Hamiltonian replica-exchange in GROMACS: a flexible implementation
Bussi, Giovanni
2013-01-01
A simple and general implementation of Hamiltonian replica exchange for the popular molecular-dynamics software GROMACS is presented. In this implementation, arbitrarily different Hamiltonians can be used for the different replicas without incurring in any significant performance penalty. The implementation was validated on a simple toy model - alanine dipeptide in water - and applied to study the rearrangement of an RNA tetraloop, where it was used to compare recently proposed force-field co...
Hamiltonian replica-exchange in GROMACS: a flexible implementation
Bussi, Giovanni
2013-01-01
A simple and general implementation of Hamiltonian replica exchange for the popular molecular-dynamics software GROMACS is presented. In this implementation, arbitrarily different Hamiltonians can be used for the different replicas without incurring in any significant performance penalty. The implementation was validated on a simple toy model - alanine dipeptide in water - and applied to study the rearrangement of an RNA tetraloop, where it was used to compare recently proposed force-field corrections.
Hamiltonian replica exchange molecular dynamics using soft-core interactions.
Hritz, Jozef; Oostenbrink, Chris
2008-04-14
To overcome the problem of insufficient conformational sampling within biomolecular simulations, we have developed a novel Hamiltonian replica exchange molecular dynamics (H-REMD) scheme that uses soft-core interactions between those parts of the system that contribute most to high energy barriers. The advantage of this approach over other H-REMD schemes is the possibility to use a relatively small number of replicas with locally larger differences between the individual Hamiltonians. Because soft-core potentials are almost the same as regular ones at longer distances, most of the interactions between atoms of perturbed parts will only be slightly changed. Rather, the strong repulsion between atoms that are close in space, which in many cases results in high energy barriers, is weakened within higher replicas of our proposed scheme. In addition to the soft-core interactions, we proposed to include multiple replicas using the same Hamiltonian/level of softness. We have tested the new protocol on the GTP and 8-Br-GTP molecules, which are known to have high energy barriers between the anti and syn conformation of the base with respect to the sugar moiety. During two 25 ns MD simulations of both systems the transition from the more stable to the less stable (but still experimentally observed) conformation is not seen at all. Also temperature REMD over 50 replicas for 1 ns did not show any transition at room temperature. On the other hand, more than 20 of such transitions are observed in H-REMD using six replicas (at three different Hamiltonians) during 6.8 ns per replica for GTP and 12 replicas (at six different Hamiltonians) during 8.7 ns per replica for 8-Br-GTP. The large increase in sampling efficiency was obtained from an optimized H-REMD scheme involving soft-core potentials, with multiple simulations using the same level of softness. The optimization of the scheme was performed by fast mimicking [J. Hritz and C. Oostenbrink, J. Chem. Phys. 127, 204104 (2007)].
Ostermeir, Katja; Zacharias, Martin
2014-01-15
A Hamiltonian Replica-Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two-dimensional backbone and one-dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions.
Wang, Kai; Chodera, John D; Yang, Yanzhi; Shirts, Michael R
2013-12-01
We present a method to identify small molecule ligand binding sites and poses within a given protein crystal structure using GPU-accelerated Hamiltonian replica exchange molecular dynamics simulations. The Hamiltonians used vary from the physical end state of protein interacting with the ligand to an unphysical end state where the ligand does not interact with the protein. As replicas explore the space of Hamiltonians interpolating between these states, the ligand can rapidly escape local minima and explore potential binding sites. Geometric restraints keep the ligands from leaving the vicinity of the protein and an alchemical pathway designed to increase phase space overlap between intermediates ensures good mixing. Because of the rigorous statistical mechanical nature of the Hamiltonian exchange framework, we can also extract binding free energy estimates for all putative binding sites. We present results of this methodology applied to the T4 lysozyme L99A model system for three known ligands and one non-binder as a control, using an implicit solvent. We find that our methodology identifies known crystallographic binding sites consistently and accurately for the small number of ligands considered here and gives free energies consistent with experiment. We are also able to analyze the contribution of individual binding sites to the overall binding affinity. Our methodology points to near term potential applications in early-stage structure-guided drug discovery.
Vreede, Jocelyne; Wolf, Maarten G; de Leeuw, Simon W; Bolhuis, Peter G
2009-05-07
Hydrogen bonds play an important role in stabilizing (meta-)stable states in protein folding. Hence, they can potentially be used as a way to bias these states in molecular simulation methods. Previously, Wolf et al. showed that applying repulsive and attractive hydrogen bond biasing potentials in an alternating way significantly accelerates the folding process (Wolf, M. G.; de Leeuw, S. W. Biophys. J. 2008, 94, 3742). As the biasing potentials are only active during a fixed time interval, this alternating scheme does not represent a thermodynamic equilibrium. In this work, we present a Hamiltonian replica exchange molecular dynamics (REMD) scheme that aims to shuffle and reorder hydrogen bonds in the protein backbone. We therefore apply adapted hydrogen bond potentials in a Hamiltonian REMD scheme, which we call hydrogen bond switching (HS). To compare the performance of the HS to a standard REMD method, we performed HS and temperature REMD simulations of a beta-heptapeptide in methanol. Both methods sample the conformational space to a similar extent. As the HS simulation required only five replicas, while the REMD simulation required 20 replicas, the HS method is significantly more efficient. We tested the HS method also on a larger system, 16-residue polyalanine in water. Both of the simulations starting from a completely unfolded and a folded conformation resulted in an ensemble with, apart from the starting structure, similar conformational minima. We can conclude that the HS method provides an efficient way to sample the conformational space of a protein, without requiring knowledge of the folded states beforehand. In addition, these simulations revealed that convergence was hampered by replicas having a preference for specific biasing potentials. As this sorting effect is inherent to any Hamiltonian REMD method, finding a solution will result in an additional increase in the efficiency of Hamiltonian REMD methods in general.
Enhanced conformational sampling of carbohydrates by Hamiltonian replica-exchange simulation.
Mishra, Sushil Kumar; Kara, Mahmut; Zacharias, Martin; Koca, Jaroslav
2014-01-01
Knowledge of the structure and conformational flexibility of carbohydrates in an aqueous solvent is important to improving our understanding of how carbohydrates function in biological systems. In this study, we extend a variant of the Hamiltonian replica-exchange molecular dynamics (MD) simulation to improve the conformational sampling of saccharides in an explicit solvent. During the simulations, a biasing potential along the glycosidic-dihedral linkage between the saccharide monomer units in an oligomer is applied at various levels along the replica runs to enable effective transitions between various conformations. One reference replica runs under the control of the original force field. The method was tested on disaccharide structures and further validated on biologically relevant blood group B, Lewis X and Lewis A trisaccharides. The biasing potential-based replica-exchange molecular dynamics (BP-REMD) method provided a significantly improved sampling of relevant conformational states compared with standard continuous MD simulations, with modest computational costs. Thus, the proposed BP-REMD approach adds a new dimension to existing carbohydrate conformational sampling approaches by enhancing conformational sampling in the presence of solvent molecules explicitly at relatively low computational cost.
Zacharias, Martin
2008-03-01
Coarse-grained elastic network models (ENM) of proteins can be used efficiently to explore the global mobility of a protein around a reference structure. A new Hamiltonian-replica exchange molecular dynamics (H-RexMD) method has been designed that effectively combines information extracted from an ENM analysis with atomic-resolution MD simulations. The ENM analysis is used to construct a distance-dependent penalty (flooding or biasing) potential that can drive the structure away from its current conformation in directions compatible with the ENM model. Various levels of the penalty or biasing potential are added to the force field description of the MD simulation along the replica coordinate. One replica runs at the original force field. By focusing the penalty potential on the relevant soft degrees of freedom the method avoids the rapid increase of the replica number with increasing system size to cover a desired temperature range in conventional (temperature) RexMD simulations. The application to domain motions in lysozyme of bacteriophage T4 and to peptide folding indicates significantly improved conformational sampling compared to conventional MD simulations.
Roe, Daniel R; Bergonzo, Christina; Cheatham, Thomas E
2014-04-03
Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.
Protein-ligand docking using hamiltonian replica exchange simulations with soft core potentials.
Luitz, Manuel P; Zacharias, Martin
2014-06-23
Molecular dynamics (MD) simulations in explicit solvent allow studying receptor-ligand binding processes including full flexibility of the binding partners and an explicit inclusion of solvation effects. However, in MD simulations, the search for an optimal ligand-receptor complex geometry is frequently trapped in locally stable non-native binding geometries. A Hamiltonian replica-exchange (H-REMD)-based protocol has been designed to enhance the sampling of putative ligand-receptor complexes. It is based on softening nonbonded ligand-receptor interactions along the replicas and one reference replica under the control of the original force field. The efficiency of the method has been evaluated on two receptor-ligand systems and one protein-peptide complex. Starting from misplaced initial docking geometries, the H-REMD method reached in each case the known binding geometry significantly faster than a standard MD simulation. The approach could also be useful to identify and evaluate alternative binding geometries in a given binding region with small relative differences in binding free energy.
Curuksu, Jeremy; Zacharias, Martin
2009-03-14
Although molecular dynamics (MD) simulations have been applied frequently to study flexible molecules, the sampling of conformational states separated by barriers is limited due to currently possible simulation time scales. Replica-exchange (Rex)MD simulations that allow for exchanges between simulations performed at different temperatures (T-RexMD) can achieve improved conformational sampling. However, in the case of T-RexMD the computational demand grows rapidly with system size. A Hamiltonian RexMD method that specifically enhances coupled dihedral angle transitions has been developed. The method employs added biasing potentials as replica parameters that destabilize available dihedral substates and was applied to study coupled dihedral transitions in nucleic acid molecules. The biasing potentials can be either fixed at the beginning of the simulation or optimized during an equilibration phase. The method was extensively tested and compared to conventional MD simulations and T-RexMD simulations on an adenine dinucleotide system and on a DNA abasic site. The biasing potential RexMD method showed improved sampling of conformational substates compared to conventional MD simulations similar to T-RexMD simulations but at a fraction of the computational demand. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions including explicit solvent and ions and can be easily extended to other types of molecules.
Meng, Yilin; Dashti, Danial Sabri; Roitberg, Adrian E
2011-09-13
Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.
Zeller, Fabian; Zacharias, Martin
2014-02-11
The accurate calculation of potentials of mean force for ligand-receptor binding is one of the most important applications of molecular simulation techniques. Typically, the separation distance between ligand and receptor is chosen as a reaction coordinate along which a PMF can be calculated with the aid of umbrella sampling (US) techniques. In addition, restraints can be applied on the relative position and orientation of the partner molecules to reduce accessible phase space. An approach combining such phase space reduction with flattening of the free energy landscape and configurational exchanges has been developed, which significantly improves the convergence of PMF calculations in comparison with standard umbrella sampling. The free energy surface along the reaction coordinate is smoothened by iteratively adapting biasing potentials corresponding to previously calculated PMFs. Configurations are allowed to exchange between the umbrella simulation windows via the Hamiltonian replica exchange method. The application to a DNA molecule in complex with a minor groove binding ligand indicates significantly improved convergence and complete reversibility of the sampling along the pathway. The calculated binding free energy is in excellent agreement with experimental results. In contrast, the application of standard US resulted in large differences between PMFs calculated for association and dissociation pathways. The approach could be a useful alternative to standard US for computational studies on biomolecular recognition processes.
Jo, Sunhwan; Chipot, Christophe; Roux, Benoît
2015-05-12
The performance and accuracy of different simulation schemes for estimating the entropy inferred from free energy calculations are tested. The results obtained from replica-exchange molecular dynamics (REMD) simulations based on a simplified toy model are compared to exact numerically derived ones to assess accuracy and convergence. It is observed that the error in entropy estimation decreases by at least an order of magnitude and the quantities of interest converge much faster when the simulations are coupled via a temperature REMD algorithm and the trajectories from different temperatures are combined. Simulations with the infinite-swapping method and its variants show some improvement over the traditional nearest-neighbor REMD algorithms, but they are more computationally expensive. To test the methodologies further, the free energy profile for the reversible association of two methane molecules in explicit water was calculated and decomposed into its entropic and enthalpic contributions. Finally, a strategy based on umbrella sampling computations carried out via simultaneous temperature and Hamiltonian REMD simulations is shown to yield the most accurate entropy estimation. The entropy profile between the two methane molecules displays the characteristic signature of a hydrophobic interaction.
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.
Han, Nanyu; Mu, Yuguang
2013-01-01
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.
Protein-Ligand Binding from Distancefield Distances and Hamiltonian Replica Exchange Simulations.
de Ruiter, Anita; Oostenbrink, Chris
2013-02-12
The calculation of protein-ligand binding free energies is an important goal in the field of computational chemistry. Applying path-sampling methods for this purpose involves calculating the associated potential of mean force (PMF) and gives insight into the binding free energy along the binding process. Without a priori knowledge about the binding path, sampling reversible binding can be difficult to achieve. To alleviate this problem, we introduce the distancefield (DF) as a reaction coordinate for such calculations. DF is a grid-based method in which the shortest distance between the binding site and a ligand is determined avoiding routes that pass through the protein. Combining this reaction coordinate with Hamiltonian replica exchange molecular dynamics (HREMD) allows for the reversible binding of the ligand to the protein. A comparison is made between umbrella sampling using regular distance restraints and HREMD with DF restraints to study aspirin binding to the protein phospholipase A2. Although the free energies of binding are similar for both methods, the increased sampling with HREMD has a significant influence on the shape of the PMF. A remarkable agreement between the calculated binding free energies from the PMF and the experimental estimate is obtained.
Fan, Hao; Periole, Xavier; Mark, Alan E.
2012-01-01
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, spe
Cukier, Robert I
2011-01-28
Leucine zippers consist of alpha helical monomers dimerized (or oligomerized) into alpha superhelical structures known as coiled coils. Forming the correct interface of a dimer from its monomers requires an exploration of configuration space focused on the side chains of one monomer that must interdigitate with sites on the other monomer. The aim of this work is to generate good interfaces in short simulations starting from separated monomers. Methods are developed to accomplish this goal based on an extension of a previously introduced [Su and Cukier, J. Phys. Chem. B 113, 9595, (2009)] hamiltonian temperature replica exchange method (HTREM), which scales the hamiltonian in both potential and kinetic energies that was used for the simulation of dimer melting curves. The new method, HTREM_MS (MS designates mean square), focused on interface formation, adds restraints to the hamiltonians for all but the physical system, which is characterized by the normal molecular dynamics force field at the desired temperature. The restraints in the nonphysical systems serve to prevent the monomers from separating too far, and have the dual aims of enhancing the sampling of close in configurations and breaking unwanted correlations in the restrained systems. The method is applied to a 31-residue truncation of the 33-residue leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4. The monomers are initially separated by a distance that is beyond their capture length. HTREM simulations show that the monomers oscillate between dimerlike and monomerlike configurations, but do not form a stable interface. HTREM_MS simulations result in the dimer interface being faithfully reconstructed on a 2 ns time scale. A small number of systems (one physical and two restrained with modified potentials and higher effective temperatures) are sufficient. An in silico mutant that should not dimerize because it lacks charged residues that provide electrostatic stabilization of the dimer
Cukier, Robert I.
2011-01-01
Leucine zippers consist of alpha helical monomers dimerized (or oligomerized) into alpha superhelical structures known as coiled coils. Forming the correct interface of a dimer from its monomers requires an exploration of configuration space focused on the side chains of one monomer that must interdigitate with sites on the other monomer. The aim of this work is to generate good interfaces in short simulations starting from separated monomers. Methods are developed to accomplish this goal based on an extension of a previously introduced [Su and Cukier, J. Phys. Chem. B 113, 9595, (2009)] Hamiltonian temperature replica exchange method (HTREM), which scales the Hamiltonian in both potential and kinetic energies that was used for the simulation of dimer melting curves. The new method, HTREM_MS (MS designates mean square), focused on interface formation, adds restraints to the Hamiltonians for all but the physical system, which is characterized by the normal molecular dynamics force field at the desired temperature. The restraints in the nonphysical systems serve to prevent the monomers from separating too far, and have the dual aims of enhancing the sampling of close in configurations and breaking unwanted correlations in the restrained systems. The method is applied to a 31-residue truncation of the 33-residue leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4. The monomers are initially separated by a distance that is beyond their capture length. HTREM simulations show that the monomers oscillate between dimerlike and monomerlike configurations, but do not form a stable interface. HTREM_MS simulations result in the dimer interface being faithfully reconstructed on a 2 ns time scale. A small number of systems (one physical and two restrained with modified potentials and higher effective temperatures) are sufficient. An in silico mutant that should not dimerize because it lacks charged residues that provide electrostatic stabilization of the dimer
Yang, Mingjun; Huang, Jing; MacKerell, Alexander D
2015-06-09
Replica exchange (REX) is a powerful computational tool for overcoming the quasi-ergodic sampling problem of complex molecular systems. Recently, several multidimensional extensions of this method have been developed to realize exchanges in both temperature and biasing potential space or the use of multiple biasing potentials to improve sampling efficiency. However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions. In this study, we develop a one-dimensional (1D) REX algorithm to concurrently combine the advantages of overall enhanced sampling from Hamiltonian solute scaling and the specific enhancement of collective variables using Hamiltonian biasing potentials. In the present Hamiltonian replica exchange method, termed HREST-BP, Hamiltonian solute scaling is applied to the solute subsystem, and its interactions with the environment to enhance overall conformational transitions and biasing potentials are added along selected collective variables associated with specific conformational transitions, thereby balancing the sampling of different hierarchical degrees of freedom. The two enhanced sampling approaches are implemented concurrently allowing for the use of a small number of replicas (e.g., 6 to 8) in 1D, thus greatly reducing the computational cost in complex system simulations. The present method is applied to conformational sampling of two nitrogen-linked glycans (N-glycans) found on the HIV gp120 envelope protein. Considering the general importance of the conformational sampling problem, HREST-BP represents an efficient procedure for the study of complex saccharides, and, more generally, the method is anticipated to be of general utility for the conformational sampling in a wide range of macromolecular systems.
