Khavrutskii, Ilja V; Wallqvist, Anders
2010-11-09
This paper introduces an efficient single-topology variant of Thermodynamic Integration (TI) for computing relative transformation free energies in a series of molecules with respect to a single reference state. The presented TI variant that we refer to as Single-Reference TI (SR-TI) combines well-established molecular simulation methodologies into a practical computational tool. Augmented with Hamiltonian Replica Exchange (HREX), the SR-TI variant can deliver enhanced sampling in select degrees of freedom. The utility of the SR-TI variant is demonstrated in calculations of relative solvation free energies for a series of benzene derivatives with increasing complexity. Noteworthy, the SR-TI variant with the HREX option provides converged results in a challenging case of an amide molecule with a high (13-15 kcal/mol) barrier for internal cis/trans interconversion using simulation times of only 1 to 4 ns.
Directory of Open Access Journals (Sweden)
Nanyu Han
Full Text Available Neuraminidase (NA of influenza is a key target for antiviral inhibitors, and the 150-cavity in group-1 NA provides new insight in treating this disease. However, NA of 2009 pandemic influenza (09N1 was found lacking this cavity in a crystal structure. To address the issue of flexibility of the 150-loop, Hamiltonian replica exchange molecular dynamics simulations were performed on different groups of NAs. Free energy landscape calculated based on the volume of 150-cavity indicates that 09N1 prefers open forms of 150-loop. The turn A (residues 147-150 of the 150-loop is discovered as the most dynamical motif which induces the inter-conversion of this loop among different conformations. In the turn A, the backbone dynamic of residue 149 is highly related with the shape of 150-loop, thus can function as a marker for the conformation of 150-loop. As a contrast, the closed conformation of 150-loop is more energetically favorable in N2, one of group-2 NAs. The D147-H150 salt bridge is found having no correlation with the conformation of 150-loop. Instead the intimate salt bridge interaction between the 150 and 430 loops in N2 variant contributes the stabilizing factor for the closed form of 150-loop. The clustering analysis elaborates the structural plasticity of the loop. This enhanced sampling simulation provides more information in further structural-based drug discovery on influenza virus.
Fan, Hao; Periole, Xavier; Mark, Alan E.
The efficiency of using a variant of Hamiltonian replica-exchange molecular dynamics (Chaperone H-replica-exchange molecular dynamics [CH-REMD]) for the refinement of protein structural models generated de novo is investigated. In CH-REMD, the interaction between the protein and its environment,
Difficult Sudoku Puzzles Created by Replica Exchange Monte Carlo Method
Watanabe, Hiroshi
2013-01-01
An algorithm to create difficult Sudoku puzzles is proposed. An Ising spin-glass like Hamiltonian describing difficulty of puzzles is defined, and difficult puzzles are created by minimizing the energy of the Hamiltonian. We adopt the replica exchange Monte Carlo method with simultaneous temperature adjustments to search lower energy states efficiently, and we succeed in creating a puzzle which is the world hardest ever created in our definition, to our best knowledge. (Added on Mar. 11, the ...
Replica exchange with solute tempering: A method for sampling biological systems in explicit water
Liu, Pu; Kim, Byungchan; Friesner, Richard A.; Berne, B. J.
2005-09-01
An innovative replica exchange (parallel tempering) method called replica exchange with solute tempering (REST) for the efficient sampling of aqueous protein solutions is presented here. The method bypasses the poor scaling with system size of standard replica exchange and thus reduces the number of replicas (parallel processes) that must be used. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST is compared with standard replica exchange for an alanine dipeptide molecule in water. The comparisons confirm that REST greatly reduces the number of CPUs required by regular replica exchange and increases the sampling efficiency. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water. Author contributions: B.J.B. designed research; P.L. and B.K. performed research; P.L. and B.K. analyzed data; and P.L., B.K., R.A.F., and B.J.B. wrote the paper.Abbreviations: REST, replica exchange with solute tempering; REM, replica exchange method; MD, molecular dynamics.*P.L. and B.K. contributed equally to this work.
Kinetics from Replica Exchange Molecular Dynamics Simulations.
Stelzl, Lukas S; Hummer, Gerhard
2017-08-08
Transitions between metastable states govern many fundamental processes in physics, chemistry and biology, from nucleation events in phase transitions to the folding of proteins. The free energy surfaces underlying these processes can be obtained from simulations using enhanced sampling methods. However, their altered dynamics makes kinetic and mechanistic information difficult or impossible to extract. Here, we show that, with replica exchange molecular dynamics (REMD), one can not only sample equilibrium properties but also extract kinetic information. For systems that strictly obey first-order kinetics, the procedure to extract rates is rigorous. For actual molecular systems whose long-time dynamics are captured by kinetic rate models, accurate rate coefficients can be determined from the statistics of the transitions between the metastable states at each replica temperature. We demonstrate the practical applicability of the procedure by constructing master equation (Markov state) models of peptide and RNA folding from REMD simulations.
Itoh, Satoru G; Okumura, Hisashi
2013-03-30
We propose a new type of the Hamiltonian replica-exchange method (REM) for molecular dynamics (MD) and Monte Carlo simulations, which we refer to as the Coulomb REM (CREM). In this method, electrostatic charge parameters in the Coulomb interactions are exchanged among replicas while temperatures are exchanged in the usual REM. By varying the atom charges, the CREM overcomes free-energy barriers and realizes more efficient sampling in the conformational space than the REM. Furthermore, this method requires only a smaller number of replicas because only the atom charges of solute molecules are used as exchanged parameters. We performed Coulomb replica-exchange MD simulations of an alanine dipeptide in explicit water solvent and compared the results with those of the conventional canonical, replica exchange, and van der Waals REMs. Two force fields of AMBER parm99 and AMBER parm99SB were used. As a result, the CREM sampled all local-minimum free-energy states more frequently than the other methods for both force fields. Moreover, the Coulomb, van der Waals, and usual REMs were applied to a fragment of an amyloid-β peptide (Aβ) in explicit water solvent to compare the sampling efficiency of these methods for a larger system. The CREM sampled structures of the Aβ fragment more efficiently than the other methods. We obtained β-helix, α-helix, 3(10)-helix, β-hairpin, and β-sheet structures as stable structures and deduced pathways of conformational transitions among these structures from a free-energy landscape. Copyright © 2012 Wiley Periodicals, Inc.
Multiscale implementation of infinite-swap replica exchange molecular dynamics.
Yu, Tang-Qing; Lu, Jianfeng; Abrams, Cameron F; Vanden-Eijnden, Eric
2016-10-18
Replica exchange molecular dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular systems. The idea is to run several replicas of the system in parallel at different temperatures that are swapped periodically. These swaps are typically attempted every few MD steps and accepted or rejected according to a Metropolis-Hastings criterion. This guarantees that the joint distribution of the composite system of replicas is the normalized sum of the symmetrized product of the canonical distributions of these replicas at the different temperatures. Here we propose a different implementation of REMD in which (i) the swaps obey a continuous-time Markov jump process implemented via Gillespie's stochastic simulation algorithm (SSA), which also samples exactly the aforementioned joint distribution and has the advantage of being rejection free, and (ii) this REMD-SSA is combined with the heterogeneous multiscale method to accelerate the rate of the swaps and reach the so-called infinite-swap limit that is known to optimize sampling efficiency. The method is easy to implement and can be trivially parallelized. Here we illustrate its accuracy and efficiency on the examples of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent. In this latter example, our results indicate that the landscape of the protein is a triple funnel with two folded structures and one misfolded structure that are stabilized by H-bonds.
Lee, Kuo Hao; Chen, Jianhan
2017-11-15
Recasting temperature replica exchange (T-RE) as a special case of Gibbs sampling has led to a simple and efficient scheme for enhanced mixing (Chodera and Shirts, J. Chem. Phys., 2011, 135, 194110). To critically examine if T-RE with independence sampling (T-REis) improves conformational sampling, we performed T-RE and T-REis simulations of ordered and disordered proteins using coarse-grained and atomistic models. The results demonstrate that T-REis effectively increase the replica mobility in temperatures space with minimal computational overhead, especially for folded proteins. However, enhanced mixing does not translate well into improved conformational sampling. The convergences of thermodynamic properties interested are similar, with slight improvements for T-REis of ordered systems. The study re-affirms the efficiency of T-RE does not appear to be limited by temperature diffusion, but by the inherent rates of spontaneous large-scale conformational re-arrangements. Due to its simplicity and efficacy of enhanced mixing, T-REis is expected to be more effective when incorporated with various Hamiltonian-RE protocols. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Rauscher, Sarah; Neale, Chris; Pomès, Régis
2009-10-13
Generalized-ensemble algorithms in temperature space have become popular tools to enhance conformational sampling in biomolecular simulations. A random walk in temperature leads to a corresponding random walk in potential energy, which can be used to cross over energetic barriers and overcome the problem of quasi-nonergodicity. In this paper, we introduce two novel methods: simulated tempering distributed replica sampling (STDR) and virtual replica exchange (VREX). These methods are designed to address the practical issues inherent in the replica exchange (RE), simulated tempering (ST), and serial replica exchange (SREM) algorithms. RE requires a large, dedicated, and homogeneous cluster of CPUs to function efficiently when applied to complex systems. ST and SREM both have the drawback of requiring extensive initial simulations, possibly adaptive, for the calculation of weight factors or potential energy distribution functions. STDR and VREX alleviate the need for lengthy initial simulations, and for synchronization and extensive communication between replicas. Both methods are therefore suitable for distributed or heterogeneous computing platforms. We perform an objective comparison of all five algorithms in terms of both implementation issues and sampling efficiency. We use disordered peptides in explicit water as test systems, for a total simulation time of over 42 μs. Efficiency is defined in terms of both structural convergence and temperature diffusion, and we show that these definitions of efficiency are in fact correlated. Importantly, we find that ST-based methods exhibit faster temperature diffusion and correspondingly faster convergence of structural properties compared to RE-based methods. Within the RE-based methods, VREX is superior to both SREM and RE. On the basis of our observations, we conclude that ST is ideal for simple systems, while STDR is well-suited for complex systems.
Foundations and latest advances in replica exchange transition interface sampling
Cabriolu, Raffaela; Skjelbred Refsnes, Kristin M.; Bolhuis, Peter G.; van Erp, Titus S.
2017-10-01
Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations.
Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.
Cooke, Ben; Schmidler, Scott C
2008-10-28
We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.
Replica Exchange Simulations of the Thermodynamics of Aβ Fibril Growth
Takeda, Takako; Klimov, Dmitri K.
2009-01-01
Abstract Replica exchange molecular dynamics and an all-atom implicit solvent model are used to probe the thermodynamics of deposition of Alzheimer's Aβ monomers on preformed amyloid fibrils. Consistent with the experiments, two deposition stages have been identified. The docking stage occurs over a wide temperature range, starting with the formation of the first peptide-fibril interactions at 500 K. Docking is completed when a peptide fully adsorbs on the fibril edge at the temperature of 380 K. The docking transition appears to be continuous, and occurs without free energy barriers or intermediates. During docking, incoming Aβ monomer adopts a disordered structure on the fibril edge. The locking stage occurs at the temperature of ≈360 K and is characterized by the rugged free energy landscape. Locking takes place when incoming Aβ peptide forms a parallel β-sheet structure on the fibril edge. Because the β-sheets formed by locked Aβ peptides are typically off-registry, the structure of the locked phase differs from the structure of the fibril interior. The study also reports that binding affinities of two distinct fibril edges with respect to incoming Aβ peptides are different. The peptides bound to the concave edge have significantly lower free energy compared to those bound on the convex edge. Comparison with the available experimental data is discussed. PMID:19167295
Designed-walk replica-exchange method for simulations of complex systems
Urano, Ryo; Okamoto, Yuko
2015-01-01
We propose a new implementation of the replica-exchange method (REM) in which replicas follow a pre-planned route in temperature space instead of a random walk. Our method satisfies the detailed balance condition in the proposed route. The method forces tunneling events between the highest and lowest temperatures to happen with an almost constant period. The number of tunneling counts is proportional to that of the random-walk REM multiplied by the square root of moving distance in temperatur...
International Nuclear Information System (INIS)
Kamberaj, Hiqmet
2015-01-01
In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4, 5, and 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias
Huang, Kun; García, Angel E
2014-10-14
The lateral heterogeneity of cellular membranes plays an important role in many biological functions such as signaling and regulating membrane proteins. This heterogeneity can result from preferential interactions between membrane components or interactions with membrane proteins. One major difficulty in molecular dynamics simulations aimed at studying the membrane heterogeneity is that lipids diffuse slowly and collectively in bilayers, and therefore, it is difficult to reach equilibrium in lateral organization in bilayer mixtures. Here, we propose the use of the replica exchange with solute tempering (REST) approach to accelerate lateral relaxation in heterogeneous bilayers. REST is based on the replica exchange method but tempers only the solute, leaving the temperature of the solvent fixed. Since the number of replicas in REST scales approximately only with the degrees of freedom in the solute, REST enables us to enhance the configuration sampling of lipid bilayers with fewer replicas, in comparison with the temperature replica exchange molecular dynamics simulation (T-REMD) where the number of replicas scales with the degrees of freedom of the entire system. We apply the REST method to a cholesterol and 1,2-dipalmitoyl- sn -glycero-3-phosphocholine (DPPC) bilayer mixture and find that the lateral distribution functions of all molecular pair types converge much faster than in the standard MD simulation. The relative diffusion rate between molecules in REST is, on average, an order of magnitude faster than in the standard MD simulation. Although REST was initially proposed to study protein folding and its efficiency in protein folding is still under debate, we find a unique application of REST to accelerate lateral equilibration in mixed lipid membranes and suggest a promising way to probe membrane lateral heterogeneity through molecular dynamics simulation.
Huang, Yu-Ming M; McCammon, J Andrew; Miao, Yinglong
2018-04-10
Through adding a harmonic boost potential to smooth the system potential energy surface, Gaussian accelerated molecular dynamics (GaMD) provides enhanced sampling and free energy calculation of biomolecules without the need of predefined reaction coordinates. This work continues to improve the acceleration power and energy reweighting of the GaMD by combining the GaMD with replica exchange algorithms. Two versions of replica exchange GaMD (rex-GaMD) are presented: force constant rex-GaMD and threshold energy rex-GaMD. During simulations of force constant rex-GaMD, the boost potential can be exchanged between replicas of different harmonic force constants with fixed threshold energy. However, the algorithm of threshold energy rex-GaMD tends to switch the threshold energy between lower and upper bounds for generating different levels of boost potential. Testing simulations on three model systems, including the alanine dipeptide, chignolin, and HIV protease, demonstrate that through continuous exchanges of the boost potential, the rex-GaMD simulations not only enhance the conformational transitions of the systems but also narrow down the distribution width of the applied boost potential for accurate energetic reweighting to recover biomolecular free energy profiles.
Sidler, Dominik; Cristòfol-Clough, Michael; Riniker, Sereina
2017-06-13
Replica-exchange enveloping distribution sampling (RE-EDS) allows the efficient estimation of free-energy differences between multiple end-states from a single molecular dynamics (MD) simulation. In EDS, a reference state is sampled, which can be tuned by two types of parameters, i.e., smoothness parameters(s) and energy offsets, such that all end-states are sufficiently sampled. However, the choice of these parameters is not trivial. Replica exchange (RE) or parallel tempering is a widely applied technique to enhance sampling. By combining EDS with the RE technique, the parameter choice problem could be simplified and the challenge shifted toward an optimal distribution of the replicas in the smoothness-parameter space. The choice of a certain replica distribution can alter the sampling efficiency significantly. In this work, global round-trip time optimization (GRTO) algorithms are tested for the use in RE-EDS simulations. In addition, a local round-trip time optimization (LRTO) algorithm is proposed for systems with slowly adapting environments, where a reliable estimate for the round-trip time is challenging to obtain. The optimization algorithms were applied to RE-EDS simulations of a system of nine small-molecule inhibitors of phenylethanolamine N-methyltransferase (PNMT). The energy offsets were determined using our recently proposed parallel energy-offset (PEOE) estimation scheme. While the multistate GRTO algorithm yielded the best replica distribution for the ligands in water, the multistate LRTO algorithm was found to be the method of choice for the ligands in complex with PNMT. With this, the 36 alchemical free-energy differences between the nine ligands were calculated successfully from a single RE-EDS simulation 10 ns in length. Thus, RE-EDS presents an efficient method for the estimation of relative binding free energies.
Directory of Open Access Journals (Sweden)
Cameron Abrams
2013-12-01
Full Text Available We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods.
New force replica exchange method and protein folding pathways probed by force-clamp technique.
Kouza, Maksim; Hu, Chin-Kun; Li, Mai Suan
2008-01-28
We have developed a new extended replica exchange method to study thermodynamics of a system in the presence of external force. Our idea is based on the exchange between different force replicas to accelerate the equilibrium process. This new approach was applied to obtain the force-temperature phase diagram and other thermodynamical quantities of the three-domain ubiquitin. Using the C(alpha)-Go model and the Langevin dynamics, we have shown that the refolding pathways of single ubiquitin depend on which terminus is fixed. If the N end is fixed then the folding pathways are different compared to the case when both termini are free, but fixing the C terminal does not change them. Surprisingly, we have found that the anchoring terminal does not affect the pathways of individual secondary structures of three-domain ubiquitin, indicating the important role of the multidomain construction. Therefore, force-clamp experiments, in which one end of a protein is kept fixed, can probe the refolding pathways of a single free-end ubiquitin if one uses either the polyubiquitin or a single domain with the C terminus anchored. However, it is shown that anchoring one end does not affect refolding pathways of the titin domain I27, and the force-clamp spectroscopy is always capable to predict folding sequencing of this protein. We have obtained the reasonable estimate for unfolding barrier of ubiquitin, using the microscopic theory for the dependence of unfolding time on the external force. The linkage between residue Lys48 and the C terminal of ubiquitin is found to have the dramatic effect on the location of the transition state along the end-to-end distance reaction coordinate, but the multidomain construction leaves the transition state almost unchanged. We have found that the maximum force in the force-extension profile from constant velocity force pulling simulations depends on temperature nonlinearly. However, for some narrow temperature interval this dependence becomes
Chattopadhyay, Aditya; Zheng, Min; Waller, Mark Paul; Priyakumar, U Deva
2018-05-23
Knowledge of the structure and dynamics of biomolecules is essential for elucidating the underlying mechanisms of biological processes. Given the stochastic nature of many biological processes, like protein unfolding, it's almost impossible that two independent simulations will generate the exact same sequence of events, which makes direct analysis of simulations difficult. Statistical models like Markov Chains, transition networks etc. help in shedding some light on the mechanistic nature of such processes by predicting long-time dynamics of these systems from short simulations. However, such methods fall short in analyzing trajectories with partial or no temporal information, for example, replica exchange molecular dynamics or Monte Carlo simulations. In this work we propose a probabilistic algorithm, borrowing concepts from graph theory and machine learning, to extract reactive pathways from molecular trajectories in the absence of temporal data. A suitable vector representation was chosen to represent each frame in the macromolecular trajectory (as a series of interaction and conformational energies) and dimensionality reduction was performed using principal component analysis (PCA). The trajectory was then clustered using a density-based clustering algorithm, where each cluster represents a metastable state on the potential energy surface (PES) of the biomolecule under study. A graph was created with these clusters as nodes with the edges learnt using an iterative expectation maximization algorithm. The most reactive path is conceived as the widest path along this graph. We have tested our method on RNA hairpin unfolding trajectory in aqueous urea solution. Our method makes the understanding of the mechanism of unfolding in RNA hairpin molecule more tractable. As this method doesn't rely on temporal data it can be used to analyze trajectories from Monte Carlo sampling techniques and replica exchange molecular dynamics (REMD).
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Salma Jamal
2017-12-01
Full Text Available Intrinsically disordered proteins (IDP are a class of proteins that do not have a stable three-dimensional structure and can adopt a range of conformations playing various vital functional role. Alpha-synuclein is one such IDP which can aggregate into toxic protofibrils and has been associated largely with Parkinson's disease (PD along with other neurodegenerative diseases. Osmolytes are small organic compounds that can alter the environment around the proteins by acting as denaturants or protectants for the proteins. In the present study, we have conducted a series of replica exchange molecular dynamics simulations to explore the role of osmolytes, urea which is a denaturant and TMAO (trimethylamine N-oxide, a protecting osmolyte, in aggregation and conformations of the synuclein peptide. We observed that both the osmolytes have significantly distinct impacts on the peptide and led to transitions of the conformations of the peptide from one state to other. Our findings highlighted that urea attenuated peptide aggregation and resulted in the formation of extended peptide structures whereas TMAO led to compact and folded forms of the peptide.
Perovskite Quantum Dots Modeled Using ab Initio and Replica Exchange Molecular Dynamics
Buin, Andrei; Comin, Riccardo; Ip, Alexander H.; Sargent, Edward H.
