications of our findings with respect to learning and strategic approaches to controlling dynamic uncertainty.
Immunocontraceptives: New Approaches to Fertility Control
Directory of Open Access Journals (Sweden)
Kiranjeet Kaur
2014-01-01
Full Text Available The rapidly increasing global population has bowed the attention of family planning and associated reproductive health programmes in the direction of providing a safe and reliable method which can be used to limit family size. The world population is estimated to exceed a phenomenal 10 billion by the year 2050 A.D., thus presenting a real jeopardy of overpopulation with severe implications for the future. Despite the availability of contraceptive methods, there are over one million elective abortions globally each year due to unintended pregnancies, having devastating impact on reproductive health of women worldwide. This highlights the need for the development of newer and improved contraceptive methods. A novel contraceptive approach that is gaining substantial attention is “immunocontraception” targeting gamete production, gamete outcome, or gamete function. Amongst these, use of sperm antigens (gamete function seems to be an exciting and feasible approach. However, the variability of immune response and time lag to attain titer among vaccinated individuals after active immunization has highlighted the potential relevance of preformed antibodies in this league. This review is an attempt to analyze the current status and progress of immunocontraceptive approaches with respect to their establishment as a future fertility control agent.
Modelling very-high-eccentricity asteroidal librations with the Andoyer Hamiltonian.
Simula, A.; Ferraz-Mello, S.; Giordano, C.
High eccentricity asteroidal librations are modelled using a tailored Hamiltonian which is built from the high eccentricity non planar asymmetric expansion (Roig et al. 1998). We show that, using the reducing Sessin's rotation, the Hamiltonian of the pseudo circular model is actually a first order Andoyer Hamiltonian. This Hamiltonian has already been used by Henrard, at least for a numerical study, as a second fundamental model for resonance. A different approach was followed by Ferraz-Mello, who carried on the integration of the equations of motion in formal way by the use of the Jacobian elliptic functions. This second approach permits an explicit description of the asteroidal dynamics combined with a very precise analytical computation of the frequencies. We use this analytical approach for the study of asteroidal librations. Secular perturbations of the perturber's orbit can also be considered in the dynamics, together with the short periodic variations of Jupiter's orbit associated to the 5/2 near-commensurability between Jupiter and Saturn. Some preliminary results are shown.
Statistical mechanics of Hamiltonian adaptive resolution simulations.
Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K
2015-02-14
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
Fractal boundaries in chaotic hamiltonian systems
Viana, R. L.; Mathias, A. C.; Marcus, F. A.; Kroetz, T.; Caldas, I. L.
2017-10-01
Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.
Model Hamiltonians for atomic and molecular systems
Carlson, J.; Moskowitz, Jules W.; Schmidt, K. E.
1989-01-01
A model Hamiltonian, designed to allow larger systems to be treated with the Green's function Monte Carlo method, is introduced for atomic and molecular systems. The model reduces the statistical variance associated with Green's function Monte Carlo calculations by reducing potential energy fluctuations in the core regions. By performing calculations of Li, LiH, and Li2 we show that this method can be used to obtain energy differences with much less computer time than required for the complete interaction. Increases in efficiency for larger systems will be even greater.
Reducing the generalised Sudoku problem to the Hamiltonian cycle problem
Directory of Open Access Journals (Sweden)
Michael Haythorpe
2016-12-01
Full Text Available The generalised Sudoku problem with N symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where N is a perfect square. In particular, generalised Sudoku is equivalent to the, classical, Hamiltonian cycle problem. A constructive algorithm is given that reduces generalised Sudoku to the Hamiltonian cycle problem, where the resultant instance of Hamiltonian cycle problem is sparse, and has O(N3 vertices. The Hamiltonian cycle problem instance so constructed is a directed graph, and so a (known conversion to undirected Hamiltonian cycle problem is also provided so that it can be submitted to the best heuristics. A simple algorithm for obtaining the valid Sudoku solution from the Hamiltonian cycle is provided. Techniques to reduce the size of the resultant graph are also discussed.
CPT and effective Hamiltonians for neutral kaon and similar complexes
Urbanowski, K.
2002-01-01
We begin with a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next, the properties of the exact effective Hamiltonian for this complex are discussed. Using the Khalfin Theorem we show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t...
Datamining approaches for modeling tumor control probability.
Naqa, Issam El; Deasy, Joseph O; Mu, Yi; Huang, Ellen; Hope, Andrew J; Lindsay, Patricia E; Apte, Aditya; Alaly, James; Bradley, Jeffrey D
2010-11-01
Tumor control probability (TCP) to radiotherapy is determined by complex interactions between tumor biology, tumor microenvironment, radiation dosimetry, and patient-related variables. The complexity of these heterogeneous variable interactions constitutes a challenge for building predictive models for routine clinical practice. We describe a datamining framework that can unravel the higher order relationships among dosimetric dose-volume prognostic variables, interrogate various radiobiological processes, and generalize to unseen data before when applied prospectively. Several datamining approaches are discussed that include dose-volume metrics, equivalent uniform dose, mechanistic Poisson model, and model building methods using statistical regression and machine learning techniques. Institutional datasets of non-small cell lung cancer (NSCLC) patients are used to demonstrate these methods. The performance of the different methods was evaluated using bivariate Spearman rank correlations (rs). Over-fitting was controlled via resampling methods. Using a dataset of 56 patients with primary NCSLC tumors and 23 candidate variables, we estimated GTV volume and V75 to be the best model parameters for predicting TCP using statistical resampling and a logistic model. Using these variables, the support vector machine (SVM) kernel method provided superior performance for TCP prediction with an rs=0.68 on leave-one-out testing compared to logistic regression (rs=0.4), Poisson-based TCP (rs=0.33), and cell kill equivalent uniform dose model (rs=0.17). The prediction of treatment response can be improved by utilizing datamining approaches, which are able to unravel important non-linear complex interactions among model variables and have the capacity to predict on unseen data for prospective clinical applications.
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.
IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Borisov, Alexey V; Mamaev, Ivan S; Sokolovskiy, Mikhail A; IUTAM BOOKSERIES : Volume 6
2008-01-01
This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects of the processes of formation and evolution of various flows, wave a...
Agricultural water pollution control: An interdisciplinary approach
Miller, Watkins W.; Ching, Chauncey T. K.; Yanagida, John F.; Jakus, Paul
1985-01-01
Regulation and control of agricultural water pollution is unique and difficult to accomplish. Water quality standards are often proposed without adequate consideration of the overall economic impact on agricultural production. This article illustrates how economists and physical scientists can cooperate to develop appropriate control strategies for agricultural water pollution. Data provided by physical scientists and economists are used in a linear programming model to describe salt discharge as a function of water management, production levels, and an associated effluent charge. Four water management activities were chosen on the basis of different costs of production (including a parametrically varied effluent charge), water requirements, alfalfa yields, and levels of salt discharge. Results indicate that when the effluent charge is low (profitable. As the effluent charge is increased (0.20 0.40/metric ton salt discharged), it becomes progressively less profitable to produce alfalfa at maximum levels of pollutant discharge. When the effluent charge is >0.40/metric ton salt discharged, alfalfa production is no longer economically feasible. An important aspect of this approach is that it permits policy makers to identify explicitly the relationship between the environmental standard and the effect on agricultural production.
Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems
Doroshin, Anton V.
2010-03-01
This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a ``Spider-type System,'' also it can be called ``Rotary Hedgehog.'' These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.
A family of asymptotically stable control laws for flexible robots based on a passivity approach
Lanari, Leonardo; Wen, John T.
1991-01-01
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.
Spectral analysis of the direct sum Hamiltonian operators ...
African Journals Online (AJOL)
... the Sz.-Nagy-Foias characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces. Keywords: Hamiltonian system, dissipative operator, characteristic function, scattering matrix, ...
Bifurcations in Hamiltonian systems with a reflecting symmetry
Bosschaert, M.; Hanssmann, H.
2011-01-01
A reflecting symmetry q 7→ −q of a Hamiltonian system does not leave the symplectic structure dq∧dp invariant and is therefore usually asso- ciated with a reversible Hamiltonian system. However, if q 7→ −q leads to H 7→ −H, then the equations of motion are invariant under the re- flection. This
The Group of Hamiltonian Automorphisms of a Star Product
Energy Technology Data Exchange (ETDEWEB)
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
... v ) ) for various choices of the function (), where (, ) is the distance between vertices and in . In this paper, we give some sufficient conditions for a connected graph to be Hamiltonian, a connected graph to be traceable, and a connected bipartite graph to be Hamiltonian in terms of the Wiener-type invariants ...
Periodic Hamiltonian hierarchies and non-uniqueness of ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 1. Periodic Hamiltonian hierarchies and ... ABHIJIT BANERJEE. Regular Volume 88 Issue 1 January 2017 Article ID 1 ... Abstract. In this article, a family of periodic quantum Hamiltonians, that is subject to a closure condition is considered. In the context of the ...
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
On the minimization of Hamiltonians over pure Gaussian states
DEFF Research Database (Denmark)
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown that this proce...
Symmetry and reduction in implicit generalized Hamiltonian systems
Blankenstein, G.; van der Schaft, Arjan
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this
Symmetry and Reduction in Implicit Generalized Hamiltonian Systems
Blankenstein, G.; Schaft, A.J. van der
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding conserved quantities. Main features
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
In this article, we write the general form of the quasiexactly solvable Hamiltonian of g2 algebra via one special ... In general, there are two types of problems in such systems: the quasiexactly solvable (QES) models .... we should not consider writing the general form of the QES Hamiltonian of g2 algebra. If we take the whole ...
Boundary Liouville Theory: Hamiltonian Description and Quantization
Directory of Open Access Journals (Sweden)
Harald Dorn
2007-01-01
Full Text Available The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator $e^varphi$ in terms of free field exponentials is constructed in the hyperbolic sector.
Classical Mechanics Hamiltonian and Lagrangian Formalism
Deriglazov, Alexei
2010-01-01
Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the...
Linear Design Approach to a Fuzzy Controller
DEFF Research Database (Denmark)
Jantzen, Jan
1999-01-01
A ball-balancer, basically an inverted pendulum problem, is stabilised by a linear controller. With certain design choices, a fuzzy controller is equivalent to a summation; thus it can replace the linear controller. It can be claimed, that the fuzzy controller performs at least as well as the lin......A ball-balancer, basically an inverted pendulum problem, is stabilised by a linear controller. With certain design choices, a fuzzy controller is equivalent to a summation; thus it can replace the linear controller. It can be claimed, that the fuzzy controller performs at least as well...
Open quantum systems, effective Hamiltonians, and device characterization
Duffus, S. N. A.; Dwyer, V. M.; Everitt, M. J.
2017-10-01
High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the form X ̂P ̂+P ̂X ̂ should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.
Wang, Kai; Yang, Yanzhi; Chodera, John D.; Shirts, Michael R.
2014-01-01
We present a method to identify small molecule ligand binding sites and orientations to a given protein crystal structure using GPU-accelerated Hamiltonian replica exchange molecular dynamics simulations. The Hamiltonians used vary from the physical end state of protein interacting with the ligand to a unphysical end state where the ligand does not interact with the protein. As replicas explore the space of Hamiltonians interpolating between these states the ligand can rapidly escape local minima and explore potential binding sites. Geometric restraints keep the ligands within the protein volume, and a potential energy pathway designed to increase phase space overlap between intermediates ensures good mixing. Because of the rigorous statistical mechanical nature of the Hamiltonian exchange framework, we can also extract binding free energy estimates at all putative binding sites, which agree well with free energies computed from occupation probabilities. We present results of this methodology on the T4 lysozyme L99A model system with four ligands, including one non-binder as a control. We find that our methodology identifies the crystallographic binding sites consistently and accurately for the small number of ligands considered here and gives free energies consistent with experiment. We are also able to analyze the contribution of individual binding sites on the overall binding affinity. Our methodology points to near term potential applications in early-stage drug discovery. PMID:24297454
A shooting approach to suboptimal control
Hull, David G.; Sheen, Jyh-Jong
1991-01-01
The shooting method is used to solve the suboptimal control problem where the control history is assumed to be piecewise linear. Suboptimal solutions can be obtained without difficulty and can lead to accurate approximate controls and good starting multipliers for the regular shooting method by increasing the number of nodes. Optimal planar launch trajectories are presented for the advanced launch system.
Trait approach motivation moderates the aftereffects of self-control
Directory of Open Access Journals (Sweden)
Adrienne eCrowell
2014-09-01
Full Text Available Numerous experiments have found that exercising self-control reduces success on subsequent, seemingly unrelated self-control tasks. Such evidence lends support to a strength model that posits a limited and depletable resource underlying all manner of self-control. Recent theory and evidence suggest that exercising self-control may also increase approach-motivated impulse strength. The two studies reported here tested two implications of this increased approach motivation hypothesis. First, aftereffects of self-control should be evident even in responses that require little or no self-control. Second, participants higher in trait approach motivation should be particularly susceptible to such aftereffects. In support, exercising self-control led to increased optimism (Study 1 and broadened attention (Study 2, but only among individuals higher in trait approach motivation. These findings suggest that approach motivation is an important key to understanding the aftereffects of exercising self-control.
Trait approach motivation moderates the aftereffects of self-control
Crowell, Adrienne; Kelley, Nicholas J.; Schmeichel, Brandon J.
2014-01-01
Numerous experiments have found that exercising self-control reduces success on subsequent, seemingly unrelated self-control tasks. Such evidence lends support to a strength model that posits a limited and depletable resource underlying all manner of self-control. Recent theory and evidence suggest that exercising self-control may also increase approach-motivated impulse strength. The two studies reported here tested two implications of this increased approach motivation hypothesis. First, aftereffects of self-control should be evident even in responses that require little or no self-control. Second, participants higher in trait approach motivation should be particularly susceptible to such aftereffects. In support, exercising self-control led to increased optimism (Study 1) and broadened attention (Study 2), but only among individuals higher in trait approach motivation. These findings suggest that approach motivation is an important key to understanding the aftereffects of exercising self-control. PMID:25324814
A Hamiltonian Formulation On Tsunami Over Swell
TIAN, M.; Sheremet, A.; Kaihatu, J. M.
2012-12-01
Tsunami induced by earthquakes typically evolves shore-ward with a significant amplification of amplitude during the last stages of shoaling. This study focuses on tsunami evolution in shallow water under the effects of the oceanographic environment such as breaking and tsunami- swell interaction. One generally describes wave breaking directly with a discontinuity in the solution to the classical nonlinear shallow water equations (NLSW) (e.g., Stoker 1985). This wave-front steepness calculation, however, has the potential problem that for the case of the single wave defined by solitary wave, breaking occurs much closer to the wave crest so that the method is formally invalid (Madsen et. al. 2008). Li and Raichlen (2002) applied a weighted essentially non-oscillatory (WENO) shock-capturing scheme in the numerical NSWE model to capture the wave breaking process. The problem arises that a convenient hamiltonian formalism is lacking to describe wave breaking. One wants to evaluate breaking by deducing the decay of the tsunami energy in a straightforward manner. The linear effect of the tsunami background circulation on swell is well known (e.g., Madsen et. al. 2008). However, Kaihatu and El Safty(2011) hypothesized that this is only one "half" of the mutual interaction between the tsunami and the overlying swell field, which might have subtle effects on the tsunami front-face steepness and breaking process. These effects were observed in a laboratory experiments (Kaihatu and El Safty 2011). It was observed that the presence of swell affects the maximum surface amplitude of overall wave field and produces significant energy shifts to high frequencies, thus promoting tsunami breaking. The theoretical study for tsunami-swell interaction requires a phase-resolving wave-wave interaction model. In this study, we derive a Hamiltonian formulation for the tsunami-swell interaction using the quasi stream-function formulation. This formalism is better able to handle uneven
Enhancing sensitivity in quantum metrology by Hamiltonian extensions
Fraïsse, Julien Mathieu Elias; Braun, Daniel
2017-06-01
A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θ G . For such "phase-shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it is possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term from the original Hamiltonian. Neither method makes use of any ancillas, which shows that, for quantum channel estimation with an arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with nitrogen vacancy center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.