Ostermeir, Katja; Zacharias, Martin
2014-12-01
Coarse-grained elastic network models (ENM) of proteins offer a low-resolution representation of protein dynamics and directions of global mobility. A Hamiltonian-replica exchange molecular dynamics (H-REMD) approach has been developed that combines information extracted from an ENM analysis with atomistic explicit solvent MD simulations. Based on a set of centers representing rigid segments (centroids) of a protein, a distance-dependent biasing potential is constructed by means of an ENM analysis to promote and guide centroid/domain rearrangements. The biasing potentials are added with different magnitude to the force field description of the MD simulation along the replicas with one reference replica under the control of the original force field. The magnitude and the form of the biasing potentials are adapted during the simulation based on the average sampled conformation to reach a near constant biasing in each replica after equilibration. This allows for canonical sampling of conformational states in each replica. The application of the methodology to a two-domain segment of the glycoprotein 130 and to the protein cyanovirin-N indicates significantly enhanced global domain motions and improved conformational sampling compared with conventional MD simulations.
Laghaei, Rozita; Mousseau, Normand; Wei, Guanghong
2011-03-31
The loss of the insulin-producing β-cells in the pancreatic islets of Langerhans, responsible for type-II diabetes, is associated with islet amyloid deposits. The main component of these deposits is the amyloid fibrils formed by the 37-residue human islet amyloid polypeptide (hIAPP also known as amylin). Although the fibrils are well characterized by cross β structure, the structure of the transient oligomers formed in the early stage of aggregation remains elusive. In this study, we apply the Hamiltonian-temperature replica exchange molecular dynamics to characterize the structure and thermodynamics of a full-length hIAPP dimer in both the presence and the absence of the Cys2-Cys7 disulfide bond. We compare these results with those obtained on the monomeric and dimeric forms of rat IAPP (rIAPP) with a disulfide bridge which differ from the hIAPP by 6 amino acids in the C-terminal region, but it is unable to form fibrils. Using a coarse-grained protein force field (OPEP-the Optimized Potential for Efficient peptide structure Prediction) running for a total of 10-28 μs per system studied, we show that sequences sample α-helical structure in the N-terminal region but that the length of this secondary element is shorter and less stable for the chains without the disulfide bridge (residues 5-16 for hIAPP with the bridge vs 10-16 for hIAPP without the bridge). This α-helix is known to be an important transient stage in the formation of oligomers. In the C-terminal, the amyloidogenic region of hIAPP, β-strands are seen for residues 17-26 and 30-35. On the contrary, no significant β-sheet content in the C-terminal is observed for either the monomeric or the dimeric rIAPP. These numerical results are fully consistent with recent experimental findings that the N-terminal residues are not part of the fibril by forming α-helical structure but rather play a significant role in stabilizing the amyloidogenic region available for the fibrillation.
Mentes, Ahmet; Deng, Nan-Jie; Vijayan, R S K; Xia, Junchao; Gallicchio, Emilio; Levy, Ronald M
2016-05-10
Molecular dynamics modeling of complex biological systems is limited by finite simulation time. The simulations are often trapped close to local energy minima separated by high energy barriers. Here, we introduce Hamiltonian replica exchange (H-REMD) with torsional flattening in the Binding Energy Distribution Analysis Method (BEDAM), to reduce energy barriers along torsional degrees of freedom and accelerate sampling of intramolecular degrees of freedom relevant to protein-ligand binding. The method is tested on a standard benchmark (T4 Lysozyme/L99A/p-xylene complex) and on a library of HIV-1 integrase complexes derived from the SAMPL4 blind challenge. We applied the torsional flattening strategy to 26 of the 53 known binders to the HIV Integrase LEDGF site found to have a binding energy landscape funneled toward the crystal structure. We show that our approach samples the conformational space more efficiently than the original method without flattening when starting from a poorly docked pose with incorrect ligand dihedral angle conformations. In these unfavorable cases convergence to a binding pose within 2-3 Å from the crystallographic pose is obtained within a few nanoseconds of the Hamiltonian replica exchange simulation. We found that torsional flattening is insufficient in cases where trapping is due to factors other than torsional energy, such as the formation of incorrect intramolecular hydrogen bonds and stacking. Work is in progress to generalize the approach to handle these cases and thereby make it more widely applicable.
Jiang, Wei; Roux, Benoît
2010-07-01
Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of free energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" can improve the statistical convergence in calculations of absolute binding free energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor lambda in the extended ensemble is further coupled with a set of replicas evolving on a biased energy surface with boosting potentials used to accelerate the inter-conversion among different rotameric states of the side chains in the neighborhood of the binding site. Exchanges are allowed to occur alternatively along the axes corresponding to the thermodynamic coupling parameter lambda and the boosting potential, in an extended dual array of coupled lambda- and H-REMD simulations. The method is implemented on the basis of new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. As an illustrative example, the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme was calculated. The tests demonstrate that the dual lambda-REMD and H-REMD simulation scheme greatly accelerates the configurational sampling of the rotameric states of the side chains around the binding pocket, thereby improving the convergence of the FEP computations.
Guardiani, Carlo; Procacci, Piero
2013-06-21
The inhibitors of the Tumor Necrosis Factor-α Converting Enzyme represent promising tools for the treatment of Rheumatoid Arthritis, Multiple Sclerosis and other autoimmune diseases. In this work, using Hamiltonian Replica Exchange Molecular Dynamics simulations and atomistic force field we perform an accurate structural characterization of a group of tartrate-based inhibitors. The simulations highlight a correlation between the conformational landscape in bulk solvent and inhibition potency. Since the structures in bulk solvent are much more compact than the crystallographic bound state, we formulate the hypothesis of a two-step docking mechanism: (i) formation of an intermediate between the compact, hydroxyl exposing conformations in solution and the catalytic zinc ion; (ii) structural rearrangement in the active site of TACE of the zinc-tethered drug in the final binding conformation.
2010-10-21
transfor- mation, the hybrid potential VAB remains well-defined. Therefore, the associated reversible work can be computed. This reversible work formally...corresponds to changing the potential of the system VAB from the state that represents the original molecule A to the state that corresponds to molecule...constructed. Typically, the hybrid Hamiltonian of the system (HAB) that includes the potential VAB is linearly interpolated between the end points, molecules
Meli, Massimiliano; Colombo, Giorgio
2013-06-06
Herein, we present a novel Hamiltonian replica exchange protocol for classical molecular dynamics simulations of protein folding/unfolding. The scheme starts from the analysis of the energy-networks responsible for the stabilization of the folded conformation, by means of the energy-decomposition approach. In this framework, the compact energetic map of the native state is generated by a preliminary short molecular dynamics (MD) simulation of the protein in explicit solvent. This map is simplified by means of an eigenvalue decomposition. The highest components of the eigenvector associated with the lowest eigenvalue indicate which sites, named "hot spots", are likely to be responsible for the stability and correct folding of the protein. In the Hamiltonian replica exchange protocol, we use modified force-field parameters to treat the interparticle non-bonded potentials of the hot spots within the protein and between protein and solvent atoms, leaving unperturbed those relative to all other residues, as well as solvent-solvent interactions. We show that it is possible to reversibly simulate the folding/unfolding behavior of two test proteins, namely Villin HeadPiece HP35 (35 residues) and Protein A (62 residues), using a limited number of replicas. We next discuss possible implications for the study of folding mechanisms via all atom simulations.
Massimiliano Meli
2013-06-01
Full Text Available Herein, we present a novel Hamiltonian replica exchange protocol for classical molecular dynamics simulations of protein folding/unfolding. The scheme starts from the analysis of the energy-networks responsible for the stabilization of the folded conformation, by means of the energy-decomposition approach. In this framework, the compact energetic map of the native state is generated by a preliminary short molecular dynamics (MD simulation of the protein in explicit solvent. This map is simplified by means of an eigenvalue decomposition. The highest components of the eigenvector associated with the lowest eigenvalue indicate which sites, named “hot spots”, are likely to be responsible for the stability and correct folding of the protein. In the Hamiltonian replica exchange protocol, we use modified force-field parameters to treat the interparticle non-bonded potentials of the hot spots within the protein and between protein and solvent atoms, leaving unperturbed those relative to all other residues, as well as solvent-solvent interactions. We show that it is possible to reversibly simulate the folding/unfolding behavior of two test proteins, namely Villin HeadPiece HP35 (35 residues and Protein A (62 residues, using a limited number of replicas. We next discuss possible implications for the study of folding mechanisms via all atom simulations.
Minh, David D L
2015-01-01
A binding potential of mean force (BPMF) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid. I have developed a method to calculate BPMFs for protein-ligand systems. The method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein-ligand interaction strengths. Protein-ligand interactions are represented by interpolating precomputed electrostatic and van der Waals grids. Using a simple estimator for thermodynamic length, thermodynamic states are initialized at approximately equal intervals. The method is demonstrated on the Astex diverse set, a database of 85 protein-ligand complexes relevant to pharmacy or agriculture. Fifteen independent simulations of each complex were started using poses from crystallography, docking, or the lowest-energy pose observed in the other simulations. Benchmark simulations completed within three days on a single processor. Overall, protocols initialized using the ther...
Fan, Hao; Periole, Xavier; Mark, Alan E
2012-07-01
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, specifically, the electrostatic interaction between the protein and the solvating water, is varied leading to cycles of partial unfolding and refolding mimicking some aspects of folding chaperones. In 10 of the 15 cases examined, the CH-REMD approach sampled structures in which the root-mean-square deviation (RMSD) of secondary structure elements (SSE-RMSD) with respect to the experimental structure was more than 1.0 Å lower than the initial de novo model. In 14 of the 15 cases, the improvement was more than 0.5 Å. The ability of three different statistical potentials to identify near-native conformations was also examined. Little correlation between the SSE-RMSD of the sampled structures with respect to the experimental structure and any of the scoring functions tested was found. The most effective scoring function tested was the DFIRE potential. Using the DFIRE potential, the SSE-RMSD of the best scoring structures was on average 0.3 Å lower than the initial model. Overall the work demonstrates that targeted enhanced-sampling techniques such as CH-REMD can lead to the systematic refinement of protein structural models generated de novo but that improved potentials for the identification of near-native structures are still needed.
Itoh, Satoru G; Okumura, Hisashi
2013-11-05
We propose the Hamiltonian replica-permutation method (RPM) (or multidimensional RPM) for molecular dynamics and Monte Carlo simulations, in which parameters in the Hamiltonian are permuted among more than two replicas with the Suwa-Todo algorithm. We apply the Coulomb RPM, which is one of realization of the Hamiltonian RPM, to an alanine dipeptide and to two amyloid-β(29-42) molecules. The Hamiltonian RPM realizes more efficient sampling than the Hamiltonian replica-exchange method. We illustrate the protein misfolding funnel of amyloid-β(29-42) and reveal its dimerization pathways.
Laghaei, Rozita; Mousseau, Normand; Wei, Guanghong
2010-05-27
The human Islet amyloid polypeptide (hIAPP or amylin) is a 37-residue peptide hormone that is normally cosecreted with insulin by the pancreatic beta-cells. In patients with type 2 diabetes, hIAPP deposits as amyloid fibrils in the extracellular spaces of the pancreatic islets. Recent experimental studies show that the intramolecular disulfide bond between Cys2 and Cys7 plays a central role in the process of fibril formation. However, the effect of the disulfide bond on the intrinsic structural properties of monomeric hIAPP is yet to be determined. In this study, we characterize the atomic structure and the thermodynamics of full-length hIAPP in the presence and absence of a disulfide bond using extensive combined Hamiltonian and temperature replica exchange molecular dynamics simulations (HT-REMD) with a coarse grained protein force field. Our simulations show that HT-REMD is more efficient in sampling than temperature REMD. On the basis of a total simulation time of 28 mus, we find that, although native hIAPP (in the presence of a disulfide bond) essentially adopts a disordered conformation in solution, consistent with the signal measured by ultraviolet-circular dichroism (UV-CD) spectroscopy, it also transiently samples alpha-helical structure for residues 5-16. In comparison with the N-terminal region, the C-terminal region is highly disordered and populates a much lesser content of isolated beta-strand conformation for residues 22-26 and 30-35. Moreover, the absence of the disulfide bond greatly decreases the extent of helix formed throughout residues 5-9 in favor of random coil and beta-sheet structure. Implications of the stabilization of N-terminal helical structure by disulfide bond on the initialization of hIAPP amyloid formation are discussed.
Exchange frequency in replica exchange molecular dynamics
Sindhikara, Daniel; Meng, Yilin; Roitberg, Adrian E.
2008-01-01
The effect of the exchange-attempt frequency on sampling efficiency is studied in replica exchange molecular dynamics (REMD). We show that sampling efficiency increases with increasing exchange-attempt frequency. This conclusion is contrary to a commonly expressed view in REMD. Five peptides (1-21 residues long) are studied with a spectrum of exchange-attempt rates. Convergence rates are gauged by comparing ensemble properties between fixed length test REMD simulations and longer reference simulations. To show the fundamental correlation between exchange frequency and convergence time, a simple model is designed and studied, displaying the same basic behavior of much more complex systems.
Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.
Zhang, Bin W; Dai, Wei; Gallicchio, Emilio; He, Peng; Xia, Junchao; Tan, Zhiqiang; Levy, Ronald M
2016-08-25
Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.
A simple asynchronous replica-exchange implementation
Bussi, Giovanni
2008-01-01
We discuss the possibility of implementing asynchronous replica-exchange (or parallel tempering) molecular dynamics. In our scheme, the exchange attempts are driven by asynchronous messages sent by one of the computing nodes, so that different replicas are allowed to perform a different number of time-steps between subsequent attempts. The implementation is simple and based on the message-passing interface (MPI). We illustrate the advantages of our scheme with respect to the standard synchronous algorithm and we benchmark it for a model Lennard-Jones liquid on an IBM-LS21 blade center cluster.
Asynchronous replica exchange software for grid and heterogeneous computing
Gallicchio, Emilio; Xia, Junchao; Flynn, William F.; Zhang, Baofeng; Samlalsingh, Sade; Mentes, Ahmet; Levy, Ronald M.
2015-11-01
Parallel replica exchange sampling is an extended ensemble technique often used to accelerate the exploration of the conformational ensemble of atomistic molecular simulations of chemical systems. Inter-process communication and coordination requirements have historically discouraged the deployment of replica exchange on distributed and heterogeneous resources. Here we describe the architecture of a software (named ASyncRE) for performing asynchronous replica exchange molecular simulations on volunteered computing grids and heterogeneous high performance clusters. The asynchronous replica exchange algorithm on which the software is based avoids centralized synchronization steps and the need for direct communication between remote processes. It allows molecular dynamics threads to progress at different rates and enables parameter exchanges among arbitrary sets of replicas independently from other replicas. ASyncRE is written in Python following a modular design conducive to extensions to various replica exchange schemes and molecular dynamics engines. Applications of the software for the modeling of association equilibria of supramolecular and macromolecular complexes on BOINC campus computational grids and on the CPU/MIC heterogeneous hardware of the XSEDE Stampede supercomputer are illustrated. They show the ability of ASyncRE to utilize large grids of desktop computers running the Windows, MacOS, and/or Linux operating systems as well as collections of high performance heterogeneous hardware devices.
Asynchronous Replica Exchange Software for Grid and Heterogeneous Computing
Gallicchio, Emilio; Xia, Junchao; Flynn, William F.; Zhang, Baofeng; Samlalsingh, Sade; Mentes, Ahmet; Levy, Ronald M.
2015-01-01
Parallel replica exchange sampling is an extended ensemble technique often used to accelerate the exploration of the conformational ensemble of atomistic molecular simulations of chemical systems. Inter-process communication and coordination requirements have historically discouraged the deployment of replica exchange on distributed and heterogeneous resources. Here we describe the architecture of a software (named ASyncRE) for performing asynchronous replica exchange molecular simulations on volunteered computing grids and heterogeneous high performance clusters. The asynchronous replica exchange algorithm on which the software is based avoids centralized synchronization steps and the need for direct communication between remote processes. It allows molecular dynamics threads to progress at different rates and enables parameter exchanges among arbitrary sets of replicas independently from other replicas. ASyncRE is written in Python following a modular design conducive to extensions to various replica exchange schemes and molecular dynamics engines. Applications of the software for the modeling of association equilibria of supramolecular and macromolecular complexes on BOINC campus computational grids and on the CPU/MIC heterogeneous hardware of the XSEDE Stampede supercomputer are illustrated. They show the ability of ASyncRE to utilize large grids of desktop computers running the Windows, MacOS, and/or Linux operating systems as well as collections of high performance heterogeneous hardware devices. PMID:27103749
On a general Heisenberg exchange effective Hamiltonian
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
Enhanced Conformational Sampling using Replica Exchange with Collective-Variable Tempering
Gil-Ley, Alejandro
2015-01-01
The computational study of conformational transitions in RNA and proteins with atomistic molecular dynamics often requires suitable enhanced sampling techniques. We here introduce a novel method where concurrent metadynamics are integrated in a Hamiltonian replica-exchange scheme. The ladder of replicas is built with different strength of the bias potential exploiting the tunability of well-tempered metadynamics. Using this method, free-energy barriers of individual collective variables are significantly reduced compared with simple force-field scaling. The introduced methodology is flexible and allows adaptive bias potentials to be self-consistently constructed for a large number of simple collective variables, such as distances and dihedral angles. The method is tested on alanine dipeptide and applied to the difficult problem of conformational sampling in a tetranucleotide.
Itoh, Satoru G; Okumura, Hisashi
2014-10-02
The amyloid-β peptides form amyloid fibrils which are associated with Alzheimer's disease. Amyloid-β(29-42) is its C-terminal fragment and a critical determinant of the amyloid formation rate. This fragment forms the amyloid fibril by itself. However, the fragment conformation in the fibril has yet to be determined. The oligomerization process including the dimerization process is also still unknown. The dimerization process corresponds to an early process of the amyloidogenesis. In order to investigate the dimerization process and conformations, we applied the Hamiltonian replica-permutation method, which is a better alternative to the Hamiltonian replica-exchange method, to two amyloid-β(29-42) molecules in explicit water solvent. At the first step of the dimerization process, two amyloid-β(29-42) molecules came close to each other and had intermolecular side chain contacts. When two molecules had the intermolecular side chain contacts, the amyloid-β(29-42) tended to have intramolecular secondary structures, especially β-hairpin structures. The two molecules had intermolecular β-bridge structures by coming much closer at the second step of the dimerization process. Formation of these intermolecular β-bridge structures was induced by the β-hairpin structures. The intermolecular β-sheet structures elongated at the final step. Structures of the amyloid-β(29-42) in the monomer and dimer states are also shown with the free-energy landscapes, which were obtained by performing efficient sampling in the conformational space in our simulations.