2015-01-01
© 2015 American Chemical Society. Organometal halide perovskites have recently attracted tremendous attention at both the experimental and theoretical levels. Much of this work has been dedicated to bulk material studies, yet recent experimental work has shown the formation of highly efficient quantum-confined nanocrystals with tunable band edges. Here we investigate perovskite quantum dots from theory, predicting an upper bound of the Bohr radius of 45 Å that agrees well with literature values. When the quantum dots are stoichiometric, they are trap-free and have nearly symmetric contributions to confinement from the valence and conduction bands. We further show that surface-associated conduction bandedge states in perovskite nanocrystals lie below the bulk states, which could explain the difference in Urbach tails between mesoporous and planar perovskite films. In addition to conventional molecular dynamics (MD), we implement an enhanced phase-space sampling algorithm, replica exchange molecular dynamics (REMD). We find that in simulation of methylammonium orientation and global minima, REMD outperforms conventional MD. To the best of our knowledge, this is the first REMD implementation for realistic-sized systems in the realm of DFT calculations.
Perovskite Quantum Dots Modeled Using ab Initio and Replica Exchange Molecular Dynamics
Buin, Andrei
2015-06-18
© 2015 American Chemical Society. Organometal halide perovskites have recently attracted tremendous attention at both the experimental and theoretical levels. Much of this work has been dedicated to bulk material studies, yet recent experimental work has shown the formation of highly efficient quantum-confined nanocrystals with tunable band edges. Here we investigate perovskite quantum dots from theory, predicting an upper bound of the Bohr radius of 45 Å that agrees well with literature values. When the quantum dots are stoichiometric, they are trap-free and have nearly symmetric contributions to confinement from the valence and conduction bands. We further show that surface-associated conduction bandedge states in perovskite nanocrystals lie below the bulk states, which could explain the difference in Urbach tails between mesoporous and planar perovskite films. In addition to conventional molecular dynamics (MD), we implement an enhanced phase-space sampling algorithm, replica exchange molecular dynamics (REMD). We find that in simulation of methylammonium orientation and global minima, REMD outperforms conventional MD. To the best of our knowledge, this is the first REMD implementation for realistic-sized systems in the realm of DFT calculations.
Lu, Qing; Kim, Jaegil; Straub, John E
2013-03-14
The generalized Replica Exchange Method (gREM) is extended into the isobaric-isothermal ensemble, and applied to simulate a vapor-liquid phase transition in Lennard-Jones fluids. Merging an optimally designed generalized ensemble sampling with replica exchange, gREM is particularly well suited for the effective simulation of first-order phase transitions characterized by "backbending" in the statistical temperature. While the metastable and unstable states in the vicinity of the first-order phase transition are masked by the enthalpy gap in temperature replica exchange method simulations, they are transformed into stable states through the parameterized effective sampling weights in gREM simulations, and join vapor and liquid phases with a succession of unimodal enthalpy distributions. The enhanced sampling across metastable and unstable states is achieved without the need to identify a "good" order parameter for biased sampling. We performed gREM simulations at various pressures below and near the critical pressure to examine the change in behavior of the vapor-liquid phase transition at different pressures. We observed a crossover from the first-order phase transition at low pressure, characterized by the backbending in the statistical temperature and the "kink" in the Gibbs free energy, to a continuous second-order phase transition near the critical pressure. The controlling mechanisms of nucleation and continuous phase transition are evident and the coexistence properties and phase diagram are found in agreement with literature results.
Wang, Hongrui; Liu, Hongwei; Cai, Leixin; Wang, Caixia; Lv, Qiang
2017-07-10
In this study, we extended the replica exchange Monte Carlo (REMC) sampling method to protein-small molecule docking conformational prediction using RosettaLigand. In contrast to the traditional Monte Carlo (MC) and REMC sampling methods, these methods use multi-objective optimization Pareto front information to facilitate the selection of replicas for exchange. The Pareto front information generated to select lower energy conformations as representative conformation structure replicas can facilitate the convergence of the available conformational space, including available near-native structures. Furthermore, our approach directly provides min-min scenario Pareto optimal solutions, as well as a hybrid of the min-min and max-min scenario Pareto optimal solutions with lower energy conformations for use as structure templates in the REMC sampling method. These methods were validated based on a thorough analysis of a benchmark data set containing 16 benchmark test cases. An in-depth comparison between MC, REMC, multi-objective optimization-REMC (MO-REMC), and hybrid MO-REMC (HMO-REMC) sampling methods was performed to illustrate the differences between the four conformational search strategies. Our findings demonstrate that the MO-REMC and HMO-REMC conformational sampling methods are powerful approaches for obtaining protein-small molecule docking conformational predictions based on the binding energy of complexes in RosettaLigand.
A replica exchange Monte Carlo algorithm for protein folding in the HP model
Directory of Open Access Journals (Sweden)
Shmygelska Alena
2007-09-01
Full Text Available Abstract Background The ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics. The ab initio protein folding problem is computationally challenging and has been shown to be NP MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFneVtcqqGqbauaaa@3961@-hard even when conformations are restricted to a lattice. In this work, we implement and evaluate the replica exchange Monte Carlo (REMC method, which has already been applied very successfully to more complex protein models and other optimization problems with complex energy landscapes, in combination with the highly effective pull move neighbourhood in two widely studied Hydrophobic Polar (HP lattice models. Results We demonstrate that REMC is highly effective for solving instances of the square (2D and cubic (3D HP protein folding problem. When using the pull move neighbourhood, REMC outperforms current state-of-the-art algorithms for most benchmark instances. Additionally, we show that this new algorithm provides a larger ensemble of ground-state structures than the existing state-of-the-art methods. Furthermore, it scales well with sequence length, and it finds significantly better conformations on long biological sequences and sequences with a provably unique ground-state structure, which is believed to be a characteristic of real proteins. We also present evidence that our REMC algorithm can fold sequences which exhibit significant interaction between termini in the hydrophobic core relatively easily. Conclusion We demonstrate that REMC utilizing the pull move
International Nuclear Information System (INIS)
Nanayakkara, Asiri
2005-01-01
The pseudo Hermiticity with respect to the exchange operators of N-D complex Hamiltonians is investigated. It is shown that if an N-D Hamiltonian is pseudo Hermitian and any eigenfunction of it retains π α T symmetry then the corresponding eigen value is real, where π α is an exchange operator with respect to the permutation α of coordinates and T is the time reversal operator. We construct a special class of N-D pseudo Hermitian Hamiltonians with respect to exchange operators from both N/2-D and N-D general complex Hamiltonians. Examples are presented for Hamiltonians with πT symmetry (π:x↔y, p x ↔p y ) and the reality of these systems are investigated.
Swenson, David W. H.; Bolhuis, Peter G.
2014-07-01
The multiple state transition interface sampling (TIS) framework in principle allows the simulation of a large network of complex rare event transitions, but in practice suffers from convergence problems. To improve convergence, we combine multiple state TIS [J. Rogal and P. G. Bolhuis, J. Chem. Phys. 129, 224107 (2008)] with replica exchange TIS [T. S. van Erp, Phys. Rev. Lett. 98, 268301 (2007)]. In addition, we introduce multiple interface sets, which allow more than one order parameter to be defined for each state. We illustrate the methodology on a model system of multiple independent dimers, each with two states. For reaction networks with up to 64 microstates, we determine the kinetics in the microcanonical ensemble, and discuss the convergence properties of the sampling scheme. For this model, we find that the kinetics depend on the instantaneous composition of the system. We explain this dependence in terms of the system's potential and kinetic energy.
Directory of Open Access Journals (Sweden)
Mark A Olson
Full Text Available A central problem of computational structural biology is the refinement of modeled protein structures taken from either comparative modeling or knowledge-based methods. Simulations are commonly used to achieve higher resolution of the structures at the all-atom level, yet methodologies that consistently yield accurate results remain elusive. In this work, we provide an assessment of an adaptive temperature-based replica exchange simulation method where the temperature clients dynamically walk in temperature space to enrich their population and exchanges near steep energetic barriers. This approach is compared to earlier work of applying the conventional method of static temperature clients to refine a dataset of conformational decoys. Our results show that, while an adaptive method has many theoretical advantages over a static distribution of client temperatures, only limited improvement was gained from this strategy in excursions of the downhill refinement regime leading to an increase in the fraction of native contacts. To illustrate the sampling differences between the two simulation methods, energy landscapes are presented along with their temperature client profiles.
Figueiredo, T. P.; Rocha, J. C. S.; Costa, B. V.
2017-12-01
Although the topological Berezinskii-Kosterlitz-Thouless transition was for the first time described by 40 years ago, it is still a matter of discussion. It has been used to explain several experiments in the most diverse physical systems. In contrast with the ordinary continuous phase transitions the BKT-transition does not break any symmetry. However, in some contexts it can easily be confused with other continuous transitions, in general due to an insufficient data analysis. The two-dimensional XY (or sometimes called planar rotator) spin model is the fruit fly model describing the BKT transition. As demonstrated by Bramwell and Holdsworth (1993) the finite-size effects are more important in two-dimensions than in others due to the logarithmic system size dependence of the properties of the system. Closely related is the anisotropic two dimensional Heisenberg model (AH). Although they have the same Hamiltonian the spin variable in the former has only two degrees of freedom while the AH has three. Many works treat the AH model as undergoing a transition in the same universality class as the XY model. However, its characterization as being in the BKT class of universality deserve some investigation. This paper has two goals. First, we describe an analytical evidence showing that the AH model is in the BKT class of universality. Second, we make an extensive simulation, using the numerical Replica Exchange Wang-Landau method that corroborate our analytical calculations. From our simulation we obtain the BKT transition temperature as TBKT = 0 . 6980(10) by monitoring the susceptibility, the two point correlation function and the helicity modulus. We discuss the misuse of the fourth order Binder's cumulant to locate the transition temperature. The specific heat is shown to have a non-critical behavior as expected in the BKT transition. An analysis of the two point correlation function at low temperature, C(r) ∝r - η(T), shows that the exponent, η, is consistent
Meson-exchange Hamiltonian for NN scattering and isobar-nucleus dynamics
International Nuclear Information System (INIS)
Lee, T.S.H.
1983-01-01
We have constructed a meson-exchange Hamiltonian for π, N, Δ and N* for NN scattering up to 2 GeV. The model gives good descriptions of the Arndt phase-shifts up to 1 GeV in both the T = 0 and T = 1 channels. The calculated total cross sections sigma/sup tot/, Δsigma/sub L//sup tot/ and Δsigma/sub T//sup tot/ agree to a large extent with the data in both the magnitudes and the signs. The present calculation gives a sound starting point for future refinements. Among them, a large-scale three-body calculation could be needed to investigate the energy dependence of the effect due to NN interactions in the πNN channel. Until this effect is carefully studied, it is premature to extract information on dibaryon resonances, if they exist, from the data. Our model also gives definite predictions of np scattering. Precise np polarization measurements at higher energy > 0.6 GeV are needed to have a complete test of our model. Finally, the present model Hamiltonian can be used to carry our many-body calculations
International Nuclear Information System (INIS)
Roger, M.; Suaudeau, E.; Bernier, M.E.R.
1987-08-01
High temperature series expansions with a multiple-exchange Hamiltonian are performed to fourth order in arbitrary magnetic field for both phases of solid 3 He. The susceptibility series are analysed with Pade approximants and compared with recent experimental results. For the hcp phase we estimate the ferromagnetic ordering temperature from susceptibility series and discuss the influence of four-particle exchange in lowering the transition
Calculation of absolute protein-ligand binding free energy using distributed replica sampling.
Rodinger, Tomas; Howell, P Lynne; Pomès, Régis
2008-10-21
Distributed replica sampling [T. Rodinger et al., J. Chem. Theory Comput. 2, 725 (2006)] is a simple and general scheme for Boltzmann sampling of conformational space by computer simulation in which multiple replicas of the system undergo a random walk in reaction coordinate or temperature space. Individual replicas are linked through a generalized Hamiltonian containing an extra potential energy term or bias which depends on the distribution of all replicas, thus enforcing the desired sampling distribution along the coordinate or parameter of interest regardless of free energy barriers. In contrast to replica exchange methods, efficient implementation of the algorithm does not require synchronicity of the individual simulations. The algorithm is inherently suited for large-scale simulations using shared or heterogeneous computing platforms such as a distributed network. In this work, we build on our original algorithm by introducing Boltzmann-weighted jumping, which allows moves of a larger magnitude and thus enhances sampling efficiency along the reaction coordinate. The approach is demonstrated using a realistic and biologically relevant application; we calculate the standard binding free energy of benzene to the L99A mutant of T4 lysozyme. Distributed replica sampling is used in conjunction with thermodynamic integration to compute the potential of mean force for extracting the ligand from protein and solvent along a nonphysical spatial coordinate. Dynamic treatment of the reaction coordinate leads to faster statistical convergence of the potential of mean force than a conventional static coordinate, which suffers from slow transitions on a rugged potential energy surface.
Sidler, Dominik; Schwaninger, Arthur; Riniker, Sereina
2016-10-21
In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows to calculate multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which "envelopes" the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To resolve this, we have generalised the replica-exchange EDS (RE-EDS) approach, introduced by Lee et al. [J. Chem. Theory Comput. 10, 2738 (2014)] for constant-pH MD simulations. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. A new robust scheme to estimate the reference-state parameters from a short initial RE-EDS simulation with default parameters was developed, which allowed the calculation of 36 free-energy differences between nine small-molecule inhibitors of phenylethanolamine N-methyltransferase from a single simulation. The resulting free-energy differences were in excellent agreement with values obtained previously by TI and two-state EDS simulations.
Paschek, Dietmar; Nymeyer, Hugh; García, Angel E
2007-03-01
We simulate the folding/unfolding equilibrium of the 20-residue miniprotein Trp-cage. We use replica exchange molecular dynamics simulations of the AMBER94 atomic detail model of the protein explicitly solvated by water, starting from a completely unfolded configuration. We employ a total of 40 replicas, covering the temperature range between 280 and 538 K. Individual simulation lengths of 100 ns sum up to a total simulation time of about 4 micros. Without any bias, we observe the folding of the protein into the native state with an unfolding-transition temperature of about 440 K. The native state is characterized by a distribution of root mean square distances (RMSD) from the NMR data that peaks at 1.8A, and is as low as 0.4A. We show that equilibration times of about 40 ns are required to yield convergence. A folded configuration in the entire extended ensemble is found to have a lifetime of about 31 ns. In a clamp-like motion, the Trp-cage opens up during thermal denaturation. In line with fluorescence quenching experiments, the Trp-residue sidechain gets hydrated when the protein opens up, roughly doubling the number of water molecules in the first solvation shell. We find the helical propensity of the helical domain of Trp-cage rather well preserved even at very high temperatures. In the folded state, we can identify states with one and two buried internal water molecules interconnecting parts of the Trp-cage molecule by hydrogen bonds. The loss of hydrogen bonds of these buried water molecules in the folded state with increasing temperature is likely to destabilize the folded state at elevated temperatures.
On the exchange term of the interacting boson-fermion hamiltonian
International Nuclear Information System (INIS)
Gelberg, A.
1983-01-01
The exchange term of the Interacting Boson Fermion Model is investigated by using I. Talmi's method based on the shell model. A quadrupole operator of a three-proton system is formed; the protons are quadrupole-coupled to the neutron-bosons. Seniority conserving and seniority non conserving terms are considered. The particle number dependence of the parameters is investigated for the single-j shell. The relation between exchange and direct, seniority non conserving terms is examined. Approximate formulas are given for the multi-j shell. (orig.)
Directory of Open Access Journals (Sweden)
Zhenyu Qian
Full Text Available The aggregation of amyloid-β peptides is associated with the pathogenesis of Alzheimer's disease, in which the 30-36 fragments play an important part as a fiber-forming hydrophobic region. The fibrillar structure of Aβ30-36 has been detected by means of X-ray diffraction, but its oligomeric structural determination, biophysical characterization, and pathological mechanism remain elusive. In this study, we have investigated the structures of Aβ30-36 hexamer as well as its G33V and L34T mutants in explicit water environment using replica-exchange molecular dynamics (REMD simulations. Our results show that the wild-type (WT Aβ30-36 hexamer has a preference to form β-barrel and bilayer β-sheet conformations, while the G33V or L34T mutation disrupts the β-barrel structures: the G33V mutant is homogenized to adopt β-sheet-rich bilayers, and the structures of L34T mutant on the contrary get more diverse. The hydrophobic interaction plays a critical role in the formation and stability of oligomeric assemblies among all the three systems. In addition, the substitution of G33 by V reduces the β-sheet content in the most populated conformations of Aβ30-36 oligomers through a steric effect. The L34T mutation disturbs the interpeptide hydrogen bonding network, and results in the increased coil content and morphological diversity. Our REMD runs provide structural details of WT and G33V/L34T mutant Aβ30-36 oligomers, and molecular insight into the aggregation mechanism, which will be helpful for designing novel inhibitors or amyloid-based materials.
Watts, Charles R; Gregory, Andrew; Frisbie, Cole; Lovas, Sándor
2018-03-01
The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1-40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER-ff99sb-ILDN, AMBER-ff99sb*-ILDN, AMBER-ff99sb-NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER-ff99sb-ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α-helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER-ff99sb-NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER-ff99sb-NMR force field, the others tended to under estimate the expected amount of β-sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER-ff99sb-NMR, reproduce a theoretically expected β-sheet-turn-β-sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C-terminal hydrophobic cores from residues 17-21 and 30-36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different. © 2017 Wiley Periodicals, Inc.
Iwaoka, Michio; Suzuki, Toshiki; Shoji, Yuya; Dedachi, Kenichi; Shimosato, Taku; Minezaki, Toshiya; Hojo, Hironobu; Onuki, Hiroyuki; Hirota, Hiroshi
2017-12-01
Single amino acid potential (SAAP) would be a prominent factor to determine peptide conformations. To prove this hypothesis, we previously developed SAAP force field for molecular simulation of polypeptides. In this study, the force field was renovated to SAAP3D force field by applying more accurate three-dimensional main-chain parameters, instead of the original two-dimensional ones, for the amino acids having a long side-chain. To demonstrate effectiveness of the SAAP3D force field, replica-exchange Monte Carlo (REMC) simulation was performed for two benchmark short peptides, chignolin (H-GYDPETGTWG-OH) and C-peptide (CHO-AETAAAKFLRAHA-NH 2 ). For chignolin, REMC/SAAP3D simulation correctly produced native β-turn structures, whose minimal all-atom root-mean-square deviation value measured from the native NMR structure (except for H) was 1.2 Å, at 300 K in implicit water, along with misfolded β-hairpin structures with unpacked aromatic side chains of Tyr2 and Trp9. Similar results were obtained for chignolin analog [G1Y,G10Y], which folded more tightly to the native β-turn structure than chignolin did. For C-peptide, on the other hand, the α-helix content was larger than the β content on average, suggesting a significant helix-forming propensity. When the imidazole side chain of His12 was protonated (i.e., [His12Hip]), the α content became larger. These observations as well as the representative structures obtained by clustering analysis were in reasonable agreement not only with the structures of C-peptide that were determined in this study by NMR in 30% CD 3 CD in H 2 O at 298 K but also with the experimental and theoretical behaviors having been reported for protonated C-peptide. Thus, accuracy of the SAAP force field was improved by applying three-dimensional main-chain parameters, supporting prominent importance of SAAP for peptide conformations.
Iwaoka, Michio; Suzuki, Toshiki; Shoji, Yuya; Dedachi, Kenichi; Shimosato, Taku; Minezaki, Toshiya; Hojo, Hironobu; Onuki, Hiroyuki; Hirota, Hiroshi
2017-12-01
Single amino acid potential (SAAP) would be a prominent factor to determine peptide conformations. To prove this hypothesis, we previously developed SAAP force field for molecular simulation of polypeptides. In this study, the force field was renovated to SAAP3D force field by applying more accurate three-dimensional main-chain parameters, instead of the original two-dimensional ones, for the amino acids having a long side-chain. To demonstrate effectiveness of the SAAP3D force field, replica-exchange Monte Carlo (REMC) simulation was performed for two benchmark short peptides, chignolin (H-GYDPETGTWG-OH) and C-peptide (CHO-AETAAAKFLRAHA-NH2). For chignolin, REMC/SAAP3D simulation correctly produced native β-turn structures, whose minimal all-atom root-mean-square deviation value measured from the native NMR structure (except for H) was 1.2 Å, at 300 K in implicit water, along with misfolded β-hairpin structures with unpacked aromatic side chains of Tyr2 and Trp9. Similar results were obtained for chignolin analog [G1Y,G10Y], which folded more tightly to the native β-turn structure than chignolin did. For C-peptide, on the other hand, the α-helix content was larger than the β content on average, suggesting a significant helix-forming propensity. When the imidazole side chain of His12 was protonated (i.e., [His12Hip]), the α content became larger. These observations as well as the representative structures obtained by clustering analysis were in reasonable agreement not only with the structures of C-peptide that were determined in this study by NMR in 30% CD3CD in H2O at 298 K but also with the experimental and theoretical behaviors having been reported for protonated C-peptide. Thus, accuracy of the SAAP force field was improved by applying three-dimensional main-chain parameters, supporting prominent importance of SAAP for peptide conformations.