Nonunitary quantum computation in the ground space of local Hamiltonians
Usher, Naïri; Hoban, Matty J.; Browne, Dan E.
2017-09-01
A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.
Unconstrained Hamiltonian formulation of low energy QCD
Directory of Open Access Journals (Sweden)
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
Lusanna, Luca
1995-01-01
A review is given of the presymplectic approach to relativistic physical systems and of the determination of their Dirac's observables. After relativistic mechanics and Nambu string, the Dirac's observables of Yang-Mills theory with fermions are given for the case of massless vector bosons (like in QED). A Dirac-Yukawa-like intrinsic ultraviolet cut-off is identified from the study of the covariantization of Hamiltonian classical field theory in the Dirac-Tomonaga-Schwinger sens. The implicat...
Local control approach to ultrafast electron transfer
Energy Technology Data Exchange (ETDEWEB)
Vindel-Zandbergen, Patricia [Departamento de Química Física, Universidad Complutense, 28040 Madrid (Spain); Meier, Christoph [Laboratoire Colisions, Agrégats et Reactivité, UMR 5589, IRSAMC, Université Paul Sabatier, 31062 Toulouse (France); Sola, Ignacio R., E-mail: isola@quim.ucm.es [Departamento de Química Física, Universidad Complutense, 28040 Madrid (Spain)
2016-10-20
We study ultrafast electron transfer between separated nuclei using local control theory. By imposing electron ionization and electron transport through the continuum, different local control formulations are used to increase the yield of retrapping the electron at the desired nuclei. The control mechanism is based on impulsive de-excitation. Both symmetric and asymmetric nuclear arrangements are analyzed, as well as the role of the nuclear motion.
A cohomological obstruction for global quasi-bi-Hamiltonian fields
Energy Technology Data Exchange (ETDEWEB)
Rakotondralambo, Joseph, E-mail: joseph.rakotondralambo@unimes.f [Departement de Mathematiques et Informatique, Faculte des Sciences, Universite d' Antananarivo (Madagascar)
2011-02-14
We introduce the notion of integrating factor for a 1-form which is an inner product of a vector fields and a 2-form, and the notion of weakly bi-Hamiltonian field also, which is locally quasi-bi-Hamiltonian. A cohomological class in some first cohomology space is associated to such vector fields when this is weakly bi-Hamiltonian and defined relatively to the above 1-form. This class is a cohomological obstruction to the existence of a global integrating factor for the 1-form.
The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni
2014-12-01
We generalize the idea of "extension of Hamiltonian systems"—developed in a series of previous articles—which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call "modified extension of Hamiltonian systems," produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz system, as well as for the caged anisotropic oscillator in dimension two.
Linear Quantum Entropy and Non-Hermitian Hamiltonians
Directory of Open Access Journals (Sweden)
Alessandro Sergi
2016-12-01
Full Text Available We consider the description of open quantum systems with probability sinks (or sources in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation. Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Phase space flows for non-Hamiltonian systems with constraints.
Sergi, Alessandro
2005-09-01
In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.
Access control, security, and trust a logical approach
Chin, Shiu-Kai
2010-01-01
Access Control, Security, Trust, and Logic Deconstructing Access Control Decisions A Logical Approach to Access Control PRELIMINARIES A Language for Access ControlSets and Relations Syntax SemanticsReasoning about Access Control Logical RulesFormal Proofs and Theorems Soundness of Logical RulesBasic Concepts Reference Monitors Access Control Mechanisms: Tickets and Lists Authentication Security PoliciesConfidentiality, Integrity, and Availability Discretionary Security Policies Mandatory Security Policies Military Security Policies Commercial PoliciesDISTRIBUTED ACCESS CONTROL Digital Authenti
Mixing Properties of Stochastic Quantum Hamiltonians
Onorati, E.; Buerschaper, O.; Kliesch, M.; Brown, W.; Werner, A. H.; Eisert, J.
2017-11-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathematical description closely with the more established one of random quantum circuits, we present a unified picture for analysing local random quantum and classes of Markovian dissipative processes, for which we also discuss applications.
A new approach for strawberry disease control
Strawberry is grown around the world in different production systems and diverse environmental conditions, which creates challenges in controlling fruit-rot causing pathogens before and after harvest. Fungicides have been traditionally used to control these diseases, and in some areas, as many as 2...
Adaptive Control with Approximated Policy Search Approach
Directory of Open Access Journals (Sweden)
Agus Naba
2010-05-01
Full Text Available Most of existing adaptive control schemes are designed to minimize error between plant state and goal state despite the fact that executing actions that are predicted to result in smaller errors only can mislead to non-goal states. We develop an adaptive control scheme that involves manipulating a controller of a general type to improve its performance as measured by an evaluation function. The developed method is closely related to a theory of Reinforcement Learning (RL but imposes a practical assumption made for faster learning. We assume that a value function of RL can be approximated by a function of Euclidean distance from a goal state and an action executed at the state. And, we propose to use it for the gradient search as an evaluation function. Simulation results provided through application of the proposed scheme to a pole-balancing problem using a linear state feedback controller and fuzzy controller verify the scheme’s efficacy.
Nearly optimal quantum control: an analytical approach
Sun, Chen; Saxena, Avadh; Sinitsyn, Nikolai A.
2017-09-01
We propose nearly optimal control strategies for changing the states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for optimization. This optimization strategy can be preferred in practice because it is physically transparent and does not lead to combinatorial complexity in multistate problems. As a demonstration, we design optimized control protocols that achieve switching between orthogonal states of a naturally biased quantum two-level system.
Sustainable malaria control: transdisciplinary approaches for translational applications
Directory of Open Access Journals (Sweden)
Birkholtz Lyn-Marie
2012-12-01
Full Text Available Abstract With the adoption of the Global Malaria Action Plan, several countries are moving from malaria control towards elimination and eradication. However, the sustainability of some of the approaches taken may be questionable. Here, an overview of malaria control and elimination strategies is provided and the sustainability of each in context of vector- and parasite control is assessed. From this, it can be concluded that transdisciplinary approaches are essential for sustained malaria control and elimination in malaria-endemic communities.
Sustainable malaria control: transdisciplinary approaches for translational applications.
Birkholtz, Lyn-Marie; Bornman, Riana; Focke, Walter; Mutero, Clifford; de Jager, Christiaan
2012-12-26
With the adoption of the Global Malaria Action Plan, several countries are moving from malaria control towards elimination and eradication. However, the sustainability of some of the approaches taken may be questionable. Here, an overview of malaria control and elimination strategies is provided and the sustainability of each in context of vector- and parasite control is assessed. From this, it can be concluded that transdisciplinary approaches are essential for sustained malaria control and elimination in malaria-endemic communities.
Robust control of robots fault tolerant approaches
Siqueira, Adriano A G; Bergerman, Marcel
2014-01-01
Bridging the divide between robust control theory and its application, this volume focuses on robotic manipulators and illustrates the mathematical concepts through experimental results in reproducible detail, obtained with a two-manipulator system.
Neutraceutical approaches to control diabetes: A natural requisite approach.
Srivastava, N; Tiwari, G; Tiwari, R; Bhati, L K; Rai, Awani K
2012-07-01
The aim of this study is to screen the polyherbal preparation for antidiabetic activity in rats. The blood glucose lowering activity of the polyherbal preparation-I (1:1:1 of wheat germ oil, Coraidrum sativum, and Aloe vera) was studied in normal rats after oral administration at doses of 1.0 ml/kg and 2.0 ml/kg and polyherbal preparation-I, II (wheat germ oil, fresh juice of C. sativum, and A. vera in the ratio of 2:2:1), and III (wheat germ oil, fresh juice of C. sativum and A. vera in the ratio of 1:2:2) on alloxan-induced diabetic rats, after oral administration at doses of 1.0 ml/kg and 2.0 ml/kg. Blood samples were collected from the tail vein method at 0, 0.5, 1, 2, 4, 8, 12, and 24 h in normal rats and in diabetic rats at 0, 1, 3, 7, 15, and 30 days. Blood plasma glucose was estimated by the GOD/POD (glucose oxidase and peroxidase) method. The data were compared statistically by using the one-way ANOVA method followed by the Dunnett multiple component test. Statistical significance was set at P < 0.05. The polyherbal preparation-I produced significant (P < 0.05) reduction in the blood glucose level of normal rats and polyherbal preparation-I, II, and III produced significant (P < 0.01) reduction in the blood glucose level of diabetic rats during 30-day study and compared with that of control and glibenclamide. The polyherbal preparation-I showed a significant glucose lowering effect in normal rats and polyherbal preparation-I, II, and III in diabetic rats. This preparation is going to be promising antidiabetic preparation for masses; however, it requires further extensive studies in human beings.
On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes
Directory of Open Access Journals (Sweden)
Cao Jianxiang
2016-11-01
Full Text Available The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E, we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v, there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn is edge-hy per- Hamiltonian laceable.
The behavior-analytic approach to emotional self-control
Directory of Open Access Journals (Sweden)
Jussara Rocha Batista
2012-12-01
Full Text Available Some psychological approaches distinguish behavioral self-control from emotional self-control, the latter being approached with the reference to inside events controlled by the individual himself. This paper offers some directions to a behavior-analytic approach of what has been referred to as emotional self-control. According to Behavior Analysis, no new process is found in emotional self-control, but components that are additional to those found in behavioral self-control, which require appropriate treatment. The paper highlights some determinants of behavioral repertoires taken as instances of emotional self-control: the social context in which self-control is produced and maintained; the conflicts between consequences for the individual and for the group; and the degree of participation of the motor apparatus in the emission of emotional responses. Keywords: emotional self-control; emotional responses; inner world; behavior analysis.
A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds
Turki, Yahya
2015-04-01
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution-a class of bivector fields generalizing twisted Poisson structures that we study in detail.
Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
O'Hara, Michael J.; O'Leary, Dianne P.
2008-01-01
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the J...
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
In this section, we will give a sufficient condition of a connected graph to be Hamiltonian by means of the Wiener-type index. First we introduce the following Chvátal condition for a connected graph to be Hamiltonian. Lemma 1 [2]. Let G be a nontrivial graph of order n, n ≥ 3, with degree sequence (d1, d2,...,dn), where d1 ...
Controller design approach based on linear programming.
Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa
2013-11-01
This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.
Wind Turbine Control: Robust Model Based Approach
DEFF Research Database (Denmark)
Mirzaei, Mahmood
. Wind turbines are the most common wind energy conversion systems and are hoped to be able to compete economically with fossil fuel power plants in near future. However this demands better technology to reduce the price of electricity production. Control can play an essential part in this context...... wind turbine control using robust MPC. In general, robust MPC problems are very computationally demanding, however we have shown that with some approximations the resulting robust MPC problem can be specialized with reduced computational complexity. After a short introduction on wind energy and wind....... This is because, on the one hand, control methods can decrease the cost of energy by keeping the turbine close to its maximum efficiency. On the other hand, they can reduce structural fatigue and therefore increase the lifetime of the wind turbine. The power produced by a wind turbine is proportional...
Statistical quality control a loss minimization approach
Trietsch, Dan
1999-01-01
While many books on quality espouse the Taguchi loss function, they do not examine its impact on statistical quality control (SQC). But using the Taguchi loss function sheds new light on questions relating to SQC and calls for some changes. This book covers SQC in a way that conforms with the need to minimize loss. Subjects often not covered elsewhere include: (i) measurements, (ii) determining how many points to sample to obtain reliable control charts (for which purpose a new graphic tool, diffidence charts, is introduced), (iii) the connection between process capability and tolerances, (iv)
Chen, Yongpin P; Jiang, Li Jun; Meng, Min; Wu, Yu Mao; Chew, Weng Cho
2016-01-01
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum mechanics, a unified Maxwell-Schrodinger system is derived by the variational principle. The coupled system is well-posed and symplectic, which ensures energy conserving property during the time evolution. However, due to the disparity of wavelengths of EM waves and that of electron waves, a numerical implementation of the finite-difference time-domain (FDTD) method to the multiscale coupled system is extremely challenging. To overcome this difficulty, a reduced eigenmode expansion technique is first applied to represent the wave function of the particle. Then, a set of ordinary differential equations (ODEs) governing the time evolution of the slowly-varying expansion coefficients are derived to replace the original Schrodinger equation. Finally, Maxwell's equations represented b...
Directory of Open Access Journals (Sweden)
Karim P. Y. Thébault
2011-03-01
Full Text Available Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that “quantisation commutes with reduction” and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.
Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
Bender, Carl M.; Mannheim, Philip D.
2008-07-01
In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian HPU of the model is PT symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity transformation whose form was found exactly. The present paper explores the equal-frequency limit of the same model. It is shown that in this limit the similarity transform that was used for the unequal-frequency case becomes singular and that HPU becomes a Jordan-block operator, which is nondiagonalizable and has fewer energy eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart. Thus, the equal-frequency PT theory emerges as a distinct realization of quantum mechanics. The quantum mechanics associated with this Jordan-block Hamiltonian can be treated exactly. It is shown that the Hilbert space is complete with a set of nonstationary solutions to the Schrödinger equation replacing the missing stationary ones. These nonstationary states are needed to establish that the Jordan-block Hamiltonian of the equal-frequency Pais-Uhlenbeck model generates unitary time evolution.
Extended Hamiltonians and shift, ladder functions and operators
Chanu, Claudia Maria; Rastelli, Giovanni
2017-11-01
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in the family of extended Hamiltonians, geometrically characterized by the structure of warped manifold of their configuration manifold. For the extended Hamiltonians, the characteristic constants of motion of high degree are polynomial in the momenta of determined form. We consider here a different form of the constants of motion, based on the factorization procedure developed for systems of two degrees of freedom by S. Kuru, J. Negro and others. We show that an important subclass of the extended Hamiltonians, with arbitrary dimension, admits factorized constants of motion and we determine their expression. The classical constants can be polynomial or non-polynomial in the momenta, but the factorization procedure allows, in a type of extended Hamiltonians, their quantization via shift and ladder operators, for systems of any finite dimension.
Greenhouse climate management : an optimal control approach
Henten, van E.J.
1994-01-01
In this thesis a methodology is developed for the construction and analysis of an optimal greenhouse climate control system.
In chapter 1, the results of a literature survey are presented and the research objectives are defined. In the literature, optimal greenhouse climate
Systematic approach to balanced control technology management
Directory of Open Access Journals (Sweden)
I. N. Vorobjev
2012-01-01
Full Text Available Articulated understanding of important systemic controls that exist in the modern world. Identify and describe the key success factors of a balanced management of organizational change. Proposed register of compliance balanced scorecard target values and objectives of balanced management of industrial organizations.