Moors, Samuel L C; Michielssens, Servaas; Flors, Cristina; Dedecker, Peter; Hofkens, Johan; Ceulemans, Arnout
2008-06-01
The reversibly photoactivatable green fluorescent protein analog Dronpa holds great promise as a marker for various new cellular imaging applications. Using a replica exchange method which combines both Hamiltonian and temperature exchanges, the ground-state dynamics of Dronpa and two mutants with increased switching kinetics, Val157Gly and Met159Thr, were compared. The dominant chromophore state was found to be the cis isomer in all three proteins. The simulation data suggest that both mutations strongly increase the chromophore flexibility and cis-trans isomerization rate. We identify three key amino acids, Val157, Met159, and Phe173, which are able to impede the bottom hula-twist transition path, depending on their position and rotameric state. We believe our insights will help to understand the switching process and provide useful information for the design of new variants with improved fluorescence properties.
Replica exchange Monte Carlo applied to hard spheres.
Odriozola, Gerardo
2009-10-14
In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role.
Scalable replica-exchange framework for Wang-Landau sampling.
Vogel, Thomas; Li, Ying Wai; Wüst, Thomas; Landau, David P
2014-08-01
We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.
Scalable replica-exchange framework for Wang-Landau sampling
Vogel, Thomas; Li, Ying Wai; Wüst, Thomas; Landau, David P.
2014-08-01
We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.
Scalable replica-exchange framework for Wang Landau sampling
Vogel, Thomas [University of Georgia, Athens, GA; Li, Ying Wai [ORNL; Wuest, Thomas [Swiss Federal Research Institute, Switzerland; Landau, David P [University of Georgia, Athens, GA
2014-01-01
We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general, current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.
Kamberaj, Hiqmet, E-mail: hkamberaj@ibu.edu.mk [Department of Computer Engineering, International Balkan University, Tashko Karadza 11A, Skopje (Macedonia, The Former Yugoslav Republic of)
2015-09-28
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.
Vogel, Thomas
2015-01-01
We recently introduced a novel replica-exchange scheme in which an individual replica can sample from states encountered by other replicas at any previous time by way of a global configuration database, enabling the fast propagation of relevant states through the whole ensemble of replicas. This mechanism depends on the knowledge of global thermodynamic functions which are measured during the simulation and not coupled to the heat bath temperatures driving the individual simulations. Therefore, this setup also allows for a continuous adaptation of the temperature set. In this paper, we will review the new scheme and demonstrate its capability. The method is particularly useful for the fast and reliable estimation of the microcanonical temperature T(U) or, equivalently, of the density of states g(U) over a wide range of energies.
Yucesoy, Burcu; Machta, Jonathan; Katzgraber, Helmut G.
2012-02-01
We present the results of a large-scale numerical study of the equilibrium three-dimensional Ising spin glass with Gaussian disorder. Using replica exchange (parallel tempering) Monte Carlo, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the replica exchange Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations (N <=10^3 spins) down to very low temperatures (T 0.2Tc) is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free energy landscape. We also discuss the size dependence of several static quantities.
Ito, Shingo; Irle, Stephan; Okamoto, Yuko
2016-07-01
The replica-exchange umbrella sampling (REUS) method combines replica-exchange and umbrella sampling methods and allows larger conformational sampling than conventional simulation methods. This method has been used in many studies to understand docking mechanisms and the functions of molecules. However, REUS has not been combined with quantum chemical codes. Therefore, we implemented the REUS simulation technique in the DFTB + quantum chemistry code utilizing approximate density functional theory. We performed REUS simulations of an intra-molecular proton transfer reaction of malonaldehyde and a formation of a phthalocyanine from four phthalonitriles and one iron atom to validate the reliability of our implemented REUS-DFTB + combination.
Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study.
Perera, Dilina; Vogel, Thomas; Landau, David P
2016-10-01
Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.
Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study
Perera, Dilina; Vogel, Thomas; Landau, David P.
2016-10-01
Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.
Lee, Juyong; Miller, Benjamin T; Damjanović, Ana; Brooks, Bernard R
2014-07-08
We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.
Shea, Joan-Emma; Levine, Zachary A
2016-01-01
The simulation of protein aggregation poses several computational challenges due to the disparate time and lengths scales that are involved. This chapter focuses on the use of atomistically detailed simulations to probe the initial steps of aggregation, with an emphasis on the Tau peptide as a model system, run under a replica exchange molecular dynamics protocol.
Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space
Valentim, Alexandra; Rocha, Julio C. S.; Tsai, Shan-Ho; Li, Ying Wai; Eisenbach, Markus; Fiore, Carlos E.; Landau, David P.
2015-09-01
We considered a higher-dimensional extension for the replica-exchange Wang- Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.
Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space
Valentim, Alexandra [University of Georgia, Athens, GA; Rocha, Julio C. S. [Universidade Federal de Minas Gerais; Tsai, Shan-Ho [University of Georgia, Athens, GA; Li, Ying Wai [ORNL; Eisenbach, Markus [ORNL; Fiore, Carlos E [University of Sao Paulo, BRAZIL; Landau, David P [University of Georgia, Athens, GA
2015-01-01
We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this diculty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.
Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space
Valentim, Alexandra; Tsai, Shan-Ho; Li, Ying Wai; Eisenbach, Markus; Fiore, Carlos E; Landau, David P
2015-01-01
We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty,...
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.
Brown, Sandra E
2014-01-01
Classical free energies for the cage and prism isomers of water hexamer computed by the self- consistent phonons (SCP) method and reversible scaling (RS) method are presented for several flexible water potentials. Both methods have been augmented with a rotational correction for improved accuracy when working with clusters. Comparison of the SCP results with the RS results suggests a fairly broad temperature range over which the SCP approximation can be expected to give accurate results for systems of water clusters, and complements a previously reported assessment of SCP. Discrepancies between the SCP and RS results presented here, and recently published replica exchange molecular dynamics (REMD) results bring into question the convergence of the REMD and accompanying replica exchange path integral molecular dynamics results. In addition to the ever-present specter of unconverged results, several possible sources for the discrepancy are explored based on inherent characteristics of the methods used.
Performance of replica-exchange Wang-Landau sampling for the study of spin systems
Li, Ying Wai; Eisenbach, Markus; Vogel, Thomas; Wüst, Thomas; Landau, David P.
2014-03-01
The recently proposed replica-exchange Wang-Landau sampling (REWL) is a novel, massively parallel Monte Carlo method which allows for the parallelization of Wang-Landau sampling based on a replica-exchange framework. The robustness of the scheme is demonstrated by its broad applicability on a variety of spin systems: from the simplest models with discrete or continuous energy domains, to complex systems captured by large-scale first principles density functional theory calculations. The accuracy of REWL is studied by comparing the thermodynamic properties with exact solutions and results obtained by the original, serial Wang-Landau sampling. The principles for the speed-up, the strong and weak scaling behavior of REWL are also investigated when different parameter settings are employed. We will show, with the aid of selected spin systems, that the method accelerates the simulations significantly with a possible improved accuracy. Phys. Rev. Lett. 110, 210603 (2013)
A new paradigm for petascale Monte Carlo simulation: Replica exchange Wang-Landau sampling
Li, Ying Wai; Wüst, Thomas; Landau, David P
2014-01-01
We introduce a generic, parallel Wang-Landau method that is naturally suited to implementation on massively parallel, petaflop supercomputers. The approach introduces a replica-exchange framework in which densities of states for overlapping sub-windows in energy space are determined iteratively by traditional Wang-Landau sampling. The advantages and general applicability of the method are demonstrated for several distinct systems that possess discrete or continuous degrees of freedom, including those with complex free energy landscapes and topological constraints.
A new paradigm for petascale Monte Carlo simulation: Replica exchange Wang-Landau sampling
Li, Ying Wai; Vogel, Thomas; Wüst, Thomas; Landau, David P.
2014-05-01
We introduce a generic, parallel Wang-Landau method that is naturally suited to implementation on massively parallel, petaflop supercomputers. The approach introduces a replica-exchange framework in which densities of states for overlapping sub-windows in energy space are determined iteratively by traditional Wang-Landau sampling. The advantages and general applicability of the method are demonstrated for several distinct systems that possess discrete or continuous degrees of freedom, including those with complex free energy landscapes and topological constraints.
A new paradigm for petascale Monte Carlo simulation: Replica exchange Wang Landau sampling
Li, Ying Wai [ORNL; Vogel, Thomas [Los Alamos National Laboratory (LANL); Wuest, Thomas [Swiss Federal Research Institute, Switzerland; Landau, David P [University of Georgia, Athens, GA
2014-01-01
We introduce a generic, parallel Wang Landau method that is naturally suited to implementation on massively parallel, petaflop supercomputers. The approach introduces a replica-exchange framework in which densities of states for overlapping sub-windows in energy space are determined iteratively by traditional Wang Landau sampling. The advantages and general applicability of the method are demonstrated for several distinct systems that possess discrete or continuous degrees of freedom, including those with complex free energy landscapes and topological constraints.
Nagai, Tetsuro
2017-01-01
Replica-exchange molecular dynamics (REMD) has demonstrated its efficiency by combining trajectories of a wide range of temperatures. As an extension of the method, the author formalizes the mass-manipulating replica-exchange molecular dynamics (MMREMD) method that allows for arbitrary mass scaling with respect to temperature and individual particles. The formalism enables the versatile application of mass-scaling approaches to the REMD method. The key change introduced in the novel formalism is the generalized rules for the velocity and momentum scaling after accepted replica-exchange attempts. As an application of this general formalism, the refinement of the viscosity-REMD (V-REMD) method [P. H. Nguyen, https://doi.org/10.1063/1.3369626" xlink:type="simple">J. Chem. Phys. 132, 144109 (2010)] is presented. Numerical results are provided using a pilot system, demonstrating easier and more optimized applicability of the new version of V-REMD as well as the importance of adherence to the generalized velocity scaling rules. With the new formalism, more sound and efficient simulations will be performed.
Xia, Junchao; Flynn, William F; Gallicchio, Emilio; Zhang, Bin W; He, Peng; Tan, Zhiqiang; Levy, Ronald M
2015-09-05
We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.
Perera, Meewanage Dilina N [ORNL; Li, Ying Wai [ORNL; Eisenbach, Markus [ORNL; Vogel, Thomas [Los Alamos National Laboratory (LANL); Landau, David P [University of Georgia, Athens
2015-01-01
We describe the study of thermodynamics of materials using replica-exchange Wang Landau (REWL) sampling, a generic framework for massively parallel implementations of the Wang Landau Monte Carlo method. To evaluate the performance and scalability of the method, we investigate the magnetic phase transition in body-centered cubic (bcc) iron using the classical Heisenberg model parameterized with first principles calculations. We demonstrate that our framework leads to a significant speedup without compromising the accuracy and precision and facilitates the study of much larger systems than is possible with its serial counterpart.
Doi, Hideo; Yasuoka, Kenji
2017-05-01
Confined systems exhibit interesting properties that are applied to the fields of lubrication, adhesion and nanotechnology. The replica exchange molecular simulation method was applied to calculate the phase equilibrium points of Lennard-Jones particles in a two-dimensional confined system. The liquid-solid phase equilibrium points and the solid structure with a dependency of the slit width were determined and the order parameter of the solid structure was analyzed. Such confined systems are shown to be favorable for manipulation of the phase equilibrium points.
Combining Coarse-Grained Protein Models with Replica-Exchange All-Atom Molecular Dynamics
Wabik, Jacek; Gront, Dominik; Kouza, Maksim; Kolinski, Andrzej
2013-01-01
We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.
Combining Coarse-Grained Protein Models with Replica-Exchange All-Atom Molecular Dynamics
Andrzej Koliński
2013-05-01
Full Text Available We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.
Combining coarse-grained protein models with replica-exchange all-atom molecular dynamics.
Wabik, Jacek; Kmiecik, Sebastian; Gront, Dominik; Kouza, Maksim; Koliński, Andrzej
2013-05-10
We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.
Folding of SAM-II riboswitch explored by replica-exchange molecular dynamics simulation.
Xue, Xu; Yongjun, Wang; Zhihong, Li
2015-01-21
Riboswitches are cis-acting RNA fragments that function via a conformational transition mechanism when a specific target molecule binds to its binding pocket, representing an inviting new class of biomolecular target for the development of antibiotics. To understand the folding mechanism of SAM-II riboswitch, occurring predominantly in proteobacteria, a 100ns replica-exchange molecular dynamics simulation in explicit solvent is performed. Our results show that this RNA pseudoknot has multiple folding pathways, and various intermediate structures. The resultant riboswitch conformational transition map is well consistent with the recent fluorescence measurement, which confirms the dynamical properties of this pseudoknot. Moreover, a novel transition pathway is predicted. The global folding dynamics is mainly coupled with the helix rather than the loop region. The potential folding pathways of the riboswitch presented here should lead to a deeper understanding of the folding mechanism of the riboswitch, as well as the conformational change of RNA pseudoknot.
Characterizing folding funnels with replica exchange Wang-Landau simulation of lattice proteins.
Shi, Guangjie; Wüst, Thomas; Landau, David P
2016-11-01
We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional "neutral" monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.
Replica-exchange Wang-Landau simulations of the H0P lattice protein model
Shi, Guangjie; Wüst, Thomas; Li, Ying Wai; Landau, David P.
The hydrophobic-polar (HP) lattice protein model has been the subject of intensive investigation in an effort to aid our understanding of protein folding. However, the high ground state degeneracies caused by its simplification stands in contrast to the generally unique native states of natural proteins. Here we proposed a simple modification, by introducing a new type of ``neutral'' monomer, 0, i.e. neither hydrophobic nor polar, thus rendering the model more realistic without increasing the difficulties of sampling significantly. With the replica exchange Wang-Landau (REWL) scheme we investigated several widely studied HP proteins and their H0P counterparts. Dramatic differences in both ground state and thermodynamic properties have been found. For example, the H0P version of Crambin shows more clear two-step folding and 3 order of magnitudes less ground state degeneracy than its HP counterpart. Supported by NSF.
Characterizing folding funnels with replica exchange Wang-Landau simulation of lattice proteins
Shi, Guangjie; Wüst, Thomas; Landau, David P.
2016-11-01
We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional "neutral" monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
Itoh, Satoru G; Okumura, Hisashi
2016-07-14
Oligomers of amyloid-β peptides (Aβ) are formed during the early stage of the amyloidogenesis process and exhibit neurotoxicity. The oligomer formation process of Aβ and even that of Aβ fragments are still poorly understood, though understanding of these processes is essential for remedying Alzheimer's disease. In order to better understand the oligomerization process of the C-terminal Aβ fragment Aβ(29-42) at the atomic level, we performed the Hamiltonian replica-permutation molecular dynamics simulation with Aβ(29-42) molecules using the explicit water solvent model. We observed that oligomers increased in size through the sequential addition of monomers to the oligomer, rather than through the assembly of small oligomers. Moreover, solvent effects played an important role in this oligomerization process.
Replica exchange molecular dynamics study of the truncated amyloid beta (11-40) trimer in solution.
Ngo, Son Tung; Hung, Huynh Minh; Truong, Duc Toan; Nguyen, Minh Tho
2017-01-18
Amyloid beta (Aβ) oligomers are neurotoxic compounds that destroy the brain of Alzheimer's disease patients. Recent studies indicated that the trimer is one of the most cytotoxic forms of low molecular weight Aβ oligomers. As there was limited information about the structure of the Aβ trimer, either by experiment or by computation, we determined in this work the structure of the 3Aβ11-40 oligomer for the first time using the temperature replica exchange molecular dynamics simulations in the presence of an explicit solvent. More than 20.0 μs of MD simulations were performed. The probability of the β-content and random coil structure of the solvated trimer amounts to 42 ± 6 and 49 ± 7% which is in good agreement with experiments. Intermolecular interactions in central hydrophobic cores play a key role in stabilizing the oligomer. Intermolecular polar contacts between D23 and residues 24-29 replace the salt bridge D23-K28 to secure the loop region. The hydrophilic region of the N-terminus is maintained by the intermolecular polar crossing contacts H13A-Q15B and H13B-Q15C. The difference in the free energy of binding between the constituting monomers and the others amounts to -36 ± 8 kcal mol(-1). The collision cross section of the representative structures of the trimer was computed to be 1330 ± 47 Å(2), which is in good agreement with previous experiments.
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.
Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent.
Chebaro, Yassmine; Dong, Xiao; Laghaei, Rozita; Derreumaux, Philippe; Mousseau, Normand
2009-01-08
Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.
Replica-exchange Wang-Landau simulations of the H0P model of protein folding
Shi, Guangjie; Landau, David P.; Wüst, Thomas; Li, Ying Wai Li
2015-03-01
The hydrophobic-polar (HP) model has served as a coarse-grained lattice protein folding model attracting scientists from various disciplines. However, simplification into H and P monomers may yield high ground state degeneracies which stands in contrast to the generally unique native states of natural proteins. We propose a simple modification, by introducing a new type of ``neutral'' monomer, 0, i.e. neither hydrophobic nor polar, rendering the model more realistic without increasing the difficulties of sampling significantly. With the newly developed parallel Wang-Landau (replica exchange Wang-Landau) scheme and an innovative method of estimating the ground state degeneracies, we investigated some widely studied HP proteins and their H0P counterparts. Dramatic differences in ground state and thermodynamic properties have been observed, e.g. the estimation of ground state degeneracy for the 46mer is 460,000 for the HP version and only 20 for the H0P mapping. Similarly, the specific heat and structural properties: radius of gyration and etc. show more pronounced signals associated with folding. Supported by NSF.
Małolepsza, Edyta; Secor, Maxim; Keyes, Tom
2015-10-22
A prescription for sampling isobaric generalized ensembles with molecular dynamics is presented and applied to the generalized replica exchange method (gREM), which was designed to simulate first-order phase transitions. The properties of the isobaric gREM ensemble are discussed, and a study is presented for the liquid-vapor equilibrium of the guest molecules given for gas hydrate formation with the mW water model. Phase diagrams, critical parameters, and a law of corresponding states are obtained.
Vreede, J.; Wolf, M.G.; de Leeuw, S.W.; Bolhuis, P.G.
2009-01-01
Hydrogen bonds play an important role in stabilizing (meta-)stable states in protein folding. Hence, they can potentially be used as a way to bias these states in molecular simulation methods. Previously, Wolf et al. showed that applying repulsive and attractive hydrogen bond biasing potentials in a
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.