Replica Approach for Minimal Investment Risk with Cost
Shinzato, Takashi
2018-06-01
In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where an objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Hamiltonians in the Hopfield model and the Sherrington-Kirkpatrick model, show that we can analyze this portfolio optimization problem by using replica analysis, and derive the minimal investment risk with cost and the investment concentration of the optimal portfolio. Furthermore, we validate our proposed method through numerical simulations.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of
Krstevski, Vangel
2013-01-01
a in various deployment scenarios.Hyper-V Replica Essentials is for Windows Server administrators who want to improve their system availability and speed up disaster recovery. You will need experience in Hyper-V deployment because Hyper-V Replica is built in the Hyper-V platform.
Fedorov, Dmitri G; Sugita, Yuji; Choi, Cheol Ho
2013-07-03
An efficient parallel implementation of QM/MM-based replica-exchange molecular dynamics (REMD) as well as umbrella samplings techniques was proposed by adopting the generalized distributed data interface (GDDI). Parallelization speed-up of 40.5 on 48 cores was achieved, making our QM/MM-MD engine a robust tool for studying complex chemical dynamics in solution. They were comparatively used to study the torsional isomerization of hydrogen peroxide in aqueous solution. All results by QM/MM-REMD and QM/MM umbrella sampling techniques yielded nearly identical potentials of mean force (PMFs) regardless of the particular QM theories for solute, showing that the overall dynamics are mainly determined by solvation. Although the entropic penalty of solvent rearrangements exists in cisoid conformers, it was found that both strong intermolecular hydrogen bonding and dipole-dipole interactions preferentially stabilize them in solution, reducing the torsional free-energy barrier at 0° by about 3 kcal/mol as compared to that in gas phase.
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
Directory of Open Access Journals (Sweden)
M. SARCINELLI
2013-12-01
Full Text Available L'articolo è una breve nota critica alcuni elementi essenziali di Jager e De Jong del potenziale impatto del dell'ECU privato sulla stabilità dei tassi di cambio mondiale ed europeo ( 1988 . L'autore fornisce tre punti di critica che minano l'analisi di quel articolo. In primo luogo , l'ECU deve essere considerata in tutte le sue funzioni di una valuta di riserva internazionale e non solo come valuta di investimento . In secondo luogo, la restrittività delle assunzioni sottostanti l'approccio di portafoglio fanno esito degli autori inutile nella pratica . In terzo luogo, il risultato dei loro calcoli favorisce l'ipotesi che la centralina crea stabilità dei cambi The article is a brief note criticising some essential elements of Jager and De Jong’s The private ECU’s potential impact on Global and European exchange-rate stability (1988. The author provides three points of criticism which undermine that article’s analysis. Firstly, the ECU ought to be considered in all its functions of an international reserve currency and not only as an investment currency. Secondly, the restrictiveness of the assumptions underlying the portfolio approach make the authors’ outcome useless in practice. Thirdly, the outcome of their calculations favours the hypothesis that the ECU creates exchange-rate stability.JEL: F33, F36
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
Directory of Open Access Journals (Sweden)
Lulu Ning
Full Text Available The fragment 106-126 of prion protein exhibits similar properties to full-length prion. Experiments have shown that the A117V mutation enhances the aggregation of PrP106-126, while the H111S mutation abolishes the assembly. However, the mechanism of the change in the aggregation behavior of PrP106-126 upon the two mutations is not fully understood. In this study, replica exchange molecular dynamics simulations were performed to investigate the conformational ensemble of the WT PrP106-126 and its two mutants A117V and H111S. The obtained results indicate that the three species are all intrinsically disordered but they have distinct morphological differences. The A117V mutant has a higher propensity to form β-hairpin structures than the WT, while the H111S mutant has a higher population of helical structures. Furthermore, the A117V mutation increases the hydrophobic solvent accessible surface areas of PrP106-126 and the H111S mutation reduces the exposure of hydrophobic residues. It can be concluded that the difference in populations of β-hairpin structures and the change of hydrophobic solvent accessible areas may induce the different aggregation behaviors of the A117V and the H111S mutated PrP106-126. Understanding why the two mutations have contrary effects on the aggregation of PrP106-126 is very meaningful for further elucidation of the mechanism underlying aggregation and design of inhibitor against aggregation process.
Tsyganov, D. L.
2017-11-01
A new model for calculating the rates of reactions of excitation, ionization, and atomic exchange is proposed. Diatomic molecule AB is an unstructured particle M upon the exchange of elastic-vibrational (VT) energy, i.e., a model of a shock forceful oscillator with a change in Hamiltonian (SFOH). The SFOH model is based on the quantum theory of strong perturbations. The SFOH model allows generalization in simulating the rates of the reactions of excitation, ionization, and atomic exchange in the vibrational-vibrational (VV) energy exchange of diatomic molecules, and the exchange of VV- and VT-energy of polyatomic molecules. The rate constants of the excitation of metastables A 3Σ u +, B 3Π g , W 3Δ u , B'3Σ u -, a'3Σ u -, and the ionization of a nitrogen molecules from ground state X2Σ g + upon a collision with a heavy structureless particle (a nitrogen molecule), are found as examples.
Broken symmetry in the mean field theory of the ising spin glass: replica way and no replica way
International Nuclear Information System (INIS)
De Dominicis, C.
1983-06-01
We review the type of symmetry breaking involved in the solution discovered by Parisi and in the static derivation of the solution first introduced via dynamics by Sompolinsky. We turn to a formulation of the problem due to Thouless, Anderson and Palmer (TAP) that put a set of equations for the magnetization. A probability law for the magnetization is then built. We consider two cases: (i) a canonical distribution which is shown to give indentical results to the Hamiltonian formulation under a weak and physical assumption and (ii) a white distribution characterized by two matrices and a response. We show what symmetry breaking is necessary to recover Sompolinsky free energy. In section III we supplement replica indices in the Hamiltonian approach by ''time'' indices ans show in particular that the analytic continuation involved in Sompolinsky's equilibrium derivation, is trying to mimick a translational symmetry breaking in ''time'' that incorporates Sompolinsky's ansatz of a long time scale sequence. In section IV we apply the same treatment to the white average approach and show that, replicas can be altogether discorded and replaced by ''time''. Finally, we briefly discuss the attribution of distinct answers for the standard spin glass order parameter depending on the physical situation: equilibrium or non equilibrium associated with canonical or white (non canonical) initial conditions and density matrices
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.
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.
Kunszt, Peter Z; Stockinger, Heinz; Stockinger, Kurt
2005-01-01
Data replication is one of the best known strategies to achieve high levels of availability and fault tolerance, as well as minimal access times for large, distributed user communities using a world-wide Data Grid. In certain scientific application domains, the data volume can reach the order of several petabytes; in these domains, data replication and access optimization play an important role in the manageability and usability of the Grid. In this paper, we present the design and implementation of a replica management Grid middleware that was developed within the EDG project left bracket European Data Grid Project (EDG), http://www.eu-egee.org right bracket and is designed to be extensible so that user communities can adjust its detailed behavior according to their QoS requirements.
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
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 ...
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Garrido, L M; Pascual, P
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Validation of the replica trick for simple models
Shinzato, Takashi
2018-04-01
We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the replica analysis, which is used in a wide range of fields related to large-scale complex systems. While replica analysis consists of two analytical techniques—the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion)—we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
Replica consistency in a Data Grid
International Nuclear Information System (INIS)
Domenici, Andrea; Donno, Flavia; Pucciani, Gianni; Stockinger, Heinz; Stockinger, Kurt
2004-01-01
A Data Grid is a wide area computing infrastructure that employs Grid technologies to provide storage capacity and processing power to applications that handle very large quantities of data. Data Grids rely on data replication to achieve better performance and reliability by storing copies of data sets on different Grid nodes. When a data set can be modified by applications, the problem of maintaining consistency among existing copies arises. The consistency problem also concerns metadata, i.e., additional information about application data sets such as indices, directories, or catalogues. This kind of metadata is used both by the applications and by the Grid middleware to manage the data. For instance, the Replica Management Service (the Grid middleware component that controls data replication) uses catalogues to find the replicas of each data set. Such catalogues can also be replicated and their consistency is crucial to the correct operation of the Grid. Therefore, metadata consistency generally poses stricter requirements than data consistency. In this paper we report on the development of a Replica Consistency Service based on the middleware mainly developed by the European Data Grid Project. The paper summarises the main issues in the replica consistency problem, and lays out a high-level architectural design for a Replica Consistency Service. Finally, results from simulations of different consistency models are presented
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
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...
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
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...
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Replica methods for loopy sparse random graphs
International Nuclear Information System (INIS)
Coolen, ACC
2016-01-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)
3D printed replicas for endodontic education.
Reymus, M; Fotiadou, C; Kessler, A; Heck, K; Hickel, R; Diegritz, C
2018-06-14
To assess the feasibility of producing artificial teeth for endodontic training using 3D printing technology, to analyse the accuracy of the printing process, and to evaluate the teeth by students when used during training. Sound extracted human teeth were selected, digitalized by cone beam computed tomography (CBCT) and appropriate software and finally reproduced by a stereolithographic printer. The printed teeth were scanned and compared with the original ones (trueness) and to one another (precision). Undergraduate dental students in the third and fourth years performed root canal treatment on printed molars and were subsequently asked to evaluate their experience with these compared to real teeth. The workflow was feasible for manufacturing 3D printed tooth replicas. The absolute deviation after printing (trueness) ranged from 50.9μm to 104.3μm. The values for precision ranged from 43.5μm to 68.2μm. Students reported great benefits in the use of the replicated teeth for training purposes. The presented workflow is feasible for any dental educational institution who has access to a CBCT unit and a stereolithographic printer. The accuracy of the printing process is suitable for the production of tooth replicas for endodontic training. Undergraduate students favoured the availability of these replicas and the fairness they ensured in training due to standardization. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
A critical inventory of preoperative skull replicas.
Fasel, J H D; Beinemann, J; Schaller, K; Gailloud, P
2013-09-01
Physical replicas of organs are used increasingly for preoperative planning. The quality of these models is generally accepted by surgeons. In view of the strong trend towards minimally invasive and personalised surgery, however, the aim of this investigation was to assess qualitatively the accuracy of such replicas, using skull models as an example. Skull imaging was acquired for three cadavers by computed tomography using clinical routine parameters. After digital three-dimensional (3D) reconstruction, physical replicas were produced by 3D printing. The facsimilia were analysed systematically and compared with the best gold standard possible: the macerated skull itself. The skull models were far from anatomically accurate. Non-conforming rendering was observed in particular for foramina, sutures, notches, fissures, grooves, channels, tuberosities, thin-walled structures, sharp peaks and crests, and teeth. Surgeons should be aware that preoperative models may not yet render the exact anatomy of the patient under consideration and are advised to continue relying, in specific conditions, on their own analysis of the native computed tomography or magnetic resonance imaging.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Robust online Hamiltonian learning
International Nuclear Information System (INIS)
Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G
2012-01-01
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)
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...
Foundations and latest advances in replica exchange transition interface sampling
Cabriolu, R.; Refsnes, K.M.S; Bolhuis, P.G.; van Erp, T.S.
2017-01-01
Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short
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.
A Validation Study of the Impression Replica Technique.
Segerström, Sofia; Wiking-Lima de Faria, Johanna; Braian, Michael; Ameri, Arman; Ahlgren, Camilla
2018-04-17
To validate the well-known and often-used impression replica technique for measuring fit between a preparation and a crown in vitro. The validation consisted of three steps. First, a measuring instrument was validated to elucidate its accuracy. Second, a specimen consisting of male and female counterparts was created and validated by the measuring instrument. Calculations were made for the exact values of three gaps between the male and female. Finally, impression replicas were produced of the specimen gaps and sectioned into four pieces. The replicas were then measured with the use of a light microscope. The values received from measuring the specimen were then compared with the values received from the impression replicas, and the technique was thereby validated. The impression replica technique overvalued all measured gaps. Depending on location of the three measuring sites, the difference between the specimen and the impression replicas varied from 47 to 130 μm. The impression replica technique overestimates gaps within the range of 2% to 11%. The validation of the replica technique enables the method to be used as a reference when testing other methods for evaluating fit in dentistry. © 2018 by the American College of Prosthodontists.
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems
Modeling Vocal Fold Intravascular Flow using Synthetic Replicas
Terry, Aaron D.; Ricks, Matthew T.; Thomson, Scott L.
2017-11-01
Vocal fold vibration that is induced by air flowing from the lungs is believed to decrease blood flow through the vocal folds. This is important due to the critical role of blood flow in maintaining tissue health. However, the precise mechanical relationships between vocal fold vibration and blood perfusion remain understudied. A platform for studying liquid perfusion in a synthetic, life-size, self-oscillating vocal fold replica has recently been developed. The replicas are fabricated using molded silicone with material properties comparable to those of human vocal fold tissues and that include embedded microchannels through which liquid is perfused. The replicas are mounted on an air flow supply tube to initiate flow-induced vibration. A liquid reservoir is attached to the microchannel to cause liquid to perfuse through replica in the anterior-posterior direction. As replica vibration is initiated and amplitude increases, perfusion flow rate decreases. In this presentation, the replica design will be presented, along with data quantifying the relationships between parameters such as replica vibration amplitude, stiffness, microchannel diameter, and perfusion flow rate. This work was supported by Grant NIDCD R01DC005788 from the National Institutes of Health.
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.
Variational identities and Hamiltonian structures
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Gamma-ray dosimetry measurements of the Little Boy replica
International Nuclear Information System (INIS)
Plassmann, E.A.; Pederson, R.A.
1984-01-01
We present the current status of our gamma-ray dosimetry results for the Little Boy replica. Both Geiger-Mueller and thermoluminescent detectors were used in the measurements. Future work is needed to test assumptions made in data analysis
SRF Cavity Surface Topography Characterization Using Replica Techniques
Energy Technology Data Exchange (ETDEWEB)
C. Xu, M.J. Kelley, C.E. Reece
2012-07-01
To better understand the roll of topography on SRF cavity performance, we seek to obtain detailed topographic information from the curved practical cavity surfaces. Replicas taken from a cavity interior surface provide internal surface molds for fine Atomic Force Microscopy (AFM) and stylus profilometry. In this study, we confirm the replica resolution both on surface local defects such as grain boundary and etching pits and compare the surface uniform roughness with the aid of Power Spectral Density (PSD) where we can statistically obtain roughness parameters at different scales. A series of sampling locations are at the same magnetic field chosen at the same latitude on a single cell cavity to confirm the uniformity. Another series of sampling locations at different magnetic field amplitudes are chosen for this replica on the same cavity for later power loss calculation. We also show that application of the replica followed by rinsing does not adversely affect the cavity performance.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Patrol Detection for Replica Attacks on Wireless Sensor Networks
Wang, Liang-Min; Shi, Yang
2011-01-01
Replica attack is a critical concern in the security of wireless sensor networks. We employ mobile nodes as patrollers to detect replicas distributed in different zones in a network, in which a basic patrol detection protocol and two detection algorithms for stationary and mobile modes are presented. Then we perform security analysis to discuss the defense strategies against the possible attacks on the proposed detection protocol. Moreover, we show the advantages of the proposed protocol by d...
Accuracy of three-dimensional printing for manufacturing replica teeth
Lee, Keun-Young; Cho, Jin-Woo; Chang, Na-Young; Chae, Jong-Moon; Kang, Kyung-Hwa; Kim, Sang-Cheol; Cho, Jin-Hyoung
2015-01-01
Objective Three-dimensional (3D) printing is a recent technological development that may play a significant role in orthodontic diagnosis and treatment. It can be used to fabricate skull models or study models, as well as to make replica teeth in autotransplantation or tooth impaction cases. The aim of this study was to evaluate the accuracy of fabrication of replica teeth made by two types of 3D printing technologies. Methods Fifty extracted molar teeth were selected as samples. They were sc...
Bayesian ensemble refinement by replica simulations and reweighting
Hummer, Gerhard; Köfinger, Jürgen
2015-12-01
We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.
Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
de Dominicis, C.; Carlucci, D. M.; Temesvári, T.
1997-01-01
The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices M^{α β;γ^δ}, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work. On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice M^{α β;γ^δ} dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
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 ...
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 formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
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
Neurovascular Modeling: Small-Batch Manufacturing of Silicone Vascular Replicas
Chueh, J.Y.; Wakhloo, A.K.; Gounis, M.J.
2009-01-01
BACKGROUND AND PURPOSE Realistic, population based cerebrovascular replicas are required for the development of neuroendovascular devices. The objective of this work was to develop an efficient methodology for manufacturing realistic cerebrovascular replicas. MATERIALS AND METHODS Brain MR angiography data from 20 patients were acquired. The centerline of the vasculature was calculated, and geometric parameters were measured to describe quantitatively the internal carotid artery (ICA) siphon. A representative model was created on the basis of the quantitative measurements. Using this virtual model, we designed a mold with core-shell structure and converted it into a physical object by fused-deposit manufacturing. Vascular replicas were created by injection molding of different silicones. Mechanical properties, including the stiffness and luminal coefficient of friction, were measured. RESULTS The average diameter, length, and curvature of the ICA siphon were 4.15 ± 0.09 mm, 22.60 ± 0.79 mm, and 0.34 ± 0.02 mm-1 (average ± standard error of the mean), respectively. From these image datasets, we created a median virtual model, which was transformed into a physical replica by an efficient batch-manufacturing process. The coefficient of friction of the luminal surface of the replica was reduced by up to 55% by using liquid silicone rubber coatings. The modulus ranged from 0.67 to 1.15 MPa compared with 0.42 MPa from human postmortem studies, depending on the material used to make the replica. CONCLUSIONS Population-representative, smooth, and true-to-scale silicone arterial replicas with uniform wall thickness were successfully built for in vitro neurointerventional device-testing by using a batch-manufacturing process. PMID:19321626
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
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
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
The Hamiltonian of QED. Zero mode
International Nuclear Information System (INIS)
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Accuracy of three-dimensional printing for manufacturing replica teeth.
Lee, Keun-Young; Cho, Jin-Woo; Chang, Na-Young; Chae, Jong-Moon; Kang, Kyung-Hwa; Kim, Sang-Cheol; Cho, Jin-Hyoung
2015-09-01
Three-dimensional (3D) printing is a recent technological development that may play a significant role in orthodontic diagnosis and treatment. It can be used to fabricate skull models or study models, as well as to make replica teeth in autotransplantation or tooth impaction cases. The aim of this study was to evaluate the accuracy of fabrication of replica teeth made by two types of 3D printing technologies. Fifty extracted molar teeth were selected as samples. They were scanned to generate high-resolution 3D surface model stereolithography files. These files were converted into physical models using two types of 3D printing technologies: Fused deposition modeling (FDM) and PolyJet technology. All replica teeth were scanned and 3D images generated. Computer software compared the replica teeth to the original teeth with linear measurements, volumetric measurements, and mean deviation measurements with best-fit alignment. Paired t-tests were used to statistically analyze the measurements. Most measurements of teeth formed using FDM tended to be slightly smaller, while those of the PolyJet replicas tended to be slightly larger, than those of the extracted teeth. Mean deviation measurements with best-fit alignment of FDM and PolyJet group were 0.047 mm and 0.038 mm, respectively. Although there were statistically significant differences, they were regarded as clinically insignificant. This study confirms that FDM and PolyJet technologies are accurate enough to be usable in orthodontic diagnosis and treatment.
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Weak KAM for commuting Hamiltonians
International Nuclear Information System (INIS)
Zavidovique, M
2010-01-01
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)
Hamiltonian dynamics of extended objects
Capovilla, R.; Guven, J.; Rojas, E.
2004-12-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.
A Hamiltonian approach to Thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
Hamiltonian dynamics of extended objects
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2004-01-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations
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.
A Hamiltonian approach to Thermodynamics
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; Molina, C.
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
On the domain of the Nelson Hamiltonian
Griesemer, M.; Wünsch, A.
2018-04-01
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.
Hamiltonian systems in accelerator physics
International Nuclear Information System (INIS)
Laslett, L.J.
1985-06-01
General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production
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.
Hamiltonian dynamics of preferential attachment
International Nuclear Information System (INIS)
Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2016-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)
Reconstruction of Monte Carlo replicas from Hessian parton distributions
Energy Technology Data Exchange (ETDEWEB)
Hou, Tie-Jiun [Department of Physics, Southern Methodist University,Dallas, TX 75275-0181 (United States); Gao, Jun [INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology,Department of Physics and Astronomy, Shanghai Jiao-Tong University, Shanghai 200240 (China); High Energy Physics Division, Argonne National Laboratory,Argonne, Illinois, 60439 (United States); Huston, Joey [Department of Physics and Astronomy, Michigan State University,East Lansing, MI 48824 (United States); Nadolsky, Pavel [Department of Physics, Southern Methodist University,Dallas, TX 75275-0181 (United States); Schmidt, Carl; Stump, Daniel [Department of Physics and Astronomy, Michigan State University,East Lansing, MI 48824 (United States); Wang, Bo-Ting; Xie, Ke Ping [Department of Physics, Southern Methodist University,Dallas, TX 75275-0181 (United States); Dulat, Sayipjamal [Department of Physics and Astronomy, Michigan State University,East Lansing, MI 48824 (United States); School of Physics Science and Technology, Xinjiang University,Urumqi, Xinjiang 830046 (China); Center for Theoretical Physics, Xinjiang University,Urumqi, Xinjiang 830046 (China); Pumplin, Jon; Yuan, C.P. [Department of Physics and Astronomy, Michigan State University,East Lansing, MI 48824 (United States)
2017-03-20
We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section reweighting. Master formulas for computation of asymmetric standard deviations in the Monte-Carlo representation are derived. A correction is proposed to address a bias in asymmetric uncertainties introduced by the Taylor series approximation. A numerical program is made available for conversion of Hessian PDFs into Monte-Carlo replicas according to normal, log-normal, and Watt-Thorne sampling procedures.