Groothuis, Stefan S.; Stramigioli, Stefano; Carloni, Raffaella
2017-01-01
This paper proposes a modeling method for generic compliant robotic manipulators. It is based on graph theory and the port-Hamiltonian formalism, which allows a modular approach to the interconnection of rigid bodies with compliant actuators by means of kinematic pairs. This modularity enables a
Groothuis, Stefan; Stramigioli, Stefano; Carloni, Raffaella
2017-01-01
This paper proposes a modeling method for generic compliant robotic manipulators. It is based on graph theory and the port-Hamiltonian formalism, which allows a modular approach to the interconnection of rigid bodies with compliant actuators by means of kinematic pairs. This modularity enables a
A sustainable approach to controlling oil spills.
Al-Majed, Abdul Aziz; Adebayo, Abdulrauf Rasheed; Hossain, M Enamul
2012-12-30
As a result of the huge economic and environmental destruction from oil spills, studies have been directed at improving and deploying natural sorbents which are not only the least expensive but also the safest means of spill control. This research reviews the limitations and environmental impact of existing cleanup methods. It also justifies the need for concerted research effort on oil spill control using natural and sustainable technology concepts. The article proposes future guidelines for the development of a sustainable cleanup technology. Finally, guidelines for the development of a new technology for the Middle East are proposed, which is the use of an abundant resource--date palm fibers--for such techniques. Copyright © 2012 Elsevier Ltd. All rights reserved.
Confinement and fermion doubling problem in Dirac-like Hamiltonians
Messias de Resende, B.; de Lima, F. Crasto; Miwa, R. H.; Vernek, E.; Ferreira, G. J.
2017-10-01
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative k →-i ∂x skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator Bi2Se3 , for which we use ab initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-14
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Hamiltonian analysis for linearly acceleration-dependent Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, México (Mexico); Molgado, Alberto, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Avenida Salvador Nava S/N Zona Universitaria, CP 78290 San Luis Potosí, SLP, México (Mexico)
2016-06-15
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.
Different Approaches to Control of TISO Thermal System
Directory of Open Access Journals (Sweden)
Jaroslava KRÁLOVÁ
2009-06-01
Full Text Available The contribution is aimed on problematic of multivariable control. Multivariable system can be controlled by multivariable controller or we can use decentralized control. Control of thermal system with two inputs and one output is shown in the paper. The goal of paper is to find what sort of results we can get by classical approaches and by more sophisticated strategies. Two discrete-time PID controllers are selected as a representative of classical approach and split-range with discrete-time PID controller is selected as a representative of more sophisticated strategy. Control strategies are compared in the view of control quality and costs, information and knowledge required by control design and application.
Approaches to Golden Algae Control: In-Lake Mesocosm Experiments
2012-04-01
ER D C/ EL C R- 12 -1 Aquatic Plant Control Research Program Approaches to Golden Algae Control: In-Lake Mesocosm Experiments En vi ro...Approved for public release; distribution is unlimited. Aquatic Plant Control Research Program ERDC/EL CR-12-1 April 2012 Approaches to Golden...parvum cell toxicity and stable isotope ratios. Harmful Algae 8: 247-253. Lundholm, N., and O. Moestrup. 2006. The biogeography of harmful algae. In
Quality control program: the radiology technician approach
Helga Alexandra Soares Macedo; Vitor Manuel Costa Pereira Rodrigues
2009-01-01
OBJETIVO: Pretendeu-se averiguar que importância os técnicos de radiologia atribuem à implementação de um programa de controle de qualidade em radiologia, e conhecer a importância da existência de critérios de proteção. MATERIAIS E MÉTODOS: Estudo descritivo e transversal. Os dados foram recolhidos por meio de um questionário (quatro partes), tendo sido garantido o anonimato e a confidencialidade dos dados. Participaram neste estudo 48 técnicos de radiologia que exercem funções em instituiçõe...
Exact Hamiltonians with Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface
Chang, Jian-Yuan; Wu, Jhih-Sheng; Chang, Ching-Ray
2013-05-01
The exact Hamiltonians for Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface with an arbitrary shape are rigorously derived. Two orthogonal principal curvatures dominate the electronic spin transport, and the asymptotic behavior of the normal confined potential on a curved surface is insignificant. For a curved surface with a large curvature, the higher order momentum terms play an important role in controlling spin transport. The Rashba spin-orbit coupling on a curved surface only induces the extra pseudopotential term, and the cubic Dresselhaus spin-orbit coupling on a curved surface can induce the extra pseudokinetic and pseudomomentum terms. Because of the extra curvature-induced terms and the associated pseudomagnetic fields, spin transport on a curved surface is very different from that on a flat surface. The Hamiltonians on both cylindrical and spherical surfaces are explicitly derived here, and the associated physical properties of electrons are studied in detail.
Multiple Model Approaches to Modelling and Control,
DEFF Research Database (Denmark)
on the ease with which prior knowledge can be incorporated. It is interesting to note that researchers in Control Theory, Neural Networks,Statistics, Artificial Intelligence and Fuzzy Logic have more or less independently developed very similar modelling methods, calling them Local ModelNetworks, Operating......, and allows direct incorporation of high-level and qualitative plant knowledge into themodel. These advantages have proven to be very appealing for industrial applications, and the practical, intuitively appealing nature of the framework isdemonstrated in chapters describing applications of local methods...... to problems in the process industries, biomedical applications and autonomoussystems. The successful application of the ideas to demanding problems is already encouraging, but creative development of the basic framework isneeded to better allow the integration of human knowledge with automated learning...
Robust control of UAVs using the parameter space approach
Abdelmoeti, Samer; Carloni, Raffaella
2016-01-01
In this paper a robust PID controller for quadrotor unmanned aerial vehicles is proposed that uses the pa- rameter space approach. Stability and robustness analyses are carried out in the controller parameter space to determine a set of stable controller gains that guarantee also robustness against
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Over the past twelve years, ideas and methods from nonlinear dynamics system theory, in particular, group theoretical methods in bifurcation theory, have ... Also, patterns of behaviour in networks of oscillators with certain symmetry groups have been extensively studied and the results have been applied to ...
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
Nowadays, integrable systems arise naturally at various length scales: in molecular dynamics [3], underwater vehicle dynamics [4], in magnetic- and electric-field sensors. [5–8], hydroelastic rotating systems and boats/ships [9–12], in complex systems such as telecommunication infrastructures [13], and in power grids [14].
Accreting fluids onto regular black holes via Hamiltonian approach
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); University of Central Punjab, CAMS, UCP Business School, Lahore (Pakistan)
2017-08-15
We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sfetsos black holes and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The accreting fluid is being classified through the equation of state according to the features of regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. It is noted that the three-velocity depends on critical points and the equation of state parameter on phase space. (orig.)
Olsen, Seth
2012-01-01
We propose a single effective Hamiltonian to describe the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are all bridge-substituted derivatives of Michler's Hydrol Blue. Three-state diabatic Hamiltonians for the dyes are calculated using four-electron three-orbital state-averaged complete active space self-consistent field and multi-state multi-reference perturbation theory models. The approach takes advantage of an isolobal analogy that can be established between the orbitals spanning the active spaces of the different substituted dyes. The solutions of the chemical problem are expressed in a diabatic Hilbert space that is analogous to classical resonance models. The effective Hamiltonians for all dyes can be fit to a single functional form that depends on the mixing angle between a bridge-charged diabatic state and a superposition representing the canonical resonance. We find that the structure of the bridge-charged state changes in a regular fashion across the serie...
Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano
Falaize, Antoine; Hélie, Thomas
2017-03-01
This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.
Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics.
Bauer, Sebastian; Tavan, Paul; Mathias, Gerald
2014-03-14
In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.
Energy Technology Data Exchange (ETDEWEB)
Yang, Chao
2009-07-17
We present a practical approach to calculate the complex band structure of an electrode for quantum transport calculations. This method is designed for plane wave based Hamiltonian with nonlocal pseudopotentials and the auxiliary periodic boundary condition transport calculation approach. Currently there is no direct method to calculate all the evanescent states for a given energy for systems with nonlocal pseudopotentials. On the other hand, in the auxiliary periodic boundary condition transport calculation, there is no need for all the evanescent states at a given energy. The current method fills this niche. The method has been used to study copper and gold nanowires and bulk electrodes.
Mechanical systems a unified approach to vibrations and controls
Gans, Roger F
2015-01-01
This essential textbook covers analysis and control of engineering mechanisms, which include almost any apparatus with moving parts used in daily life, from musical instruments to robots. The text presents both vibrations and controls with considerable breadth and depth using a unified notation. It strikes a nice balance between the analytical and the practical. This text contains enough material for a two semester sequence, but it can also be used in a single semester course combining the two topics. Mechanical Systems: A Unified Approach to Vibrations and Controls presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text. This book also: · Presents a unified approach to vibrations and controls, including an excellent diagram that simultaneously discusses embedding classical vibrations (mechanical systems) in a discussion of models, inverse models, and open and closed loop control ...
Sliding mode control the delta-sigma modulation approach
Sira-Ramírez, Hebertt
2015-01-01
This monograph presents a novel method of sliding mode control for switch-regulated nonlinear systems. The Delta Sigma modulation approach allows one to implement a continuous control scheme using one or multiple, independent switches, thus effectively merging the available linear and nonlinear controller design techniques with sliding mode control. Sliding Mode Control: The Delta-Sigma Modulation Approach, combines rigorous mathematical derivation of the unique features of Sliding Mode Control and Delta-Sigma modulation with numerous illustrative examples from diverse areas of engineering. In addition, engineering case studies demonstrate the applicability of the technique and the ease with which one can implement the exposed results. This book will appeal to researchers in control engineering and can be used as graduate-level textbook for a first course on sliding mode control.
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics
Directory of Open Access Journals (Sweden)
Yoshifumi Nakata
2017-04-01
Full Text Available Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.
The control-of-consumption approach to alcohol abuse prevention
DEFF Research Database (Denmark)
Ravn, Ib
1987-01-01
The single-distribution theory of alcohol consumption and the derived prevention strategy, the control-of-consumption approach, are conceptualized as three probabilistic relationships between four variables, collectively called "the Ledermann string": availability, average consumption, proportion...
Wilson, David G [Tijeras, NM; Robinett, III, Rush D.
2012-02-21
A control system design method and concomitant control system comprising representing a physical apparatus to be controlled as a Hamiltonian system, determining elements of the Hamiltonian system representation which are power generators, power dissipators, and power storage devices, analyzing stability and performance of the Hamiltonian system based on the results of the determining step and determining necessary and sufficient conditions for stability of the Hamiltonian system, creating a stable control system based on the results of the analyzing step, and employing the resulting control system to control the physical apparatus.
Impedance Control for Robotic Rehabilitation: A Robust Markovian Approach
Directory of Open Access Journals (Sweden)
Andres L. Jutinico
2017-08-01
Full Text Available The human-robot interaction has played an important role in rehabilitation robotics and impedance control has been used in the regulation of interaction forces between the robot actuator and human limbs. Series elastic actuators (SEAs have been an efficient solution in the design of this kind of robotic application. Standard implementations of impedance control with SEAs require an internal force control loop for guaranteeing the desired impedance output. However, nonlinearities and uncertainties hamper such a guarantee of an accurate force level in this human-robot interaction. This paper addresses the dependence of the impedance control performance on the force control and proposes a control approach that improves the force control robustness. A unified model of the human-robot system that considers the ankle impedance by a second-order dynamics subject to uncertainties in the stiffness, damping, and inertia parameters has been developed. Fixed, resistive, and passive operation modes of the robotics system were defined, where transition probabilities among the modes were modeled through a Markov chain. A robust regulator for Markovian jump linear systems was used in the design of the force control. Experimental results show the approach improves the impedance control performance. For comparison purposes, a standard H∞ force controller based on the fixed operation mode has also been designed. The Markovian control approach outperformed the H∞ control when all operation modes were taken into account.
PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics
Fring, Andreas; Jones, Hugh; Znojil, Miloslav
2008-06-01
growing community of this subject. It is, for instance, well understood that the reality of the spectrum can be attributed either to the unbroken PT-symmetry of the entire system, that is, invariance of the Hamiltonian and the corresponding wavefunctions under a simultaneous parity transformation and time reversal, or more generally to its pseudo-Hermiticity . When the spectrum is real and discrete the Hamiltonian is actually quasi-Hermitian, with a positive-definite metric operator, and can in principle be related by a similarity transformation to an isospectral Hermitian counterpart. For all approaches well-defined procedures have been developed, which allow one to construct metric operators and therefore a consistent description of the underlying quantum mechanical observables. Even though the general principles have been laid out, it remains a challenge in most concrete cases to implement the entire procedure. Solvable models in this sense, some of which may be found in this issue, remain a rare exception. Nonetheless, despite this progress some important questions are still unanswered. For instance, according to the current understanding the non-Hermitian Hamiltonian does not uniquely define the physics of the system since a meaningful metric can no longer be associated with the system in a non-trivial and unambiguous manner. A fully consistent scattering theory has also not yet been formulated. Other issues remain controversial, such as the quantum brachistochrone problem, the problem of forming a mixture between a Hermitian and non-Hermitian system, the new phenomenological possibilities of forming a kind of worm-hole effect, etc. We would like to acknowledge the financial support of the London Mathematical Society, the Institute of Physics, the Doppler Institute in Prague and the School of Engineering and Mathematical Science of City University London. We hope this special issue will be useful to the newcomer as well as to the expert in the subject. Workshop
Regulating Cognitive Control through Approach-Avoidance Motor Actions
Koch, Severine; Holland, Rob W.; van Knippenberg, Ad
2008-01-01
In two studies, the regulatory function of approach-avoidance cues in activating cognitive control processes was investigated. It was hypothesized that avoidance motor actions, relative to approach motor actions, increase the recruitment of cognitive resources, resulting in better performance on tasks that draw on these capacities. In Study 1,…
Magnetic field lines, Hamiltonian dynamics, and nontwist systems
Energy Technology Data Exchange (ETDEWEB)
Morrison, P. J. [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)
2000-06-01
Magnetic field lines typically do not behave as described in the symmetrical situations treated in conventional physics textbooks. Instead, they behave in a chaotic manner; in fact, magnetic field lines are trajectories of Hamiltonian systems. Consequently the quest for fusion energy has interwoven, for 50 years, the study of magnetic field configurations and Hamiltonian systems theory. The manner in which invariant tori breakup in symplectic twist maps, maps that embody one and a half degree-of-freedom Hamiltonian systems in general and describe magnetic field lines in tokamaks in particular, will be reviewed, including symmetry methods for finding periodic orbits and Greene's residue criterion. In nontwist maps, which describe, e.g., reverse shear tokamaks and zonal flows in geophysical fluid dynamics, a new theory is required for describing tori breakup. The new theory is discussed and comments about renormalization are made. (c) 2000 American Institute of Physics.
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
Extended Hamiltonian learning on Riemannian manifolds: numerical aspects.