Seismic wavefield imaging based on the replica exchange Monte Carlo method
Kano, Masayuki; Nagao, Hiromichi; Ishikawa, Daichi; Ito, Shin-ichi; Sakai, Shin'ichi; Nakagawa, Shigeki; Hori, Muneo; Hirata, Naoshi
2016-11-01
Earthquakes sometimes cause serious disasters not only directly by ground motion itself but also secondarily by infrastructure damage, particularly in densely populated urban areas that have capital functions. To reduce the number and severity of secondary disasters, it is important to evaluate seismic hazards rapidly by analyzing the seismic responses of individual structures to input ground motions. We propose a method that integrates physics-based and data-driven approaches in order to obtain a seismic wavefield for use as input to a seismic response analysis. The new contribution of this study is the use of the replica exchange Monte Carlo (REMC) method, which is one of the Markov chain Monte Carlo (MCMC) methods, for estimation of a seismic wavefield, together with a one-dimensional (1-D) local subsurface structure and source information. Numerical tests were conducted to verify the proposed method, using synthetic observation data obtained from analytical solutions for two horizontally-layered subsurface structure models. The geometries of the observation sites were determined from the dense seismic observation array called the Metropolitan Seismic Observation network (MeSO-net), which has been in operation in the Tokyo metropolitan area in Japan since 2007. The results of the numerical tests show that the proposed method is able to search the parameters related to the source and the local subsurface structure in a broader parameter space than the Metropolis method, which is an ordinary MCMC method. The proposed method successfully reproduces a seismic wavefield consistent with a true wavefield. In contrast, ordinary kriging, which is a classical data-driven interpolation method for spatial data, is hardly able to reproduce a true wavefield, even in the low frequency bands. This suggests that it is essential to employ both physics-based and data-driven approaches in seismic wavefield imaging, utilizing seismograms from a dense seismic array. The REMC method
Seismic wavefield imaging based on the replica exchange Monte Carlo method
Kano, Masayuki; Nagao, Hiromichi; Ishikawa, Daichi; Ito, Shin-ichi; Sakai, Shin'ichi; Nakagawa, Shigeki; Hori, Muneo; Hirata, Naoshi
2017-01-01
Earthquakes sometimes cause serious disasters not only directly by ground motion itself but also secondarily by infrastructure damage, particularly in densely populated urban areas that have capital functions. To reduce the number and severity of secondary disasters, it is important to evaluate seismic hazards rapidly by analysing the seismic responses of individual structures to input ground motions. We propose a method that integrates physics-based and data-driven approaches in order to obtain a seismic wavefield for use as input to a seismic response analysis. The new contribution of this study is the use of the replica exchange Monte Carlo (REMC) method, which is one of the Markov chain Monte Carlo (MCMC) methods, for estimation of a seismic wavefield, together with a 1-D local subsurface structure and source information. Numerical tests were conducted to verify the proposed method, using synthetic observation data obtained from analytical solutions for two horizontally layered subsurface structure models. The geometries of the observation sites were determined from the dense seismic observation array called the Metropolitan Seismic Observation network, which has been in operation in the Tokyo metropolitan area in Japan since 2007. The results of the numerical tests show that the proposed method is able to search the parameters related to the source and the local subsurface structure in a broader parameter space than the Metropolis method, which is an ordinary MCMC method. The proposed method successfully reproduces a seismic wavefield consistent with a true wavefield. In contrast, ordinary kriging, which is a classical data-driven interpolation method for spatial data, is hardly able to reproduce a true wavefield, even in the low frequency bands. This suggests that it is essential to employ both physics-based and data-driven approaches in seismic wavefield imaging, utilizing seismograms from a dense seismic array. The REMC method, which provides not only
A replica exchange Monte Carlo algorithm for protein folding in the HP model
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
Jiang, Wei; Luo, Yun; Maragliano, Luca; Roux, Benoît
2012-11-13
An extremely scalable computational strategy is described for calculations of the potential of mean force (PMF) in multidimensions on massively distributed supercomputers. The approach involves coupling thousands of umbrella sampling (US) simulation windows distributed to cover the space of order parameters with a Hamiltonian molecular dynamics replica-exchange (H-REMD) algorithm to enhance the sampling of each simulation. In the present application, US/H-REMD is carried out in a two-dimensional (2D) space and exchanges are attempted alternatively along the two axes corresponding to the two order parameters. The US/H-REMD strategy is implemented on the basis of parallel/parallel multiple copy protocol at the MPI level, and therefore can fully exploit computing power of large-scale supercomputers. Here the novel technique is illustrated using the leadership supercomputer IBM Blue Gene/P with an application to a typical biomolecular calculation of general interest, namely the binding of calcium ions to the small protein Calbindin D9k. The free energy landscape associated with two order parameters, the distance between the ion and its binding pocket and the root-mean-square deviation (rmsd) of the binding pocket relative the crystal structure, was calculated using the US/H-REMD method. The results are then used to estimate the absolute binding free energy of calcium ion to Calbindin D9k. The tests demonstrate that the 2D US/H-REMD scheme greatly accelerates the configurational sampling of the binding pocket, thereby improving the convergence of the potential of mean force calculation.
Fujisaki, Hiroshi; Shiga, Motoyuki; Kidera, Akinori
2010-04-07
For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.
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.
Asiri Nanayakkara
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 παT symmetry then the corresponding eigen value is real, where πα 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, px(→) py) and the reality of these systems are investigated.
Zheng, Weihua; Andrec, Michael; Gallicchio, Emilio; Levy, Ronald M
2009-08-27
We present an approach to recover kinetics from a simplified protein folding model at different temperatures using the combined power of replica exchange (RE), a kinetic network, and effective stochastic dynamics. While RE simulations generate a large set of discrete states with the correct thermodynamics, kinetic information is lost due to the random exchange of temperatures. We show how we can recover the kinetics of a 2D continuous potential with an entropic barrier by using RE-generated discrete states as nodes of a kinetic network. By choosing the neighbors and the microscopic rates between the neighbors appropriately, the correct kinetics of the system can be recovered by running a kinetic simulation on the network. We fine-tune the parameters of the network by comparison with the effective drift velocities and diffusion coefficients of the system determined from short-time stochastic trajectories. One of the advantages of the kinetic network model is that the network can be built on a high-dimensional discretized state space, which can consist of multiple paths not consistent with a single reaction coordinate.
Olson, Mark A; Lee, Michael S; Yeh, In-Chul
2017-01-28
This work presents replica-exchange molecular dynamics simulations of inserting a 16-residue Ebola virus fusion peptide into a membrane bilayer. A computational approach is applied for modeling the peptide at the explicit all-atom level and the membrane-aqueous bilayer by a generalized Born continuum model with a smoothed switching function (GBSW). We provide an assessment of the model calculations in terms of three metrics: (1) the ability to reproduce the NMR structure of the peptide determined in the presence of SDS micelles and comparable structural data on other fusion peptides; (2) determination of the effects of the mutation Trp-8 to Ala and sequence discrimination of the homologous Marburg virus; and (3) calculation of potentials of mean force for estimating the partitioning free energy and their comparison to predictions from the Wimley-White interfacial hydrophobicity scale. We found the GBSW implicit membrane model to produce results of limited accuracy in conformational properties of the peptide when compared to the NMR structure, yet the model resolution is sufficient to determine the effect of sequence differentiation on peptide-membrane integration. © 2016 Wiley Periodicals, Inc.
Replica trick for rare samples
Rizzo, Tommaso
2014-05-01
In the context of disordered systems with quenched Hamiltonians I address the problem of characterizing rare samples where the thermal average of a specific observable has a value different from the typical one. These rare samples can be selected through a variation of the replica trick which amounts to replicating the system and dividing the replicas intwo two groups containing, respectively, M and -M replicas. Replicas in the first (second) group experience a positive (negative) small field O (1/M) conjugate to the observable considered and the M →∞ limit is to be taken in the end. Applications to the random-field Ising model and to the Sherrington-Kirkpatrick model are discussed.
Ionic Hamiltonians for transition metal atoms: effective exchange coupling and Kondo temperature
Flores, F.; Goldberg, E. C.
2017-02-01
An ionic Hamiltonian for describing the interaction between a metal and a d-shell transition metal atom having an orbital singlet state is introduced and its properties analyzed using the Schrieffer-Wolf transformation (exchange coupling) and the poor man’s scaling method (Kondo temperature). We find that the effective exchange coupling between the metal and the atom has an antiferromagnetic or a ferromagnetic interaction depending on the kind of atomic fluctuations, either S\\to S-1/2 or S\\to S+1/2 , associated with the metal-atom coupling. We present a general scheme for all those processes and calculate, for the antiferromagnetic interaction, the corresponding Kondo-temperature.
Replica exchange molecular dynamics simulation of cross-fibrillation of IAPP and PrP106-126.
Chua, Khi Pin; Chew, Lock Yue; Mu, Yuguang
2016-08-01
Aggregation of proteins into amyloid is the central hallmark of a number of protein diseases. Most studies were carried out on the aggregation between proteins of similar species. However, it was observed that some patients with certain protein disease can easily acquire another unrelated protein disease. As such, it is also important to examine aggregation between proteins of different species. Usually aggregation between proteins of the same species can be attributed to the similarity between their respective amino acid sequences. In this article, we were motivated by an experimental study of aggregation between amylin (Islet Amyloid Polypeptide, IAPP) and prion106-126 (PrP106-126) fragment (JACS, 2013, 135, 13582-9). It was found that the two non-homologous peptides can aggregate quickly to form fibrils in the presence of negatively charged lipid bilayer. We attempted to elucidate the molecular mechanism of the early stage of dimerization of these two peptides through extensive replica exchange molecular dynamics simulations. Conformations consisting of various degrees of β-sheets structures, both intra-chain and inter-chain, were found in the simulations. The conformations of the aggregated complex are very diverse, which suggests that the cross-species fibrils formed between the two proteins are highly polymorphic. The driving forces are mainly hydrophobic interactions, including aromatic-aliphatic interactions. The palindromic region of PrP106-126 and SNNFGAIL region of IAPP were found to play important roles in the interaction. Our study sheds insight into the exciting research of protein cross-fibrillation. Proteins 2016; 84:1134-1146. © 2016 Wiley Periodicals, Inc.
Wang, Lang; Wang, Zheng; Jiang, Run; Yin, Yuhua; Li, Baohui
2017-03-15
The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.
Kano, Masayuki; Nagao, Hiromichi; Nagata, Kenji; Ito, Shin-ichi; Sakai, Shin'ichi; Nakagawa, Shigeki; Hori, Muneo; Hirata, Naoshi
2017-04-01
Earthquakes sometimes cause serious disasters not only directly by ground motion itself but also secondarily by infrastructure damage, particularly in densely populated urban areas. To reduce these secondary disasters, it is important to rapidly evaluate seismic hazards by analyzing the seismic responses of individual structures due to the input ground motions. Such input motions are estimated utilizing an array of seismometers that are distributed more sparsely than the structures. We propose a methodology that integrates physics-based and data-driven approaches in order to obtain the seismic wavefield to be input into seismic response analysis. This study adopts the replica exchange Monte Carlo (REMC) method, which is one of the Markov chain Monte Carlo (MCMC) methods, for the estimation of the seismic wavefield together with one-dimensional local subsurface structure and source information. Numerical tests show that the REMC method is able to search the parameters related to the source and the local subsurface structure in broader parameter space than the Metropolis method, which is an ordinary MCMC method. The REMC method well reproduces the seismic wavefield consistent with the true one. In contrast, the ordinary kriging, which is a classical data-driven interpolation method for spatial data, is hardly able to reproduce the true wavefield even at low frequencies. This indicates that it is essential to take both physics-based and data-driven approaches into consideration for seismic wavefield imaging. Then the REMC method is applied to the actual waveforms observed by a dense seismic array MeSO-net (Metropolitan Seismic Observation network), in which 296 accelerometers are continuously in operation with several kilometer intervals in the Tokyo metropolitan area, Japan. The estimated wavefield within a frequency band of 0.10-0.20 Hz is absolutely consistent with the observed waveforms. Further investigation suggests that the seismic wavefield is successfully
Mignon, David; Simonson, Thomas
2016-07-15
Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.
Zanxia Cao; Lei Liu; Ping Wu; Jihua Wang
2011-01-01
The structural and thermodynamics characters of α-syn12 (residues 1-12 of the human α-synuclein protein) peptide in aqueous solution were investigated through temperature replica-exchange molecular dynamics (T-REMD) simulations with the GROMOS 43A1 force field. The two independent T-REMD simulations were completed starting from an initial conformational α-helix and an irregular structure,respectively. Each replica was run for 300ns. The structural and thermodynamics characters were studied based on parameters such as distributions of backbone dihedral angles, free energy surface, stability of folded β-hairpin structure, and favorite conformations. The results showed that the isolated α-syn12 peptide in water adopted four different conformational states: the first state was a β-hairpin ensemble with Turno-6 and four hydrogen bonds, the second state was a β-hairpin ensemble with two turns (Turn9-6 and Turn5-2) and three hydrogen bonds, the third state was a disordered structure with both Turn8-5 and Turn5-2, and the last state was a π-helix ensemble. Meanwhile, we studied the free energy change of α-syn12 peptide from the unfolded state to the β-hairpin state, which was in good agreement with the experiments and molecular dynamics simulations for some other peptides. We also analyzed the driving force of the peptide transition.The results indicated that the driving forces were high solvent exposure of hydrophobic Leu8 and hydrophobic residues in secondary structure. To our knowledge, this was the first report to study the isolated α-syn12 peptide in water by T-REMD.
Osipov, Vladimir Al
2007-01-01
Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.
Tong Zhang
Full Text Available Crystal structures of Thermotoga maritima magnesium transporter CorA, reported in 2006, revealed its homo-pentameric constructions. However, the structure of the highly conserved extracellular interhelical loops remains unsolved, due to its high flexibility. We have explored the configurations of the loops through extensive replica exchange molecular dynamics simulations in explicit solvent model with the presence of either Co(III Hexamine ions or Mg(2+ ions. We found that there are multiple binding sites available on the interhelical loops in which the negatively charged residues, E316 and E320, are located notably close to the positively charged ions during the simulations. Our simulations resolved the distinct binding patterns of the two kinds of ions: Co(III Hexamine ions were found to bind stronger with the loop than Mg(2+ ions with binding free energy -7.3 kJ/mol lower, which is nicely consistent with the previous data. Our study provides an atomic basis description of the initial binding process of Mg(2+ ions on the extracellular interhelical loops of CorA and the detailed inhibition mechanism of Co(III Hexamine ions on CorA ions transportation.
Swadling, Jacob B; Wright, David W; Suter, James L; Coveney, Peter V
2015-03-01
Compared with proteins, the relationship between structure, dynamics, and function of RNA enzymes (known as ribozymes) is far less well understood, despite the fact that ribozymes are found in many organisms and are often conceived as "molecular fossils" of the first self-replicating molecules to have arisen on Earth. To investigate how ribozymal function is governed by structure and dynamics, we study the full hammerhead ribozyme in bulk water and in an aqueous clay mineral environment by computer simulation using replica-exchange molecular dynamics. Through extensive sampling of the major conformational states of the hammerhead ribozyme, we are able to show that the hammerhead manifests a free-energy landscape reminiscent of that which is well known in proteins, exhibiting a "funnel" topology that guides the ribozyme into its globally most stable conformation. The active-site geometry is found to be closely correlated to the tertiary structure of the ribozyme, thereby reconciling conflicts between previously proposed mechanisms for the self-scission of the hammerhead. The conformational analysis also accounts for the differences reported experimentally in the catalytic activity of the hammerhead ribozyme, which is reduced when interacting with clay minerals as compared with bulk water.
De Simone, Alfonso; Derreumaux, Philippe
2010-04-01
The self-assembly of proteins and peptides into amyloid fibrils is connected to over 40 pathological conditions including neurodegenerative diseases and systemic amyloidosis. Diffusible, low molecular weight protein and peptide oligomers that form in the early steps of aggregation appear to be the harmful cytotoxic species in the molecular etiology of these diseases. So far, the structural characterization of these oligomers has remained elusive owing to their transient and dynamic features. We here address, by means of full atomistic replica exchange molecular dynamics simulations, the energy landscape of heptamers of the amyloidogenic peptide NHVTLSQ from the beta-2 microglobulin protein. The simulations totaling 5 μs show that low molecular weight oligomers in explicit solvent consist of β-barrels in equilibrium with amorphous states and fibril-like assemblies. The results, also accounting for the influence of the pH on the conformational properties, provide a strong evidence of the formation of transient β-barrel assemblies in the early aggregation steps of amyloid-forming systems. Our findings are discussed in terms of oligomers cytotoxicity.
Zhou, Chen-Yang; Jiang, Fan; Wu, Yun-Dong
2015-11-10
To test whether our recently developed residue-specific force field RSFF2 can reproduce the mutational effect on the thermal stability of Trp-cage mini-protein and decipher its detailed folding mechanism, we carried out long-time replica-exchange molecular dynamics (REMD) simulations on five Trp-cage variants, including TC5b and TC10b. Initiated from their unfolded structures, the simulations not only well-reproduce their experimental structures but also their melting temperatures and folding enthalpies reasonably well. For each Trp-cage variant, the overall folding free energy landscape is apparently two-state, but some intermediate states can be observed when projected on more detailed coordinates. We also found different variants have the same major folding pathway, including the well formed PII-helix in the unfolded state, the formation of W6-P12/P18/P19 contacts and the α-helix before the transition state, the following formation of most native contacts, and the final native loop formation. The folding mechanism derived here is consistent with many previous simulations and experiments.
Zhang, Tong; Mu, Yuguang
2012-01-01
Crystal structures of Thermotoga maritima magnesium transporter CorA, reported in 2006, revealed its homo-pentameric constructions. However, the structure of the highly conserved extracellular interhelical loops remains unsolved, due to its high flexibility. We have explored the configurations of the loops through extensive replica exchange molecular dynamics simulations in explicit solvent model with the presence of either Co(III) Hexamine ions or Mg(2+) ions. We found that there are multiple binding sites available on the interhelical loops in which the negatively charged residues, E316 and E320, are located notably close to the positively charged ions during the simulations. Our simulations resolved the distinct binding patterns of the two kinds of ions: Co(III) Hexamine ions were found to bind stronger with the loop than Mg(2+) ions with binding free energy -7.3 kJ/mol lower, which is nicely consistent with the previous data. Our study provides an atomic basis description of the initial binding process of Mg(2+) ions on the extracellular interhelical loops of CorA and the detailed inhibition mechanism of Co(III) Hexamine ions on CorA ions transportation.