Standard practice for production and evaluation of field metallographic replicas
American Society for Testing and Materials. Philadelphia
2001-01-01
1.1 This practice covers recognized methods for the preparation and evaluation of cellulose acetate or plastic film replicas which have been obtained from metallographically prepared surfaces. It is designed for the evaluation of replicas to ensure that all significant features of a metallographically prepared surface have been duplicated and preserved on the replica with sufficient detail to permit both LM and SEM examination with optimum resolution and sensitivity. 1.2 This practice may be used as a controlling document in commercial situations. 1.3 The values stated in SI units are to be regarded as the standard. Inch-pound units given in parentheses are for information only. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
Yamauchi, Masataka; Okumura, Hisashi
2017-11-01
We developed a two-dimensional replica-permutation molecular dynamics method in the isothermal-isobaric ensemble. The replica-permutation method is a better alternative to the replica-exchange method. It was originally developed in the canonical ensemble. This method employs the Suwa-Todo algorithm, instead of the Metropolis algorithm, to perform permutations of temperatures and pressures among more than two replicas so that the rejection ratio can be minimized. We showed that the isothermal-isobaric replica-permutation method performs better sampling efficiency than the isothermal-isobaric replica-exchange method and infinite swapping method. We applied this method to a β-hairpin mini protein, chignolin. In this simulation, we observed not only the folded state but also the misfolded state. We calculated the temperature and pressure dependence of the fractions on the folded, misfolded, and unfolded states. Differences in partial molar enthalpy, internal energy, entropy, partial molar volume, and heat capacity were also determined and agreed well with experimental data. We observed a new phenomenon that misfolded chignolin becomes more stable under high-pressure conditions. We also revealed this mechanism of the stability as follows: TYR2 and TRP9 side chains cover the hydrogen bonds that form a β-hairpin structure. The hydrogen bonds are protected from the water molecules that approach the protein as the pressure increases.
Patrol Detection for Replica Attacks on Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Yang Shi
2011-02-01
Full Text Available Replica attack is a critical concern in the security of wireless sensor networks. We employ mobile nodes as patrollers to detect replicas distributed in different zones in a network, in which a basic patrol detection protocol and two detection algorithms for stationary and mobile modes are presented. Then we perform security analysis to discuss the defense strategies against the possible attacks on the proposed detection protocol. Moreover, we show the advantages of the proposed protocol by discussing and comparing the communication cost and detection probability with some existing methods.
Creating technical heritage object replicas in a virtual environment
Egorova, Olga; Shcherbinin, Dmitry
2016-03-01
The paper presents innovative informatics methods for creating virtual technical heritage replicas, which are of significant scientific and practical importance not only to researchers but to the public in general. By performing 3D modeling and animation of aircrafts, spaceships, architectural-engineering buildings, and other technical objects, the process of learning is achieved while promoting the preservation of the replicas for future generations. Modern approaches based on the wide usage of computer technologies attract a greater number of young people to explore the history of science and technology and renew their interest in the field of mechanical engineering.
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.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
Integrable and nonintegrable Hamiltonian systems
International Nuclear Information System (INIS)
Percival, I.
1986-01-01
Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications
Entanglement entropy with a time-dependent Hamiltonian
Sivaramakrishnan, Allic
2018-03-01
The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT2 with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher-order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS3/CFT2 and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to "entanglement diagrams," proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.
Replica-Based High-Performance Tuple Space Computing
DEFF Research Database (Denmark)
Andric, Marina; De Nicola, Rocco; Lluch Lafuente, Alberto
2015-01-01
of concurrency and data access. We investigate issues related to replica consistency, provide an operational semantics that guides the implementation of the language, and discuss the main synchronization mechanisms of our prototypical run-time framework. Finally, we provide a performance analysis, which includes...
Replica scaling studies of hard missile impacts on reinforced concrete
International Nuclear Information System (INIS)
Barr, P.; Carter, P.G.; Howe, W.D.; Neilson, A.J.
1982-01-01
Missile and target combinations at three different liners scales have been used in an experimental assessment of the applicability of replica scaling to the dynamic behaviour of reinforced concrete structures impacted by rigid missiles. Experimental results are presented for models with relative linear scales of 1, 0.37 and 0.12. (orig.) [de
Perspective: Quantum Hamiltonians for optical interactions
Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy
2018-01-01
The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
General technique to produce isochronous Hamiltonians
International Nuclear Information System (INIS)
Calogero, F; Leyvraz, F
2007-01-01
We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra
Collective Hamiltonians for dipole giant resonances
International Nuclear Information System (INIS)
Weiss, L.I.
1991-07-01
The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1981-11-01
A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions
Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator
International Nuclear Information System (INIS)
Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.
1984-01-01
Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator
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
Hamiltonian analysis of Plebanski theory
International Nuclear Information System (INIS)
Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph
2004-01-01
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity
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 Direct Method of Hamiltonian Structure
International Nuclear Information System (INIS)
Li Qi; Chen Dengyuan; Su Shuhua
2011-01-01
A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)
Port Hamiltonian modeling of Power Networks
van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R
2012-01-01
In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
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...
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
On Distributed Port-Hamiltonian Process Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Almost periodic Hamiltonians: an algebraic approach
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians
Nested Sampling with Constrained Hamiltonian Monte Carlo
Betancourt, M. J.
2010-01-01
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.
Storing files in a parallel computing system using list-based index to identify replica files
Faibish, Sorin; Bent, John M.; Tzelnic, Percy; Zhang, Zhenhua; Grider, Gary
2015-07-21
Improved techniques are provided for storing files in a parallel computing system using a list-based index to identify file replicas. A file and at least one replica of the file are stored in one or more storage nodes of the parallel computing system. An index for the file comprises at least one list comprising a pointer to a storage location of the file and a storage location of the at least one replica of the file. The file comprises one or more of a complete file and one or more sub-files. The index may also comprise a checksum value for one or more of the file and the replica(s) of the file. The checksum value can be evaluated to validate the file and/or the file replica(s). A query can be processed using the list.
International Nuclear Information System (INIS)
Zimmer, F.M.; Magalhaes, S.G.
2007-01-01
The one-step replica symmetry breaking is used to study the competition between spin glass (SG) and antiferromagnetic order (AF) in two-sublattice fermionic Ising SG models in the presence of a transverse Γ and a parallel H magnetic fields. Inter- and intra-sublattice exchange interactions following Gaussian distributions are considered. The problem is formulated in a Grassmann path integral formalism within the static ansatz. Results show that H favors the non-ergodic mixed phase (AF+SG) and it destroys the AF. The Γ suppresses the magnetic orders, and the intra-sublattice interaction can introduce a discontinuous phase transition
Physical replicas and the Bose glass in cold atomic gases
International Nuclear Information System (INIS)
Morrison, S; Kantian, A; Daley, A J; Zoller, P; Katzgraber, H G; Lewenstein, M; Buechler, H P
2008-01-01
We study cold atomic gases in a disorder potential and analyse the correlations between different systems subjected to the same disorder landscape. Such independent copies with the same disorder landscape are known as replicas. While, in general, these are not accessible experimentally in condensed matter systems, they can be realized using standard tools for controlling cold atomic gases in an optical lattice. Of special interest is the overlap function which represents a natural order parameter for disordered systems and is a correlation function between the atoms of two independent replicas with the same disorder. We demonstrate an efficient measurement scheme for the determination of this disorder-induced correlation function. As an application, we focus on the disordered Bose-Hubbard model and determine the overlap function within the perturbation theory and a numerical analysis. We find that the measurement of the overlap function allows for the identification of the Bose-glass phase in certain parameter regimes
Physical replicas and the Bose glass in cold atomic gases
Energy Technology Data Exchange (ETDEWEB)
Morrison, S; Kantian, A; Daley, A J; Zoller, P [Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck (Austria); Katzgraber, H G [Theoretische Physik, ETH Zurich, CH-8093 Zuerich (Switzerland); Lewenstein, M [ICAO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, E-08860 Castelldefels, Barcelona (Spain); Buechler, H P [Institute for Theoretical Physics III, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart (Germany)], E-mail: sarah.morrison@uibk.ac.at
2008-07-15
We study cold atomic gases in a disorder potential and analyse the correlations between different systems subjected to the same disorder landscape. Such independent copies with the same disorder landscape are known as replicas. While, in general, these are not accessible experimentally in condensed matter systems, they can be realized using standard tools for controlling cold atomic gases in an optical lattice. Of special interest is the overlap function which represents a natural order parameter for disordered systems and is a correlation function between the atoms of two independent replicas with the same disorder. We demonstrate an efficient measurement scheme for the determination of this disorder-induced correlation function. As an application, we focus on the disordered Bose-Hubbard model and determine the overlap function within the perturbation theory and a numerical analysis. We find that the measurement of the overlap function allows for the identification of the Bose-glass phase in certain parameter regimes.
Replica approach to mean-variance portfolio optimization
Varga-Haszonits, Istvan; Caccioli, Fabio; Kondor, Imre
2016-12-01
We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for r = N/T optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.
Platinum replica electron microscopy: Imaging the cytoskeleton globally and locally.
Svitkina, Tatyana M
2017-05-01
Structural studies reveal how smaller components of a system work together as a whole. However, combining high resolution of details with full coverage of the whole is challenging. In cell biology, light microscopy can image many cells in their entirety, but at a lower resolution, whereas electron microscopy affords very high resolution, but usually at the expense of the sample size and coverage. Structural analyses of the cytoskeleton are especially demanding, because cytoskeletal networks are unresolvable by light microscopy due to their density and intricacy, whereas their proper preservation is a challenge for electron microscopy. Platinum replica electron microscopy can uniquely bridge the gap between the "comfort zones" of light and electron microscopy by allowing high resolution imaging of the cytoskeleton throughout the entire cell and in many cells in the population. This review describes the principles and applications of platinum replica electron microscopy for studies of the cytoskeleton. Copyright © 2017 Elsevier Ltd. All rights reserved.
Replica treatment of the Calogero-Sutherland model
International Nuclear Information System (INIS)
Gangardt, Dimitry M.; Kamenev, Alex
2001-01-01
Employing Forrester-Ha method of Jack polynomials, we derive an integral identity connecting certain N-fold coordinate average of the Calogero-Sutherland model with the n-fold replica integral. Subsequent analytical continuation in n leads to asymptotic expressions for the (static and dynamic) density-density correlation function of the model as well as the Green's function for an arbitrary coupling constant λ
A port-Hamiltonian approach to image-based visual servo control for dynamic systems
Mahony, R.; Stramigioli, Stefano
2012-01-01
This paper introduces a port-Hamiltonian framework for the design of image-based visual servo control for dynamic mechanical systems. The approach taken introduces the concept of an image effort and provides an interpretation of energy exchange between the dynamics of the physical system and virtual
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Single-particle dynamics - Hamiltonian formulation
International Nuclear Information System (INIS)
Montague, B.W.
1977-01-01
In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Quantum Hamiltonian Physics with Supercomputers
International Nuclear Information System (INIS)
Vary, James P.
2014-01-01
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed
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.
Jacobi fields of completely integrable Hamiltonian systems
International Nuclear Information System (INIS)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2003-01-01
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
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.
Spectral properties of almost-periodic Hamiltonians
International Nuclear Information System (INIS)
Lima, R.
1983-12-01
We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr
Air parcels and air particles: Hamiltonian dynamics
Bokhove, Onno; Lynch, Peter
We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
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.
Variable Delay in port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2006-01-01
In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.
On local Hamiltonians and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)
2006-11-15
We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
Replica field theory for a polymer in random media
International Nuclear Information System (INIS)
Goldschmidt, Yadin Y.
2000-01-01
In this paper we revisit the problem of a (non-self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM) [J. Chem. Phys. 89, 2435 (1988)]. As noticed by Cates and Ball (CB) [J. Phys. (France) 49, 2009 (1988)] there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ''localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d -1/(4-d) ∼(g ln V) -1/(4-d) , where R is the radius of gyration, g is the strength of the disorder, μ is the spring constant associated with the confining potential, and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln V as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d V ' ∼exp(g 2/(2-d) L (4-d)/(2-d) ) the annealed results are recovered and R∼(Lg) 1/(d-2) , where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The one-step replica symmetry breaking solution is crucial for obtaining the above results. (c) 2000 The American Physical Society
Replica Analysis for Portfolio Optimization with Single-Factor Model
Shinzato, Takashi
2017-06-01
In this paper, we use replica analysis to investigate the influence of correlation among the return rates of assets on the solution of the portfolio optimization problem. We consider the behavior of an optimal solution for the case where the return rate is described with a single-factor model and compare the findings obtained from our proposed methods with correlated return rates with those obtained with independent return rates. We then analytically assess the increase in the investment risk when correlation is included. Furthermore, we also compare our approach with analytical procedures for minimizing the investment risk from operations research.
Application of extraction replicas and analytical electron microscopy to precipitate phase studies
International Nuclear Information System (INIS)
Kenik, E.A.; Maziasz, P.J.
1984-01-01
Extraction replicas provide a powerful extension of AEM techniques for analysis of fine precipitates. In many cases, replicas allow more accurate analyses to be performed and, in some cases, allow unique analyses which cannot be performed in-foil. However, there are limitations to the use of extraction replicas in AEM, of which the analyst must be aware. Many can be eliminated by careful preparation. Often, combined AEM studies of precipitates in-foil and on extraction replicas provide complementary and corroborative information for the fullest analysis of precipitate phases
Replica calibration artefacts for optical 3D scanning of micro parts
DEFF Research Database (Denmark)
De Chiffre, Leonardo; Carmignato, S.; Cantatore, Angela
2009-01-01
This work deals with development of calibration artefacts produced by using hard replica materials, achieving high quality geometrical reproduction of suitable reference artefacts, high stability, and high surface cooperativeness. An investigation was carried out using a replica material for dental...... applications to reproduce the geometry of a step artefact, a miniature step gauge, and a curve standard for optical measuring machines. The replica artefacts were calibrated using a tactile coordinate measuring machine and measured on two different optical scanners. Replication quality and applicability...... of the artefacts to verify the accuracy of optical measurements as well as thermal expansion coefficient and stability of the replica artefacts over time were documented....
Energy Technology Data Exchange (ETDEWEB)
Diaz Giron, P. a.; Ortega, F.; Rivero, N.
2011-07-01
Nuclear power plants full scope replica simulators were in the past solely designed following operational personnel training criteria. Nevertheless, these simulators not only feature a high replica control room but also provide an accurate process response. Control room replica simulators are presently based on complex technological platforms permitting highest physical and functional fidelity, allowing to be used as versatile and value added tools in diverse plants operation and maintenance activities. In recent years. Tecnatom has extended the use of such simulators to different engineering applications. this article intends to identify the simulators use in training and other applications beyond training. (Author)
International Nuclear Information System (INIS)
Bunder, J.E.J.E.; McKenzie, R.H.Ross H.
2001-01-01
We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states. Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled 'spins' which are elements of u(1,1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams
Fabrication of free-standing replicas of fragile, laminar, chitinous biotemplates
International Nuclear Information System (INIS)
Lakhtakia, Akhlesh; Motyka, Michael A; MartIn-Palma, Raul J; Pantano, Carlo G
2009-01-01
The conformal-evaporated-film-by-rotation technique, followed by the dissolution of chitin in an aqueous solution of orthophosphoric acid, can be used to fabricate free-standing replicas of fragile, laminar, chitinous biotemplates. This novel approach was demonstrated using butterfly wings as biotemplates and GeSeSb chalcogenide glass for replicas. (communication)
Fabrication of free-standing replicas of fragile, laminar, chitinous biotemplates
Energy Technology Data Exchange (ETDEWEB)
Lakhtakia, Akhlesh; Motyka, Michael A [Materials Research Institute and Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802 (United States); MartIn-Palma, Raul J; Pantano, Carlo G [Materials Research Institute and Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 (United States)], E-mail: akhlesh@psu.edu
2009-09-01
The conformal-evaporated-film-by-rotation technique, followed by the dissolution of chitin in an aqueous solution of orthophosphoric acid, can be used to fabricate free-standing replicas of fragile, laminar, chitinous biotemplates. This novel approach was demonstrated using butterfly wings as biotemplates and GeSeSb chalcogenide glass for replicas. (communication)
Verbanic, Samuel; Brady, Owen; Sanda, Ahmed; Gustafson, Carolina; Donhauser, Zachary J.
2014-01-01
Biomimetic replicas of superhydrophobic lotus and taro leaf surfaces can be made using polydimethylsiloxane. These replicas faithfully reproduce the microstructures of the leaves' surface and can be analyzed using contact angle goniometry, self-cleaning experiments, and optical microscopy. These simple and adaptable experiments were used to…
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.
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Hamiltonian boundary term and quasilocal energy flux
International Nuclear Information System (INIS)
Chen, C.-M.; Nester, James M.; Tung, R.-S.
2005-01-01
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Hamiltonian dynamics for complex food webs
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Convergence to equilibrium under a random Hamiltonian
Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
Replica analysis for the duality of the portfolio optimization problem.
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
Replica analysis for the duality of the portfolio optimization problem
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
Beyond Virtual Replicas: 3D Modeling and Maltese Prehistoric Architecture
Directory of Open Access Journals (Sweden)
Filippo Stanco
2013-01-01
Full Text Available In the past decade, computer graphics have become strategic for the development of projects aimed at the interpretation of archaeological evidence and the dissemination of scientific results to the public. Among all the solutions available, the use of 3D models is particularly relevant for the reconstruction of poorly preserved sites and monuments destroyed by natural causes or human actions. These digital replicas are, at the same time, a virtual environment that can be used as a tool for the interpretative hypotheses of archaeologists and as an effective medium for a visual description of the cultural heritage. In this paper, the innovative methodology and aims and outcomes of a virtual reconstruction of the Borg in-Nadur megalithic temple, carried out by Archeomatica Project of the University of Catania, are offered as a case study for a virtual archaeology of prehistoric Malta.
Adaptive control of port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András
2010-01-01
In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for
Iterated Hamiltonian type systems and applications
Tiba, Dan
2018-04-01
We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
2000-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
1999-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
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...
The hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-01-01
We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)
Hamiltonian structure for rescaled integrable Lorenz systems
International Nuclear Information System (INIS)
Haas, F.; Goedert, J.
1993-01-01
It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)
Singularities of Poisson structures and Hamiltonian bifurcations
Meer, van der J.C.
2010-01-01
Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom
Transparency in port-Hamiltonian based telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2005-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian based teleoperators. Furthermore we provide a transparency analysis of
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Hamiltonian formulation of anomaly free chiral bosons
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.
1988-01-01
Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt
Hamiltonian structure of gravitational field theory
International Nuclear Information System (INIS)
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
The Hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-08-01
We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs
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.
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...
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
QCD string with quarks. 2. Light cone Hamiltonian
International Nuclear Information System (INIS)
Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.
1994-01-01
The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom
Internal structure analysis of particle-double network gels used in a gel organ replica
Abe, Mei; Arai, Masanori; Saito, Azusa; Sakai, Kazuyuki; Kawakami, Masaru; Furukawa, Hidemitsu
2016-04-01
In recent years, the fabrication of patient organ replicas using 3D printers has been attracting a great deal of attention in medical fields. However, the cost of these organ replicas is very high as it is necessary to employ very expensive 3D printers and printing materials. Here we present a new gel organ replica, of human kidney, fabricated with a conventional molding technique, using a particle-double network hydrogel (P-DN gel). The replica is transparent and has the feel of a real kidney. It is expected that gel organ replicas produced this way will be a useful tool for the education of trainee surgeons and clinical ultrasonography technologists. In addition to developing a gel organ replica, the internal structure of the P-DN gel used is also discussed. Because the P-DN gel has a complex structure comprised of two different types of network, it has not been possible to investigate them internally in detail. Gels have an inhomogeneous network structure. If it is able to get a more uniform structure, it is considered that this would lead to higher strength in the gel. In the present study we investigate the structure of P-DN gel, using the gel organ replica. We investigated the internal structure of P-DN gel using Scanning Microscopic Light Scattering (SMILS), a non-contacting and non-destructive.