Fiori, Simone
2012-01-01
This paper is the second part of a study initiated with the paper S. Fiori, "Extended Hamiltonian learning on Riemannian manifolds: Theoretical aspects," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 687-700, May 2011, which aimed at introducing a general framework to develop a theory of learning on differentiable manifolds by extended Hamiltonian stationary-action principle. This paper discusses the numerical implementation of the extended Hamiltonian learning paradigm by making use of notions from geometric numerical integration to numerically solve differential equations on manifolds. The general-purpose integration schemes and the discussion of several cases of interest show that the implementation of the dynamical learning equations exhibits a rich structure. The behavior of the discussed learning paradigm is illustrated via several numerical examples and discussions of case studies. The numerical examples confirm the theoretical developments presented in this paper as well as in its first part.
On the Hamiltonian formalism of the tetrad-connection gravity
Lagraa, M. H.; Lagraa, M.; Touhami, N.
2017-06-01
We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamic part of the spatial connection is fixed to zero by an adequate gauge transformation. This new action leads to a coherent Hamiltonian formalism where the Lorentz, scalar and vectorial first-class constraints obey a closed algebra in terms of Poisson brackets. This algebra closes with structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints, where the second-class constraints are eliminated as strong equalities, is obtained in terms of Dirac brackets. These first-class constraints lead to the same physical degrees of freedom of the general relativity.
Directory of Open Access Journals (Sweden)
Rudowicz Czesław
2015-07-01
Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.
Control approach to Queue Theory | Omolehin | Journal of the ...
African Journals Online (AJOL)
The rigid condition for simple queue problem is minimized by considering multiple channels through control approach. The result control problem is solved using Conventional Conjugate Gradient Method and the optimal system performance is obtained. Journal of the Nigerian Association of Mathematical Physics Vol.
Hamiltonian LGT in the complete Fourier analysis basis
Energy Technology Data Exchange (ETDEWEB)
Burgio, G.; De Pietri, R.; Morales-Tecotl, H.A.; Urrutia, L.F.; Vergara, J.D
2000-03-01
The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We short-cut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Our analysis is based only on properties of the tensor category of Lie-Group representations. The Hamiltonian of such theories is calculated yielding a sparse matrix whose spectrum and eigenstates could be exactly derived as functions of the coupling g{sup 2}.
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.
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Directory of Open Access Journals (Sweden)
Jovanović Božidar
2016-01-01
Full Text Available We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.
Hamiltonian Monte Carlo with Constrained Molecular Dynamics as Gibbs Sampling.
Spiridon, Laurentiu; Minh, David D L
2017-10-10
Compared to fully flexible molecular dynamics, simulations of constrained systems can use larger time steps and focus kinetic energy on soft degrees of freedom. Achieving ergodic sampling from the Boltzmann distribution, however, has proven challenging. Using recent generalizations of the equipartition principle and Fixman potential, here we implement Hamiltonian Monte Carlo based on constrained molecular dynamics as a Gibbs sampling move. By mixing Hamiltonian Monte Carlo based on fully flexible and torsional dynamics, we are able to reproduce free energy landscapes of simple model systems and enhance sampling of macrocycles.
Notch Filters for Port-Hamiltonian Systems
Dirksz, Danny; Scherpen, Jacquelien M.A.; van der Schaft, Abraham J.; Steinbuch, Maarten
Many powerful tools exist for control design in the frequency domain, but are theoretically only justified for linear systems. On the other hand, nonlinear control deals with control design methodologies that are theoretically justified for a larger and more realistic class of systems, but primarily
A control approach for plasma density in tokamak machines
Energy Technology Data Exchange (ETDEWEB)
Boncagni, Luca, E-mail: luca.boncagni@enea.it [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Pucci, Daniele; Piesco, F.; Zarfati, Emanuele [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy); Mazzitelli, G. [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Monaco, S. [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy)
2013-10-15
Highlights: •We show a control approach for line plasma density in tokamak. •We show a control approach for pressure in a tokamak chamber. •We show experimental results using one valve. -- Abstract: In tokamak machines, chamber pre-fill is crucial to attain plasma breakdown, while plasma density control is instrumental for several tasks such as machine protection and achievement of desired plasma performances. This paper sets the principles of a new control strategy for attaining both chamber pre-fill and plasma density regulation. Assuming that the actuation mean is a piezoelectric valve driven by a varying voltage, the proposed control laws ensure convergence to reference values of chamber pressure during pre-fill, and of plasma density during plasma discharge. Experimental results at FTU are presented to discuss weaknesses and strengths of the proposed control strategy. The whole system has been implemented by using the MARTe framework [1].
Robust decentralized power system controller design: Integrated approach
Veselý, Vojtech
2017-09-01
A unique approach to the design of gain scheduled controller (GSC) is presented. The proposed design procedure is based on the Bellman-Lyapunov equation, guaranteed cost and robust stability conditions using the parameter dependent quadratic stability approach. The obtained feasible design procedures for robust GSC design are in the form of BMI with guaranteed convex stability conditions. The obtained design results and their properties are illustrated in the simultaneously design of controllers for simple model (6-order) turbogenerator. The results of the obtained design procedure are a PI automatic voltage regulator (AVR) for synchronous generator, a PI governor controller and a power system stabilizer for excitation system.
Mass segregation phenomena using the Hamiltonian Mean Field model
Steiner, J. R.; Zolacir, T. O.
2018-02-01
Mass segregation problem is thought to be entangled with the dynamical evolution of young stellar clusters (Olczak, 2011 [1]). This is a common sense in the astrophysical community. In this work, the Hamiltonian Mean Field (HMF) model with different masses is studied. A mass segregation phenomenon (MSP) arises from this study as a dynamical feature. The MSP in the HMF model is a consequence of the Landau damping (LD) and it appears in systems that the interactions belongs to a long range regime. Actually HMF is a toy model known to show up the main characteristics of astrophysical systems due to the mean field character of the potential and for different masses, as stellar and galaxies clusters, also exhibits MSP. It is in this sense that computational simulations focusing in what happens over the mass distribution in the phase space are performed for this system. What happens through the violent relaxation period and what stands for the quasi-stationary states (QSS) of this dynamics is analyzed. The results obtained support the fact that MSP is observed already in the violent relaxation time and is maintained during the QSS. Some structures in the mass distribution function are observed. As a result of this study the mass distribution is determined by the system dynamics and is independent of the dimensionality of the system. MSP occurs in a one dimensional system as a result of the long range forces that acts in the system. In this approach MSP emerges as a dynamical feature. We also show that for HMF with different masses, the dynamical time scale is N.
Holonic Approach for Control and Coordination of Distributed Sensors
2008-08-01
computationally efficient soft (or fuzzy ) lookup table that can continually adjust to system changes. In robotic control, the CMAC can maintain...approach consists therefore in combining the holonic system paradigm with hybrid control schemes , i.e., designs that make use of both discrete and... scheme as depicted in Figure 6. The sensor control system must also be capable of addressing two types of data timing: data that are generated at
A Goal-Function Approach to Analysis of Control Situations
DEFF Research Database (Denmark)
Lind, Morten
2010-01-01
The concept of situations plays a central role in all theories of meaning and context. and serve to frame or group events and other occurrences into coherent meaningful wholes. Situations are typed, may be interconnected and organized into higher level structures. In operation of industrial...... processes situations should identify operational aspects relevant for control agent’s decision making in plant supervision and control. Control situations can be understood as recurrent and interconnected patterns of control with important implications for control and HMI design. Goal-Function approaches...
Parametric Approach to Trajectory Tracking Control of Robot Manipulators
Directory of Open Access Journals (Sweden)
Shijie Zhang
2013-01-01
Full Text Available The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.
Nonlinear identification and control a neural network approach
Liu, G P
2001-01-01
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies . . . , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series otTers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The time for nonlinear control to enter routine application seems to be approaching. Nonlinear control has had a long gestation period but much ofthe past has been concerned with methods that involve formal nonlinear functional model representations. It seems more likely that the breakthough will come through the use of other more flexible and ame...
Fring, Andreas; Frith, Thomas
2017-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
Quesne, C.
2010-02-01
In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.
Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL
2015-01-01
The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.
Lipparini, Filippo; Cappelli, Chiara; Barone, Vincenzo
2012-11-13
A fully polarizable quantum/classical Hamiltonian including SCF (HF or DFT), fluctuating charge, and polarizable continuum regions is introduced and implemented for electronic energies of ground and excited states, using, in the latter case, a linear response formulation. After calibration and validation of the approach, preliminary results are presented for pyrimidine in aqueous solution and for retinal in a rhodopsin mimic. The results are consistent with more tested methodologies and pave the route toward fully consistent yet effective simulations of large systems of technological and/or biological interest in their natural environments.
Directory of Open Access Journals (Sweden)
A. Weissblut
2012-03-01
Full Text Available This article – introduction to the structural theory of general view dynamical systems, based on construction of dynamic quantum models (DQM, offered by the author. This model is simply connected with traditional model of quantum mechanics (i.e. with the Schrodinger equation. At the same time obtained thus non – Hamiltonian quantum dynamics is easier than classical one: it allow building the clear structural theory and effective algorithms of research for concrete systems. This article is devoted mainly to such task. The algorithm of search for DQM attractors, based on this approach, is offered here.
An infinite family of superintegrable Hamiltonians with reflection in the plane
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128, QC H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-12-16
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schroedinger equations admit the separation of variables in polar coordinates and are exactly solvable. The angular part of the wavefunction is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit 'accidental' degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher order) constants of motion are constructed and the structure equations of the symmetry algebra are obtained. (paper)
Kinematic Compensation in Port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2007-01-01
A bilateral telemanipulator is a robotic system that allows the interaction with remote environments and it is composed by a controlled local robot (the master) and a controlled remote robot (the slave) interconnected through a communication channel. The motion imposed to the master by the human is
A new approach of active compliance control via fuzzy logic control for multifingered robot hand
Jamil, M. F. A.; Jalani, J.; Ahmad, A.
2016-07-01
Safety is a vital issue in Human-Robot Interaction (HRI). In order to guarantee safety in HRI, a model reference impedance control can be a very useful approach introducing a compliant control. In particular, this paper establishes a fuzzy logic compliance control (i.e. active compliance control) to reduce impact and forces during physical interaction between humans/objects and robots. Exploiting a virtual mass-spring-damper system allows us to determine a desired compliant level by understanding the behavior of the model reference impedance control. The performance of fuzzy logic compliant control is tested in simulation for a robotic hand known as the RED Hand. The results show that the fuzzy logic is a feasible control approach, particularly to control position and to provide compliant control. In addition, the fuzzy logic control allows us to simplify the controller design process (i.e. avoid complex computation) when dealing with nonlinearities and uncertainties.
Generalized Hamiltonian biodynamics and topology invariants of humanoid robots
Vladimir Ivancevic
2002-01-01
Humanoid robots are anthropomorphic mechanisms with biodynamics that resembles human musculo-skeletal dynamics. This paper proposes a new generalized (dissipative, muscle-driven, stochastic) Hamiltonian model of humanoid biodynamics. Also, (co)homological analysis is performed on its Lie-group based configuration and momentum phase-space manifolds.
Many-body Hamiltonian with screening parameter and ionization ...
Indian Academy of Sciences (India)
Yukawa-type potential; ionization and excitation energies; many-body. Hamiltonian; spin-orbit coupling; energy-level splitting. PACS Nos 71.10.-w; 31.10.+z; 03.65.Ca. 1. Introduction. Finding even an approximate but an accurate solution to a Coulombian many-body problem (many-electron atoms and solids) is no doubt, ...
Effect of three-body transformed Hamiltonian ( ) using full connected ...
Indian Academy of Sciences (India)
KALIPADA ADHIKARI
2018-02-13
Feb 13, 2018 ... Indian Academy of Sciences https://doi.org/10.1007/s12043-018-1523-3. Effect of three-body transformed Hamiltonian ( ˜H3) using full connected triple excitation coupled cluster operators on valence ionisation potentials of Cl2 and F2 computed via. EIP-VUMRCCSDτ scheme. KALIPADA ADHIKARI.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
... involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (′/)-expansion methodc, where = () satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Theoretical studies of the spin-Hamiltonian parameters for the ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 70; Issue 4. Theoretical studies of the spin-Hamiltonian parameters for the orthorhombic Pr4+ centers in Sr2CeO4 ... Author Affiliations. Wen-Lin Feng1. Department of Applied Physics, Chongqing Institute of Technology, Chongqing 400050, People Republic of China ...
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
S Ghosh, B Talukdar and S Chakraborti. The Hamiltonian structure of non-linear evolution equations solvable by the inverse spectral method was discovered in 1971 by Zakharov and Faddeev [2] and by Gardner [3] who interpreted the Kortweg-de Vries (KdV) equation as a completely integrable Hamilto- nian system in an ...
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property. Author Affiliations. S Ghosh1 B Talukdar1 S Chakraborti2. Department of Physics ...
Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro
2017-04-01
We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S =1 /2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension ... collected by a conscious observer (for example, as is the case in the quantum mea- surement problem or the ..... property of a function is bound to break down, say for an open system or in the presence of subjectivity.
Bohr Hamiltonian with deformation-dependent mass term
Energy Technology Data Exchange (ETDEWEB)
Bonatsos, Dennis, E-mail: bonat@inp.demokritos.g [Institute of Nuclear Physics, N.C.S.R. ' Demokritos' , GR-15310 Aghia Paraskevi, Attiki (Greece); Georgoudis, P.; Lenis, D. [Institute of Nuclear Physics, N.C.S.R. ' Demokritos' , GR-15310 Aghia Paraskevi, Attiki (Greece); Minkov, N. [Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784 Sofia (Bulgaria); Quesne, C. [Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2010-01-25
The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a gamma-unstable Davidson potential, using techniques of supersymmetric quantum mechanics. Numerical results in the Xe-Ba region are discussed.
Horizontal circulation and jumps in Hamiltonian wave models
Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno
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
Horizontal circulation and jumps in Hamiltonian wave models
Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno
2013-01-01
We are interested in the numerical modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian
Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 83; Issue 1. 2 Algebra and two-dimensional ... Then, by choosing an appropriate set of coefficients and making a gauge rotation, we show that this Hamiltonian leads to the solvable Poschl–Teller model on an open infinite strip. Finally, we assign 2 hidden algebra ...
Approximate first integrals of a chaotic Hamiltonian system | Unal ...
African Journals Online (AJOL)
Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been ...
Spectral Results on Some Hamiltonian Properties of Graphs
Directory of Open Access Journals (Sweden)
Rao Li
2014-10-01
Full Text Available Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs
Port-Hamiltonian discretization for open channel flows
Pasumarthy, R.; Ambati, V.R.; Schaft, A.J. van der
A finite-dimensional Port-Hamiltonian formulation for the presented. A numerical scheme based on this formulation is shallow water equations. The scheme is verified against conservation of mass and energy to the discrete level. dynamics of smooth open channel flows is developed for both the linear
Conditional Reducibility of Certain Unbounded Nonnegative Hamiltonian Operator Functions
Azizov, T.Ya.; Dijksma, A.; Gridneva, I.V.