Gai, Lili; Vogel, Thomas; Maerzke, Katie A; Iacovella, Christopher R; Landau, David P; Cummings, Peter T; McCabe, Clare
2013-08-07
Two different techniques - replica-exchange Wang-Landau (REWL) and statistical temperature molecular dynamics (STMD) - were applied to systematically study the phase transition behavior of self-assembling lipids as a function of temperature using an off-lattice lipid model. Both methods allow the direct calculation of the density of states with improved efficiency compared to the original Wang-Landau method. A 3-segment model of amphiphilic lipids solvated in water has been studied with varied particle interaction energies (ε) and lipid concentrations. The phase behavior of the lipid molecules with respect to bilayer formation has been characterized through the calculation of the heat capacity as a function of temperature, in addition to various order parameters and general visual inspection. The simulations conducted by both methods can go to very low temperatures with the whole system exhibiting well-ordered structures. With optimized parameters, several bilayer phases are observed within the temperature range studied, including gel phase bilayers with frozen water, mixed water (i.e., frozen and liquid water), and liquid water, and a more fluid bilayer with liquid water. The results obtained from both methods, STMD and REWL, are consistently in excellent agreement with each other, thereby validating both the methods and the results.
Gai, Lili; Vogel, Thomas; Maerzke, Katie A.; Iacovella, Christopher R.; Landau, David P.; Cummings, Peter T.; McCabe, Clare
2013-08-01
Two different techniques - replica-exchange Wang-Landau (REWL) and statistical temperature molecular dynamics (STMD) - were applied to systematically study the phase transition behavior of self-assembling lipids as a function of temperature using an off-lattice lipid model. Both methods allow the direct calculation of the density of states with improved efficiency compared to the original Wang-Landau method. A 3-segment model of amphiphilic lipids solvated in water has been studied with varied particle interaction energies (ɛ) and lipid concentrations. The phase behavior of the lipid molecules with respect to bilayer formation has been characterized through the calculation of the heat capacity as a function of temperature, in addition to various order parameters and general visual inspection. The simulations conducted by both methods can go to very low temperatures with the whole system exhibiting well-ordered structures. With optimized parameters, several bilayer phases are observed within the temperature range studied, including gel phase bilayers with frozen water, mixed water (i.e., frozen and liquid water), and liquid water, and a more fluid bilayer with liquid water. The results obtained from both methods, STMD and REWL, are consistently in excellent agreement with each other, thereby validating both the methods and the results.
Ferraro, E.; De Michielis, M.; Fanciulli, M.; Prati, E.
2015-01-01
Double-dot exchange-only qubit represents a promising compromise between high speed and simple fabrication in solid-state implementations. A couple of interacting double-dot exchange-only qubits, each composed by three electrons distributed in a double quantum dot, is exploited to realize controlled-NOT (CNOT) operations. The effective Hamiltonian model of the composite system is expressed by only exchange interactions between pairs of spins. Consequently, the evolution operator has a simple form and represents the starting point for the research of sequences of operations that realize CNOT gates. Two different geometrical configurations of the pair are considered, and a numerical mixed simplex and genetic algorithm is used. We compare the nonphysical case in which all the interactions are controllable from the external and the realistic condition in which intra-dot interactions are fixed by the geometry of the system. In the latter case, we find the CNOT sequences for both the geometrical configurations and we considered a qubit system where electrons are electrostatically confined in two quantum dots in a silicon nanowire. The effects of the geometrical sizes of the nanowire and of the gates on the fundamental parameters controlling the qubit are studied by exploiting a spin-density-functional theory-based simulator. Consequently, CNOT gate performances are evaluated.
Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang
2014-07-17
Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.
Ajamian, John
2016-09-01
The A2 collaboration of the Institute for Nuclear Physics of Johannes Gutenberg University performs research on (multiple) meson photoproduction and nucleon structure and dynamics using a high energy polarized photon beam at specific targets. Particles scattered from the target are detected in the Crystal Ball, or CB. The CB is composed of 672 NaI crystals that surround the target and can analyze particle type and energy of ejected particles. Our project was to create a replica of the CB that could display what was happening in real time on a 3 Dimensional scale replica. Our replica was constructed to help explain the physics to the general public, be used as a tool when calibrating each of the 672 NaI crystals, and to better analyze the electron showering of particles coming from the target. This poster will focus on the hardware steps necessary to construct the replica and wire the 672 programmable LEDS in such a way that they can be mapped to correspond to the Crystal Ball elements. George Washington NSF Grant.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Modular Hamiltonian of Excited States in Conformal Field Theory
Lashkari, Nima
2015-01-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the replica Z_n symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
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.
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of lik
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
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
Replica trick and string winding
Prudenziati, Andrea; Trancanelli, Diego
2017-07-01
We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from nonperturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, in both the open and closed string picture.
Replica trick and string winding
Prudenziati, Andrea
2016-01-01
We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, both in the open and closed string picture.
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.
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir;
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Garrido, L. M.; Pascual, P.
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Replica symmetry breaking for anisotropic magnets with quenched disorder
Kogan, E.; Kaveh, M.
2017-01-01
We study critical behaviour of a magnet with cubic anisotropy and quenched scalar disorder which is taken into account by replica method. We derive to first order in ε approximation the renormalization group equations taking into account possible replica symmetry breaking. We study the stability of the replica symmetric fixed points with respect to perturbations without (in general case) replica symmetry. However, we find that if a fixed point is stable with respect to replica symmetric deviations, it is also stable with respect to deviations without replica symmetry.
Replica symmetric spin glass field theory
Temesvari, T. [Research Group for Theoretical Physics of the Hungarian Academy of Sciences, Eoetvoes University, Pazmany Peter setany 1/A, H-1117 Budapest (Hungary)]. E-mail: temtam@helios.elte.hu
2007-06-18
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d < or approx. 6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Replica symmetric spin glass field theory
Temesvári, T.
2007-06-01
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d≲6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Replica Fourier Transform: Properties and applications
A. Crisanti
2015-02-01
Full Text Available 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.
Two phase decision algorithm of replica allocation
Zuo Chaoshu; Liu Xinsong; Wang Zheng; Li Yi
2006-01-01
In distributed parallel server system, location and redundancy of replicas have great influence on availability and efficiency of the system. In order to improve availahility and efficiency of the system, two phase decision algorithm of replica allocation is proposed. The algorithm which makes use of auto-regression model dynamically predicts the future count of READ and WRITE operation, and then determines location and redundancy of replicas by considering availability, CPU and bands of the network. The algorithm can not only ensure the requirement of availability, but also reduce the system resources consumed by all the operations in a great scale. Analysis and test show that communication complexity and time complexity of the algorithm satisfy O( n ), resource optimizing scale increases with the increase of READ count.
Generalized gravitational entropy without replica symmetry
Camps, Joan; Kelly, William R.
2015-03-01
We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study EinsteinGauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.
Generalized gravitational entropy without replica symmetry
Camps, Joan
2014-01-01
We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study Einstein-Gauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Entangling capacities of noisy non-local Hamiltonians
Bandyopadhyay, S; Bandyopadhyay, Somshubhro; Lidar, Daniel A.
2003-01-01
We show that intrinsic Gaussian fluctuations in system control parameters impose limits on the ability of non-local (exchange) Hamiltonians to generate entanglement in the presence of mixed initial states. We find three equivalence classes. For the Ising and XYZ models there are qualitatively distinct sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Vertices from replica in a random matrix theory
Brezin, E [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond 75231, Paris Cedex 05 (France); Hikami, S [Department of Basic Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo 153 (Japan)
2007-11-09
Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral. In our work we consider the correlation functions of vertices in a Gaussian random matrix theory, with an external matrix source. We deal with operator products of the form <{pi}{sub i=1}{sup n}1/N tr M{sup k{sub i}}>, in a 1/N expansion. For large values of the powers k{sub i}, in an appropriate scaling limit relating large k's to large N, universal scaling functions are derived. Furthermore, we show that the replica method applied to characteristic polynomials of the random matrices, together with a duality exchanging N and the number of points, provides a new way to recover Kontsevich's results on these intersection numbers.
Boltz, J.C. (ed.)
1992-09-01
EXCHANGE is published monthly by the Idaho National Engineering Laboratory (INEL), a multidisciplinary facility operated for the US Department of Energy (DOE). The purpose of EXCHANGE is to inform computer users about about recent changes and innovations in both the mainframe and personal computer environments and how these changes can affect work being performed at DOE facilities.
RRS: Replica Registration Service for Data Grids
Shoshani, Arie; Sim, Alex; Stockinger, Kurt
2005-07-15
Over the last few years various scientific experiments and Grid projects have developed different catalogs for keeping track of their data files. Some projects use specialized file catalogs, others use distributed replica catalogs to reference files at different locations. Due to this diversity of catalogs, it is very hard to manage files across Grid projects, or to replace one catalog with another. In this paper we introduce a new Grid service called the Replica Registration Service (RRS). It can be thought of as an abstraction of the concepts for registering files and their replicas. In addition to traditional single file registration operations, the RRS supports collective file registration requests and keeps persistent registration queues. This approach is of particular importance for large-scale usage where thousands of files are copied and registered. Moreover, the RRS supports a set of error directives that are triggered in case of registration failures. Our goal is to provide a single uniform interface for various file catalogs to support the registration of files across multiple Grid projects, and to make Grid clients oblivious to the specific catalog used.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
Remarks on hamiltonian digraphs
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Massively parallelized replica-exchange simulations of polymers on GPUs
Groß, Jonathan; Bachmann, Michael
2011-01-01
We discuss the advantages of parallelization by multithreading on graphics processing units (GPUs) for parallel tempering Monte Carlo computer simulations of an exemplified bead-spring model for homopolymers. Since the sampling of a large ensemble of conformations is a prerequisite for the precise estimation of statistical quantities such as typical indicators for conformational transitions like the peak structure of the specific heat, the advantage of a strong increase in performance of Monte Carlo simulations cannot be overestimated. Employing multithreading and utilizing the massive power of the large number of cores on GPUs, being available in modern but standard graphics cards, we find a rapid increase in efficiency when porting parts of the code from the central processing unit (CPU) to the GPU.
Novel algorithm for distributed replicas management based on dynamic programming
Wang Tao; Lu Xianliang; Hou Mengshu
2006-01-01
Replicas can improve the data reliability in distributed system. However, the traditional algorithms for replica management are based on the assumption that all replicas have the uniform reliability, which is inaccurate in some actual systems. To address such problem, a novel algorithm is proposed based on dynamic programming to manage the number and distribution of replicas in different nodes. By using Markov model, replicas management is organized as a multi-phase process, and the recursion equations are provided. In this algorithm, the heterogeneity of nodes, the expense for maintaining replicas and the engaged space have been considered. Under these restricted conditions, this algorithm realizes high data reliability in a distributed system. The results of case analysis prove the feasibility of the algorithm.
An Adaptive Replica Allocation Algorithm in Mobile Ad Hoc Networks
JingZheng; JinshuSu; KanYang
2004-01-01
In mobile ad hoc networks (MANET), nodes move freely and the distribution of access requests changes dynamically. Replica allocation in such a dynamic environment is a significant challenge. In this paoer, a dynamic adaptive replica allocation algorithm that can adapt to the nodes motion is proposed to minimize the communication cost of object access. When changes occur in the access requests of the object or the network topology, each replica node collects access requests from its neighbors and makes decisions locally to expand replica to neighbors or to relinquish the replica. The algorithm dynamically adapts the replica allocation scheme to a local optimal one. Simulation results show that our algorithms efficiently reduce the communication cost of object access in MANET environment.
An Arbitrary 2D Structured Replica Control Protocol
Basmadjian, Robert; Meer, Hermann,
2011-01-01
Traditional replication protocols that logically arrange the replicas into a specific structure have reasonable availability, lower communication cost as well as system load than those that do not require any logical organisation of replicas. We propose in this paper the A2DS protocol: a single protocol that, unlike the existing proposed protocols, can be adapted to any 2D structure. Its read operation is carried out on any replica of every level of the structure whereas write operations are ...
Reliability of the impression replica technique.
Falk, Anders; Vult von Steyern, Per; Fransson, Håkan; Thorén, Margareta Molin
2015-01-01
The aim of this study was to evaluate the reliability of the impression replica technique with a four-unit zirconia fixed dental prosthesis (FDP). Marginal and internal fit were measured by repeatedly placing the FDP on an epoxy cast using light-body silicone material corresponding to cement. All measured marginal and internal fit points showed varying values. The greatest variations were seen at the most distal margin (33 μm) and at the distal abutment of the FDP (77 μm). The results showed that the technique gives moderate variations and is a useful method to evaluate marginal and internal fit.
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...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
Fedorenko, A. A.
2003-02-01
A field-theory approach is used to investigate the 'spin-glass effects' on the critical behaviour of systems with weak temperature-like quenched disorder. The renormalization group (RG) analysis of the effective Hamiltonian of a model with replica symmetry breaking (RSB) potentials of a general type is carried out in the two-loop approximation. The fixed point (FP) stability, recently found within the one-step RSB RG treatment, is further explored in terms of replicon eigenvalues. We find that the traditional FPs, which are usually considered to describe the disorder-induced universal critical behaviour, remain stable when the continuous RSB modes are taken into account.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
Spin Glass Field Theory with Replica Fourier Transforms
Pimentel, Iveta R.; De Dominicis, Cirano
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any i-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi's solution for the free-energy of an Ising spin glass.
Fret Replica Inspection Laser Scanner (FRILS)
Kretz, S.; Hanley, K., E-mail: steve.kretz@opg.com, E-mail: kelly.hanley@opg.com [Ontario Power Generation, Inspection Maintenance and Commercial Services, Pickering, Ontario (Canada)
2008-07-01
In the stress analysis of flaws and artifacts found in pressure tubes, it is crucial to have detailed knowledge of the flaw geometry. Fuel channel inspections by ultrasonic or eddy current inspection methods alone cannot provide the complete required geometry information. Replicas, which are a negative impression of surface pressure tube indications, are scanned with a laser system which will provide the additional detail required. FRILS was initially developed in 1993 to establish in-house capability of profiling indications on the inside diameter surface of pressure tubes. The need of this profiling was initially a response to the discovery of fuel bundle bearing pad fretting (FBBPF) caused by flow induced fuel bundle vibration. The benefits of the system were soon realized as a tool for profiling debris type indications. Although the primary use of FRILS is to profile FBBBF and Debris Fretting, since its inception the FRILS inspection system has become an instrumental tool in flaw assessment for: Fuel Bundle Bearing Pad Frets (FBBPF); Debris Frets; Scratches; Crevice Corrosion; Oxide Jacking; Areas of surface roughness; and, Weld Profiling. Replicas are collected via acquisition from tooling on both the Channel and Gauging Apparatus for Reactors (CIGAR) and the Advanced Non-Destructive Examination (ANDE) systems. The ANDE system is a high speed data acquisition system which includes both an ultrasonic inspection tool and a replication tool. Although both of these tools were designed to be delivered with the UDM, the platform for these tools was built with flexibility allowing for adoption to other delivery systems. These tools were based on the experience of the CIGAR inspection system. The CIGAR system has also undergone many system upgrades resulting in reduced inspection times. The FRILS system - Fret Replication Inspection Laser Scanner system was developed and has been upgraded to meet the demands of the improved inspection and replication systems. FRILS
Response Time Optimization for Replica Selection Service in Data Grids
Husni H.E. AL-Mistarihi
2008-01-01
Full Text Available Problem Statement: Data Grid architecture provides a scalable infrastructure for grid services in order to manage data files and their corresponding replicas that were distributed across the globe. The grid services are designed to support a variety of data grid applications (jobs and projects. Replica selection is a high-level service that chooses a replica location from among many distributed replicas with the minimum response time for the users' jobs. Estimating the response time accurately in the grid environment is not an easy task. The current systems expose high response time in selecting the required replicas because the response time is estimated by considering the data transfer time only. Approach: We proposed a replica selection system that selects the best replica location for the users' running jobs in a minimum response time that can be estimated by considering new factors besides the data transfer time, namely, the storage access latency and the replica requests that waiting in the storage queue. Results: The performance of the proposed system was compared with a similar system that exists in the literature namely, SimpleOptimiser. The simulation results demonstrated that our system performed better than the SimpleOptimiser on an average of 6%. Conclusions: The proposed system can select the best replica location in a lesser response time than the SimpleOptimise. The efficiency of the proposed system is 6% higher than the SimpleOptimise. The efficiency level has a high impact on the quality of service that is perceived by grid users in a data grid environment where the data files are relatively big. For example, the data files produced from the scientific applications are of the size hundreds of Terabytes.
Chromatic roots and hamiltonian paths
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
SRF Cavity Surface Topography Characterization Using Replica Techniques
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.
Elastomer and resin replicas for sem observation of metallic materials
Palin-Luc, Thierry; Sellier, E.; D?Errico, F.; Vanhaeren, M.
2002-01-01
International audience; The replica technique is often used to study damage evolution at the surface of specimens or industrial components and understand the physicial phenomena responsible for fatigue crack initiation before failure. Replicas are usually made from acetate cellulose film. This paper presents an alternative technique generally used by archaeologists to study lithic use-wear and bone modification. A mold is made from a dental elastomer (silicon based impression material) and a ...
JavaFIRE: A Replica and File System for Grids
Petek, Marko; da Silva Gomes, Diego; Resin Geyer, Claudio Fernando; Santoro, Alberto; Gowdy, Stephen
2012-12-01
The work is focused on the creation of a replica and file transfers system for Computational Grids inspired on the needs of the High Energy Physics (HEP). Due to the high volume of data created by the HEP experiments, an efficient file and dataset replica system may play an important role on the computing model. Data replica systems allow the creation of copies, distributed between the different storage elements on the Grid. In the HEP context, the data files are basically immutable. This eases the task of the replica system, because given sufficient local storage resources any dataset just needs to be replicated to a particular site once. Concurrent with the advent of computational Grids, another important theme in the distributed systems area that has also seen some significant interest is that of peer-to-peer networks (p2p). P2p networks are an important and evolving mechanism that eases the use of distributed computing and storage resources by end users. One common technique to achieve faster file download from possibly overloaded storage elements over congested networks is to split the files into smaller pieces. This way, each piece can be transferred from a different replica, in parallel or not, optimizing the moments when the network conditions are better suited to the transfer. The main tasks achieved by the system are: the creation of replicas, the development of a system for replicas transfer (RFT) and for replicas location (RLS) with a different architecture that the one provided by Globus and the development of a system for file transfer in pieces on computational grids with interfaces for several storage elements. The RLS uses a p2p overlay based on the Kademlia algorithm.