Han, Zhiwu; Li, Bo; Mu, Zhengzhi; Yang, Meng; Niu, Shichao; Zhang, Junqiu; Ren, Luquan
2015-11-01
The polydimethylsiloxane (PDMS) positive replica templated twice from the excellent light trapping surface of butterfly Trogonoptera brookiana wing scales was fabricated by a simple and promising route. The exact SiO2 negative replica was fabricated by using a synthesis method combining a sol-gel process and subsequent selective etching. Afterwards, a vacuum-aided process was introduced to make PDMS gel fill into the SiO2 negative replica, and the PDMS gel was solidified in an oven. Then, the SiO2 negative replica was used as secondary template and the structures in its surface was transcribed onto the surface of PDMS. At last, the PDMS positive replica was obtained. After comparing the PDMS positive replica and the original bio-template in terms of morphology, dimensions and reflectance spectra and so on, it is evident that the excellent light trapping structures of butterfly wing scales were inherited by the PDMS positive replica faithfully. This bio-inspired route could facilitate the preparation of complex light trapping nanostructure surfaces without any assistance from other power-wasting and expensive nanofabrication technologies.
Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors
International Nuclear Information System (INIS)
Wang, C.-x.
2006-01-01
A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.
On integrable Hamiltonians for higher spin XXZ chain
International Nuclear Information System (INIS)
Bytsko, Andrei G.
2003-01-01
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Effective Hamiltonians in quantum physics: resonances and geometric phase
International Nuclear Information System (INIS)
Rau, A R P; Uskov, D
2006-01-01
Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian
The added value of the replica simulators in the exploitation of nuclear power plants
International Nuclear Information System (INIS)
Diaz Giron, P. a.; Ortega, F.; Rivero, N.
2011-01-01
Nuclear power plants full scope replica simulators were in the past solely designed following operational personnel training criteria. Nevertheless, these simulators not only feature a high replica control room but also provide an accurate process response. Control room replica simulators are presently based on complex technological platforms permitting highest physical and functional fidelity, allowing to be used as versatile and value added tools in diverse plants operation and maintenance activities. In recent years. Tecnatom has extended the use of such simulators to different engineering applications. this article intends to identify the simulators use in training and other applications beyond training. (Author)
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Effective Hamiltonian for high Tc Cu oxides
International Nuclear Information System (INIS)
Fukuyama, H.; Matsukawa, H.
1989-01-01
Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived
Partial quantization of Lagrangian-Hamiltonian systems
International Nuclear Information System (INIS)
Amaral, C.M. do; Soares Filho, P.C.
1979-05-01
A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Quantum mechanical Hamiltonian models of discrete processes
International Nuclear Information System (INIS)
Benioff, P.
1981-01-01
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
Hamiltonian reduction of Kac-Moody algebras
International Nuclear Information System (INIS)
Kimura, Kazuhiro
1991-01-01
Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
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.
A diagrammatic construction of formal E-independent model hamiltonian
International Nuclear Information System (INIS)
Kvasnicka, V.
1977-01-01
A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian
Boson mapping and the microscopic collective nuclear Hamiltonian
International Nuclear Information System (INIS)
Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.
1990-01-01
Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Hamiltonian theory of guiding-center motion
International Nuclear Information System (INIS)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1982-01-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic Geometric Algorithms for Hamiltonian Systems
Feng, Kang
2010-01-01
"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
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.
Quantization of non-Hamiltonian physical systems
International Nuclear Information System (INIS)
Bolivar, A.O.
1998-09-01
We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1981-12-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic topology of integrable Hamiltonian systems
International Nuclear Information System (INIS)
Nguyen Tien Zung.
1993-08-01
We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs
Hamiltonian description and quantization of dissipative systems
Enz, Charles P.
1994-09-01
Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.
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.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
Human skulls with turquoise inlays: pre hispanic origin or replicas?
International Nuclear Information System (INIS)
Silva V, Y.; Castillo M, M.T.; Bautista M, J.P.; Arenas A, J.
2006-01-01
The lack of archaeological context determining if the manufacture of two human skulls adorned with turquoise inlays have pre-Columbian origin or not (replicas), led to perform other studies. Under these conditions, besides orthodox methodology commonly used to assign chronology and cultural aspects as form, style, decoration, iconography, etc., it was necessary to obtain more results based on the use of characterization techniques. The techniques employed were Scanning Electron Microscopy (SEM), X-Ray Energy Dispersive Spectroscopy (EDS), Transmission Electron Microscopy (TEM) and Fourier Transform Infrared Spectroscopy (FTIR), in order to determine the manufacture techniques and chemical composition of the materials used for the cementant. SEM analysis showed the presence of zones composed by Ca, O, C and Al. In some cases Mg, Cl, Fe and Pb were identified. High concentration of Cu was present in all samples, due to residues of turquoise inlays (CuAI 6 (PO 4 ) 4 (OH) 8 (H 2 O) 4 ) with which the skulls were decorated. In the cementant was identified the Ca as base element of the cementant, as well as particles < 100 nm with irregular morphology and other amorphous zones. FTIR spectrums indicated the presence of organic substances that could be used as agglutinating in the cementant. The current work shows a progress identifying involved techniques in the manufacturing of two human skulls with turquoise inlays. (Author)
Parylene C coating for high-performance replica molding.
Heyries, Kevin A; Hansen, Carl L
2011-12-07
This paper presents an improvement to the soft lithography fabrication process that uses chemical vapor deposition of poly(chloro-p-xylylene) (parylene C) to protect microfabricated masters and to improve the release of polymer devices following replica molding. Chemical vapor deposition creates nanometre thick conformal coatings of parylene C on silicon wafers having arrays of 30 μm high SU8 pillars with densities ranging from 278 to 10,040 features per mm(2) and aspect ratios (height : width) from 1 : 1 to 6 : 1. A single coating of parylene C was sufficient to permanently promote poly(dimethyl)siloxane (PDMS) mold release and to protect masters for an indefinite number of molding cycles. We also show that the improved release properties of parylene treated masters allow for fabrication with hard polymers, such as poly(urethane), that would otherwise not be compatible with SU8 on silicon masters. Parylene C provides a robust and high performance mold release coating for soft lithography microfabrication that extends the life of microfabricated masters and improves the achievable density and aspect ratio of replicated features.
Critiques, replicas and proposals for the New Urbanism Vision
Directory of Open Access Journals (Sweden)
Alaide Retana
2014-03-01
Full Text Available The new urbanism (NU is a vision of planning and urban design emerged in 1993, which finds its basis in the design of traditional communities. This trend has had various criticisms and replicas, which were reviewed in relation to urban sprawl, transportation, re-densifying, mix of uses of land, design, gentrification, pedestrianization and safety, which were analyzed in the neighborhood of Santa Barbara in Toluca, Mexico. This area was chosen for being traditional and forming part of the historical center of the city, which even though it was not designed under the guidelines of the NU, it has the quality of traditional, from which the NU would theoretically has taken its essence. The objective of this analysis is to establish whether the NU has the essence of a traditional Mexican neighborhood, as well as to check if the criticisms of the NU are informed when applied to a space belonging to a Mexican historic center that has been abandoned by problems of insecurity and degradation. The general conclusion is that the traditional neighborhoods have provided design elements to the NU, which will refute some of the criticisms, however, proposals for NU in neighborhoods of his-toric centers have to be based on the community, the architecture and existing urbanism, since these elements are those that give the identity.
Stability and replica symmetry in the ising spin glass: a toy model
International Nuclear Information System (INIS)
De Dominicis, C.; Mottishaw, P.
1986-01-01
Searching for possible replica symmetric solutions in an Ising spin glass (in the tree approximation) we investigate a toy model whose bond distribution has two non vanishing cumulants (instead of one only as in a gaussian distribution)
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
NLO renormalization in the Hamiltonian truncation
Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.
2017-09-01
Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.
Redesign of the DFT/MRCI Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Utility of replica techniques for x-ray microanalysis of second phase particles
International Nuclear Information System (INIS)
Bentley, J.
1984-01-01
X-ray microanalysis of second phase particles in ion-milled or electropolished thin foils is often complicated by the presence of the matrix nearby. Extraction replica techniques provide a means to avoid many of the complications of thin-foil analyses. In this paper, three examples of the analysis of second phase particles are described and illustrate the improvement obtained by the use of extraction replicas for qualitative analysis, quantitative analysis, and analysis of radioactive specimens
Data Sets Replicas Placements Strategy from Cost-Effective View in the Cloud
Directory of Open Access Journals (Sweden)
Xiuguo Wu
2016-01-01
Full Text Available Replication technology is commonly used to improve data availability and reduce data access latency in the cloud storage system by providing users with different replicas of the same service. Most current approaches largely focus on system performance improvement, neglecting management cost in deciding replicas number and their store places, which cause great financial burden for cloud users because the cost for replicas storage and consistency maintenance may lead to high overhead with the number of new replicas increased in a pay-as-you-go paradigm. In this paper, towards achieving the approximate minimum data sets management cost benchmark in a practical manner, we propose a replicas placements strategy from cost-effective view with the premise that system performance meets requirements. Firstly, we design data sets management cost models, including storage cost and transfer cost. Secondly, we use the access frequency and the average response time to decide which data set should be replicated. Then, the method of calculating replicas’ number and their store places with minimum management cost is proposed based on location problem graph. Both the theoretical analysis and simulations have shown that the proposed strategy offers the benefits of lower management cost with fewer replicas.
Rare events via multiple reaction channels sampled by path replica exchange
Bolhuis, P.G.
2008-01-01
Transition path sampling (TPS) was developed for studying activated processes in complex systems with unknown reaction coordinate. Transition interface sampling (TIS) allows efficient evaluation of the rate constants. However, when the transition can occur via more than one reaction channel
Model many-body Stoner Hamiltonian for binary FeCr alloys
Nguyen-Manh, D.; Dudarev, S. L.
2009-09-01
We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
Integrable Time-Dependent Quantum Hamiltonians
Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen
2018-05-01
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
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...
Resonant driving of a nonlinear Hamiltonian system
International Nuclear Information System (INIS)
Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro
2013-01-01
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.
Nonabelian N=2 superstrings: Hamiltonian structure
International Nuclear Information System (INIS)
Isaev, A.P.; Ivanov, E.A.
1991-04-01
We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
Hamiltonian Description of Convective-cell Generation
International Nuclear Information System (INIS)
Krommes, J.A.; Kolesnikov, R.A.
2004-01-01
The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
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
A new perturbative treatment of pentadiagonal Hamiltonians
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.
Hamiltonian structure of the Lotka-Volterra equations
Nutku, Y.
1990-03-01
The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians
Temme, Kristan
2017-03-01
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.
Normal form for mirror machine Hamiltonians
International Nuclear Information System (INIS)
Dragt, A.J.; Finn, J.M.
1979-01-01
A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior
Nonextensive formalism and continuous Hamiltonian systems
International Nuclear Information System (INIS)
Boon, Jean Pierre; Lutsko, James F.
2011-01-01
A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.
Hamiltonian Anomalies from Extended Field Theories
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Effective Hamiltonians for phosphorene and silicene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Matchings Extend to Hamiltonian Cycles in 5-Cube
Directory of Open Access Journals (Sweden)
Wang Fan
2018-02-01
Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Spectral and resonance properties of the Smilansky Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)
2017-02-26
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.
Synthesis and properties of ZnFe2O4 replica with biological hierarchical structure
International Nuclear Information System (INIS)
Liu, Hongyan; Guo, Yiping; Zhang, Yangyang; Wu, Fen; Liu, Yun; Zhang, Di
2013-01-01
Highlights: • ZFO replica with hierarchical structure was synthesized from butterfly wings. • Biotemplate has a significant impact on the properties of ZFO material. • Our method opens up new avenues for the synthesis of spinel ferrites. -- Abstract: ZnFe 2 O 4 replica with biological hierarchical structure was synthesized from Papilio paris by a sol–gel method followed by calcination. The crystallographic structure and morphology of the obtained samples were characterized by X-ray diffraction, field-emission scanning electron microscope, and transmittance electron microscope. The results showed that the hierarchical structures were retained in the ZFO replica of spinel structure. The magnetic behavior of such novel products was measured by a vibrating sample magnetometer. A superparamagnetism-like behavior was observed due to nanostructuration size effects. In addition, the ZFO replica with “quasi-honeycomb-like structure” showed a much higher specific capacitance of 279.4 F g −1 at 10 mV s −1 in comparison with ZFO powder of 137.3 F g −1 , attributing to the significantly increased surface area. These results demonstrated that ZFO replica is a promising candidate for novel magnetic devices and supercapacitors
A distance-aware replica adaptive data gathering protocol for Delay Tolerant Mobile Sensor Networks.
Feng, Yong; Gong, Haigang; Fan, Mingyu; Liu, Ming; Wang, Xiaomin
2011-01-01
In Delay Tolerant Mobile Sensor Networks (DTMSNs) that have the inherent features of intermitted connectivity and frequently changing network topology it is reasonable to utilize multi-replica schemes to improve the data gathering performance. However, most existing multi-replica approaches inject a large amount of message copies into the network to increase the probability of message delivery, which may drain each mobile node's limited battery supply faster and result in too much contention for the restricted resources of the DTMSN, so a proper data gathering scheme needs a trade off between the number of replica messages and network performance. In this paper, we propose a new data gathering protocol called DRADG (for Distance-aware Replica Adaptive Data Gathering protocol), which economizes network resource consumption through making use of a self-adapting algorithm to cut down the number of redundant replicas of messages, and achieves a good network performance by leveraging the delivery probabilities of the mobile sensors as main routing metrics. Simulation results have shown that the proposed DRADG protocol achieves comparable or higher message delivery ratios at the cost of the much lower transmission overhead than several current DTMSN data gathering schemes.
Implementation and performance analysis of the LHCb LFC replica using Oracle streams technology
Düllmann, D; Martelli, B; Peco, G; Bonifazzi, F; Da Fonte Perez, E; Baranowski, Z; Vagnoni, V
2007-01-01
The presentation will describe the architecture and the deployment of the LHCb read-only File Catalogue for the LHC Computing Grid (LFC) replica implemented at the Italian INFN National Centre for Telematics and Informatics (CNAF), and evaluate a series of tests on the LFC with replica. The LHCb computing model foresees the replication of the central LFC database in every Tier-1, in order to assure more scalability and fault tolerance to LHCb applications Scientific data intensive applications use a large collection of files for storing data. In particular, as regards the HEP community, data generated by large detectors will be managed and stored using databases. The intensive access to information stored in databases by the Grid computing applications requires a distributed database replication in order to guarantee the scalability and, in case of failure, redundancy. Besides the results of the tests will be an important reference for all the Grid users This talk will describe the replica implementation of L...
Microlens fabrication by replica molding of frozen laser-printed droplets
Surdo, Salvatore; Diaspro, Alberto; Duocastella, Martí
2017-10-01
In this work, we synergistically combine laser-induced forward transfer (LIFT) and replica molding for the fabrication of microlenses with control of their geometry and size independent of the material or substrate used. Our approach is based on a multistep process in which liquid microdroplets of an aqueous solution are first printed on a substrate by LIFT. Following a freezing step, the microdroplets are used as a master to fabricate a polydimethylsiloxane (PDMS) mold. A subsequent replica molding step enables the creation of microlenses and microlens arrays on arbitrary selected substrates and by using different curable polymers. Thus, our method combines the rapid fabrication capabilities of LIFT and the perfectively smooth surface quality of the generated microdroplets, with the advantages of replica molding in terms of parallelization and materials flexibility. We demonstrate our strategy by generating microlenses of different photocurable polymers and by characterizing their optical and morphological properties.
International Nuclear Information System (INIS)
Kihara, Tomohiko; Tanaka, Yuuko; Furuhata, Kentaro
1995-01-01
The use of three-dimensional replicas created using laserlithography has recently become popular for surgical planning and intraoperative navigation in plastic surgery and oral maxillofacial surgery. In this study, we investigated many clinical applications that we have been involved in regarding the production of three-dimensional replicas. We have also analyzed the features, application classes, and advantages of this method. As a result, clinical applications are categorized into three classes, which are 'three-dimensional shape recognition', 'simulated surgery', and 'template'. The distinct features of three-dimensional replicas are 'direct recognition', 'fast manipulation', and 'free availability'. Meeting the requirements of surgical planning and intraoperative navigation, they have produced satisfactory results in clinical applications. (author)
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Hamiltonian indices and rational spectral densities
Byrnes, C. I.; Duncan, T. E.
1980-01-01
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
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.
A Hamiltonian five-field gyrofluid model
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)
2015-11-15
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.
Hamiltonian circuited simulations in reactor physics
International Nuclear Information System (INIS)
Rio Hirowati Shariffudin
2002-01-01
In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)
Hamiltonian inclusive fitness: a fitter fitness concept.
Costa, James T
2013-01-01
In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.
Renormalized semiclassical quantization for rescalable Hamiltonians
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum
Effective hamiltonian calculations using incomplete model spaces
International Nuclear Information System (INIS)
Koch, S.; Mukherjee, D.
1987-01-01
It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations
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.
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.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.
Local Hamiltonians for maximally multipartite-entangled states
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-10-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Local Hamiltonians for maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-01-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Model reduction of port-Hamiltonian systems as structured systems
Polyuga, R.V.; Schaft, van der A.J.
2010-01-01
The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Port-Hamiltonian approaches to motion generation for mechanical systems
Sakai, Satoru; Stramigioli, Stefano
This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system
Structure preserving port-Hamiltonian model reduction of electrical circuits
Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.
2011-01-01
This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Replica analysis of partition-function zeros in spin-glass models
International Nuclear Information System (INIS)
Takahashi, Kazutaka
2011-01-01
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distributions of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.
A generalized AKNS hierarchy and its bi-Hamiltonian structures
International Nuclear Information System (INIS)
Xia Tiecheng; You Fucai; Chen Dengyuan
2005-01-01
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator
Local modular Hamiltonians from the quantum null energy condition
Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
2018-03-01
The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
Sdg interacting boson hamiltonian in the seniority scheme
Energy Technology Data Exchange (ETDEWEB)
Yoshinaga, N.
1989-03-06
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
sdg Interacting boson hamiltonian in the seniority scheme
Yoshinaga, N.
1989-03-01
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
Frustration-free Hamiltonians supporting Majorana zero edge modes
International Nuclear Information System (INIS)
Jevtic, Sania; Barnett, Ryan
2017-01-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)
Frustration-free Hamiltonians supporting Majorana zero edge modes
Jevtic, Sania; Barnett, Ryan
2017-10-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
Risser, Steven Michael
This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb
The Efficacy of Epidemic Algorithms on Detecting Node Replicas in Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Narasimha Shashidhar
2015-12-01
Full Text Available A node replication attack against a wireless sensor network involves surreptitious efforts by an adversary to insert duplicate sensor nodes into the network while avoiding detection. Due to the lack of tamper-resistant hardware and the low cost of sensor nodes, launching replication attacks takes little effort to carry out. Naturally, detecting these replica nodes is a very important task and has been studied extensively. In this paper, we propose a novel distributed, randomized sensor duplicate detection algorithm called Discard to detect node replicas in group-deployed wireless sensor networks. Our protocol is an epidemic, self-organizing duplicate detection scheme, which exhibits emergent properties. Epidemic schemes have found diverse applications in distributed computing: load balancing, topology management, audio and video streaming, computing aggregate functions, failure detection, network and resource monitoring, to name a few. To the best of our knowledge, our algorithm is the first attempt at exploring the potential of this paradigm to detect replicas in a wireless sensor network. Through analysis and simulation, we show that our scheme achieves robust replica detection with substantially lower communication, computational and storage requirements than prior schemes in the literature.
Replicas Strategy and Cache Optimization of Video Surveillance Systems Based on Cloud Storage
Directory of Open Access Journals (Sweden)
Rongheng Li
2018-04-01
Full Text Available With the rapid development of video surveillance technology, especially the popularity of cloud-based video surveillance applications, video data begins to grow explosively. However, in the cloud-based video surveillance system, replicas occupy an amount of storage space. Also, the slow response to video playback constrains the performance of the system. In this paper, considering the characteristics of video data comprehensively, we propose a dynamic redundant replicas mechanism based on security levels that can dynamically adjust the number of replicas. Based on the location correlation between cameras, this paper also proposes a data cache strategy to improve the response speed of data reading. Experiments illustrate that: (1 our dynamic redundant replicas mechanism can save storage space while ensuring data security; (2 the cache mechanism can predict the playback behaviors of the users in advance and improve the response speed of data reading according to the location and time correlation of the front-end cameras; and (3 in terms of cloud-based video surveillance, our proposed approaches significantly outperform existing methods.
Saorin, José Luis; Carbonell-Carrera, Carlos; Cantero, Jorge de la Torre; Meier, Cecile; Aleman, Drago Diaz
2017-01-01
Spatial interpretation features as a skill to acquire in the educational curricula. The visualization and interpretation of three-dimensional objects in tactile devices and the possibility of digital manufacturing with 3D printers, offers an opportunity to include replicas of sculptures in teaching and, thus, facilitate the 3D interpretation of…
Energy Technology Data Exchange (ETDEWEB)
Storesund, Jan [Det Norske Veritas AB, Stockholm (Sweden); Roennholm, Markku [Fortum (Sweden)
2002-04-01
Creep damage development in high temperature components can be monitored by the replica method. Damage is classified and an experience based time period for safe operation is recommended where a re-inspection should be conducted. Original recommendations are still commonly used but there are also developed ones are mostly less conservative. A data base of more than 6000 replicas, collected from welded components in Swedish and Finnish power plants, has been evaluated with respect to damage development in the present project. The results are in general in good agreement to the existing developed recommendations for re-inspections. Important factors that should be considered for use of the recommendations are highlighted: Service history, Material, welding and heat treatment, Measure of pressure and temperature, System stresses, Geometrical stress concentrations, stress distributions, Design of components and welds, Creep crack growth, Starts and stops, Extent and performance of the replica method. These factors have been analysed with respect to the evaluated data resulting in comments to the existing recommendations. In addition, recommendations and conditions for a high reliability of the replica method are described. The comments and recommendations can be read in separate sections in the end of the report.