Let and be operators on a Hilbert space which are both self-adjoint and unitary and satisfy . We consider an operator function on [0, 1] of the form , , where is a closed densely defined Hamiltonian ( -skew-self-adjoint) operator on with and is a function on [0, 1] whose values are bounded operators
Symplectic Hamiltonian HDG methods for wave propagation phenomena
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2017-12-01
We devise the first symplectic Hamiltonian hybridizable discontinuous Galerkin (HDG) methods for the acoustic wave equation. We discretize in space by using a Hamiltonian HDG scheme, that is, an HDG method which preserves the Hamiltonian structure of the wave equation, and in time by using symplectic, diagonally implicit and explicit partitioned Runge-Kutta methods. The fundamental feature of the resulting scheme is that the conservation of a discrete energy, which is nothing but a discrete version of the original Hamiltonian, is guaranteed. We present numerical experiments which indicate that the method achieves optimal approximations of order k + 1 in the L2-norm when polynomials of degree k ≥ 0 and Runge-Kutta time-marching methods of order k + 1 are used. In addition, by means of post-processing techniques and by increasing the order of the Runge-Kutta method to k + 2, we obtain superconvergent approximations of order k + 2 in the L2-norm for the displacement and the velocity. We also present numerical examples that corroborate that the methods conserve energy and that they compare favorably with dissipative HDG schemes, of similar accuracy properties, for long-time simulations.
Measure synchronization in a coupled Hamiltonian associated with ...
African Journals Online (AJOL)
We report here, the existence of measure synchronization (MS) in a coupled Hamiltonian system associated with the motion of particles in a periodic potential of the pendulum type. We show that the oscillators can assume chaotic MS stares vis quasiperiodic measure desynchrononized state. In the chaotic MS state, the ...
The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
Johnson-Freyd, Theo
2016-12-01
We show that the Morita equivalences Cliff(4) ≃ H, Cliff(7) ≃ Cliff(-1), and Cliff(8) ≃ R arise from quantizing the Hamiltonian reductions R^{0|4} // Spin(3), R^{0|7} // G_2, and R^{0|8} // Spin(7), respectively.
On self-adjointness of singular Floquet Hamiltonians
DEFF Research Database (Denmark)
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Contact Hamiltonian Dynamics: The Concept and Its Use
Directory of Open Access Journals (Sweden)
Alessandro Bravetti
2017-10-01
Full Text Available We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provided along the way. We conclude by giving insights into possible future directions.
Steiner systems and large non-Hamiltonian hypergraphs
Directory of Open Access Journals (Sweden)
Zsolt Tuza
2006-10-01
Full Text Available From Steiner systems S(k − 2, 2k − 3, v, we construct k-uniform hyper- graphs of large size without Hamiltonian cycles. This improves previous estimates due to G. Y. Katona and H. Kierstead [J. Graph Theory 30 (1999, pp. 205–212].
Many-body Hamiltonian with screening parameter and ionization ...
Indian Academy of Sciences (India)
We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature (0) and the ionization energy (). We show that the existence of this total energy eigenvalue, 0 ± , does not violate ...
Port-Hamiltonian modeling for soft-finger manipulation
Ficuciello, F.; Carloni, R.; Visser, L. C.; Stramigioli, S.
2010-01-01
In this paper, we present a port-Hamiltonian model of a multi-fingered robotic hand, with soft-pads, while grasping and manipulating an object. The algebraic constraints of the interconnected systems are represented by a geometric object, called Dirac structure. This provides a powerful way to
Geometry and topology in hamiltonian dynamics and statistical mechanics
Pettini, Marco
2007-01-01
Explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. This book provides an overview of the research in the area. Using geometrical thinking to solve fundamental problems in these areas could be highly productive
Geometry of KAM tori for nearly integrable Hamiltonian systems
Broer, Hendrik; Cushman, Richard; Fassò, Francesco; Takens, Floris
We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangian tori by gluing together local KAM conjugacies with the help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to the
Geometry of torus bundles in integrable Hamiltonian systems
Lukina, Olga
2008-01-01
Thesis is concerned with global properties of Lagrangian bundles, i.e. symplectic n-torus bundles, as these occur in integrable Hamiltonian systems. It treats obstructions to triviality and concerns with classification of such bundles, as well as with manifestations of global invariants in
Hamiltonian systems, Titchmarsh-Weyl coefficients, and models
Dijksma, A.
1996-01-01
This note concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations in an L(2)-space with a boundary condition depending linearly on the eigenvalue parameter. We show that the spectral properties (in particular, the embedded eigenvalues) of this problem can be
On the Hamiltonian Formulation of Nonholonomic Mechanical Systems
Schaft, A.J. van der; Maschke, B.M.
1994-01-01
A simple procedure is provided to write the equations of motion of mechanical systems with constraints as Hamiltonian equations with respect to a “Poisson” bracket on the constrained state space, which does not necessarily satisfy the Jacobi identity. It is shown that the Jacobi identity is
On the Hamiltonian formulation of nonholonomic mechanical systems
van der Schaft, Arjan; Maschke, B.M.
1994-01-01
A simple procedure is provided to write the equations of motion of mechanical systems with constraints as Hamiltonian equations with respect to a ¿Poisson¿ bracket on the constrained state space, which does not necessarily satisfy the Jacobi identity. It is shown that the Jacobi identity is
On the Curvature and Heat Flow on Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Ohta Shin-ichi
2014-01-01
Full Text Available We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.
Bohr Hamiltonian with different mass parameters applied to band ...
Indian Academy of Sciences (India)
pp. 1055–1066. Bohr Hamiltonian with different mass parameters applied to band structures of Eu isotopes built on Nilsson orbitals. M J ERMAMATOV1,∗, H YÉPEZ-MARTÍNEZ2 and P C SRIVASTAVA3. 1Institute of Nuclear Physics, Ulughbek, Tashkent 100214, Uzbekistan. 2Universidad Autónoma de la Ciudad de México ...
An ecosystem approach to malaria control in an urban setting
Directory of Open Access Journals (Sweden)
Carrasquilla Gabriel
2001-01-01
Full Text Available We conducted a research project aimed at strengthening local government and the community for a sustainable malaria control strategy. The project began with a baseline diagnosis of malaria prevalence, a KAP survey, entomology, and health services delivery, after which an epidemiological study was performed to identify risk factors associated with malaria, thereafter used to plan intervention measures. A program evaluation was conducted five years later. By using an ecosystem approach to reanalyze data, this paper discusses how malaria arises from a complex interaction of cultural, economic, ecological, social, and individual factors. Intervention measures require an intersectorial and transdisciplinary approach that does not exist at the moment. Health sector leadership is limited, and there is no true community participation. Implications for research, including the use of qualitative and quantitative methods, study design, and complexity of data analysis are discussed. Finally, implications for malaria control are discussed, stressing the differences between the ecosystem and integrated disease control approaches.
Controller synthesis for negative imaginary systems: a data driven approach
Mabrok, Mohamed
2016-02-17
The negative imaginary (NI) property occurs in many important applications. For instance, flexible structure systems with collocated force actuators and position sensors can be modelled as negative imaginary systems. In this study, a data-driven controller synthesis methodology for NI systems is presented. In this approach, measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function. Then, this controller response is used to identify the controller transfer function using system identification methods. © The Institution of Engineering and Technology 2016.
Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
The control-of-consumption approach to alcohol abuse prevention
DEFF Research Database (Denmark)
Ravn, Ib
1987-01-01
Key empirical studies of the postulates of the single-distribution theory and the associated control-of-consumption approach are reviewed. The review is organized in terms of the six links possible between the four variables of the "Ledermann string" (availability, average consumption, proportion...... of heavy consumers, and prevalence of damage) presented in Part I. It is concluded that, on the whole, the available evidence is too inconsistent to support the control-of-consumption approach and that a more comprehensive understanding of alcohol abuse and prevention is needed....
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.
Model predictive control approach for a CPAP-device
Directory of Open Access Journals (Sweden)
Scheel Mathias
2017-09-01
Full Text Available The obstructive sleep apnoea syndrome (OSAS is characterized by a collapse of the upper respiratory tract, resulting in a reduction of the blood oxygen- and an increase of the carbon dioxide (CO2 - concentration, which causes repeated sleep disruptions. The gold standard to treat the OSAS is the continuous positive airway pressure (CPAP therapy. The continuous pressure keeps the upper airway open and prevents the collapse of the upper respiratory tract and the pharynx. Most of the available CPAP-devices cannot maintain the pressure reference [1]. In this work a model predictive control approach is provided. This control approach has the possibility to include the patient’s breathing effort into the calculation of the control variable. Therefore a patient-individualized control strategy can be developed.
An integrated approach to the control of magnetically confined plasmas
Energy Technology Data Exchange (ETDEWEB)
Albanese, R.; Ambrosino, G.; Ariola, M.; Bagatin, M.; Bellina, F.; Bettini, P.; Borghi, C.A.; Chitarin, G.; Coccorese, E.; Formisano, A.; Fresa, R.; De Magistris, M.; Gnesotto, F.; Guarnieri, M.; Marchiori, G.; Martone, R.; Pironti, A.; Ribani, P.L.; Rubinacci, G.; Stella, A. E-mail: stella@uniud.it; Trevisan, F.; Villone, F
2001-10-01
In this paper, a short review of the work done in the framework of a nation-wide research programme on 'Models and Methods for Plasma Control in Magnetically Confined Fusion Experiments' is presented. The broad aim of the overall programme is to develop and propose a new effective and reliable approach to the on-line plasma control for future fusion experiments, starting from the today's theoretical background, validated by experimental evidence from a number of tests performed on existing experiments. The proposed formulation to approach the control problem is a linearized model in terms of suitable state variables and input/output relationships. The basic project has been subdivided into four major areas of investigation: the linearized response plasma model, the three-dimensional electromagnetic model, the identification techniques and finally the plasma control requirements. The most remarkable results, achieved so far in each area above, are presented in the paper.
New approaches in intelligent control techniques, methodologies and applications
Kountchev, Roumen
2016-01-01
This volume introduces new approaches in intelligent control area from both the viewpoints of theory and application. It consists of eleven contributions by prominent authors from all over the world and an introductory chapter. This volume is strongly connected to another volume entitled "New Approaches in Intelligent Image Analysis" (Eds. Roumen Kountchev and Kazumi Nakamatsu). The chapters of this volume are self-contained and include summary, conclusion and future works. Some of the chapters introduce specific case studies of various intelligent control systems and others focus on intelligent theory based control techniques with applications. A remarkable specificity of this volume is that three chapters are dealing with intelligent control based on paraconsistent logics.
[Individual, community, regulatory, and systemic approaches to tobacco control interventions].
Gorini, Giuseppe
2011-01-01
During the 60s and the 70s strategies for decreasing initiation or quitting have been developed, in order to find those with high success rates. Unfortunately, interventions with an individual approach involved few smokers, so their impact in decreasing smoking prevalence was limited. The socio-ecological model offers a theoretical framework to community interventions for smoking cessation developed during the 80s, in which smoking was considered not only an individual, but also a social problem. In the 80s and the 90s smoking cessation community trials were developed, such as the Community Intervention Trial for Smoking Cessation (COMMIT). Afterwards, policy interventions (price policy; smoking bans in public places; advertising bans; bans of sales to minors) were developed, such as the American Stop Smoking Intervention Study for Cancer Prevention (ASSIST). California has been the first State all over the world to develop a comprehensive Tobacco Control Program in 1988, becoming the place for an ever-conducted natural experiment. All policy interventions in tobacco control have been finally grouped together in the World Health Organization - Framework Convention on Tobacco Control (WHO-FCTC), the first Public Health Treaty. Study designs have changed, according to the individual, community, or regulatory approaches: the classical randomized controlled trials (RCTs), in which the sampling unit is the individual, have been carried out for the evaluation of smoking cessation treatments, whereas cluster RCTs, in which the sampling unit is the community, have been conducted for evaluating community interventions, such as COMMIT. Finally, quasi-experimental studies (before/after study; prospective cohorts, both with a control group), in which the observational unit is a State, have been used for evaluating tobacco control policies, such as ASSIST and the International Tobacco Control Policy Evaluation Project. Although the successes of the last 20 years, tobacco
Urbanowski, K.
2003-01-01
We start from a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next we show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses CPT transformation properties, which differ from those of the LOY effective Hamiltonian. These properties of the mentioned effective Hamiltonians ar...
Effective Floquet Hamiltonian for spin I = 1 in magic angle spinning ...
Indian Academy of Sciences (India)
WINTEC
S S H. = +. −. (5). The diagonal part of the above Hamiltonian gives diagonal correction of order λ2 to the zeroth order. Hamiltonian in addition to the diagonal term of H2. Thus the Hamiltonian (1). (1). 2. (1). 0. 1. 2 d d. H. H. H λ λ. +. + is more effective than the Hamiltonian. 2. 0. 1. 2 . d d. H. H. H λ λ. +. +. The general term (1).
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
Passive vibration control: a structure-immittance approach
Zhang, Sara Ying; Jiang, Jason Zheng; Neild, Simon A.
2017-05-01
Linear passive vibration absorbers, such as tuned mass dampers, often contain springs, dampers and masses, although recently there has been a growing trend to employ or supplement the mass elements with inerters. When considering possible configurations with these elements broadly, two approaches are normally used: one structure-based and one immittance-based. Both approaches have their advantages and disadvantages. In this paper, a new approach is proposed: the structure-immittance approach. Using this approach, a full set of possible series-parallel networks with predetermined numbers of each element type can be represented by structural immittances, obtained via a proposed general formulation process. Using the structural immittances, both the ability to investigate a class of absorber possibilities together (advantage of the immittance-based approach), and the ability to control the complexity, topology and element values in resulting absorber configurations (advantages of the structure-based approach) are provided at the same time. The advantages of the proposed approach are demonstrated through two case studies on building vibration suppression and automotive suspension design, respectively.
Mananga, Eugene Stephane
2018-01-01
The utility of the average Hamiltonian theory and its antecedent the Magnus expansion is presented. We assessed the concept of convergence of the Magnus expansion in quadrupolar spectroscopy of spin-1 via the square of the magnitude of the average Hamiltonian. We investigated this approach for two specific modified composite pulse sequences: COM-Im and COM-IVm. It is demonstrated that the size of the square of the magnitude of zero order average Hamiltonian obtained on the appropriated basis is a viable approach to study the convergence of the Magnus expansion. The approach turns to be efficient in studying pulse sequences in general and can be very useful to investigate coherent averaging in the development of high resolution NMR technique in solids. This approach allows comparing theoretically the two modified composite pulse sequences COM-Im and COM-IVm. We also compare theoretically the current modified composite sequences (COM-Im and COM-IVm) to the recently published modified composite pulse sequences (MCOM-I, MCOM-IV, MCOM-I_d, MCOM-IV_d).
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Cervera, J.; van der Schaft, Arjan; Baños, A.
2007-01-01
Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Cervera, J.; Schaft, A.J. van der; Baños, A.
Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results
A "Hybrid" Approach for Synthesizing Optimal Controllers of Hybrid Systems
DEFF Research Database (Denmark)
Zhao, Hengjun; Zhan, Naijun; Kapur, Deepak
2012-01-01
We propose an approach to reduce the optimal controller synthesis problem of hybrid systems to quantifier elimination; furthermore, we also show how to combine quantifier elimination with numerical computation in order to make it more scalable but at the same time, keep arising errors due...
Design support for motion control systems : a mechatronic approach
Coelingh, H.J.
2000-01-01
This thesis discusses the development of a design support for motion control systems, using a mechatronic design approach. The placement module of the Philips Fast Component Mounter (FCM), an industrial pick-and-place machine, is used as a running example. To fully exploit the advantages of
From integrated control to integrated farming, an experimental approach
Vereijken, P.H.