Injection Compression Molding of Replica Molds for Nanoimprint Lithography
Keisuke Nagato
2014-03-01
Full Text Available As a breakthrough in the cost and durability of molds for nanoimprint lithography (NIL, replica molds are fabricated by injection compression molding (ICM. ICM is commonly used for optical disks such as DVDs or Blu-ray disks and is also a practical fabrication method for nanostructures. In this paper, I successfully demonstrated the fabrication of cycloolefin polymer replica molds with structures smaller than 60 nm by ICM. Furthermore, ultraviolet (UV-NIL using these replica molds was demonstrated. UV-cured resist was replicated over an area of 60 mm diameter. The degree of replication by UV-NIL in the first usage of each replica mold had good repeatability. Because ICM is a high-throughput, low-cost process, the replica mold can be disposed of after a certain time for UV-NIL. This method leads to a high-integrity UV-NIL process of patterned media because multiple large-area replica molds can be fabricated simultaneously.
Bayesian ensemble refinement by replica simulations and reweighting.
Hummer, Gerhard; Köfinger, Jürgen
2015-12-28
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.
On the Reaction Path Hamiltonian
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
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.
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Hamiltonian Structure of PI Hierarchy
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Alternative Hamiltonian representation for gravity
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Hamiltonian analysis of interacting fluids
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Hamiltonian description of the ideal fluid
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Modelling spin Hamiltonian parameters of molecular nanomagnets.
Gupta, Tulika; Rajaraman, Gopalan
2016-07-12
Molecular nanomagnets encompass a wide range of coordination complexes possessing several potential applications. A formidable challenge in realizing these potential applications lies in controlling the magnetic properties of these clusters. Microscopic spin Hamiltonian (SH) parameters describe the magnetic properties of these clusters, and viable ways to control these SH parameters are highly desirable. Computational tools play a proactive role in this area, where SH parameters such as isotropic exchange interaction (J), anisotropic exchange interaction (Jx, Jy, Jz), double exchange interaction (B), zero-field splitting parameters (D, E) and g-tensors can be computed reliably using X-ray structures. In this feature article, we have attempted to provide a holistic view of the modelling of these SH parameters of molecular magnets. The determination of J includes various class of molecules, from di- and polynuclear Mn complexes to the {3d-Gd}, {Gd-Gd} and {Gd-2p} class of complexes. The estimation of anisotropic exchange coupling includes the exchange between an isotropic metal ion and an orbitally degenerate 3d/4d/5d metal ion. The double-exchange section contains some illustrative examples of mixed valance systems, and the section on the estimation of zfs parameters covers some mononuclear transition metal complexes possessing very large axial zfs parameters. The section on the computation of g-anisotropy exclusively covers studies on mononuclear Dy(III) and Er(III) single-ion magnets. The examples depicted in this article clearly illustrate that computational tools not only aid in interpreting and rationalizing the observed magnetic properties but possess the potential to predict new generation MNMs.
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.
Time evolution of the autocorrelation function in dynamical replica theory
Sakata, A.
2013-04-01
Asynchronous dynamics given by the master equation in the Sherrington-Kirkpatrick (SK) spin-glass model is studied based on dynamical replica theory (DRT) with an extension to take into account the autocorrelation function. The dynamical behaviour of the system is approximately described by dynamical equations of the macroscopic quantities: magnetization, energy contributed by randomness and the autocorrelation function. The dynamical equations under the replica symmetry assumption are derived by introducing the subshell equipartitioning assumption and exploiting the replica method. The obtained dynamical equations are compared with Monte Carlo simulations, and it is demonstrated that the proposed formula describes well the time evolution of the autocorrelation function in some parameter regions. The study offers a reasonable description of the autocorrelation function in the SK spin-glass system.
Multiple replica repulsion technique for efficient conformational sampling of biological systems.
Malevanets, Anatoly; Wodak, Shoshana J
2011-08-17
Here, we propose a technique for sampling complex molecular systems with many degrees of freedom. The technique, termed "multiple replica repulsion" (MRR), does not suffer from poor scaling with the number of degrees of freedom associated with common replica exchange procedures and does not require sampling at high temperatures. The algorithm involves creation of multiple copies (replicas) of the system, which interact with one another through a repulsive potential that can be applied to the system as a whole or to portions of it. The proposed scheme prevents oversampling of the most populated states and provides accurate descriptions of conformational perturbations typically associated with sampling ground-state energy wells. The performance of MRR is illustrated for three systems of increasing complexity. A two-dimensional toy potential surface is used to probe the sampling efficiency as a function of key parameters of the procedure. MRR simulations of the Met-enkephalin pentapeptide, and the 76-residue protein ubiquitin, performed in presence of explicit water molecules and totaling 32 ns each, investigate the ability of MRR to characterize the conformational landscape of the peptide, and the protein native basin, respectively. Results obtained for the enkephalin peptide reflect more closely the extensive conformational flexibility of this peptide than previously reported simulations. Those obtained for ubiquitin show that conformational ensembles sampled by MRR largely encompass structural fluctuations relevant to biological recognition, which occur on the microsecond timescale, or are observed in crystal structures of ubiquitin complexes with other proteins. MRR thus emerges as a very promising simple and versatile technique for modeling the structural plasticity of complex biological systems. Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Fractographic ceramic failure analysis using the replica technique
Scherrer, Susanne S.; Quinn, Janet B.; Quinn, George D.; Anselm Wiskott, H. W.
2007-01-01
Objectives To demonstrate the effectiveness of in vivo replicas of fractured ceramic surfaces for descriptive fractography as applied to the analysis of clinical failures. Methods The fracture surface topography of partially failed veneering ceramic of a Procera Alumina molar and an In Ceram Zirconia premolar were examined utilizing gold-coated epoxy poured replicas viewed using scanning electron microscopy. The replicas were inspected for fractographic features such as hackle, wake hackle, twist hackle, compression curl and arrest lines for determination of the direction of crack propagation and location of the origin. Results For both veneering ceramics, replicas provided an excellent reproduction of the fractured surfaces. Fine details including all characteristic fracture features produced by the interaction of the advancing crack with the material's microstructure could be recognized. The observed features are indicators of the local direction of crack propagation and were used to trace the crack's progression back to its initial starting zone (the origin). Drawbacks of replicas such as artifacts (air bubbles) or imperfections resulting from inadequate epoxy pouring were noted but not critical for the overall analysis of the fractured surfaces. Significance The replica technique proved to be easy to use and allowed an excellent reproduction of failed ceramic surfaces. It should be applied before attempting to remove any failed part remaining in situ as the fracture surface may be damaged during this procedure. These two case studies are intended as an introduction for the clinical researcher in using qualitative (descriptive) fractography as a tool for understanding fracture processes in brittle restorative materials and, secondarily, to draw conclusions as to possible design inadequacies in failed restorations. PMID:17270267
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
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.
Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.
2016-02-01
In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
Replica calibration artefacts for optical 3D scanning of micro parts
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...
Data-Replicas Scheduler for Heterogeneous MapReduce Cluster
Yang Yang
2013-05-01
Full Text Available Large scale data processing has rapidly increased in nowadays. MapReduce programming model, which is firstly mentioned in functional languages, appeared in distributed system and perform excellently in large scale data processing since 2006. Hadoop, which is the most popular framework of open-sourced MapReduce runtime environment, supplies reliable, scalable and distributed system processing large scale data across clusters of computers using this virtue programming model. In this system, files are split into many blocks and all blocks are replicated over several computers in clusters. To process these blocks efficiently, each job runs parallel and is divided into many tasks which deals with a file block. In order to fully take advantage of network bandwidth these systems, data locality is paid more and more attentions. Considering the existence of data-replica blocks, we propose a data-replicas scheduler which includes task scheduling and data allocation. The data-replicas scheduler takes fully advantage of data replicas in local Data node, reduce the costs of data transfer and improve the system performance. The results of experiments show that our scheduler not only improves the CPU ratio, but also reduces the packets that transfer in the network.
Replicas in Caravaggio's paintings: the correct use of scientific analysis
Diana, Maurizio; Moioli, Pietro; Seccaroni, Claudio
1998-05-01
Painting techniques and materials employed by Caravaggio are analyzed by X-ray fluorescence and radiography of unquestioned genuine works and compared to replicas of his earlier work. This approach is important in the attribution of recently discovered paintings and copies from the XVII century.
Replica-Based High-Performance Tuple Space Computing
Andric, Marina; De Nicola, Rocco; Lluch Lafuente, Alberto
2015-01-01
We present the tuple-based coordination language RepliKlaim, which enriches Klaim with primitives for replica-aware coordination. Our overall goal is to offer suitable solutions to the challenging problems of data distribution and locality in large-scale high performance computing. In particular,...
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Maslov index for Hamiltonian systems
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Dynamical stability of Hamiltonian systems
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Derivation of Hamiltonians for accelerators
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Geometric Hamiltonian structures and perturbation theory
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
Mouhanna, D.; Tarjus, G.
2010-05-01
We investigate the relation between spontaneous and explicit replica symmetry breaking in the theory of disordered systems. On general ground, we prove the equivalence between the replicon operator associated with the stability of the replica-symmetric solution in the standard replica scheme and the operator signaling a breakdown of the solution with analytic field dependence in a scheme in which replica symmetry is explicitly broken by applied sources. This opens the possibility to study, via the recently developed functional renormalization group, unresolved questions related to spontaneous replica symmetry breaking and spin-glass behavior in finite-dimensional disordered systems.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Hamiltonian dynamics of extended objects
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
On Hamiltonian formulation of cosmologies
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
A Hamiltonian approach to Thermodynamics
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Production and transfer of energy and information in Hamiltonian systems.
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.
Production and transfer of energy and information in Hamiltonian systems.
Antonopoulos, Chris G; Bianco-Martinez, Ezequiel; Baptista, Murilo S
2014-01-01
We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.
ATLAS Replica Management in Rucio: Replication Rules and Subscriptions
Barisits, M; The ATLAS collaboration; Garonne, V; Lassnig, M; Stewart, G; Beermann, T; Vigne, R; Goossens, L; Nairz, A; Molfetas, A
2014-01-01
The ATLAS Distributed Data Management system stores more than 150PB of physics data across 120 sites globally. To cope with the anticipated ATLAS workload of the coming decade, Rucio, the next-generation data management system has been developed. Replica management, as one of the keys aspects of the system, has to satisfy critical performance requirements in order to keep pace with the experiment’s high rate of continual data generation. The challenge lies in meeting these performance objectives while still giving the system users and applications a powerful toolkit to control their data workflows. In this work we present the concept, design and implementation of the replica management in Rucio. We will specifically introduce the workflows behind replication rules, their formal language definition, weighting and site selection. Furthermore we will present the subscription component, which offers functionality for users to proclaim interest in data that has not been created yet. This contribution describes t...
ATLAS Replica Management in Rucio: Replication Rules and Subscriptions
Barisits, M; The ATLAS collaboration; Garonne, V; Lassnig, M; Stewart, G; Beermann, T; Vigne, R; Goossens, L; Nairz, A; Molfetas, A
2013-01-01
The ATLAS Distributed Data Management system stores more than 150PB of physics data across 120 sites globally. To cope with the anticipated ATLAS workload of the coming decade, Rucio, the next-generation data management system has been developed. Replica management, as one of the keys aspects of the system, has to satisfy critical performance requirements in order to keep pace with the experiment’s high rate of continual data generation. The challenge lies in meeting these performance objectives while still giving the system users and applications a powerful toolkit to control their data workflows. In this work we present the concept, design and implementation of the replica management in Rucio. We will specifically introduce the workflows behind replication rules, their formal language definition, weighting and site selection. Furthermore we will present the subscription component, which offers functionality for users to proclaim interest in data that has not been created yet. This contribution describes t...
An adaptive range-query optimization technique with distributed replicas
Sayar Ahmet; Pierce Marlon; Fox C.Geoffrey
2014-01-01
Replication is an approach often used to speed up the execution of queries submitted to a large dataset. A compile-time/run-time approach is presented for minimizing the response time of 2-dimensional range when a distributed replica of a dataset exists. The aim is to partition the query payload (and its range) into subsets and distribute those to the replica nodes in a way that minimizes a client’s response time. However, since query size and distribution characteristics of data (data dense/sparse regions) in varying ranges are not known a priori, performing efficient load balancing and parallel processing over the unpredictable workload is difficult. A technique based on the creation and manipulation of dynamic spatial indexes for query payload estimation in distributed queries was proposed. The effectiveness of this technique was demonstrated on queries for analysis of archived earthquake-generated seismic data records.
Replica symmetry breaking in cold atoms and spin glasses
Rotondo, P.; Tesio, E.; Caracciolo, S.
2015-01-01
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero-field limit the system exactly realizes the Sherrington-Kirkpatrick model. Upon a redefinition of the temperature, the same dynamics is realized in the dispersive, strong-field limit. This regime also gives access to spin-glass observables which can be used to detect replica symmetry breaking.
Replica inference approach to unsupervised multiscale image segmentation.
Hu, Dandan; Ronhovde, Peter; Nussinov, Zohar
2012-01-01
We apply a replica-inference-based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters ("communities" or "solutes") against a background or "solvent." Within our multiresolution approach, we compute information-theory-based correlations among multiple solutions ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations manifest by information theory overlaps. We further employ such information theory measures (such as normalized mutual information and variation of information), thermodynamic quantities such as the system entropy and energy, and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases. Within the solvable phase, transitions between contending solutions (such as those corresponding to segmentations on different scales) may also appear. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed at both zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentations appear within the "easy phase" of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images.
Rash, John E; Kamasawa, Naomi; Davidson, Kimberly G V; Yasumura, Thomas; Pereda, Alberto E; Nagy, James I
2012-06-01
Despite the combination of light-microscopic immunocytochemistry, histochemical mRNA detection techniques and protein reporter systems, progress in identifying the protein composition of neuronal versus glial gap junctions, determination of the differential localization of their constituent connexin proteins in two apposing membranes and understanding human neurological diseases caused by connexin mutations has been problematic due to ambiguities introduced in the cellular and subcellular assignment of connexins. Misassignments occurred primarily because membranes and their constituent proteins are below the limit of resolution of light microscopic imaging techniques. Currently, only serial thin-section transmission electron microscopy and freeze-fracture replica immunogold labeling have sufficient resolution to assign connexin proteins to either or both sides of gap junction plaques. However, freeze-fracture replica immunogold labeling has been limited because conventional freeze fracturing allows retrieval of only one of the two membrane fracture faces within a gap junction, making it difficult to identify connexin coupling partners in hemiplaques removed by fracturing. We now summarize progress in ascertaining the connexin composition of two coupled hemiplaques using matched double-replicas that are labeled simultaneously for multiple connexins. This approach allows unambiguous identification of connexins and determination of the membrane "sidedness" and the identities of connexin coupling partners in homotypic and heterotypic gap junctions of vertebrate neurons.
Beukelaer Herman De
2012-11-01
Full Text Available Abstract Background Sampling core subsets from genetic resources while maintaining as much as possible the genetic diversity of the original collection is an important but computationally complex task for gene bank managers. The Core Hunter computer program was developed as a tool to generate such subsets based on multiple genetic measures, including both distance measures and allelic diversity indices. At first we investigate the effect of minimum (instead of the default mean distance measures on the performance of Core Hunter. Secondly, we try to gain more insight into the performance of the original Core Hunter search algorithm through comparison with several other heuristics working with several realistic datasets of varying size and allelic composition. Finally, we propose a new algorithm (Mixed Replica search for Core Hunter II with the aim of improving the diversity of the constructed core sets and their corresponding generation times. Results Our results show that the introduction of minimum distance measures leads to core sets in which all accessions are sufficiently distant from each other, which was not always obtained when optimizing mean distance alone. Comparison of the original Core Hunter algorithm, Replica Exchange Monte Carlo (REMC, with simpler heuristics shows that the simpler algorithms often give very good results but with lower runtimes than REMC. However, the performance of the simpler algorithms is slightly worse than REMC under lower sampling intensities and some heuristics clearly struggle with minimum distance measures. In comparison the new advanced Mixed Replica search algorithm (MixRep, which uses heterogeneous replicas, was able to sample core sets with equal or higher diversity scores than REMC and the simpler heuristics, often using less computation time than REMC. Conclusion The REMC search algorithm used in the original Core Hunter computer program performs well, sometimes leading to slightly better results
Monte Carlo Hamiltonian: Linear Potentials
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Hamiltonian cosmology in bigravity and massive gravity
Soloviev, Vladimir O
2015-01-01
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María; Głazek, Stanisław D.
2016-07-01
We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
Zhang, Wang; Zhang, Di; Fan, Tongxiang; Ding, Jian; Gu, Jiajun; Guo, Qixin; Ogawa, Hiroshi
2006-09-01
Nano-structured colorful zinc oxide (ZnO) replicas were produced using the wings of the Ideopsis similis butterfly as templates. The ZnO replicas we obtained exhibit iridescence, which was clearly observed under an optical microscope (OM). Field emission scanning electron microscope analysis shows that all the microstructure details are maintained faithfully in the ZnO replica. A computer model was established to simulate the diffraction spectral results, which agreed well with the OM images.
Replica location mechanism in data grid based on ED-Chord
2008-01-01
A peer-to-peer hierarchical replica location mechanism(PRLM)was designed for data grids to provide better load balancing capability and scalability.Global replica indexes of the PRLM are organized based on even distributed Chord(ED-Chord)structure.The locality can optimize queries on local replica indexes of virtual organizations.ED-Chord protocol collects the node identifiers information using a distributed method and assigns optimal identifiers for new nodes to make them more uniformly distributed in the entire identifier space.Theoretical analysis and simulations show that PRLM provides good performance,scalability and load balancing capability for replica location in data grids.
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.