International Nuclear Information System (INIS)
Laak, Jeroen A.W.M. van der; Dijkman, Henry B.P.M.; Pahlplatz, Martin M.M.
2006-01-01
The magnification factor in transmission electron microscopy is not very precise, hampering for instance quantitative analysis of specimens. Calibration of the magnification is usually performed interactively using replica specimens, containing line or grating patterns with known spacing. In the present study, a procedure is described for automated magnification calibration using digital images of a line replica. This procedure is based on analysis of the power spectrum of Fourier transformed replica images, and is compared to interactive measurement in the same images. Images were used with magnification ranging from 1,000x to 200,000x. The automated procedure deviated on average 0.10% from interactive measurements. Especially for catalase replicas, the coefficient of variation of automated measurement was considerably smaller (average 0.28%) compared to that of interactive measurement (average 3.5%). In conclusion, calibration of the magnification in digital images from transmission electron microscopy may be performed automatically, using the procedure presented here, with high precision and accuracy
Systematic expansion in the order parameter for replica theory of the dynamical glass transition.
Jacquin, Hugo; Zamponi, Francesco
2013-03-28
It has been shown recently that predictions from mode-coupling theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one focuses on the regime around the dynamical transition in three dimensions, mode-coupling results are far more convincing than replica theory predictions. It seems thus necessary to reconcile the two theoretic approaches in order to obtain a theory that interpolates between low-dimensional, mode-coupling results, and "mean-field" results from replica theory. Even though quantitative results for the dynamical transition issued from replica theory are not accurate in low dimensions, two different approximation schemes--small cage expansion and replicated hyper-netted-chain (RHNC)--provide the correct qualitative picture for the transition, namely, a discontinuous jump of a static order parameter from zero to a finite value. The purpose of this work is to develop a systematic expansion around the RHNC result in powers of the static order parameter, and to calculate the first correction in this expansion. Interestingly, this correction involves the static three-body correlations of the liquid. More importantly, we separately demonstrate that higher order terms in the expansion are quantitatively relevant at the transition, and that the usual mode-coupling kernel, involving two-body direct correlation functions of the liquid, cannot be recovered from static computations.
Fast Optimal Replica Placement with Exhaustive Search Using Dynamically Reconfigurable Processor
Directory of Open Access Journals (Sweden)
Hidetoshi Takeshita
2011-01-01
Full Text Available This paper proposes a new replica placement algorithm that expands the exhaustive search limit with reasonable calculation time. It combines a new type of parallel data-flow processor with an architecture tuned for fast calculation. The replica placement problem is to find a replica-server set satisfying service constraints in a content delivery network (CDN. It is derived from the set cover problem which is known to be NP-hard. It is impractical to use exhaustive search to obtain optimal replica placement in large-scale networks, because calculation time increases with the number of combinations. To reduce calculation time, heuristic algorithms have been proposed, but it is known that no heuristic algorithm is assured of finding the optimal solution. The proposed algorithm suits parallel processing and pipeline execution and is implemented on DAPDNA-2, a dynamically reconfigurable processor. Experiments show that the proposed algorithm expands the exhaustive search limit by the factor of 18.8 compared to the conventional algorithm search limit running on a Neumann-type processor.
Comparison of pulsed versus continuous oxygen delivery using realistic adult nasal airway replicas
Directory of Open Access Journals (Sweden)
Chen JZ
2017-08-01
Full Text Available John Z Chen,1 Ira M Katz,2 Marine Pichelin,2 Kaixian Zhu,3 Georges Caillibotte,2 Michelle L Noga,4 Warren H Finlay,1 Andrew R Martin1 1Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada; 2Medical R&D, Air Liquide Santé International, Centre de Recherche Paris-Saclay, Les Loges-en-Josas, 3Centre Explor!, Air Liquide Healthcare, Gentilly, France; 4Radiology and Diagnostic Imaging, University of Alberta, Edmonton, AB, Canada Background: Portable oxygen concentrators (POCs typically include pulse flow (PF modes to conserve oxygen. The primary aims of this study were to develop a predictive in vitro model for inhaled oxygen delivery using a set of realistic airway replicas, and to compare PF for a commercial POC with steady flow (SF from a compressed oxygen cylinder. Methods: Experiments were carried out using a stationary compressed oxygen cylinder, a POC, and 15 adult nasal airway replicas based on airway geometries derived from medical images. Oxygen delivery via nasal cannula was tested at PF settings of 2.0 and 6.0, and SF rates of 2.0 and 6.0 L/min. A test lung simulated three breathing patterns representative of a chronic obstructive pulmonary disease patient at rest, during exercise, and while asleep. Volume-averaged fraction of inhaled oxygen (FiO2 was calculated by analyzing oxygen concentrations sampled at the exit of each replica and inhalation flow rates over time. POC pulse volumes were also measured using a commercial O2 conserver test system to attempt to predict FiO2 for PF. Results: Relative volume-averaged FiO2 using PF ranged from 68% to 94% of SF values, increasing with breathing frequency and tidal volume. Three of 15 replicas failed to trigger the POC when used with the sleep breathing pattern at the 2.0 setting, and four of 15 replicas failed to trigger at the 6.0 setting. FiO2 values estimated from POC pulse characteristics followed similar trends but were lower than those derived from
Effect of cation nature of zeolite on carbon replicas and their electrochemical capacitance
International Nuclear Information System (INIS)
Zhou, Jin; Li, Wen; Zhang, Zhongshen; Wu, Xiaozhong; Xing, Wei; Zhuo, Shuping
2013-01-01
Graphical abstract: Cation nature of zeolite influences the porosity, surface chemical properties of carbon replicas of zeolite, resulting in different electrochemical capacitance. Highlights: ► The porosity of carbon replica strongly depends on zeolite's effective pore size. ► The surface chemical properties influence by the cation nature of zeolite. ► The N-doping introduces large pseudo-capacitance. ► The HYC800 carbon showed a high capacitance of up to 312 F g −1 in 1 M H 2 SO 4 . ► The prepared carbons show good durability of galvanostatic cycle. -- Abstract: N-doped carbon replicas of zeolite Y are prepared, and the effect of cation nature of zeolite (H + or Na + ) on the carbon replicas is studied. The morphology, structure and surface properties of the carbon materials are investigated by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), N 2 adsorption, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FT-IR). The pore regularity, pore parameter and surface chemical properties of the carbons may strongly depend on the cation nature of the zeolite Y. The carbon replicas of zeolite HY (H-form of zeolite Y) possesses higher pore regularity and much larger surface area than those of zeolite NaY (Na-form of zeolite Y), while the latter carbons seem to possess higher carbonization degrees. Electrochemical measurements show a large faradaic capacitance related to the N- or O-containing groups for the prepared carbons. Owing to the large specific surface area, high pore regularity and heteroatom-doping, the HYC800 sample derived from zeolite HY presents very high gravimetric capacitance, up to 312.4 F g −1 in H 2 SO 4 electrolyte, and this carbon can operate at 1.2 V with good retention ratio in the range of 0.25 to 10 A g −1
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.
Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.
2011-12-01
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Cornea, Octavian
2001-01-01
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
The Hamiltonian structure of general relativistic perfect fluids
International Nuclear Information System (INIS)
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Toric codes and quantum doubles from two-body Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)
2011-05-15
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.
Greenberger-Horne-Zeilinger states and few-body Hamiltonians.
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V
2011-12-23
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Quantum bootstrapping via compressed quantum Hamiltonian learning
International Nuclear Information System (INIS)
Wiebe, Nathan; Granade, Christopher; Cory, D G
2015-01-01
A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1981-01-01
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
International Nuclear Information System (INIS)
Bellum, J.C.; McGuire, P.
1983-01-01
We investigate forms of the molecular system Hamiltonian valid for rigorous quantum-mechanical treatments of inelastic atom--diatom collisions characterized by exchange of energy between electronic, vibrational, and rotational degrees of freedom. We analyze this Hamiltonian in terms of various choices of independent coordinates which unambiguously specify the electronic and nuclear positions in the context of space-fixed and body-fixed reference frames. In particular we derive forms of the Hamiltonian in the context of the following four sets of independent coordinates: (1) a so-called space-fixed set, in which both electronic and nuclear positions are relative to the space-fixed frame; (2) a so-called mixed set, in which nuclear positions are relative to the body-fixed frame while electronic positions are relative to the space-fixed frame; (3) a so-called body-fixed set, in which both electronic and nuclear positions are relative to the body-fixed frame; and (4) another mixed set, in which nuclear positions are relative to the space-fixed frame while electronic positions are relative to the body-fixed frame. Based on practical considerations in accounting for electronic structure and nonadiabatic coupling of electronic states of the collision complex we find the forms of the Hamiltonian in the context of coordinate sets (3) and (4) above to be most appropriate, respectively, for body-fixed and space-fixed treatments of nuclear dynamics in collisional transfer of electronic, vibrational, and rotational energies
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
Towards practical characterization of quantum systems with quantum Hamiltonian learning
Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.
2017-01-01
Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.
On the quantization of sectorially Hamiltonian dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)
2009-10-15
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
On the quantization of sectorially Hamiltonian dissipative systems
International Nuclear Information System (INIS)
Castagnino, M.; Gadella, M.; Lara, L.P.
2009-01-01
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Directory of Open Access Journals (Sweden)
Krzysztof Andrzejewski
2014-12-01
Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.
Experimental Hamiltonian identification for controlled two-level systems
International Nuclear Information System (INIS)
Schirmer, S.G.; Kolli, A.; Oi, D.K.L.
2004-01-01
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
Hamiltonian Approach to 2+1 Dimensional Gravity
Cantini, L.; Menotti, P.; Seminara, D.
2002-12-01
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Pawłowski, Tomasz
2012-04-06
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
On the topological entropy of an optical Hamiltonian flow
Niche, Cesar J.
2000-01-01
In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.
SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS
Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.
2006-01-01
In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
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)
Orbits and variational principles for conservative Hamiltonian systems
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1989-01-01
It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)
Oscillator representations for self-adjoint Calogero Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)
2011-10-21
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Oscillator representations for self-adjoint Calogero Hamiltonians
International Nuclear Information System (INIS)
Gitman, D M; Tyutin, I V; Voronov, B L
2011-01-01
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Hamiltonian quantum simulation with bounded-strength controls
International Nuclear Information System (INIS)
Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza
2014-01-01
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)
Zeolite-templated carbon replica: a Grand Canonical Monte-Carlo simulation study
International Nuclear Information System (INIS)
Thomas Roussel; Roland J M Pellenq; Christophe Bichara; Roger Gadiou; Antoine Didion; Cathie Vix Guterl; Fabrice Gaslain; Julien Parmentier; Valentin Valtchev; Joel Patarin
2005-01-01
Microporous carbon materials are interesting for several applications such as hydrogen storage, catalysis or electrical double layer capacitors. The development of the negative templating method to obtain carbon replicas from ordered templates, has lead to the synthesis of several new materials which have interesting textural properties, attractive for energy storage. Among the possible templates, zeolites can be used to obtain highly microporous carbon materials. Nevertheless, the phenomena involved in the replica synthesis are not fully understood, and the relationships between the structure of the template, the carbon precursor and the resulting carbon material need to be investigated. Experimental results for carbon zeolite-templated nano-structures can be found in a series of papers; see for instance ref. [1] in which Wang et al describe a route to ultra-small Single Wall Carbon Nano-tubes (SWNTs) using the porosity of zeolite AlPO 4 -5. After matrix removal, the resulting structure is a free-standing bundle of 4 Angstroms large nano-tubes. However, it is highly desirable to obtain an ordered porous carbon structure that forms a real 3D network to be used for instance in gas storage applications. Carbon replica of faujasite and EMT zeolites can have these properties since these zeolites have a 3D porous network made of 10 Angstroms cages connected to each other through 7 Angstroms large windows. The first step of this study was to generate a theoretical carbon replica structure of various zeolites (faujasite, EMT, AlPO 4 -5, silicalite). For this purpose, we used the Grand Canonical Monte-Carlo (GCMC) technique in which the carbon-carbon interactions were described within the frame of a newly developed Tight Binding approach and the carbon-zeolite interactions assumed to be characteristic of physi-sorption. The intrinsic stability of the subsequent carbon nano-structures was then investigated after mimicking the removal of the inorganic phase by switching
Naz, Rehana
2018-01-01
Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.
Evaluation of generalized degrees of freedom for sparse estimation by replica method
Sakata, A.
2016-12-01
We develop a method to evaluate the generalized degrees of freedom (GDF) for linear regression with sparse regularization. The GDF is a key factor in model selection, and thus its evaluation is useful in many modelling applications. An analytical expression for the GDF is derived using the replica method in the large-system-size limit with random Gaussian predictors. The resulting formula has a universal form that is independent of the type of regularization, providing us with a simple interpretation. Within the framework of replica symmetric (RS) analysis, GDF has a physical meaning as the effective fraction of non-zero components. The validity of our method in the RS phase is supported by the consistency of our results with previous mathematical results. The analytical results in the RS phase are calculated numerically using the belief propagation algorithm.
Neutron and gamma dose and spectra measurements on the Little Boy replica
International Nuclear Information System (INIS)
Hoots, S.; Wadsworth, D.
1984-01-01
The radiation-measurement team of the Weapons Engineering Division at Lawrence Livermore National Laboratory (LLNL) measured neutron and gamma dose and spectra on the Little Boy replica at Los Alamos National Laboratory (LANL) in April 1983. This assembly is a replica of the gun-type atomic bomb exploded over Hiroshima in 1945. These measurements support the National Academy of Sciences Program to reassess the radiation doses due to atomic bomb explosions in Japan. Specifically, the following types of information were important: neutron spectra as a function of geometry, gamma to neutron dose ratios out to 1.5 km, and neutron attenuation in the atmosphere. We measured neutron and gamma dose/fission from close-in to a kilometer out, and neutron and gamma spectra at 90 and 30 0 close-in. This paper describes these measurements and the results. 12 references, 13 figures, 5 tables
Proactive replica checking to assure reliability of data in cloud storage with minimum replication
Murarka, Damini; Maheswari, G. Uma
2017-11-01
The two major issues for cloud storage systems are data reliability and storage costs. For data reliability protection, multi-replica replication strategy which is used mostly in current clouds acquires huge storage consumption, leading to a large storage cost for applications within the loud specifically. This paper presents a cost-efficient data reliability mechanism named PRCR to cut back the cloud storage consumption. PRCR ensures data reliability of large cloud information with the replication that might conjointly function as a price effective benchmark for replication. The duplication shows that when resembled to the standard three-replica approach, PRCR will scale back to consume only a simple fraction of the cloud storage from one-third of the storage, thence considerably minimizing the cloud storage price.
International Nuclear Information System (INIS)
Ng, C.K.M.; Chong, E.Y.W.; Roy, V.A.L.; Cheung, K.M.C.; Yeung, K.W.K.; Yu, K.N.
2012-01-01
We proposed a simple method to fabricate micropillar substrates. Polyallyldiglycol carbonate (PADC) films were irradiated by alpha particles and then chemically etched to form a cast with micron-scale spherical pores. A polydimethylsiloxane (PDMS) replica of this PADC film gave a micropillar substrate with micron-scale spherical pillars. HeLa cells cultured on such a micropillar substrate had significantly larger percentage of cells entering S-phase, attached cell numbers and cell spreading areas. - Highlights: ► We proposed a simple method to fabricate micropillar substrates. ► Polyallyldiglycol carbonate films were irradiated and etched to form casts. ► Polydimethylsiloxane replica then formed the micropillar substrates. ► Attachment and proliferation of HeLa cells were enhanced on these substrates.
Energy Technology Data Exchange (ETDEWEB)
Ng, C.K.M. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong); Chong, E.Y.W. [Department of Orthopaedics and Traumatology, University of Hong Kong (Hong Kong); Roy, V.A.L. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong); Cheung, K.M.C.; Yeung, K.W.K. [Department of Orthopaedics and Traumatology, University of Hong Kong (Hong Kong); Yu, K.N., E-mail: appetery@cityu.edu.hk [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong)
2012-07-15
We proposed a simple method to fabricate micropillar substrates. Polyallyldiglycol carbonate (PADC) films were irradiated by alpha particles and then chemically etched to form a cast with micron-scale spherical pores. A polydimethylsiloxane (PDMS) replica of this PADC film gave a micropillar substrate with micron-scale spherical pillars. HeLa cells cultured on such a micropillar substrate had significantly larger percentage of cells entering S-phase, attached cell numbers and cell spreading areas. - Highlights: Black-Right-Pointing-Pointer We proposed a simple method to fabricate micropillar substrates. Black-Right-Pointing-Pointer Polyallyldiglycol carbonate films were irradiated and etched to form casts. Black-Right-Pointing-Pointer Polydimethylsiloxane replica then formed the micropillar substrates. Black-Right-Pointing-Pointer Attachment and proliferation of HeLa cells were enhanced on these substrates.
Neutron and gamma-ray dose-rates from the Little Boy replica
International Nuclear Information System (INIS)
Plassmann, E.A.; Pederson, R.A.
1984-01-01
We report dose-rate information obtained at many locations in the near vicinity of, and at distances out to 0.64 km from, the Little Boy replica while it was operated as a critical assembly. The measurements were made with modified conventional dosimetry instruments that used an Anderson-Braun detector for neutrons and a Geiger-Mueller tube for gamma rays with suitable electronic modules to count particle-induced pulses. Thermoluminescent dosimetry methods provide corroborative data. Our analysis gives estimates of both neutron and gamma-ray relaxation lengths in air for comparison with earlier calculations. We also show the neutron-to-gamma-ray dose ratio as a function of distance from the replica. Current experiments and further data analysis will refine these results. 7 references, 8 figures
Impact of Channel Estimation Errors on Multiuser Detection via the Replica Method
Directory of Open Access Journals (Sweden)
Li Husheng
2005-01-01
Full Text Available For practical wireless DS-CDMA systems, channel estimation is imperfect due to noise and interference. In this paper, the impact of channel estimation errors on multiuser detection (MUD is analyzed under the framework of the replica method. System performance is obtained in the large system limit for optimal MUD, linear MUD, and turbo MUD, and is validated by numerical results for finite systems.
Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection
International Nuclear Information System (INIS)
Tassi, E
2014-01-01
We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems
International Nuclear Information System (INIS)
Zhang Wang; Zhang Di; Fan Tongxiang; Ding Jian; Gu Jiajun; Guo Qixin; Ogawa, Hiroshi
2009-01-01
Papilio paris butterflies have an iridescent blue color patch on their hind wings which is visible over a wide viewing angle. Optical and scanning electron microscopy observations of scales from the wings show that the blue color scales have very different microstructure to the matt black ones which also populate the wings. Scanning electron micrographs of the blue scales show that their surfaces comprise a regular two-dimensional array of concavities. By contrast the matt black scales have fine, sponge-like structure, between the ridges and the cross ribs in the scales. Using both types of scale as bio-templates, we obtain zinc oxide (ZnO) replicas of the microstructures of the original scales. Room temperature (T = 300 K) cathodoluminescence spectra of these ZnO replicas have also been studied. Both spectra show a similar sharp near-band-edge emission, but have different green emission, which we associate with the different microstructures of the ZnO replicas
Energy Technology Data Exchange (ETDEWEB)
Zhang Wang [State Key Lab of Metal Matrix Composites, Shanghai Jiao Tong University, 200240, Shanghai (China); Zhang Di [State Key Lab of Metal Matrix Composites, Shanghai Jiao Tong University, 200240, Shanghai (China)], E-mail: zhangdi@sjtu.edu.cn; Fan Tongxiang; Ding Jian; Gu Jiajun [State Key Lab of Metal Matrix Composites, Shanghai Jiao Tong University, 200240, Shanghai (China); Guo Qixin; Ogawa, Hiroshi [Department of Electrical and Electronic Engineering, Saga University, Saga 840-8502 (Japan)
2009-01-01
Papilio paris butterflies have an iridescent blue color patch on their hind wings which is visible over a wide viewing angle. Optical and scanning electron microscopy observations of scales from the wings show that the blue color scales have very different microstructure to the matt black ones which also populate the wings. Scanning electron micrographs of the blue scales show that their surfaces comprise a regular two-dimensional array of concavities. By contrast the matt black scales have fine, sponge-like structure, between the ridges and the cross ribs in the scales. Using both types of scale as bio-templates, we obtain zinc oxide (ZnO) replicas of the microstructures of the original scales. Room temperature (T = 300 K) cathodoluminescence spectra of these ZnO replicas have also been studied. Both spectra show a similar sharp near-band-edge emission, but have different green emission, which we associate with the different microstructures of the ZnO replicas.