1989-01-01
Integrated control or integrated pest management (IPM), as envisaged originally, is not being practised to any large extent in arable farming, notwithstanding considerable research efforts. The reasons for this are discussed. A more basic approach called integrated farming is suggested. Preliminary
Modeling Alaska boreal forests with a controlled trend surface approach
Mo Zhou; Jingjing Liang
2012-01-01
An approach of Controlled Trend Surface was proposed to simultaneously take into consideration large-scale spatial trends and nonspatial effects. A geospatial model of the Alaska boreal forest was developed from 446 permanent sample plots, which addressed large-scale spatial trends in recruitment, diameter growth, and mortality. The model was tested on two sets of...
Cost effective and shape controlled approach to synthesize ...
Indian Academy of Sciences (India)
Cost effective and shape controlled approach to synthesize hierarchically assembled NiO nanoflakes for the removal of toxic heavy metal ions in aqueous solution. K Yogesh Kumar H B Muralidhara Y Arthoba Nayaka H Hanumanthappa M S Veena S R Kiran Kumar. Volume 38 Issue 1 February 2015 pp 271-282 ...
A novel practical control approach for rate independent hysteretic systems.
Goforth, Frank J; Zheng, Qing; Gao, Zhiqiang
2012-05-01
A disturbance rejection based control approach, active disturbance rejection control (ADRC), is proposed for hysteretic systems with unknown characteristics. It is an appealing alternative to hysteresis compensation because it does not require a detailed model of hysteresis, by treating the nonlinear hysteresis as a common disturbance and actively rejecting it. The stability characteristic of the ADRC is analyzed. It is shown that, in the face of the inherent dynamic uncertainties, the estimation and closed-loop tracking errors of ADRC are bounded, with their bounds monotonously decreasing with the observer and controller bandwidths, respectively. Simulation results on a typical hysteretic system further demonstrate the effectiveness of the proposed approach. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
John Cortés-Romero
2013-01-01
Full Text Available This work proposes an active disturbance rejection approach for the establishment of a sliding mode control strategy in fault-tolerant operations. The core of the proposed active disturbance rejection assistance is a Generalized Proportional Integral (GPI observer which is in charge of the active estimation of lumped nonlinear endogenous and exogenous disturbance inputs related to the creation of local sliding regimes with limited control authority. Possibilities are explored for the GPI observer assisted sliding mode control in fault-tolerant schemes. Convincing improvements are presented with respect to classical sliding mode control strategies. As a collateral advantage, the observer-based control architecture offers the possibility of chattering reduction given that a significant part of the control signal is of the continuous type. The case study considers a classical DC motor control affected by actuator faults, parametric failures, and perturbations. Experimental results and comparisons with other established sliding mode controller design methodologies, which validate the proposed approach, are provided.
Trajectory tracking in quadrotor platform by using PD controller and LQR control approach
Islam, Maidul; Okasha, Mohamed; Idres, Moumen Mohammad
2017-11-01
The purpose of the paper is to discuss a comparative evaluation of performance of two different controllers i.e. Proportional-Derivative Controller (PD) and Linear Quadratic Regulation (LQR) in Quadrotor dynamic system that is under-actuated with high nonlinearity. As only four states can be controlled at the same time in the Quadrotor, the trajectories are designed on the basis of the four states whereas three dimensional position and rotation along an axis, known as yaw movement are considered. In this work, both the PD controller and LQR control approach are used for Quadrotor nonlinear model to track the trajectories. LQR control approach for nonlinear model is designed on the basis of a linear model of the Quadrotor because the performance of linear model and nonlinear model around certain nominal point is almost similar. Simulink and MATLAB software is used to design the controllers and to evaluate the performance of both the controllers.
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.
Periodic Solutions of Hamiltonian Systems: A Survey.
1980-12-01
where z = (p, q) and P ( , J being the identity matrix in j 0 R . Also of interest is the forced analogue of (HS) (FHS) PH =Hzlt, Z) where H depends...oscillazioni periodiche d’une sistema dinamico , Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 19, (1934), 234-237. [15] Arnold, V. I... CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE See Item 18 below J/ ~),~~~* ** / Dpcembere 1980 Fl //,(I~..*.- .4. / 13 . NUMBER OF PAGES 23 14
A nonlinear optimal control approach for chaotic finance dynamics
Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.
2017-11-01
A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.
Anyons are not energy eigenspaces of quantum double Hamiltonians
Kómár, Anna; Landon-Cardinal, Olivier
2017-11-01
Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a two-dimensional spin lattice. Their Hamiltonian defines the ground space by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among nontrivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice.
Fluctuations in a Spin Chain and the Entanglement Hamiltonian
Turner, Ari; Demler, Eugene
2014-03-01
How are quantum fluctuations and thermal fluctuations different in many-body systems? I will compare the variance of the fluctuations of spin in a segment of a spin chain in the ground state and at a finite temperature, showing that fluctuations in the ground state are much more correlated than in the thermal state. The full distribution function of spin can also be determined, and is non-Gaussian. These effects could possibly be measured in a chain of sodium atoms in an optical lattice. The method involves mapping the system to an imaginary thermal system called the ``entanglement Hamiltonian.'' Measuring the ground state fluctuations of the spin chain gives an indirect way of measuring the entanglement Hamiltonian.
Applications of the trilinear Hamiltonian with three trapped ions
Hablutzel Marrero, Roland Esteban; Ding, Shiqian; Maslennikov, Gleb; Gan, Jaren; Nimmrichter, Stefan; Roulet, Alexandre; Dai, Jibo; Scarani, Valerio; Matsukevich, Dzmitry
2017-04-01
The trilinear Hamiltonian a† bc + ab†c† , which describes a nonlinear interaction between harmonic oscillators, can be implemented to study different phenomena ranging from simple quantum models to quantum thermodynamics. We engineer this coupling between three modes of motion of three trapped 171Yb+ ions, where the interaction arises naturally from their mutual (anharmonic) Coulomb repulsion. By tuning our trapping parameters we are able to turn on / off resonant exchange of energy between the modes on demand. We present applications of this Hamiltonian for simulations of the parametric down conversion process in the regime of depleted pump, a simple model of Hawking radiation, and the Tavis-Cummings model. We also discuss the implementation of the quantum absorption refrigerator in such system and experimentally study effects of quantum coherence on its performance. This research is supported by the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.
RG-Whitham dynamics and complex Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Gorsky
2015-06-01
Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.
Metastable states in parametrically excited multimode Hamiltonian systems
Kirr, E
2003-01-01
Consider a linear autonomous Hamiltonian system with time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, bound states directly to bound states, as well as coupling among bound states, which is mediate...
Geometrical approach to neural net control of movements and posture
Pellionisz, A. J.; Ramos, C. F.
1993-01-01
In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.
Tsunami generation by ocean floor rupture front propagation: Hamiltonian description
Directory of Open Access Journals (Sweden)
V. I. Pavlov
2009-02-01
Full Text Available The Hamiltonian method is applied to the problem of tsunami generation caused by a propagating rupture front and deformation of the ocean floor. The method establishes an alternative framework for analyzing the tsunami generation process and produces analytical expressions for the power and directivity of tsunami radiation (in the far-field for two illustrative cases, with constant and gradually varying speeds of rupture front propagation.
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.
Hamiltonian ODE's on a Space of Deficient Measures
Chayes, L.; Gangbo, W.; Lei, H. K.
2011-01-01
We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained b...
Hamiltonian ODEs on a space of deficient measures
Chayes, L.; Gangbo, W.; Lei, H. K
2013-01-01
We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained b...
Escapes in Hamiltonian systems with multiple exit channels: Part II
Zotos, Euaggelos E.
2015-01-01
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape towards the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four diffe...
Theoretical studies of the spin-Hamiltonian parameters for the ...
Indian Academy of Sciences (India)
Theoretical studies of spin-Hamiltonian (SH) parameters associated with. Pr4+ in Sr2CeO4 single crystals have been made by ... other is the perturbation theory method (PTM) [7,8]. As suggested in previous studies [7–10], the PTM ... k (θj,φj) can be obtained from the local lattice struc- tural parameters of the studied system.
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Jovanović Božidar
2016-01-01
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on ...
Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions
Directory of Open Access Journals (Sweden)
Capozziello S.
2005-07-01
Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.
Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.
Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos
2017-07-14
In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩
Production and transfer of energy and information in Hamiltonian systems.
Antonopoulos, Chris G; Bianco-Martinez, Ezequiel; Baptista, Murilo S
2014-01-01
We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.
Production and transfer of energy and information in Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Chris G Antonopoulos
Full Text Available We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.
Runtime of unstructured search with a faulty Hamiltonian oracle
Temme, Kristan
2014-08-01
We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003)., 10.1103/PhysRevA.68.052313]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773-781]. Here, we extend this result to the continuous-time setting.
Optimized t-expansion method for the Rabi Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Travenec, Igor, E-mail: fyzitrav@savba.sk [Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Samaj, Ladislav [Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia)
2011-10-31
A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E{sub 0} of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E{sub 0} is assumed to be stationary with respect to the free parameters. A high accuracy of E{sub 0} estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10{sup -4} (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E{sub 1}, with the relative error smaller than 10{sup -2} (1%). -- Highlights: → We study the ground state energy of the Rabi Hamiltonian. → We use the t-expansion method with an optimized trial function. → High accuracy of estimates is achieved, the relative error being smaller than 0.01%. → The calculation of the first excited state energy is made. The method has a general applicability.
Active control of nonlinear aseismic structures: MRAC approach
Zou, Yin Sheng; Zou, Xiang; Wang, Jian Ping
1996-05-01
The responses of structures under seismic conditions present very high nonlinearity due to both the parameter variations of the structures and the nonlinearities of the forces induced by ground motions. On the other hand, an adaptive controller (stabilizer) can adjust itself continuously to the changes in the system. Therefore, this paper examines the applicability of the adaptive controller to the nonlinear seismic structures so as to enable us to design economic and attractive structures which can successfully withstand the earthquake loading. The approach to the desired active control employs model reference adaptive control (MRAC) technique. Initial parameters of the system, which are mass matrix, damping matrix and stiffness matrix, are identified using off-line algorithms. An adaptive controller is, then, introduced to change the system characteristics of the target structure so that the responses of the controlled structure, under seismic conditions, will follow the expected ideal responses which are the output of a reference model. The reference model is constructed according to the specifications on the performance requirements of structures under earthquake excitation. It is shown that the MRAC technique can be applied to solve the active control problem of nonlinear seismic responses of structures in an effective and efficient fashion. The controller proposed demonstrates rational self-tuning capability to the random changes of earthquake excitation as well as to the time-varying property of nonlinear seismic structures under strong- motion earthquake. The theoretical results obtained are illustrated and verified with numerical examples.
Multimodel Predictive Control Approach for UAV Formation Flight
Directory of Open Access Journals (Sweden)
Chang-jian Ru
2014-01-01
Full Text Available Formation flight problem is the most important and interesting problem of multiple UAVs (unmanned aerial vehicles cooperative control. In this paper, a novel approach for UAV formation flight based on multimodel predictive control is designed. Firstly, the state equation of relative motion is obtained and then discretized. By the geometrical method, the characteristic points of state are determined. Afterwards, based on the linearization technique, the standard linear discrete model is obtained at each characteristic state point. Then, weighted model set is proposed using the idea of T-S (Takagi-Sugeno fuzzy control and the predictive control is carried out based on the multimodel method. Finally, to verify the performance of the proposed method, two different simulation scenarios are performed.
Novel approaches to control of parasites—a workshop.
Waller, P J; Thamsborg, S M; Larsen, M; Knox, M R; Peter, R; Miller, J E; Molento, M B; Beriajaya; Hood, G M
2004-10-28
With the advent of helminth parasite populations that have developed resistance to anthelmintics over the last decade or so, especially in small ruminants, sustainable productivity has been threatened. This workshop on novel approaches to control was held at the 19th International Conference of the World Association for the Advancement of Veterinary Parasitology (WAAVP) at New Orleans,LA, USA, during 10–14 August 2003. The workshop was organized and chaired by J.E. Miller and P.J. Waller. Novel or alternative approaches to control have been the focus of research (basic and applied) in many parts of the world. The objective of the workshop was to discuss where we have been and what direction(s) appears to be viable for both the short and long term future. In the long term, all represented regions at the workshop have promulgated programs where breeding for resistance may be the best approach as genes for resistance can be fixed in host populations. However,it does take many years to achieve results and the question of tradeoff concerning alteration of production traits needs further evaluation. Vaccination, especially against Haemonchus contortus,has been a thrust of laboratories in Scotland and Australia where natural “hidden gut” antigens have shown promise, but recombinant products have yet to be developed. In Europe, North and South America, Australia, South Africa and Asia, biocontrol using the nematode-trapping fungus Duddingtonia flagrans has been shown to be effective under experimental conditions, but some field evaluations have been disappointing. Most recently, the FAMACHA system was developed in South Africa. This system is directly and immediately applicable to all regions where H. contortus is a problem. Although not a new or novel approach, copper-oxide wire particles have been revived as a means to control H. contortus.Work being done in Europe, North and South America,South Africa and Australia have shown very encouraging results and can
Mathematical models for therapeutic approaches to control HIV disease transmission
Roy, Priti Kumar
2015-01-01
The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...
A direct approach to linear-quadratic stochastic control
Directory of Open Access Journals (Sweden)
Tyrone E. Duncan
2017-01-01
Full Text Available A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
Lagrangian controllability of inviscid perfect fluids: a constructive approach
Horsin, T.; Kavian, O
2016-01-01
We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal com- putations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical si...
Sun, L.G.; De Visser, C.C.; Chu, Q.P.; Falkena, W.
2013-01-01
Recently, an incremental type sensor based backstepping (SBB) control approach, based on singular perturbation theory and Tikhonov’s theorem, has been proposed. This Lyapunov function based method uses measurements of control variables and less model knowledge, and it is not susceptible to the model
A model predictive control approach to design a parameterized adaptive cruise control
Naus, G.J.L.; Ploeg, J.; Molengraft, M.J.G. van de; Heemels, W.P.M.H.; Steinbuch, M.
2010-01-01
The combination of different desirable characteristics and situation-dependent behavior cause the design of adaptive cruise control (ACC) systems to be time consuming and tedious. This chapter presents a systematic approach for the design and tuning of an ACC, based on model predictive control
Geospatial Approaches to Cancer Control and Population Sciences.
Schootman, Mario; Gomez, Scarlett Lin; Henry, Kevin A; Paskett, Electra D; Ellison, Gary L; Oh, April; Taplin, Stephen H; Tatalovich, Zaria; Berrigan, David A
2017-04-01
Cancer incidence and mortality display strong geographic patterns worldwide and in the United States (1, 2). The environment where individuals live, work, and play is increasingly being recognized as important across the cancer control continuum, including the risk of cancer development, detection, diagnosis, treatment, mortality, and survivorship (3-5). At the same time, emergent technological capacity in geographic information systems (GIS) and mapping, along with increasing sophistication in applied spatial methods, has resulted in a growing research community developing and applying geospatial approaches in health research (5). Through collaborative, transdisciplinary efforts, and continued data collection efforts, there is great potential to apply these emerging geospatial approaches to various aspects of cancer prevention and control to inform etiology and target interventions and implementation of efficacious risk-reducing strategies. Cancer Epidemiol Biomarkers Prev; 26(4); 472-5. ©2017 AACRSee all the articles in this CEBP Focus section, "Geospatial Approaches to Cancer Control and Population Sciences." ©2017 American Association for Cancer Research.
[Integrated approach to prevention and control of cardiovascular diseases].
Rakić, Dušica; Jakovljević, Djordje
2011-01-01
From 1984 to 2004, the city of Novi Sad participated in the international MONICA (Multinational MONItoring of trends and determinants in CArdiovascular disease) project, as one of the 38 research centres form 21 countries around the world and in CINDI (Countrywide Integrated Noncommunicable Disease Intervention Programme) programme. Objective was to indicate the advantages of the integrated approach to prevention and control of the cardiovascular disease (CVD) over mono-programmes and still present curative approach. Additional objective was the assessment of the vulnerability from the leading risk factors of the population of Novi Sad, based on the results and experience gained in realization of international projects. We analysed the results obtained in the countries where MONICA project and CINDI programme have been applied. The results of their application in Novi Sad are analysed (the trend of the prevalence of risk factors, the incidence of coronary and cerebrovascular events). The prevalence of risk factors (except smoking), the incidence of coronary and cerebrovascular events are significantly increasing and are in positive correlation with the values of the linear trend.The decrease was only recorded in 1987 (the implementation of the intervention programme). The review of results and experiences in international projects and programs, clearly indicate the advantage of an integrated approach to prevention and control of CVD in relation to monoprograme. The great vulnerability of the population of Novi Sad of the risk factors of CVD points out the necessity of their reductions by the principles of integrated programmes of prevention and control.
Human rights-based approach to tobacco control.
Dresler, Carolyn; Lando, Harry; Schneider, Nick; Sehgal, Hitakshi
2012-03-01
The Framework Convention for Tobacco Control (FCTC) is currently the most potent tool for implementation of tobacco control laws across the globe. The FCTC is derivative from previously constructed international human rights conventions. These previous conventions have enforcement mechanisms, unlike the FCTC. However, the FCTC relies on state parties to report periodically on its implementation rather than on a continuous monitoring system. The Human Rights and Tobacco Control Network proposes that abiding by the principles of human rights delineated by international treaties, citizens across the globe can demand effective action for tobacco control. This paper explains the link between fundamental human rights and the right to tobacco control. Mechanisms are described to link the FCTC and its principles with human rights-based monitoring reports, which are provided to oversight committees for the other human rights conventions. The initial work of the Human Rights and Tobacco Control Network is summarised and considers the future directions for the human rights-based approach to tobacco control.
Energy Technology Data Exchange (ETDEWEB)
Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit
2012-08-15
Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.
The search for a Hamiltonian whose energy spectrum coincides with the Riemann zeta zeroes
Aschheim, Raymond; Perelman, Carlos Castro; Irwin, Klee
Inspired by the Hilbert-Polya proposal to prove the Riemann Hypothesis we have studied the Schroedinger QM equation involving a highly nontrivial potential, and whose self-adjoint Hamiltonian operator has for its energy spectrum one which approaches the imaginary parts of the zeta zeroes only in the asymptotic (very large N) region. The ordinates λn are the positive imaginary parts of the nontrivial zeta zeroes in the critical line :sn = 1 2 + iλn. The latter results are consistent with the validity of the Bohr-Sommerfeld semi-classical quantization condition. It is shown how one may modify the parameters which define the potential, and fine tune its values, such that the energy spectrum of the (modified) Hamiltonian matches not only the first two zeroes but the other consecutive zeroes. The highly nontrivial functional form of the potential is found via the Bohr-Sommerfeld quantization formula using the full-fledged Riemann-von Mangoldt counting formula (without any truncations) for the number N(E) of zeroes in the critical strip with imaginary part greater than 0 and less than or equal to E.
A bioinspired approach for a multizone temperature control system
Energy Technology Data Exchange (ETDEWEB)
Pantoja, A; Quijano, N [Departamento de IngenierIa Electrica y Electronica, Universidad de los Andes, Bogota (Colombia); Leirens, S, E-mail: ad.pantoja24@uniandes.edu.c, E-mail: nquijano@uniandes.edu.c, E-mail: sylvain.leirens@orange.fr [La Pillayre, 63160 Montmorin (France)
2011-03-15
Bioinspired design approaches seek to exploit nature in order to construct optimal solutions for engineering problems as uniform temperature control in multizone systems. The ideal free distribution (IFD) is a concept from behavioural ecology, which describes the arrangement of individuals in different habitats such that at equilibrium, all habitats are equally suitable. Here, we relax the IFD's main assumptions using the standing-crop idea to introduce dynamics into the supplies of each habitat. Then, we make an analogy with a multizone thermal system to propose a controller based on the replicator dynamics model, in order to obtain a maximum uniform temperature subject to constant power injection. Besides, we analytically show that the equilibrium point of the controlled system is asymptotically stable. Finally, some practical results obtained with a testbed and comparisons with the theoretical results are presented.
Stochastic control approaches for sensor management in search and exploitation
Hitchings, Darin Chester
Recent improvements in the capabilities of autonomous vehicles have motivated their increased use in such applications as defense, homeland security, environmental monitoring, and surveillance. To enhance performance in these applications, new algorithms are required to control teams of robots autonomously and through limited interactions with human operators. In this dissertation we develop new algorithms for control of robots performing information-seeking missions in unknown environments. These missions require robots to control their sensors in order to discover the presence of objects, keep track of the objects, and learn what these objects are, given a fixed sensing budget. Initially, we investigate control of multiple sensors, with a finite set of sensing options and finite-valued measurements, to locate and classify objects given a limited resource budget. The control problem is formulated as a Partially Observed Markov Decision Problem (POMDP), but its exact solution requires excessive computation. Under the assumption that sensor error statistics are independent and time-invariant, we develop a class of algorithms using Lagrangian Relaxation techniques to obtain optimal mixed strategies using performance bounds developed in previous research. We investigate alternative Receding Horizon (RH) controllers to convert the mixed strategies to feasible adaptive-sensing strategies and evaluate the relative performance of these controllers in simulation. The resulting controllers provide superior performance to alternative algorithms proposed in the literature and obtain solutions to large-scale POMDP problems several orders of magnitude faster than optimal Dynamic Programming (DP) approaches with comparable performance quality. We extend our results for finite action, finite measurement sensor control to scenarios with moving objects. We use Hidden Markov Models (HMMs) for the evolution of objects, according to the dynamics of a birth-death process. We develop a
S-variable approach to LMI-based robust control
Ebihara, Yoshio; Arzelier, Denis
2015-01-01
This book shows how the use of S-variables (SVs) in enhancing the range of problems that can be addressed with the already-versatile linear matrix inequality (LMI) approach to control can, in many cases, be put on a more unified, methodical footing. Beginning with the fundamentals of the SV approach, the text shows how the basic idea can be used for each problem (and when it should not be employed at all). The specific adaptations of the method necessitated by each problem are also detailed. The problems dealt with in the book have the common traits that: analytic closed-form solutions are not available; and LMIs can be applied to produce numerical solutions with a certain amount of conservatism. Typical examples are robustness analysis of linear systems affected by parametric uncertainties and the synthesis of a linear controller satisfying multiple, often conflicting, design specifications. For problems in which LMI methods produce conservative results, the SV approach is shown to achieve greater accuracy...
Present and future approaches for the control of caries.
Anusavice, Kenneth J
2005-05-01
This article summarizes current and potential future approaches for the management of caries. Current surveys suggest that traditional "drill, fill, and bill" dentistry is still widely practiced in the United States in spite of considerable evidence that supports a minimally invasive treatment approach. Because there is a wide variability in treatment decisions on when and how to prevent new lesions, on how to arrest the progression of existing lesions, and on when and how to place initial and replacement restorations, the findings from some studies differ significantly from the results of other studies. While fluoride treatments are known to prevent a percentage of new lesions, they do not have the ability to prevent all caries lesions. Modern management of caries entails treating patients according to risk and monitoring early lesions in tooth surfaces that are not cavitated. Although we know that the dmfs score for children is a powerful predictor of caries increment in permanent teeth of these children a few years later, this score is rarely used in private practice as a measure of risk or as a measure of treatment success. Although these modern methods for caries management offer great promise for controlling the disease, they may take decades to apply in a standardized way so that the variability in treatment is reduced. However, during the next two decades, an alternative approach to caries prevention such as replacement therapy and a caries vaccine may become available as a more consistent method of controlling this disease.
Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G
2017-02-17
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Quorum Quenching Mediated Approaches for Control of Membrane Biofouling
Lade, Harshad; Paul, Diby; Kweon, Ji Hyang
2014-01-01
Membrane biofouling is widely acknowledged as the most frequent adverse event in wastewater treatment systems resulting in significant loss of treatment efficiency and economy. Different strategies including physical cleaning and use of antimicrobial chemicals or antibiotics have been tried for reducing membrane biofouling. Such traditional practices are aimed to eradicate biofilms or kill the bacteria involved, but the greater efficacy in membrane performance would be achieved by inhibiting biofouling without interfering with bacterial growth. As a result, the search for environmental friendly non-antibiotic antifouling strategies has received much greater attention among scientific community. The use of quorum quenching natural compounds and enzymes will be a potential approach for control of membrane biofouling. This approach has previously proven useful in diseases and membrane biofouling control by triggering the expression of desired phenotypes. In view of this, the present review is provided to give the updated information on quorum quenching compounds and elucidate the significance of quorum sensing inhibition in control of membrane biofouling. PMID:24910534
Mandra, Salvatore
2017-01-01
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Intelligent Approach to Inventory Control in Logistics under Uncertainty Conditions
Energy Technology Data Exchange (ETDEWEB)
Więcek, P.
2016-07-01
The article presents a proposal for a combined application of fuzzy logic and genetic algorithms to control the procurement process in the enterprise. The approach presented in this paper draws particular attention to the impact of external random factors in the form of demand and lead time uncertainty. The model uses time-variable membership function parameters in a dynamic fashion to describe the modelled output fuzzy (sets) values. An additional element is the use of genetic algorithms for optimisation of fuzzy rule base in the proposed method. The approach presented in this paper was veryfied according to four criteria based on a computer simulation performed on the basis of the actual data from an enterprise. (Author)
Quantum Ensemble Classification: A Sampling-Based Learning Control Approach.
Chen, Chunlin; Dong, Daoyi; Qi, Bo; Petersen, Ian R; Rabitz, Herschel
2017-06-01
Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.
Robust and optimal control a two-port framework approach
Tsai, Mi-Ching
2014-01-01
A Two-port Framework for Robust and Optimal Control introduces an alternative approach to robust and optimal controller synthesis procedures for linear, time-invariant systems, based on the two-port system widespread in electrical engineering. The novel use of the two-port system in this context allows straightforward engineering-oriented solution-finding procedures to be developed, requiring no mathematics beyond linear algebra. A chain-scattering description provides a unified framework for constructing the stabilizing controller set and for synthesizing H2 optimal and H∞ sub-optimal controllers. Simple yet illustrative examples explain each step. A Two-port Framework for Robust and Optimal Control features: · a hands-on, tutorial-style presentation giving the reader the opportunity to repeat the designs presented and easily to modify them for their own programs; · an abundance of examples illustrating the most important steps in robust and optimal design; and · �...
Degree of rate control approach to computational catalyst screening
Energy Technology Data Exchange (ETDEWEB)
Wolcott, Christopher A.; Medford, Andrew J.; Studt, Felix; Campbell, Charles T.
2015-10-01
A new method for computational catalyst screening that is based on the concept of the degree of rate control (DRC) is introduced. It starts by developing a full mechanism and microkinetic model at the conditions of interest for a reference catalyst (ideally, the best known material) and then determines the degrees of rate control of the species in the mechanism (i.e., all adsorbed intermediates and transition states). It then uses the energies of the few species with the highest DRCs for this reference catalyst as descriptors to estimate the rates on related materials and predict which are most active. The predictions of this method regarding the relative rates of twelve late transition metals for methane steam reforming, using the Rh(2 1 1) surface as the reference catalyst, are compared to the most commonly-used approach for computation catalyst screening, the Nørskov–Bligaard (NB) method which uses linear scaling relationships to estimate the energies of all adsorbed intermediates and transition states. It is slightly more accurate than the NB approach when the metals are similar to the reference metal (<0.5 eV different on a plot where the axes are the bond energies to C and O adatoms), but worse when too different from the reference. It is computationally faster than the NB method when screening a moderate number of materials (<100), thus adding a valuable complement to the NB approach. It can be implemented without a microkinetic model if the degrees of rate control are already known approximately, e.g., from experiments.
Mobilising communities for Aedes aegypti control: the SEPA approach
Directory of Open Access Journals (Sweden)
Robert J. Ledogar
2017-05-01
Full Text Available Abstract Camino Verde (the Green Way is an evidence-based community mobilisation tool for prevention of dengue and other mosquito-borne viral diseases. Its effectiveness was demonstrated in a cluster-randomised controlled trial conducted in 2010–2013 in Nicaragua and Mexico. The common approach that brought functional consistency to the Camino Verde intervention in both Mexico and Nicaragua is Socialisation of Evidence for Participatory Action (SEPA. In this article, we explain the SEPA concept and its theoretical origins, giving examples of its previous application in different countries and contexts. We describe how the approach was used in the Camino Verde intervention, with details that show commonalities and differences in the application of the approach in Mexico and Nicaragua. We discuss issues of cost, replicability and sustainability, and comment on which components of the intervention were most important to its success. In complex interventions, multiple components act in synergy to produce change. Among key factors in the success of Camino Verde were the use of community volunteers called brigadistas, the house-to-house visits they conducted, the use of evidence derived from the communities themselves, and community ownership of the undertaking. Communities received the intervention by random assignment; dengue was not necessarily their greatest concern. The very nature of the dengue threat dictated many of the actions that needed to be taken at household and neighbourhood levels to control it. But within these parameters, communities exercised a large degree of control over the intervention and displayed considerable ingenuity in the process. Trial registration ISRCTN27581154 .
Intermediacy between political control and institutional autonomy: A transformative approach
Directory of Open Access Journals (Sweden)
Nirmala Dorasamy
2015-06-01
Full Text Available The public sector is about providing services, managing resources efficiently and securing a return on investment. Producing results and managing performance depends on adaptation, flexibility and creativity. While one may argue for greater control to achieve performance indicators, this has to be underpinned by managerial control systems both internally and externally. Post NPM reforms have tried to respond to the problem of single purpose organisations that have distanced political control. While post NPM reforms tipped the scale toward more political control, it did not restore the balance between control and autonomy. In view of the NPM and post NPM reforms and the accompanying challenges, the paper argues that it is not possible to device a “one size fits all” response to these challenges. In trying to analyse the dilemma of balancing political control and institutional autonomy an institutional theoretical perspective is used by analysing structural and instrumental features (national political environment, cultural features (historical administrative traditions and external constraints (technical and institutional environments. It needs to be recognised that the aforementioned features have constraints. The structural and instrumental features specify the formal constraints on leaderships decisions. These constraints may give political leaders strong hierarchical control or may not give them much direction, but a lot of potential discretionary influence. The cultural features specify that public organisations develop informal norms and values which lead to a distinct institutional culture. While these informal norms and values are infused in formal structures and decision making, it may be inconsistent with the sub-culture, thereby giving it less systemic influence. The technical and institutional environment which focuses on efficiency production and internal culture may develop beliefs over time that cannot be ignored. Christensen
Matrix converter controlled with the direct transfer function approach
DEFF Research Database (Denmark)
Rodriguez, J.; Silva, E.; Blaabjerg, Frede
2005-01-01
Power electronics is an emerging technology. New power circuits are invented and have to be introduced into the power electronics curriculum. One of the interesting new circuits is the matrix converter (MC), and this paper analyses its working principles. A simple model is proposed to represent...... the power circuit, including the input filter. The power semiconductors are modelled as ideal bidirectional switches and the MC is controlled using a direct transfer function approach. The modulation strategy of the converter is explained in a complete and clear form. The commutation problem of two switches...