Gonzalez-Lopez, David; Faerber, Gloria; Diab, Mahmoud; Amorim, Paulo; Zeynalov, Natig; Doenst, Torsten
2017-10-01
Current sizing strategies suggest valve selection based on annulus diameter despite supra-annular placement of biological prostheses potentially allowing placement of a larger size. We assessed the frequency of selecting a larger prosthesis if prosthesis size was selected using a replica (upsizing) and evaluated its impact on haemodynamics. We analysed all discharge echocardiograms between June 2012 and June 2014, where a replica sizer was used for isolated aortic valve replacement (Epic Supra: 266 patients, Trifecta: 49 patients). Upsizing was possible in 71% of the Epic Supra valves (by 1 size: 168, by 2 sizes: 20) and in 59% of the Trifectas (by 1 size: 26, by 2 sizes: 3). Patients for whom upsizing was possible had the lowest pressure gradients within their annulus size groups. The difference was significant in annulus diameters of 21-22 or 25-26 mm (Epic Supra) and 23-24 mm (Trifecta). Trifecta gradients were the lowest. However, the ability to upsize the Epic Supra by 2 sizes eliminated the differences between Epic Supra and Trifecta. Upsizing did not cause intraoperative complications. Using replica sizers for aortic prosthesis size selection allows the implantation of bigger prostheses than recommended in most cases and reduces postoperative gradients, specifically for Epic Supra. © The Author 2017. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.
Characterization of Nb SRF cavity materials by white light interferometry and replica techniques
Energy Technology Data Exchange (ETDEWEB)
Xu, Chen [Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States); The Applied Science Department, The College of William and Mary, Williamsburg, VA 23185 (United States); Reece, Charles [Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States); Kelley, Michael, E-mail: mkelley@jlab.org [Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States); The Applied Science Department, The College of William and Mary, Williamsburg, VA 23185 (United States)
2013-06-01
Much work has shown that the topography of the interior surface is an important contributor to the performance of Nb superconducting radiofrequency (SRF) accelerator cavities. Micron-scale topography is implicated in non-linear loss mechanisms that limit the useful accelerating gradient range and impact cryogenic cost. Aggressive final chemical treatments in cavity production seek to reliably obtain “smoothest” surfaces with superior performance. Process development suffers because the cavity interior surface cannot be viewed directly without cutting out pieces, rendering the cavities unavailable for further study. Here we explore replica techniques as an alternative, providing imprints of cavity internal surface that can be readily examined. A second matter is the topography measurement technique used. Atomic force microscopy (AFM) has proven successful, but too time intensive for routine use in this application. We therefore introduce white light interferometry (WLI) as an alternative approach. We examined real surfaces and their replicas, using AFM and WLI. We find that the replica/WLI is promising to provide the large majority of the desired information, recognizing that a trade-off is being made between best lateral resolution (AFM) and the opportunity to examine much more surface area (WLI).
Dey, Ranabir; Raj M, Kiran; Bhandaru, Nandini; Mukherjee, Rabibrata; Chakraborty, Suman
2014-05-21
The present work comprehensively addresses the hydrodynamic characteristics through microchannels with lotus leaf replica (exhibiting low adhesion and superhydrophobic properties) walls. The lotus leaf replica is fabricated following an efficient, two-step, soft-molding process and is then integrated with rectangular microchannels. The inherent biomimetic, superhydrophobic surface-liquid interfacial hydrodynamics, and the consequential bulk flow characteristics, are critically analyzed by the micro-particle image velocimetry technique. It is observed that the lotus leaf replica mediated microscale hydrodynamics comprise of two distinct flow regimes even within the low Reynolds number paradigm, unlike the commonly perceived solely apparent slip-stick dominated flows over superhydrophobic surfaces. While the first flow regime is characterized by an apparent slip-stick flow culminating in an enhanced bulk throughput rate, the second flow regime exhibits a complete breakdown of the aforementioned laminar and uni-axial flow model, leading to a predominantly no-slip flow. Interestingly, the critical flow condition dictating the transition between the two hydrodynamic regimes is intrinsically dependent on the micro-confinement effect. In this regard, an energetically consistent theoretical model is also proposed to predict the alterations in the critical flow condition with varying microchannel configurations, by addressing the underlying biomimetic surface-liquid interfacial conditions. Hence, the present research endeavour provides a new design-guiding paradigm for developing multi-functional microfluidic devices involving biomimetic, superhydrophobic surfaces, by judicious exploitation of the tunable hydrodynamic characteristics in the two regimes.
Effect of roughness and material strength on the mechanical properties of fracture replicas
International Nuclear Information System (INIS)
Wibowo, J.; Amadei, B.; Sture, S.
1995-08-01
This report presents the results of 11 rotary shear tests conducted on replicas of three hollow cylinders of natural fractures with JRC values of 7.7, 9.4 and 12.0. The JRC values were determined from the results of laser profilometer measurements. The replicas were created from gypsum cement. By varying the water-to-gypsum cement ratio from 30 to 45%, fracture replicas with different values of compressive strength (JCS) were created. The rotary shear experiments were performed under constant normal (nominal) stresses ranging between 0.2 and 1.6 MPa. In this report, the shear test results are compared with predictions using Barton's empirical peak shear strength equation. observations during the experiments indicate that only certain parts of the fracture profiles influence fracture shear strength and dilatancy. Under relatively low applied normal stresses, the JCS does not seem to have a significant effect on shear behavior. As an alternative, a new procedure for predicting the shear behavior of fractures was developed. The approach is based on basic fracture properties such as fracture surface profile data and the compressive strength, modulus of elasticity, and Poisson's ratio of the fracture walls. Comparison between predictions and actual shear test results shows that the alternative procedure is a reliable method
Energy Technology Data Exchange (ETDEWEB)
Avram, C.N. [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania); Gruia, A.S., E-mail: adigruia@yahoo.com [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania); Brik, M.G. [College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Institute of Physics, University of Tartu, Ravila 14C, Tartu 50411 (Estonia); Institute of Physics, Jan Dlugosz University, Armii Krajowej 13/15, PL-42200 Czestochowa (Poland); Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw (Poland); Barb, A.M. [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania)
2015-12-01
Calculations of the Cr{sup 3+} energy levels, spin-Hamiltonian parameters and vibrational spectra for the layered CrCl{sub 3} crystals are reported for the first time. The crystal field parameters and the energy level scheme were calculated in the framework of the Exchange Charge Model of crystal field. The spin-Hamiltonian parameters (zero-field splitting parameter D and g-factors) for Cr{sup 3+} ion in CrCl{sub 3} crystals were obtained using two independent techniques: i) semi-empirical crystal field theory and ii) density functional theory (DFT)-based model. In the first approach, the spin-Hamiltonian parameters were calculated from the perturbation theory method and the complete diagonalization (of energy matrix) method. The infrared (IR) and Raman frequencies were calculated for both experimental and fully optimized geometry of the crystal structure, using CRYSTAL09 software. The obtained results are discussed and compared with the experimental available data.
Directory of Open Access Journals (Sweden)
Alekha Kumar Mishra
2017-01-01
Full Text Available Node replication attack possesses a high level of threat in wireless sensor networks (WSNs and it is severe when the sensors are mobile. A limited number of replica detection schemes in mobile WSNs (MWSNs have been reported till date, where most of them are centralized in nature. The centralized detection schemes use time-location claims and the base station (BS is solely responsible for detecting replica. Therefore, these schemes are prone to single point of failure. There is also additional communication overhead associated with sending time-location claims to the BS. A distributed detection mechanism is always a preferred solution to the above kind of problems due to significantly lower communication overhead than their counterparts. In this paper, we propose a distributed replica detection scheme for MWSNs. In this scheme, the deviation in the distance traveled by a node and its replica is recorded by the observer nodes. Every node is an observer node for some nodes in the network. Observers are responsible for maintaining a sliding window of recent time-distance broadcast of the nodes. A replica is detected by an observer based on the degree of violation computed from the deviations recorded using the time-distance sliding window. The analysis and simulation results show that the proposed scheme is able to achieve higher detection probability compared to distributed replica detection schemes such as Efficient Distributed Detection (EDD and Multi-Time-Location Storage and Diffusion (MTLSD.
An extended discrete gradient formula for oscillatory Hamiltonian systems
International Nuclear Information System (INIS)
Liu Kai; Shi Wei; Wu Xinyuan
2013-01-01
In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)
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)
Non-stoquastic Hamiltonians in quantum annealing via geometric phases
Vinci, Walter; Lidar, Daniel A.
2017-09-01
We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.
Effective Hamiltonian for protected edge states in graphene
International Nuclear Information System (INIS)
Winkler, R.; Deshpande, H.
2017-01-01
Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.
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.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
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.
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
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...
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
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.
Blocking Radial Diffusion in a Double-Waved Hamiltonian Model
International Nuclear Information System (INIS)
Martins, Caroline G L; De Carvalho, R Egydio; Marcus, F A; Caldas, I L
2011-01-01
A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
[1, D], or Wf (G) ≥ f (1). 2 n2 + [f(2) − 3. 2 f(1)]n − 2[f(2) − f(1)] for a monotonically decreasing function f(x) on x ∈ [1, D], then G is Hamiltonian, unless G ∼= K∗ n or K2∨3K1. Proof. Assume that G is not a Hamiltonian graph with degree sequence (d1,d2,...,dn), where d1 ≤ d2 ≤ ··· ≤ dn and n ≥ 3. By Lemma 1, there is a ...
Painlevé IV Hamiltonian systems and coherent states
International Nuclear Information System (INIS)
Bermudez, D; Contreras-Astorga, A; Fernández C, D J
2015-01-01
Schrödinger Hamiltonians with third-order differential ladder operators are linked to the Painlevé IV equation. Some of these appear from applying SUSY QM to the harmonic oscillator. Departing from them, we will build coherent states as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as displaced extremal states using linearized ladder operators. To each Hamiltonian corresponds two families of coherent states for fixed ladder operators: one in the infinite dimension subspace associated with the oscillator spectrum and another in the finite dimension one generated by the eigenstates created by SUSY QM. (paper)
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.
Topological color codes and two-body quantum lattice Hamiltonians
Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.
2010-02-01
Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the
Necessary conditions for super-integrability of Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: maria.przybylska@astri.uni.torun.pl; Yoshida, Haruo [National Astronomical Observatory, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo (Japan)], E-mail: h.yoshida@nao.ac.jp
2008-08-18
We formulate a general theorem which gives a necessary condition for the maximal super-integrability of a Hamiltonian system. This condition is expressed in terms of properties of the differential Galois group of the variational equations along a particular solution of the considered system. An application of this general theorem to natural Hamiltonian systems of n degrees of freedom with a homogeneous potential gives easily computable and effective necessary conditions for the super-integrability. To illustrate an application of the formulated theorems, we investigate: three known families of integrable potentials, and the three body problem on a line.
A progressive diagonalization scheme for the Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan, Feng; Guan, Xin; Wang, Yin; Draayer, J P
2010-01-01
A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.
A Class of Quasi-exact Solutions of Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.
2007-01-01
A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.
Phase transition in the non-degenerate Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1976-01-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques, using the epsilon = 4 - d expansion to first order in epsilon, is studied. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. The possibility of tricritical behavior then emerges. The effects of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
Additional integrals of the motion of classical Hamiltonian wave systems
International Nuclear Information System (INIS)
Shul'man, E.I.
1989-01-01
It is shown that a classical Hamiltonian wave system that possesses at least one additional integral of the motion with quadratic principal part has an infinite number of such integrals in the cases of both nondegenerate and degenerate dispersion laws. Conditions under which in a space of dimension d ≥ 2 a system with nondegenerate dispersion law is completely integratable and its Hamiltonian can be reduced to normal form are found. In the case of a degenerate dispersion law integrals are not sufficient for complete integrability
Floquet-Green function formalism for harmonically driven Hamiltonians
International Nuclear Information System (INIS)
Martinez, D F
2003-01-01
A method is proposed for the calculation of the Floquet-Green function of a general Hamiltonian with harmonic time dependence. We use matrix continued fractions to derive an expression for the 'dynamical effective potential' that can be used to calculate the Floquet-Green function of the system. We demonstrate the formalism for the simple case of a space-periodic (in the tight-binding approximation) Hamiltonian with a defect whose on-site energy changes harmonically with time. We study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system
Divide and conquer approach to quantum Hamiltonian simulation
Hadfield, Stuart; Papageorgiou, Anargyros
2018-04-01
We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.
Hamiltonian formulation of QCD in the Schwinger gauge
International Nuclear Information System (INIS)
Schutte, D.
1989-01-01
The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed
Scattering theory of infrared divergent Pauli-Fierz Hamiltonians
Derezinski, J
2003-01-01
We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called {\\em coherent sectors} describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of {\\em inclusive and non-inclusive scattering cross-sections} for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.
The detectability lemma and its applications to quantum Hamiltonian complexity
International Nuclear Information System (INIS)
Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph
2011-01-01
Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general
The intrinsic stochasticity of near-integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1989-09-01
Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).
Hamiltonian models for the Madelung fluid and generalized Langevin equations
International Nuclear Information System (INIS)
Nonnenmacher, T.F.
1985-01-01
We present a Hamiltonian formulation of some type of an 'electromagnetic' Madelung fluid leading to a fluid mechanics interpretation of the Aharonov-Bohm effect and to a subsidary condition to be required in order to make the correspondence between Schroedinger's quantum mechanics and Madelung's fluid mechanics unique. Then we discuss some problems related with the Brownian oscillator. Our aim is to start out with a Hamiltonian for the composite system with surrounding heat bath) and to finally arrive at a stochastic differential equation with completely determined statistical properties. (orig./HSI)
Continuum-time Hamiltonian for the Baxter's model
International Nuclear Information System (INIS)
Libero, V.L.
1983-01-01
The associated Hamiltonian for the symmetric eight-vertex model is obtained by taking the time-continuous limit in an equivalent Ashkin-Teller model. The result is a Heisenberg Hamiltonian with coefficients J sub(x), J sub(y) and J sub(z) identical to those found by Sutherland for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form. (Author) [pt
Quantum-circuit model of Hamiltonian search algorithms
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover's algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover's algorithm
Constraints and Hamiltonian in light-front quantized field theory
International Nuclear Information System (INIS)
Srivastava, P.P.
1993-01-01
Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)
Useful forms of the Hamiltonian for ion-optical systems
International Nuclear Information System (INIS)
Davies, W.G.
1991-04-01
The symbiosis of differential algebra and the Lie-algebraic formulation of optics provides a set of very powerful tools for analyzing and understanding the orbit dynamics of complex accelerators up to very high orders. In order to use these tools effectively it is usually necessary to express the Hamiltonian in the appropriate coordinate system. In this report, the relativistic Hamiltonian is derived in curvilinear (the fundamental coordinate system for ion-optics), Cartesian and polar coordinates, in forms suitable for solving problems in ion optics and accelerator physics both with and without the help of differential algebra
Zeolite-templated carbon replica: a grand canonical Monte-Carlo simulation study
International Nuclear Information System (INIS)
Roussel, Th.; Pellenq, R.J.M.; Bichara, Ch.; Gadiou, R.; Didion, A.; Vix-Guterl, C.; Gaslain, F.; Parmentier, J.; Valtchev, V.; Patarin, J.
2005-01-01
Microporous carbon materials are interesting for several applications such as hydrogen storage, catalysis or electrical double layer capacitors. The development of the negative templating method to obtain carbon replicas from ordered templates, has lead to the synthesis of several new materials which have interesting textural properties, attractive for energy storage. Among the possible templates, zeolites can be used to obtain highly microporous carbon materials. Nevertheless, the phenomena involved in the replica synthesis are not fully understood, and the relationships between the structure of the template, the carbon precursor and the resulting carbon material need to be investigated. Experimental results for carbon zeolite-templated nano-structures can be found in a series of papers; see for instance ref. [1] in which Wang et al describe a route to ultra-small Single Wall Carbon Nano-tubes (SWNTs) using the porosity of zeolite AlPO 4 -5. After matrix removal, the resulting structure is a free-standing bundle of 4 Angstroms large nano-tubes. However, it is highly desirable to obtain an ordered porous carbon structure that forms a real 3D network to be used for instance in gas storage applications. Carbon replica of faujasite and EMT zeolites can have these properties since these zeolites have a 3D porous network made of 10 Angstroms cages connected to each other through 7 Angstroms large windows. The first step of this study was to generate a theoretical carbon replica structure of various zeolites (faujasite, EMT, AlPO 4 -5, silicalite). For this purpose, we used the Grand Canonical Monte-Carlo (GCMC) technique in which the carbon-carbon interactions were described within the frame of a newly developed Tight Binding approach and the carbon-zeolite interactions assumed to be characteristic of physisorption. The intrinsic stability of the subsequent carbon nano-structures was then investigated after mimicking the removal of the inorganic phase by switching
Inferring predator behavior from attack rates on prey-replicas that differ in conspicuousness.
Directory of Open Access Journals (Sweden)
Yoel E Stuart
Full Text Available Behavioral ecologists and evolutionary biologists have long studied how predators respond to prey items novel in color and pattern. Because a predatory response is influenced by both the predator's ability to detect the prey and a post-detection behavioral response, variation among prey types in conspicuousness may confound inference about post-prey-detection predator behavior. That is, a relatively high attack rate on a given prey type may result primarily from enhanced conspicuousness and not predators' direct preference for that prey. Few studies, however, account for such variation in conspicuousness. In a field experiment, we measured predation rates on clay replicas of two aposematic forms of the poison dart frog Dendrobates pumilio, one novel and one familiar, and two cryptic controls. To ask whether predators prefer or avoid a novel aposematic prey form independently of conspicuousness differences among replicas, we first modeled the visual system of a typical avian predator. Then, we used this model to estimate replica contrast against a leaf litter background to test whether variation in contrast alone could explain variation in predator attack rate. We found that absolute predation rates did not differ among color forms. Predation rates relative to conspicuousness did, however, deviate significantly from expectation, suggesting that predators do make post-detection decisions to avoid or attack a given prey type. The direction of this deviation from expectation, though, depended on assumptions we made about how avian predators discriminate objects from the visual background. Our results show that it is important to account for prey conspicuousness when investigating predator behavior and also that existing models of predator visual systems need to be refined.
Naz, Rehana; Naeem, Imran
2018-03-01
The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.
EPR of exchange coupled systems
Bencini, Alessandro
2012-01-01
From chemistry to solid state physics to biology, the applications of Electron Paramagnetic Resonance (EPR) are relevant to many areas. This unified treatment is based on the spin Hamiltonian approach and makes extensive use of irreducible tensor techniques to analyze systems in which two or more spins are magnetically coupled. This edition contains a new Introduction by coauthor Dante Gatteschi, a pioneer and scholar of molecular magnetism.The first two chapters review the foundations of exchange interactions, followed by examinations of the spectra of pairs and clusters, relaxation in oligon
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
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…
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 ...
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 ...
Periodic Hamiltonian hierarchies and non-uniqueness of ...
Indian Academy of Sciences (India)
2016-12-02
Dec 2, 2016 ... Ca. 1. Introduction. Through the past few decades, research in supersym- ... The subject of periodic Hamiltonians has been exam- ined for a long time ... The plan of this paper is as follows: In §2, a brief resume of SUSYQM is ...
Nuclear properties with realistic Hamiltonians through spectral distribution theory
International Nuclear Information System (INIS)
Vary, J.P.; Belehrad, R.; Dalton, B.J.
1979-01-01
Motivated by the need of non-perturbative methods for utilizing realistic nuclear Hamiltonians H, the authors use spectral distribution theory, based on calculated moments of H, to obtain specific bulk and valence properties of finite nuclei. The primary emphasis here is to present results for the binding energies of nuclei obtained with and without an assumed core. (Auth.)
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems
Directory of Open Access Journals (Sweden)
Chao-Nien Chen
1997-03-01
Full Text Available Homoclinic orbits play an important role in the study of qualitative behavior of dynamical systems. Such kinds of orbits have been studied since the time of Poincare. In this paper, we discuss how to use variational methods to study the existence of homoclinic orbits of Hamiltonian systems.
Multi-component bi-Hamiltonian Dirac integrable equations
Energy Technology Data Exchange (ETDEWEB)
Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu
2009-01-15
A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.
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].
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics
Conventional hamiltonian for first-order differential systems
International Nuclear Information System (INIS)
Farias, J.R.
1984-01-01
Lagrangian systems corresponding to a given set of 2n first-order ordinary differential equations are singular ones. In despite this, it is shown that these systems can be put into a Hamiltonian form in the usual manner. (Author) [pt
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 ...
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
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
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.
Spectra of PT -symmetric Hamiltonians on tobogganic contours
Indian Academy of Sciences (India)
The term PT -symmetric quantum mechanics, although defined to be of a much broader use, was coined in tight connection with C. Bender's analysis of one- ... on the other hand, the other members of the family were strange Hamiltonians with imaginary potentials which do not appear physical at all. The aim of the.
On the minimization of Hamiltonians over pure Gaussian states
DEFF Research Database (Denmark)
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only terms that can be interpreted as quasiparticles excitations. We propose to call this fact Beliaev's Theorem, since to our knowledge it was mentioned for the first time in a paper...