Toda, Masayoshi
2016-01-01
This book provides readers with alternative robust approaches to control design for an important class of systems characteristically associated with ocean-going vessels and structures. These systems, which include crane vessels, on-board cranes, radar gimbals, and a conductivity temperature and depth winch, are modelled as manipulators with oscillating bases. One design approach is based on the H-infinity control framework exploiting an effective combination of PD control, an extended matrix polytope and a robust stability analysis method with a state-dependent coefficient form. The other is based on sliding-mode control using some novel nonlinear sliding surfaces. The model demonstrates how successful motion control can be achieved by suppressing base oscillations and in the presence of uncertainties. This is important not only for ocean engineering systems in which the problems addressed here originate but more generally as a benchmark platform for robust motion control with disturbance rejection. Researche...
Data-Driven Controller Design The H2 Approach
Sanfelice Bazanella, Alexandre; Eckhard, Diego
2012-01-01
Data-driven methodologies have recently emerged as an important paradigm alternative to model-based controller design and several such methodologies are formulated as an H2 performance optimization. This book presents a comprehensive theoretical treatment of the H2 approach to data-driven control design. The fundamental properties implied by the H2 problem formulation are analyzed in detail, so that common features to all solutions are identified. Direct methods (VRFT) and iterative methods (IFT, DFT, CbT) are put under a common theoretical framework. The choice of the reference model, the experimental conditions, the optimization method to be used, and several other designer’s choices are crucial to the quality of the final outcome, and firm guidelines for all these choices are derived from the theoretical analysis presented. The practical application of the concepts in the book is illustrated with a large number of practical designs performed for different classes of processes: thermal, fluid processing a...
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
2015-01-01
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.
Third derivatives of the integrable part of an asteroid Hamiltonian
Directory of Open Access Journals (Sweden)
Pavlović R.
2007-01-01
Full Text Available To apply the theorem of Nekhoroshev (1977 to asteroids, one first has to check whether a necessary geometrical condition is fulfilled: either convexity, or quasi-convexity, or only a 3-jet non-degeneracy. This requires computation of the derivatives of the integrable part of the corresponding Hamiltonian up to the third order over actions and a thorough analysis of their properties. In this paper we describe in detail the procedure of derivation and we give explicit expressions for the obtained derivatives. .
Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics
Dankowicz, Harry
1997-01-01
In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM t
Relativistic tidal heating of Hamiltonian quasi-local boundary expressions
So, Lau Loi
2015-01-01
Purdue and Favata calculate the tidal heating used certain classical pseudotensors. Booth and Creighton employed the quasi-local mass formalism of Brown and York to demonstrate the same subject. All of them give the result matched with the Newtonian theory. Here we present another Hamiltonian quasi-local boundary expressions and all give the same desired value. This indicates that the tidal heating is unique as Thorne predicted. Moreover, we discovered that the pseudo-tensor method and quasi-local method are fundamentally different.
Quantum mechanics of non-Hamiltonian and dissipative systems
Tarasov, Vasily
2008-01-01
Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. Requires no preliminary knowledge of graduate and advanced mathematics Discusses the fundamental results of last 15 years in this theory Suitable for cours
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Periodic Solutions of Hamiltonian Systems of 3-Body Type
1989-08-01
As has been noted earlier. a(C) < 4(4 + C2) - 1 implies this is impossible. Thus I has no critical points in this region and there does not exist a...unstable manifolds for Z 12 in the region e1 <- J 1 2(q) -< M + 1 have a transversal intersection. Points on the unstable manifold between levels ci...Hamiltonian systems, Nonlinear Analysis: TMA, 12, (1988), 259-270. [7] Marino, A. and G. Prodi, Metodi perturbativi nella teoria di Morse, Boll. Un. Mat
Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems
Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.
2018-02-01
A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.
An Interval Approach for Robust Control of a Large PHWR with PID Controllers
Banerjee, Shohan; Halder, Kaushik; Dasgupta, Soumya; Mukhopadhyay, Siddhartha; Ghosh, Koushik; Gupta, Amitava
2015-02-01
A nuclear reactor exhibits changing behavior with variation in reactor power. Further, uncertainties in the measurement of the actual power produced by the reactor, the heat transfer from the fuel to the coolant and the reactivity change due to the change in the fuel and coolant temperatures and condition of the core, make it necessary to adopt a robust control approach for design of control systems for such plants. In this paper a 540 MWe Indian PHWR consisting of 14 zones has been modeled using inexact models incorporating bounded parametric variations in power, heat transfer from the fuel to the coolant and temperature coefficients of reactivity of fuel and coolant. These inexact models are then used to obtain a robust and optimal PID controller gains for controlling the reactor power with specified time response under parametric variations, using an interval approach. The methodology is established with credible MATLAB simulations.
15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics
Passante, Roberto; Trapani, Camillo
2016-01-01
This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.
Fault Tolerant Control for Civil Structures Based on LMI Approach
Directory of Open Access Journals (Sweden)
Chunxu Qu
2013-01-01
Full Text Available The control system may lose the performance to suppress the structural vibration due to the faults in sensors or actuators. This paper designs the filter to perform the fault detection and isolation (FDI and then reforms the control strategy to achieve the fault tolerant control (FTC. The dynamic equation of the structure with active mass damper (AMD is first formulated. Then, an estimated system is built to transform the FDI filter design problem to the static gain optimization problem. The gain is designed to minimize the gap between the estimated system and the practical system, which can be calculated by linear matrix inequality (LMI approach. The FDI filter is finally used to isolate the sensor faults and reform the FTC strategy. The efficiency of FDI and FTC is validated by the numerical simulation of a three-story structure with AMD system with the consideration of sensor faults. The results show that the proposed FDI filter can detect the sensor faults and FTC controller can effectively tolerate the faults and suppress the structural vibration.
Sex Control in Fish: Approaches, Challenges and Opportunities for Aquaculture
Directory of Open Access Journals (Sweden)
Alyssa M. Budd
2015-05-01
Full Text Available At present, aquaculture is the fastest growing sector of animal food production and holds great potential as a sustainable solution for world food security. The ability to control sex is one of the most important factors for the commercialisation and efficient propagation of fish species, due to influences on reproduction, growth and product quality. Accordingly, there is a large body of research that targets sexual development in commercially important species in an attempt to understand and control fish sex and reproductive function. In this review, we provide an introduction to sex determination and differentiation in fish, including the genetic, epigenetic and environmental factors that can influence fish sex ratios. We also summarise the major approaches used to control sex in fish and discuss their application in commercially important species. Specifically, we discuss the use of exogenous steroid hormones, chromosome ploidy, environmental manipulations, sex-linked genetic markers, selection for altered sex ratios, and transgenics and comment on the challenges associated with controlling sex in a commercial environment.
Live Vaccination Tactics: Possible Approaches for Controlling Visceral Leishmaniasis
Saljoughian, Noushin; Taheri, Tahareh; Rafati, Sima
2014-01-01
Vaccination with durable immunity is the main goal and fundamental to control leishmaniasis. To stimulate the immune response, small numbers of parasites are necessary to be presented in the mammalian host. Similar to natural course of infection, strategy using live vaccine is more attractive when compared to other approaches. Live vaccines present the whole spectrum of antigens to the host immune system in the absence of any adjuvant. Leishmanization was the first effort for live vaccination and currently used in a few countries against cutaneous leishmaniasis, in spite of their obstacle and safety. Then, live attenuated vaccines developed with similar promotion of creating long-term immunity in the host with lower side effect. Different examples of attenuated strains are generated through long-term in vitro culturing, culturing under drug pressure, temperature sensitivity, and chemical mutagenesis, but none is safe enough and their revision to virulent form is possible. Attenuation through genetic manipulation and disruption of virulence factors or essential enzymes for intracellular survival are among other approaches that are intensively under study. Other designs to develop live vaccines for visceral form of leishmaniasis are utilization of live avirulent microorganisms such as Lactococcus lactis, Salmonella enterica, and Leishmania tarentolae called as vectored vaccine. Apparently, these vaccines are intrinsically safer and can harbor the candidate antigens in their genome through different genetic manipulation and create more potential to control Leishmania parasite as an intracellular pathogen. PMID:24744757
THE THEORETHICAL APPROACH AND PRACTICE OF CONTROLLING AND BUSSINESS RISK
Directory of Open Access Journals (Sweden)
István HÁGEN
2015-07-01
Full Text Available Achieving the controlling approach at the companies has the obvious advantage that it is getting easier to exactly define the strategic and operative objectives, the planning system encourages the increase of performance and the decrease of costs and it helps by comparing plan-fact data. By defining the indices and continuous monitoring it is easier to get the fact data closer to the plans, so in case of careful planning business risk can be reduced. With the application of the controlling approach enterprises can be made economical, efficient and effective, so the activity naturally involving several risks, namely weather conditions, biological hazards, can be made more predictable. To sum up, the application of the Balanced Scorecard at the enterprises on the one hand helps short-term profitability and on the other hand designates what to do to reach long-term financial profitability and competitiveness. The objective of the research was to conduct a survey via questionnaires suitable for analysis as well as relevant deep interviews among the small and medium sized enterprises from different branches in the Carpathian Basin.
Density control in ITER: an iterative learning control and robust control approach
Ravensbergen, T.; de Vries, P. C.; Felici, F.; Blanken, T. C.; Nouailletas, R.; Zabeo, L.
2018-01-01
Plasma density control for next generation tokamaks, such as ITER, is challenging because of multiple reasons. The response of the usual gas valve actuators in future, larger fusion devices, might be too slow for feedback control. Both pellet fuelling and the use of feedforward-based control may help to solve this problem. Also, tight density limits arise during ramp-up, due to operational limits related to divertor detachment and radiative collapses. As the number of shots available for controller tuning will be limited in ITER, in this paper, iterative learning control (ILC) is proposed to determine optimal feedforward actuator inputs based on tracking errors, obtained in previous shots. This control method can take the actuator and density limits into account and can deal with large actuator delays. However, a purely feedforward-based density control may not be sufficient due to the presence of disturbances and shot-to-shot differences. Therefore, robust control synthesis is used to construct a robustly stabilizing feedback controller. In simulations, it is shown that this combined controller strategy is able to achieve good tracking performance in the presence of shot-to-shot differences, tight constraints, and model mismatches.
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
Gugercin, Serkan; Polyuga, Rostyslav V.; Beattie, Christopher; van der Schaft, Arjan
2011-01-01
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a rational tangential interpolant but also retains the port-Hamiltonian structure; hence is passive. This reduction methodology is described ...
Keshtkar, F.; Erjaee, G.; Boutefnouchet, M.
2014-01-01
In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts. NPRP . Grant Number: NP...
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
Sheftel, M. B.; Yazıcı, D.; Malykh, A. A.
2017-06-01
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian structures of the two-component general heavenly system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We discover that in the two-component form we have only a single nonlocal recursion operator. Composing the recursion operator with the first Hamiltonian operator we obtain second Hamiltonian operator. We check the Jacobi identities for the second Hamiltonian operator and compatibility of the two Hamiltonian structures using P. Olver's theory of functional multi-vectors. Our well-founded conjecture is that P. Olver's method works fine for nonlocal operators. We show that the general heavenly equation in the two-component form is a bi-Hamiltonian system integrable in the sense of Magri. We demonstrate how to obtain nonlocal Hamiltonian flows generated by local Hamiltonians by using formal adjoint recursion operator.
Electronic properties, low-energy Hamiltonian, and superconducting instabilities in CaKFe4As4
Lochner, Felix; Ahn, Felix; Hickel, Tilmann; Eremin, Ilya
2017-09-01
We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe4As4 by combining an ab initio approach and a projection of the band structure to a low-energy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3 d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe4As4 and the parent systems CaFe2As2 and KFe2As2 . In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe4As4 by employing the leading angular harmonics approximation and find two potential A1 g-symmetry representations of the superconducting gap to be the dominant instabilities in this system.
Berman, Robert J.
2017-09-01
In the present paper and the companion paper (Berman, Kähler-Einstein metrics, canonical random point processes and birational geometry. arXiv:1307.3634, 2015) a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on complex algebraic varieties X is introduced by sampling "temperature deformed" determinantal point processes. The main new ingredient is a large deviation principle for Gibbs measures with singular Hamiltonians, which is proved in the present paper. As an application we show that the unique Kähler-Einstein metric with negative Ricci curvature on a canonically polarized algebraic manifold X emerges in the many particle limit of the canonical point processes on X. In the companion paper (Berman in 2015) the extension to algebraic varieties X with positive Kodaira dimension is given and a conjectural picture relating negative temperature states to the existence problem for Kähler-Einstein metrics with positive Ricci curvature is developed.
Tarenzi, Thomas; Calandrini, Vania; Potestio, Raffaello; Giorgetti, Alejandro; Carloni, Paolo
2017-11-14
The recently proposed Hamiltonian adaptive resolution scheme (H-AdResS) allows the performance of molecular simulations in an open boundary framework. It allows changing, on the fly, the resolution of specific subsets of molecules (usually the solvent), which are free to diffuse between the atomistic region and the coarse-grained reservoir. So far, the method has been successfully applied to pure liquids. Coupling the H-AdResS methodology to hybrid models of proteins, such as the molecular mechanics/coarse-grained (MM/CG) scheme, is a promising approach for rigorous calculations of ligand binding free energies in low-resolution protein models. Toward this goal, here we apply for the first time H-AdResS to two atomistic proteins in dual-resolution solvent, proving its ability to reproduce structural and dynamic properties of both the proteins and the solvent, as obtained from atomistic simulations.
Failure of the work-Hamiltonian connection for free-energy calculations.
Vilar, Jose M G; Rubi, J Miguel
2008-01-18
Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial differentialH(x,t)/partial differentialt, which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free-energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.
Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
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Tamás Fülöp
2007-11-01
Full Text Available For a class of singular potentials, including the Coulomb potential (in three and less dimensions and $V(x = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
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.
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Keller, Sebastian; Dolfi, Michele; Troyer, Matthias; Reiher, Markus
2015-12-01
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.
Daskin, Anmer; Kais, Sabre
2011-04-14
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.
A Hamiltonian Model of Dissipative Wave-particle Interactions and the Negative-mass Effect
Energy Technology Data Exchange (ETDEWEB)
A. Zhmoginov
2011-02-07
The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negativemass eff ect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m! are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due to cyclotron cooling, whereas some of those with positive m! undergo cyclotron heating instead, extracting energy from the pump wave.
L\\'eon Rosenfeld's invention of constrained Hamiltonian dynamics
Salisbury, Donald
2016-01-01
This commentary reflects on the 1930 discoveries of L\\'eon Rosenfeld in the domain of phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that a...
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.
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.