Hamiltonian formulation of QED in the superaxial gauge
International Nuclear Information System (INIS)
Girotti, H.O.; Rothe, H.J.
A Hamiltonian formulation of QED in a fully fixed axial gauge is presented. The equal-time commutators for all field variables are computed and are shown to lead to the correct equations of motion. The constraints and gauge conditions hold as strong operator relations. (Author) [pt
Fractional Hamiltonian analysis of higher order derivatives systems
International Nuclear Information System (INIS)
Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan
2006-01-01
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
On Interconnections of Infinite-dimensional Port-Hamiltonian Systems
Pasumarthy, Ramkrishna; Schaft, Arjan J. van der
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
On interconnections of infinite-dimensional port-Hamiltonian systems
Ramkrishna Pasumarthy, R.P.; van der Schaft, Arjan
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
Hamiltonian model analysis of ππ scattering and production
International Nuclear Information System (INIS)
Obu, Mitsuaki
2000-01-01
A simple Hamiltonian model for ππ scattering and production is presented which incorporates resonant and background interactions. Analysis of isoscalar S wave ππ phase shift indicates that the background interaction plays only a minor role and the σ may be a dynamical resonance which is not originated from a corresponding bare state. (author)
Energy preserving integration of bi-Hamiltonian partial differential equations
Karasozen, B.; Simsek, G.
2013-01-01
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the
On resonances and bound states of Smilansky Hamiltonian
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Lotoreichik, Vladimir; Tater, Miloš
2016-01-01
Roč. 7, č. 5 (2016), s. 789-802 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Smilansky Hamiltonian * resonances * resonance free region * weak coupling asymptotics * Riemann surface * bound states Subject RIV: BE - Theoretical Physics
Statistical properties of the nuclear shell-model Hamiltonian
International Nuclear Information System (INIS)
Dias, H.; Hussein, M.S.; Oliveira, N.A. de
1986-01-01
The statistical properties of realistic nuclear shell-model Hamiltonian are investigated in sd-shell nuclei. The probability distribution of the basic-vector amplitude is calculated and compared with the Porter-Thomas distribution. Relevance of the results to the calculation of the giant resonance mixing parameter is pointed out. (Author) [pt
The Lagrangians and Hamiltonians of damped coupled vibrations
International Nuclear Information System (INIS)
Ding Guangtao; Gan Huilan; Zheng Xianfeng; Cui Zhifeng
2012-01-01
In this paper, the analytical mechanization of two kinds of damped coupled vibrations is studied. First, by use of coordinate transformations the equations of motion are transformed into the self-ad- joint form. Secondly, the Lagrangians are obtained according to Engels method. Finally the Lagrangians and Hamiltonians of the original equations are deduced by using the inverse transformation. (authors)
Maxwell-Vlasov equations as a continuous Hamiltonian system
International Nuclear Information System (INIS)
Morrison, P.J.
1980-09-01
The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion
New bi-Hamiltonian systems on the plane
Tsiganov, A. V.
2017-06-01
We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth, and sixth orders in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets, and recursion operators are also presented in the framework of the Jacobi method.
A Hamiltonian structure for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1991-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)
Hamiltonian Cycles on a Random Three-coordinate Lattice
DEFF Research Database (Denmark)
Eynard, B.; Guitter, E.; Kristjansen, C.
1998-01-01
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition...
Hamiltonian theory of vacuum helical torus lines of magnetic force
International Nuclear Information System (INIS)
Gnudi, Giovanni; Hatori, Tadatsugu
1994-01-01
For making plasma into equilibrium state, the lines of magnetic force must have magnetic surfaces. However in a helical system, space is divided into the region having magnetic surface structure and the region that does not have it. Accordingly, it is an important basic research for the plasma confinement in a helical system to examine where is the boundary of both regions and how is the large area structure of the lines of magnetic force in the boundary region. The lines of magnetic force can be treated as a Hamilton mechanics system, and it has been proved that the Hamiltonian for the lines of magnetic force can be expressed by a set of canonical variables and the function of time. In this research, the Hamiltonian that describes the lines of magnetic force of helical system torus coordination in vacuum was successfully determined concretely. Next, the development of new linear symplectic integration method was carried out. The important supports for the theory of determining Hamiltonian are Lie transformation and paraxial expansion. The procedure is explained. In Appendix, Lie transformation, Hamiltonian for the lines of magnetic force, magnetic potential, Taylor expansion of the potential, cylindrical limit approximation, helical toroidal potential and integrable model are described. (K.I.)
Error Estimates for the Approximation of the Effective Hamiltonian
International Nuclear Information System (INIS)
Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.
2008-01-01
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting
On squaring the primary constraints in a generalized Hamiltonian dynamics
International Nuclear Information System (INIS)
Nesterenko, V.V.
1993-01-01
Consideration of the model of the relativistic particle with curvature and torsion in the three-dimensional space-time shows that the squaring of the primary constraints entails a wrong result. The complete set of the Hamiltonian constraints arising here corresponds to another model with an action similar but not identical with the initial action. 16 refs
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
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
Relating Lagrangian and Hamiltonian Formalisms of LC Circuits
Clemente-Gallardo, Jesús; Scherpen, Jacquelien M.A.
2003-01-01
The Lagrangian formalism earlier defined for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other
Quantum finance Hamiltonian for coupon bond European and barrier options.
Baaquie, Belal E
2008-03-01
Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.
Anti-stiction coating of PDMS moulds for rapid microchannel fabrication by double replica moulding
DEFF Research Database (Denmark)
Zhuang, Guisheng; Kutter, Jörg Peter
2011-01-01
), which resulted in an anti-stiction layer for the improved release after PDMS casting. The deposition of FDTS on an O2 plasma-activated surface of PDMS produced a reproducible and well-performing anti-stiction monolayer of fluorocarbon, and we used the FDTS-coated moulds as micro-masters for rapid......In this paper, we report a simple and precise method to rapidly replicate master structures for fast microchannel fabrication by double replica moulding of polydimethylsiloxane (PDMS). A PDMS mould was surface-treated by vapour phase deposition of 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FDTS...
A sequence of Clifford algebras and three replicas of Dirac particle
International Nuclear Information System (INIS)
Krolikowski, W.; Warsaw Univ.
1990-01-01
The embedding of Dirac algebra into a sequence N=1, 2, 3,... of Clifford algebras is discussed, leading to Dirac equations with N=1 additional, electromagnetically ''hidden'' spins 1/2. It is shown that there are three and only three replicas N=1, 3, 5 of Dirac particle if the theory of relativity together with the probability interpretation of wave function is applied both to the ''visible'' spin and ''hidden'' spins, and a new ''hidden exclusion principle''is imposed on the wave function (then ''hidden'' spins add up to zero). It is appealing to explore this idea in order to explain the puzzle of three generations of lepton and quarks. (author)
Time-reversal focusing of an expanding soliton gas in disordered replicas
Fratalocchi, Andrea
2011-05-31
We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time-reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schrödinger equation.
Time-reversal focusing of an expanding soliton gas in disordered replicas
Fratalocchi, Andrea; Armaroli, A.; Trillo, S.
2011-01-01
We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time-reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schrödinger equation.
Directory of Open Access Journals (Sweden)
L. S. Sindhuja
2016-01-01
Full Text Available Security of Mobile Wireless Sensor Networks is a vital challenge as the sensor nodes are deployed in unattended environment and they are prone to various attacks. One among them is the node replication attack. In this, the physically insecure nodes are acquired by the adversary to clone them by having the same identity of the captured node, and the adversary deploys an unpredictable number of replicas throughout the network. Hence replica node detection is an important challenge in Mobile Wireless Sensor Networks. Various replica node detection techniques have been proposed to detect these replica nodes. These methods incur control overheads and the detection accuracy is low when the replica is selected as a witness node. This paper proposes to solve these issues by enhancing the Single Hop Detection (SHD method using the Clonal Selection algorithm to detect the clones by selecting the appropriate witness nodes. The advantages of the proposed method include (i increase in the detection ratio, (ii decrease in the control overhead, and (iii increase in throughput. The performance of the proposed work is measured using detection ratio, false detection ratio, packet delivery ratio, average delay, control overheads, and throughput. The implementation is done using ns-2 to exhibit the actuality of the proposed work.
Synthesis and properties of ZnFe{sub 2}O{sub 4} replica with biological hierarchical structure
Energy Technology Data Exchange (ETDEWEB)
Liu, Hongyan; Guo, Yiping, E-mail: ypguo@sjtu.edu.cn; Zhang, Yangyang; Wu, Fen; Liu, Yun; Zhang, Di, E-mail: zhangdi@sjtu.edu.cn
2013-09-20
Highlights: • ZFO replica with hierarchical structure was synthesized from butterfly wings. • Biotemplate has a significant impact on the properties of ZFO material. • Our method opens up new avenues for the synthesis of spinel ferrites. -- Abstract: ZnFe{sub 2}O{sub 4} replica with biological hierarchical structure was synthesized from Papilio paris by a sol–gel method followed by calcination. The crystallographic structure and morphology of the obtained samples were characterized by X-ray diffraction, field-emission scanning electron microscope, and transmittance electron microscope. The results showed that the hierarchical structures were retained in the ZFO replica of spinel structure. The magnetic behavior of such novel products was measured by a vibrating sample magnetometer. A superparamagnetism-like behavior was observed due to nanostructuration size effects. In addition, the ZFO replica with “quasi-honeycomb-like structure” showed a much higher specific capacitance of 279.4 F g{sup −1} at 10 mV s{sup −1} in comparison with ZFO powder of 137.3 F g{sup −1}, attributing to the significantly increased surface area. These results demonstrated that ZFO replica is a promising candidate for novel magnetic devices and supercapacitors.
Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
International Nuclear Information System (INIS)
Dias, Goncalo A. S.; Lemos, Jose P. S.
2008-01-01
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P M ;Q,P Q ), where M is the mass parameter, which for ω M is the conjugate momenta of M, Q is the charge parameter, and P Q is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field φ. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.
Hamiltonian reductions in plasma physics about intrinsic gyrokinetic
International Nuclear Information System (INIS)
Guillebon de Resnes, L. de
2013-01-01
Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including
Hamiltonian formalism for perfect fluids in general relativity
International Nuclear Information System (INIS)
Demaret, J.; Moncrief, V.
1980-01-01
Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models
Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
International Nuclear Information System (INIS)
Zhang, Yufeng; Fan, Engui
2006-01-01
A scheme for deducing Hamiltonian structures of the higher-dimensional hierarchies of evolution equations is presented which is devoting to obtaining the Hamiltonian structures of integrable coupling of the Jaulent-Miodek hierarchy
Integrable quadratic classical Hamiltonians on so(4) and so(3, 1)
International Nuclear Information System (INIS)
Sokolov, Vladimir V; Wolf, Thomas
2006-01-01
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions
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Qi Wang
2013-01-01
Full Text Available By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.
Phonon replica dynamics in high quality GaN epilayers and AlGaN/GaN quantum wells
Energy Technology Data Exchange (ETDEWEB)
Alderighi, D.; Vinattieri, A.; Colocci, M. [Ist. Nazionale Fisica della Materia, Firenze (Italy); Dipt. di Fisica and LENS, Firenze (Italy); Bogani, F. [Ist. Nazionale Fisica della Materia, Firenze (Italy); Dipt. di Energetica, Firenze (Italy); Gottardo, S. [Dipt. di Fisica and LENS, Firenze (Italy); Grandjean, N.; Massies, J. [Centre de Recherche sur l' Hetero-Epitaxie et ses Applications, CNRS, Valbonne (France)
2001-01-01
We present an experimental study of the exciton and phonon replica dynamics in high quality GaN epilayers and AlGaN/GaN quantum wells (QW) by means of picosecond time-resolved photoluminescence (PL) measurements. A non-exponential decay is observed both at the zero phonon line (ZPL) and at the n = 1 LO replica. Time-resolved spectra unambiguously assign the replica to the free exciton A recombination. Optical migration effects are detected both in the epilayer and the QWs samples and disappear as the temperature increases up to 60-90 K. Even though the sample quality is comparable to state-of-the-art samples, localization effects dominate the exciton dynamics at low temperature in the studied GaN based structures. (orig.)
Wu, Sangwook
2009-03-01
We investigate dynamical self-arrest in a diblock copolymer melt using a replica approach within a self-consistent local method based on dynamical mean-field theory (DMFT). The local replica approach effectively predicts (chiN)_{A} for dynamical self-arrest in a block copolymer melt for symmetric and asymmetric cases. We discuss the competition of the cubic and quartic interactions in the Landau free energy for a block copolymer melt in stabilizing a glassy state depending on the chain length. Our local replica theory provides a universal value for the dynamical self-arrest in block copolymer melts with (chiN)_{A} approximately 10.5+64N;{-3/10} for the symmetric case.
How could the replica method improve accuracy of performance assessment of channel coding?
Energy Technology Data Exchange (ETDEWEB)
Kabashima, Yoshiyuki [Department of Computational Intelligence and Systems Science, Tokyo Institute of technology, Yokohama 226-8502 (Japan)], E-mail: kaba@dis.titech.ac.jp
2009-12-01
We explore the relation between the techniques of statistical mechanics and information theory for assessing the performance of channel coding. We base our study on a framework developed by Gallager in IEEE Trans. Inform. Theory IT-11, 3 (1965), where the minimum decoding error probability is upper-bounded by an average of a generalized Chernoff's bound over a code ensemble. We show that the resulting bound in the framework can be directly assessed by the replica method, which has been developed in statistical mechanics of disordered systems, whereas in Gallager's original methodology further replacement by another bound utilizing Jensen's inequality is necessary. Our approach associates a seemingly ad hoc restriction with respect to an adjustable parameter for optimizing the bound with a phase transition between two replica symmetric solutions, and can improve the accuracy of performance assessments of general code ensembles including low density parity check codes, although its mathematical justification is still open.
PHYSICAL DISABILITY, STIGMA, AND PHYSICAL ACTIVITY IN CHILDREN: A REPLICA STUDY
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Markus GEBHARDT
2016-04-01
Full Text Available Introduction: Stereotypes can be reduced through positive descriptions. A stigma that able-bodied adults have towards children with physical disability can be reduced when the child is portrayed as being active. The study found out that a sporty active child, who uses a wheelchair, is perceived as more competent than the sporty active able-bodied child. Objective: This study is a replica study to support the hypotheses and to examine the stereotypes of able-bodied adults towards children with and without (physical disabilities. Methods: This study presents two experimental replica studies using a 2 (physical activity x 2 (sporty activities. The dependent variables were the perception of competencies and warmth according to Stereotype Content Model (SCM. Study 1 is an online experiment with 355 students of the Open University of Hagen. Study 2 surveys 1176 participants (from Munich and Graz with a paper-pencil-questionnaire. Results: The significant interaction effect was not supported by our studies. The sporty able-bodied child was rated higher in competences than the sporty child, who use a wheelchair. Sporting activity only reduces the stigma towards children with a physical disability slightly. Conclusion: The stigma towards children with physical disability can be reduced when the child is portrayed as being active, but the effect was not strong enough to chance the original classification by the SCM.
Nuclear research emulsion neutron spectrometry at the Little-Boy replica
International Nuclear Information System (INIS)
Gold, R.; Roberts, J.H.; Preston, C.C.
1985-10-01
Nuclear research emulsions (NRE) have been used to characterize the neutron spectrum emitted by the Little-Boy replica. NRE were irradiated at the Little-Boy surface as well as approximately 2 m from the center of the Little-Boy replica using polar angles of 0 0 , 30 0 , 60 0 and 90 0 . For the NRE exposed at 2 m, neutron background was determined using shadow shields of borated polyethylene. Emulsion scanning to date has concentrated exclusively on the 2-m, 0 0 and 2-m, 90 0 locations. Approximately 5000 proton-recoil tracks have been measured in NRE irradiated at each of these locations. Neutron spectra obtained from these NRE proton-recoil spectra are compared with both liquid scintillator neutron spectrometry and Monte Carlo calculations. NRE and liquid scintillator neutron spectra generally agree within experimental uncertainties at the 2-m, 90 0 location. However, at the 2-m, 0 0 location, the neutron spectra derived from these two independent experimental methods differ significantly. NRE spectra and Monte Carlo calculations exhibit general agreement with regard to both intensity as well as energy dependence. Better agreement is attained between theory and experiment at the 2-m, 90 0 location, where the neutron intensity is considerably higher. 14 refs., 18 figs., 11 tabs
One step replica symmetry breaking and extreme order statistics of logarithmic REMs
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Xiangyu Cao, Yan V. Fyodorov, Pierre Le Doussal
2016-12-01
Full Text Available Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.
A new creep-strain-replica method for evaluating the remaining life time of components
International Nuclear Information System (INIS)
Joas, H.D.
2001-01-01
To realise a safe and economic operation of older power- or chemical plants a strategy for maintenance is necessary, which makes it possible to operate a component or the plant longer than 300,000 operating hours, this also for the situation that the mode of operation has changed meanwhile. In Germany a realistic evaluation of the remaining life-time is done by comparing the actual calculated test data of a component with the code TRD 301 and TRD 508 and additional non-destructive tests or other codes like ASME, Sec. II, BS 5500, AFCEN (1985). According to many boundary conditions, the calculated data are inaccurate and the measuring of creep-strain at temperatures of about 600 o C with capacitive strain-gauges very expensive. Description of the approach of the problems: spotwelding of two gauges to the surface of a component (in a defined distance), forming a gap, producing of replica of the gap after certain operating hours at shut-down conditions by trained personal, evaluation of the replica to gain the amount of creep-strain using a scanning electron microscope, assessment of the creep-strain data. (Author)
International Nuclear Information System (INIS)
Geller, J.T.
1998-02-01
Laboratory experiments to simulate two-phase (gas and water) flow in fractured rock evolving from groundwater degassing were conducted in transparent replicas of natural rock fractures. These experiments extend the work by Geller et al. (1995) and Jarsjo and Geller (1996) that tests the hypothesis that groundwater degassing caused observed flow reductions in the Stripa Simulated Drift Experiment (SDE). Understanding degassing effects over a range of gas contents is needed due to the uncertainty in the gas contents of the water at the SDE. The main objectives of this study were to: (1) measure the effect of groundwater degassing on liquid flow rates for lower gas contents than the values used in Geller for linear flow geometry in the same fracture replicas of Geller; (2) provide a data set to develop a predictive model of two-phase flow in fractures for conditions of groundwater degassing; and (3) improve the certainty of experimental gas contents (this effort included modifications to the experimental system used by Geller et al. and separate gas-water equilibration tests). The Stripa site is being considered for a high-level radioactive waste repository
Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds
International Nuclear Information System (INIS)
Krouglikov, B.S.
1994-10-01
Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs
Determination of Hamiltonian matrix for IBM4 and compare it is self value with shells model
International Nuclear Information System (INIS)
Slyman, S.; Hadad, S.; Souman, H.
2004-01-01
The Hamiltonian is determined using the procedure OAI and the mapping of (IBM4) states into the shell model, which is based on the seniority classification scheme. A boson sub-matrix of the shell model Hamiltonian for the (sd) 4 configuration is constructed, and is proved to produce the same eigenvalues as the shell model Hamiltonian for the corresponding fermion states. (authors)
Generalized internal long wave equations: construction, hamiltonian structure and conservation laws
International Nuclear Information System (INIS)
Lebedev, D.R.
1982-01-01
Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu
The hamiltonian index of a graph and its branch-bonds
Xiong, Liming; Broersma, Haitze J.; Li, Xueliang; Li, Xueliang; Li, MingChu
2004-01-01
Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G) ≤ 2 is given here. We
Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.
2015-01-01
We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or
van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.
A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity
New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
A generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using of differential forms and exterior derivatives of fractional orders. Example of the fractional Hamiltonian system of the C-KdV soliton equation hierarchy is constructed, which is a new Hamiltonian structure
Magneto-structural correlations in exchange coupled systems
International Nuclear Information System (INIS)
Willett, R.D.; Gatteschi, D.; Kahn, O.
1985-01-01
This book contains 19 chapters. Some of the chapter titles are: Optical Spectroscophy; The Basis of Spin-Hamiltonian Theory; Inelastic Neutorn Scattering From Clusters; Magneto-structural Correlations in Bioinorganic Chemistry; and Magnetic Exchange Interactions Propagated by Multi-Atom Bridges
Study of the multiple exchange frequencies in bcc 3He by thermodynamic measurements
International Nuclear Information System (INIS)
Bernier, M.; Suaudeau, E.; Roger, M.
1987-08-01
To study the multiple exchange hamiltonian of solid 3 He we measured the contribution of the spin exchange to the pressure of bcc solid in various magnetic fields (O≤ H≤ 7.5T). Due to the nature of the atomic exchange of a fermion system this contribution is a strong function of the spin polarization. The characteristic frequencies of the exchange hamiltonian are obtained by fitting the pressure measurements with the results of a statistical calculation using a high temperature series expansion of the hamiltonian in a temperature range where both the magnetic effect is significant and the expansion converges (7mK < T < 30mK). We discuss the results obtained for two molar volumes