REPLICA ORNSTEIN-ZERNIKE EQUATIONS FOR POSITIONALLY FROZEN HEISENBERG SYSTEMS
E.Lomba
2003-01-01
Full Text Available We present the formulation of the Replica Ornstein-Zernike equations for a model of positionally frozen disordered Heisenberg spin system. The results are obtained for various models, one in which the particle positions correspond to a frozen hard sphere fluid, another system in which the configurations are generated by a random insertion of hard spheres, a system of randomly distributed spins, and finally a system corresponding to a soft sphere fluid quenched at high and low temperatures. We will see that the orientational structure of the spin system is fairly well reproduced by the integral equation which, however, does not correctly account for the critical behaviour.
Implicit variational principle for contact Hamiltonian systems
Wang, Kaizhi; Wang, Lin; Yan, Jun
2017-02-01
We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
A parcel formulation for Hamiltonian layer models
Bokhove, O.; Oliver, M.
2009-01-01
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamilton
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS
QI Zhao-hui(齐朝晖); Alexander P. Seyranian
2002-01-01
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Normal Form for Families of Hamiltonian Systems
Zhi Guo WANG
2007-01-01
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d+1. And some dynamical consequences are obtained.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
Momentum and hamiltonian in complex action theory
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
Square conservation systems and Hamiltonian systems
王斌; 曾庆存; 季仲贞
1995-01-01
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
A Hamiltonian approach to Thermodynamics
Baldiotti, M C; Molina, C
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed ontop of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.
Effective Hamiltonians for Complexes of Unstable Particles
Urbanowski, K
2014-01-01
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \\rightarrow \\infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\\rightarrow \\infty$.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Simulating sparse Hamiltonians with star decompositions
Childs, Andrew M
2010-01-01
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts, this algorithm uses (d^2(d+log* N)||H||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||H||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
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 portfolio and T the length of the time series used to estimate the covariance matrix. At the critical point r = 1 a phase transition is taking place. The out of sample estimation error blows up at this point as 1/(1 - r), independently of the covariance matrix or the expected return, displaying the universality not only of the critical exponent, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.
Generating Scaled Replicas of Real-World Complex Networks
Staudt, Christian L; Safro, Ilya; Gutfraind, Alexander; Meyerhenke, Henning
2016-01-01
Research on generative models plays a central role in the emerging field of network science, studying how statistical patterns found in real networks can be generated by formal rules. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how models can be fitted to an original network to produce a structurally similar replica, and (c) aim for producing much larger networks than the original exemplar. In a comparative experimental study, we find ReCoN often superior to many other state-of-the-art network generation methods. Our design yields a scalable and effective tool for replicating a given network while preserving important properties at both micro- and macroscopic scales and (optionally) scaling the replica by orders of magnitude in size. We recommend ReCoN as a general practical method for creating realistic test data for the enginee...
Wu, Xin-tian
We investigate the replica symmetry breaking (RSB) in m-component ferromagnetic spin systems with a short-range disorder. Using ε-expansion the Landau-Ginzburg Hamiltonian with a RSB quartic interaction term is studied, where ε=4- d, d is the spatial dimension. The differential recursion relations of renormalization group (RG) are derived to the second order of ε. The replicon eigenvalue, which is a simple way to investigate the stability with respect to the continuous RSB modes, is defined. The fixed points and their eigenvalues are obtained. For m mc, we find a stable fixed point, which is not only stable in the one-step RSB subspace but also stable with respect to the continuous RSB. However, it is unphysical. For m> mc only the pure fixed point is physical and stable.
Stöhr, Frederik; Michael-Lindhard, Jonas; Simons, Hugh
2015-01-01
We have used replica molding and large-range atomic force microscopy to characterize the threedimensional shape of high aspect ratio microstructures. Casting inverted replicas of microstructures using polydimethylsiloxane (PDMS) circumvents the inability of AFM probes to measure deep and narrow c...
Finite size corrections in the random energy model and the replica approach
Derrida, Bernard; Mottishaw, Peter
2015-01-01
We present a systematic and exact way of computing finite size corrections for the random energy model, in its low temperature phase. We obtain explicit (though complicated) expressions for the finite size corrections of the overlap functions. In its low temperature phase, the random energy model is known to exhibit Parisi's broken symmetry of replicas. The finite size corrections given by our exact calculation can be reproduced using replicas if we make specific assumptions about the fluctuations (with negative variances!) of the number and sizes of the blocks when replica symmetry is broken. As an alternative we show that the exact expression for the non-integer moments of the partition function can be written in terms of coupled contour integrals over what can be thought of as ‘complex replica numbers’. Parisi's one step replica symmetry breaking arises naturally from the saddle point of these integrals without making any ansatz or using the replica method. The fluctuations of the ‘complex replica numbers’ near the saddle point in the imaginary direction correspond to the negative variances we observed in the replica calculation. Finally our approach allows one to see why some apparently diverging series or integrals are harmless.
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…
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…
Fabrication of free-standing replicas of fragile, laminar, chitinous biotemplates.
Lakhtakia, Akhlesh; Martín-Palma, Raúl J; Motyka, Michael A; Pantano, Carlo G
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.
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Lectures on Hamiltonian Dynamics : Theory and Applications
Benettin, Giancarlo; Kuksin, Sergei
2005-01-01
This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
EXISTENCE OF HAMILTONIAN κ-FACTOR
CAI Maocheng; FANG Qizhi; LI Yanjun
2004-01-01
A Hamiltonian k-factor is a k-factor containing a Hamiltonian cycle. An n/2-critical graph G is a simple graph of order n which satisfies δ(G) ≥ n/2 and δ(G - e) ＜ n/2for any edge e ∈ E(G). Let κ≥ 2 be an integer and G be an n/2-critical graph of even order n ≥ 8κ - 14. It is shown in this paper that for any given Hamiltonian cycle Cexcept that G - C consists of two components of odd orders when κ is odd, G has a k-factor containing C.
Orthogonal separable Hamiltonian systems on T2
无
2007-01-01
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way.
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
Yuqian GUO; Daizhan CHENG
2006-01-01
In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
Algebraic Hamiltonian for Vibrational Spectra of Stibine
HOU Xi-Wen
2004-01-01
@@ An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan,is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.
Indirect quantum tomography of quadratic Hamiltonians
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Dicycle Cover of Hamiltonian Oriented Graphs
Khalid A. Alsatami
2016-01-01
Full Text Available A dicycle cover of a digraph D is a family F of dicycles of D such that each arc of D lies in at least one dicycle in F. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.
Improved Sufficient Conditions for Hamiltonian Properties
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
An integrable case of the p + ip pairing Hamiltonian interacting with its environment
Lukyanenko, Inna; Isaac, Phillip S.; Links, Jon
2016-02-01
We consider a generalization of the p + ip pairing Hamiltonian, with external interaction terms of a particular form. These terms allow for the exchange of particles between the system and its environment. As a result the {u}(1) symmetry associated with conservation of particle number, present in the p + ip Hamiltonian, is broken. Nonetheless the generalized model is integrable. We establish integrability using the boundary quantum inverse scattering method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe ansatz equations, the roots of which parametrize the exact solution for the energy spectrum.
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.
Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions
Charbonneau, Patrick; Yaida, Sho
2017-05-01
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon—the Gardner transition—has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, du=6 . Here, we obtain evidence for the existence of these transitions in d
Searching near-replicas of images via clustering
Chang, Edward Y.; Li, Chen; Wang, James Z.; Mork, Peter; Wiederhold, Gio
1999-08-01
Internet piracy has been one of the major concerns for Web publishing. In this study we present a system, RIME, that we have prototyped for detecting unauthorized image copying on the WWW. To speed up the copy detection, RIME uses a new clustering/hashing approach that first clusters similar images on adjacent disk cylinders and then builds indexes to access the clusters made in this way. Searching for the replicas of an image often takes just one IO to loop up the location of the cluster containing similar objects and one sequential file IO to read in this cluster. Our experimental results show that RIME can detect images copies both more efficiently and effectively than the traditional content- based image retrieval systems that use tree-like structures to index images. In addition, RIME copes well with image format conversion, resampling, requantization and geometric transformation.
Beyond Virtual Replicas: 3D Modeling and Maltese Prehistoric Architecture
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.
Effective stability for generalized Hamiltonian systems
CONG; Fuzhong; LI; Yong
2004-01-01
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
Spinor-Like Hamiltonian for Maxwellian Optics
Kulyabov D.S.
2016-01-01
Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi; Nielsen, Holger Bech
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
Jacobi fields of completely integrable Hamiltonian systems
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G
2003-03-31
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion.
Polysymplectic Hamiltonian formalism and some quantum outcomes
Giachetta, G; Sardanashvily, G
2004-01-01
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\\beta$-function coincides with the one obtained in an earlier calculation using a different generator.
Hamiltonian cycle problem and Markov chains
Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T
2014-01-01
This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Hamiltonian formulation of guiding center motion
Stern, D. P.
1971-01-01
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
On Hamiltonians Generating Optimal-Speed Evolutions
2008-01-01
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality ...
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel; Wocjan, Pawel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in th...
Minimal realizations of supersymmetry for matrix Hamiltonians
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Hamiltonian Dynamics at Spatial Infinity.
Alexander, Matthew
We employ a projective construction of spatial infinity in four-dimensional spacetimes which are asymptotically flat. In this construction, points of the spatial boundary of the spacetime manifold are identified with congruences of asymptotically parallel spacelike curves that are asymptotically geodesic. It is shown that for this type of construction spatial infinity is represented by a three-dimensional timelike hyperboloid, and that this follows as a consequence of the vacuum Einstein equations. We then construct tensor fields which are defined at spatial infinity, and which embody the information carried by the gravitational field regarding the total mass, linear, and angular momentum of the spacetime. It is shown that these tensor fields must satisfy a set of second order partial differential field equations at spatial infinity. The asymptotic symmetry group implied by the projective construction is examined, and is identified with the Spi group. The field equations satisfied by the tensor fields at spatial infinity can be derived from an action principle, however this action does not appear to be related in any obvious way to the Hilbert-Einstein action of general relativity. Under mappings generated by the Spi group our Lagrangian is left form -invariant, and the corresponding Noether-conserved quantities are examined. It is found that for spacetimes which are stationary or axisymmetric, these conserved quantities are not the limits of the conserved quantities associated with the infinitesimal four-dimensional coordinate transformations. It is shown that using the tensor fields at spatial infinity one can define a set of canonical variables. Further, we show that the "time" derivatives of the configuration variables can be expressed in terms of some of the momentum densities; the remaining momentum densities are constrained. Finally, we construct the Hamiltonian, and examine the transformations generated by it.
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.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
Tokmachev, A. M.; Robb, M. A.
The spin-Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics - valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge-transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin-Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step-by-step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin-Hamiltonian valence bond theory.
Relativistic Hamiltonians and short-range structure of nuclei
Forest, Jun Lu
1998-12-01
This work is divided into two parts. In the first part, short-range structure of deuteron is studied using a nonrelativistic Hamiltonian. The equidensity surfaces for spin projection Ms = 0 distributions are found to be toroidal in shape, while those of Ms = ±1 have dumbbell shapes at large density. The toroidal shapes indicate that the tensor correlations have near maximal strength at the interparticle distance r OPEP) and the second is from boost interaction. The OPEP contribution is reduced by ~15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of ~0.4 (1.9) MeV in 3H (4He) and account for ~1/3 of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.
Hamiltonian Description of Multi-fluid Streaming
Valls, C.; de La Llave, R.; Morrison, P. J.
2001-10-01
The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.
An intuitive Hamiltonian for quantum search
Fenner, S A
2000-01-01
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can ...
Application of Replica Technique and SEM in Accuracy Measurement of Ceramic Crowns
Trifkovic, B.; Budak, I.; Todorovic, A.; Hodolic, J.; Puskar, T.; Jevremovic, D.; Vukelic, D.
2012-01-01
The paper presents a comparative study of the measuring values of the marginal gap related to the ceramic crowns made by dental CAD/CAM system using the replica technique and SEM. The study was conducted using three experimental groups, which consisted of ceramic crowns manufactured by the Cerec CAD/CAM system. The scanning procedure was carried out using three specialized dental 3D digitization systems from the Cerec family - two types of extraoral optical scanning systems and an intraoral optical scanner. Measurements of the marginal gap were carried out using the replica technique and SEM. The comparison of aggregate values of the marginal gap using the replica technique showed a statistically significant difference between the systems. The measured values of marginal gaps of ceramic crowns using the replica technique were significantly lower compared to those measured by SEM. The results indicate that the choice of technique for measuring the accuracy of ceramic crowns influences the final results of investigation.
Laak, J.A.W.M. van der; Dijkman, H.B.P.M.; Pahlplatz, M.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 pre
Rapid prototyping of replica knee implants for in vitro testing
Verjans Mark
2016-09-01
Full Text Available The understanding of the complex biomechanics of the knee is a key for an optimal implant design. To easily investigate the influence of prosthetic designs on knee biomechanics a rapid prototyping workflow for knee implants has been developed and evaluated. Therefore, different manufacturing technologies and post-treatment methods have been examined and overall seven different replica knee implants were manufactured. For evaluation, the manufacturing properties such as surface accuracy and roughness were determined and kinematic behaviour was investigated in a novel knee testing rig. It was carried out that PolyJet-Modelling with a sanded surface resulted in changed kinematic patterns compared to a usual CoCr-UHMWPE implant. However, fused deposition modelling using ABS and subsequent surface smoothening with acetone vapor showed the lowest roughness of the manufactured implants and only minor kinematic differences. For this reason this method constitutes a promising approach towards an optimal implant design for improved patient-satisfaction and long lifetime of the implant. Finally the workflow is not only limited to the knee.
Critiques, replicas and proposals for the New Urbanism Vision
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.
2011-12-01
and Biochemistry , U.S. Army Medical Research Institute of Infectious Diseases, Fort Detrick, Maryland §Computational Sciences and Engineering Branch...of motion of a system with constraints: molecular dynamics of n- alkanes . J. Comput. Phys. 1977, 23, 327–341. (29) Feig, M.; Karanicolas, J.; Brooks, C
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 separate
Replica exchange Monte Carlo simulations of the ising spin glass: Static and dynamic properties
Yucesoy, Burcu
Spin glasses have been the subject of intense study and considerable controversy for decades, and the low-temperature phase of short-range spin glasses is still poorly understood. Our main goal is to improve our understanding in this area and find an answer to the following question: Are there only a single pair or a countable infinity of pure states in the low temperature phase of the EA spin glass? To that aim we first start by introducing spin glasses and provide a brief history of their research, then proceed to describe our method of simulation, the parallel tempering Monte Carlo algorithm. Next, we present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. In order to understand how the parallel tempering algorithm works, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. We examine the correlation between static and dynamic observables for ˜ 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature, and our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape. In the following chapters, the three- and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied again via large scale Monte Carlo simulations at low temperatures, deep within the spin glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. We arrive to the following conclusion: The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states. Finally we present results for several new observables, along with a few preliminary studies and suggestions for future research.
Equivalent Hamiltonians with additional discrete states
Chinn, C.R. (Physics Department, Lawrence Livermore National Laboratory, Livermore, CA (USA)); Thaler, R.M. (Los Alamos National Laboratory, Los Alamos, NM (USA) Department of Physics, Case Western Reserve University, Cleveland, OH (USA))
1991-01-01
Given a particular Hamiltonian {ital H}, we present a method to generate a new Hamiltonian {ital {tilde H}}, which has the same discrete energy eigenvalues and the same continuum phase shifts as {ital H}, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian {ital h}{sub 1}, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Equivalent Hamiltonians with additional discrete states
Chinn, C. R.; Thaler, R. M.
1991-01-01
Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Hamiltonian Dynamics of Cosmological Quintessence Models
Ivanov, Rossen I
2016-01-01
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any pos...
Gravitational surface Hamiltonian and entropy quantization
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
3-state Hamiltonians associated to solvable 33-vertex models
Crampé, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.
2016-09-01
Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang-Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.
Cluster Monte Carlo methods for the FePt Hamiltonian
Lyberatos, A.; Parker, G. J.
2016-02-01
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.
Design of replica bit line control circuit to optimize power for SRAM
Pengjun, Wang; Keji, Zhou; Huihong, Zhang; Daohui, Gong
2016-12-01
A design of a replica bit line control circuit to optimize power for SRAM is proposed. The proposed design overcomes the limitations of the traditional replica bit line control circuit, which cannot shut off the word line in time. In the novel design, the delay of word line enable and disable paths are balanced. Thus, the word line can be opened and shut off in time. Moreover, the chip select signal is decomposed, which prevents feedback oscillations caused by the replica bit line and the replica word line. As a result, the switch power caused by unnecessary discharging of the bit line is reduced. A 2-kb SRAM is fully custom designed in an SMIC 65-nm CMOS process. The traditional replica bit line control circuit and the new replica bit line control circuit are used in the designed SRAM, and their performances are compared with each other. The experimental results show that at a supply voltage of 1.2 V, the switch power consumption of the memory array can be reduced by 53.7%. Project supported by the Zhejiang Provincial Natural Science Foundation of China (No. LQ14F040001), the National Natural Science Foundation of China (Nos. 61274132, 61234002, 61474068), and the K. C. Wong Magna Fund in Ningbo University.
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Effective Hamiltonians for phosphorene and silicene
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.;
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature...
Hamiltonian Dynamics of Protein Filament Formation.
Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J
2016-01-22
We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
Hamiltonian dynamics for complex food webs.
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Hamiltonian adaptive resolution simulation for molecular liquids.
Potestio, Raffaello; Fritsch, Sebastian; Español, Pep; Delgado-Buscalioni, Rafael; Kremer, Kurt; Everaers, Ralf; Donadio, Davide
2013-03-08
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.
Stability of Frustration-Free Hamiltonians
Michalakis, Spyridon
2011-01-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al., on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Hamiltonian theory of guiding-center motion
Cary, John R.; Brizard, Alain J. [Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States) and Tech-X Corporation, Boulder, Colorado 80303 (United States); Department of Chemistry and Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States)
2009-04-15
Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem (hence invariants follow from symmetries), and they preserve the Poincare invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields--something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time
Hamiltonian dynamics of the parametrized electromagnetic field
G., J Fernando Barbero; Villaseñor, Eduardo J S
2015-01-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Hamiltonian dynamics of the parametrized electromagnetic field
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2016-06-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Convergence to equilibrium under a random Hamiltonian.
Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
Silva V, Y. [FIME-UANL, Pedro A. del Alba s/n, Ciudad Universitaria, San Nicolas de los Garza, Nuevo Leon (Mexico); Castillo M, M.T.; Bautista M, J.P. [DRPMZA/INAH. Direccion de Registro Publico de Monumentos y Zonas Arqueologicas, Victoria 110, Copilco El Bajo, 04340 Mexico D.F. (Mexico); Arenas A, J. [IFUNAM, Circuito de la Investigacion Cientifica s/n, Ciudad Universitaria, 04510 Mexico D.F. (Mexico)]. e-mail: ysilva@fisica.unam.mx
2006-07-01
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{sub 6}(PO{sub 4}){sub 4}(OH){sub 8}(H{sub 2}O){sub 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)
An ingenious replica templated from the light trapping structure in butterfly wing scales
Han, Zhiwu; Niu, Shichao; Yang, Meng; Zhang, Junqiu; Yin, Wei; Ren, Luquan
2013-08-01
Although the physical mechanism of light trapping property of butterfly wings is well understood, it remains a challenge to create artificial replicas of these natural functional structures. Here, we synthesized a SiO2 inverse replica of a light trapping structure in butterfly wing scales using a method combining a sol-gel process and subsequent selective etching. First, the reflectance spectrum was taken to measure the reflectivity. Then, FESEM and TEM were used to observe the coupling structure of scales and the replicas. Afterwards, assisted by SEM and TEM data, 3D optimized models of the structures and fabrication process were generated by software. Finally, the parametric comparisons of the morphologies and structures between the original template and the inverse SiO2 replica were carefully conducted, and it was found that the original structures of bio-templates were well inherited by the structures of the inverse replica. This work would open up possibilities for an extensive study of mimicking novel bio-inspired functional materials, and the reported biomimetic technique confirms the feasibility of extending the functional structures in butterfly wings to particular optical devices in the field of space exploration, space equipment, photoelectrical devices and photo-induced sensors.Although the physical mechanism of light trapping property of butterfly wings is well understood, it remains a challenge to create artificial replicas of these natural functional structures. Here, we synthesized a SiO2 inverse replica of a light trapping structure in butterfly wing scales using a method combining a sol-gel process and subsequent selective etching. First, the reflectance spectrum was taken to measure the reflectivity. Then, FESEM and TEM were used to observe the coupling structure of scales and the replicas. Afterwards, assisted by SEM and TEM data, 3D optimized models of the structures and fabrication process were generated by software. Finally, the parametric
Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution
Sudha; B. G. Divyamani; A. R. Usha Devi
2011-01-01
Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically we show that among 4-qubit states obeying exchange symmetry, all states except W class (and their linear combination) lose their symmetry under time evolution with Ising Hamiltonian. Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits, we indicate that all N-qubit states (N ＞ 5) obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.%@@ Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry, all states except W class (and their linear combination) lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits, we indicate that all N-qubit states (N > 5) obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.
Szalay, Viktor
2015-05-07
A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Hamiltonian Approach to the Gribov Problem
Heinzl, T
1996-01-01
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
Edge-disjoint Hamiltonian cycles in hypertournaments
Thomassen, Carsten
2006-01-01
We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Linear Hamiltonian Behaviors and Bilinear Differential Forms
Rapisarda, P.; Trentelman, H.L.
2004-01-01
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study
Discrete variable representation for singular Hamiltonians
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Bifurcations and safe regions in open Hamiltonians
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
Hamiltonian analysis of BHT massive gravity
Blagojević, M
2010-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\\Lambda_0/m^2\
Hamiltonian and self-adjoint control systems
Schaft, A. van der; Crouch, P.E.
1987-01-01
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoin
Hamiltonian constants for several new entire solutions
2008-01-01
Using the Hamiltonian identities and the corresponding Hamilto- nian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
2008-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of p
Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation
Mane, S R
2016-01-01
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi
2011-01-01
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view. In arXiv:1104.3381[quant-ph], introducing a philosophy to keep the analyticity in parameter variables of FPI and defining a modified set of complex conjugate, hermitian conjugates and bras, we have extended $| q >$ and $| p >$ to complex $q$ and $p$ so that we can deal with a complex coordinate $q$ and a complex momentum $p$. After reviewing them briefly, we describe in terms of the newly introduced devices the time development of a $\\xi$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have t...
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems, electromec
The Maslov indices of Hamiltonian periodic orbits
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approa
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
GUO Fu-Kui; ZHANG Yu-Feng
2006-01-01
The Hamiltonian structure of the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratic-form identity.
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Berche, B; Berche, Bertrand; Lopez, Alexander
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.
Assessment of hydro/oleophobicity for shark skin replica with riblets.
Kim, Tae Wan
2014-10-01
The shark skin has a unique skin structure which enables the shark to swim faster and more efficiently due to an intriguing three-dimensional rib pattern. Shark skin has also known as having functional performances such as self cleaning and anti-fouling as well as excellent drag reduction due to a hierarchical structure built up by micro grooves and nano-long chain mucus drag reduction interface around the shark body. In this study, the wetting properties for the biomimetic surfaces that replicate shark skin are assessed. First of all, the shark skin replicas are obtained using the micro molding technique directly from a shark skin template. The quantitative replication precision of the shark skin replicas is evaluated comparing with the geometry of shark skin template using 3D and 2D surface profiles are measured. Then contact angles in the conditions of solid-air-water, solid-air-oil and solid-water-oil interfaces are evaluated for shark skin replicas. The effect of Teflon coating on the wetting properties of shark skin replicas is also observed. The results show the shark skin replica by the micro molding technique gives better effect on the wetting performance, and the micro riblets on shark skin improve the wettability feature.
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
蔡茂诚; 方奇志; 李延军
2003-01-01
A Hamiltonian [k, k + 1]-factor is a [k, k + 1]-factor containing a Hamiltonian cycle. A simple graph G of order n is n/2-critical if δ(G) ≥ n/2 but δ(G - e) ＜ n/2 for any edge e ∈ E(G). Let k ≥ 2 be an integer and G be an n/2-critical graph with n ≥ 4k - 6 and n ≥ 7. In this paper it is proved that for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. This result is an improvement on some recent results about the existence of Hamiltonian [k, k + 1]-factor.%本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性.Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\\e)＜n/2(对任意的e∈E(G)),则称G为n/2-临界图.设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子.该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Hamiltonian Approach To Dp-Brane Noncommutativity
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
Hamiltonian approach to hybrid plasma models
Tronci, Cesare
2010-01-01
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.
ON THE ELUSIVENESS OF HAMILTONIAN PROPERTY
高随祥
2001-01-01
Decision tree complexity is an important measure of computational complexity. A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set. Let P be a graph property on n vertices, if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case, then it is said that the decision tree complexity of P is k. If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case, then P is said to be elusive. Karp conjectured that every nontrivial monotone graph property is elusive. This paper concerns the elusiveness of Hamiltonian property. It is proved that if n=p+1, pq or pq+1, (where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
A Hamiltonian Formulation of Topological Gravity
Waelbroeck, Henri
2009-01-01
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.
Quantum Hamiltonian complexity and the detectability lemma
Aharonov, Dorit; Landau, Zeph; Vazirani, Umesh
2010-01-01
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint satisfaction (such as SAT), with the additional ingredient of multi-particle entanglement. This additional ingredient of course makes generalizations of celebrated theorems such as the PCP theorem from classical to the quantum domain highly non-trivial; it also raises entirely new questions such as bounds on entanglement and correlations in ground states, and in particular area laws. We propose a simple combinatorial tool that helps to handle such questions: it is a simplified, yet more general version of the detectability lemma introduced by us in the more restricted context on quantum gap amplification a year ago. Here, we argue that this lemma is applicable in much more general contexts. We use it to provide a simplified and more combinatorial proof of Hastings' 1D area law...
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.
Hamiltonian partial differential equations and applications
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Hamiltonian hierarchy and the Hulthen potential
Gönül, B
2000-01-01
We deal with the Hamiltonian hierarchy problem of the Hulth\\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulth\\'{e}n potential which gives satisfactory values for the non-zero angular momentum states.
Hamiltonian theory of guiding-center motion
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
Monte Carlo Hamiltonian:Inverse Potential
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Spectral analysis of tridiagonal Fibonacci Hamiltonians
Yessen, William
2011-01-01
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Gauge symmetry enhancement in Hamiltonian formalism
Hong, S T; Lee, T H; Oh, P; Oh, Phillial
2003-01-01
We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.
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.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, Guang Hao; Chuang, Isaac L.
2017-01-01
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Reinforcement learning for port-hamiltonian systems.
Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D
2015-05-01
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, Makoto; Chua, Leon
In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.
Nickel replicas as calibration reference standards for industrial surface texture instruments
Sammatini-Malberg, Maria-Pia
The present report is a documentation of measurements carried out at DTU on Nickel replicas. The research is performed in the frame of the project with contract SMT4-CT97-2176 with title: Calibration Standards for Surface Topography Measuring Systems down to Nanometric Scale.......The present report is a documentation of measurements carried out at DTU on Nickel replicas. The research is performed in the frame of the project with contract SMT4-CT97-2176 with title: Calibration Standards for Surface Topography Measuring Systems down to Nanometric Scale....
Baruffi, Federico; Parenti, Paolo; Cacciatore, Francesco
2017-01-01
the replica molding technology. The method consists of obtaining a replica of the feature that is inaccessible for standard measurement devices and performing its indirect measurement. This paper examines the performance of a commercial replication media applied to the indirect measurement of micromilled...
Avram, C. N.; Gruia, A. S.; Brik, M. G.; Barb, A. M.
2015-12-01
Calculations of the Cr3+ energy levels, spin-Hamiltonian parameters and vibrational spectra for the layered CrCl3 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 Cr3+ ion in CrCl3 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.
Spin Hamiltonian of hyper-kagome Na{sub 4}Ir{sub 3}O{sub 8}.
Micklitz, T.; Norman, M. R.; Materials Science Division; Freie Univ.
2010-01-01
We derive the spin Hamiltonian for the quantum spin liquid Na{sub 4}Ir{sub 3}O{sub 8}, and then estimate the direct and superexchange contributions between near neighbor iridium ions using a tight-binding parametrization of the electronic structure. We find a magnitude of the exchange interaction comparable to experiment for a reasonable value of the on-site Coulomb repulsion. For one of the two tight-binding parametrizations we have studied, the direct exchange term, which is isotropic, dominates the total exchange. This provides support for those theories proposed to describe this quantum spin liquid that assume an isotropic Heisenberg model.
Visualizing the zero order basis of the spectroscopic Hamiltonian.
Barnes, George L; Kellman, Michael E
2012-01-14
Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.
Hamiltonian realization of power system dynamic models and its applications
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hamiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
Nickel replicas as calibration reference standards for industrial surface texture instruments
Sammatini-Malberg, Maria-Pia
The present report is a documentation of measurements carried out at DTU on Nickel replicas. The research is performed in the frame of the project with contract SMT4-CT97-2176 with title: Calibration Standards for Surface Topography Measuring Systems down to Nanometric Scale....
Investigation of the Airflow inside Realistic and Semi-Realistic Replicas of Human Airways
Lizal Frantisek
2015-01-01
Full Text Available Measurement of velocity in human lungs during breathing cycle is a challenging task for researchers, since the measuring location is accessible only with significant difficulties. A special measuring rig consisting of optically transparent replica of human lungs, breathing simulator, particle generator and Laser-Doppler anemometer was developed and used for investigation of the velocity in specific locations of lungs during simulated breathing cycle. Experiments were performed on two different replicas of human lungs in corresponding measuring points to facilitate the analysis of the influence of the geometry and its simplification on the flow. The analysis of velocity course and turbulence intensity revealed that special attention should be devoted to the modelling of vocal cords position during breathing, as the position of laryngeal jet created by vocal cords significantly influences velocity profiles in trachea. The shapes of velocity courses during expiration proved to be consistent for both replicas; however magnitudes of peak expiratory velocity differ between the corresponding measuring points in both the replicas.
Fast Optimal Replica Placement with Exhaustive Search Using Dynamically Reconfigurable Processor
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.
Proton radius puzzle in Hamiltonian dynamics
Glazek, Stanislaw D
2014-01-01
Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue equations with the effective Coulomb potential that exhibits a tiny sensitivity to the characteristic momentum-scale of the bound system. The scale dependence is shown to be relevant to the theoretical interpretation of precisely measured lepton-proton bound-state energy levels in terms of a 4 percent difference between the proton radii in muon-proton and electron-proton bound states.
Linear representation of energy-dependent Hamiltonians
Znojil, Miloslav
2004-05-01
Quantum mechanics abounds in models with Hamiltonian operators which are energy-dependent. A linearization of the underlying Schrödinger equation with H= H( E) is proposed here via an introduction of a doublet of separate energy-independent representatives K and L of the respective right and left action of H( E). Both these new operators are non-Hermitian so that our formalism admits a natural extension to non-Hermitian initial H( E)s. Its applicability may range from pragmatic phenomenology and variational calculations (where all the subspace-projected effective operators depend on energy by construction) up to perturbation theory and quasi-exact constructions.
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Dyson--Schwinger Approach to Hamiltonian QCD
Campagnari, Davide R; Huber, Markus Q; Vastag, Peter; Ebadati, Ehsan
2016-01-01
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
Enumeration of Hamiltonian Cycles in 6-cube
Deza, Michel
2010-01-01
Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43 in Section 7.2.1.1 of Knuth's ' The Art of Computer Programming'; various proposed estimates are surveyed below. We computed exact value: H6=14,754,666,508,334,433,250,560=6*2^4*217,199*1,085,989*5,429,923. Also the number Aut6 of those cycles up to automorphisms of 6-cube was computed as 147,365,405,634,413,085
Hamiltonian analysis of BHT massive gravity
Blagojević, M.; Cvetković, B.
2011-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants ( Λ 0, m 2), our canonical analysis reveals the special role of the condition Λ 0/ m 2 ≠ -1. In this sector, the dimension of the physical phase space is found to be N ∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.
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
Statistical mechanics of Hamiltonian adaptive resolution simulations.
Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K
2015-02-14
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
The quantization of the Rabi Hamiltonian
Vandaele, Eva R. J.; Arvanitidis, Athanasios; Ceulemans, Arnout
2017-03-01
The Rabi Hamiltonian addresses the proverbial paradigmatic case of a two-level fermionic system coupled to a single bosonic mode. It is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which rationalize the spectrum by relating the solutions to the Juddian baselines. The relationship with Braak’s integrability claim (Braak 2011 Phys. Rev. Lett. 107 100401) is discussed.
Quantum Hamiltonian Identification from Measurement Time Traces
Zhang, Jun; Sarovar, Mohan
2014-08-01
Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.
Connecting orbits for families of Tonelli Hamiltonians
Mandorino, Vito
2011-01-01
We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the time-one maps of a family of Tonelli Hamiltonians. Such systems are known as 'polysystems' or 'iterated function systems'. When specialized to families of twist maps on the cylinder, our results are similar to those obtained by Moeckel [20] and Le Calvez [15]. Our approach is based on weak KAM theory and is close to the one used by Bernard in [3] to study the case of a single Tonell...
Hamiltonian BF theory and projected Borromean Rings
Contreras, Ernesto; Leal, Lorenzo
2011-01-01
It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consists on finding the Hamiltonian on-shell of the theory coupled to external sources with support on curves and points in the spatial plane. We explicitly calculate a non-trivial invariant that could be seen as a "projection" of the Milnor's link invariant MU(1; 2; 3), and as such, it measures the entanglement of generalized (or projected) Borromeans Rings in the Euclidean plane.
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure—in doing so we try to bring together various fundamental concepts...
Nonabelian N=2 Superstrings: Hamiltonian Structure
Isaev, A P
2009-01-01
We examine the Hamiltonian structure of nonabelian N=2 superstrings 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 choices of the background.
Subsystem's dynamics under random Hamiltonian evolution
Vinayak,
2011-01-01
We study time evolution of a subsystem's density matrix under a unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian. We exactly calculate all coherences, purity and fluctuations. The reduced density matrix is described in terms of a noncentral correlated Wishart ensemble. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.
New approaches to generalized Hamiltonian realization of autonomous nonlinear systems
王玉振; 李春文; 程代展
2003-01-01
The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally,this paper proposes several sufficient conditions for feedback dissipative realization.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
On Hamiltonian realization of time-varying nonlinear systems
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Equivalence of two sets of deformed Calogero-Moser Hamiltonians
Gorbe, T F
2015-01-01
The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BC(n) Ruijsenaars-Schneider-van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found.
Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion
Larsson, Jonas
1986-02-01
Kruskal's asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal's theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L¯) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L¯+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ɛ, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper.
Hamiltonian Cycles in Regular 2-Connected Claw-Free Graphs
李明楚
2003-01-01
A known result by Jackson Bill is that every 2-connected k-regular graph on at most 3k vertices is Hamiltonian. In this paper,it is proved that every 2-connected k-regular claw-free graph on at most 5k(k≥10)vertices is Hamiltonian. Moreover, the bound 5k is best possible. A counterexample of a 2-connected k-regular claw-free non-Hamiltonian graph on 5k+1 vertices is given, and it is conjectured that every 3-connected k-regular claw-free graph on at most 12k-7 vertices is Hamiltonian.
Hamiltonian description of closed configurations of the vacuum magnetic field
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru [National Research Centre Kurchatov Institute (Russian Federation)
2015-05-15
Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.
Covariant hamiltonian spin dynamics in curved space–time
D' Ambrosi, G., E-mail: gdambros@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Satish Kumar, S., E-mail: satish@lorentz.leidenuniv.nl [Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands); Holten, J.W. van, E-mail: t32@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands)
2015-04-09
The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space–time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern–Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
Covariant hamiltonian spin dynamics in curved space-time
d'Ambrosi, G; van Holten, J W
2015-01-01
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
How is Lorentz invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-07-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
How is Lorentz Invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-01-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
A New Scheme of Integrability for (bi)Hamiltonian PDE
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
2016-10-01
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
Position-dependent mass quantum Hamiltonians: general approach and duality
Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.
2016-03-01
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.
Hamiltonian realization of power system dynamic models and its applications
MA Jin; MEI ShengWei
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hemiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
Darboux transformations of the Jaynes-Cummings Hamiltonian
Samsonov, B F; Samsonov, Boris F; Negro, Javier
2004-01-01
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schr\\"odinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
Bagarello, Fabio
2011-01-01
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\\dagger]=0$ and $x^\\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
Solutions of the Bohr Hamiltonian, a compendium
Fortunato, L.
2005-10-01
The Bohr Hamiltonian, also called collective Hamiltonian, is one of the cornerstones of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V(β,γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ-unstable and γ-stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.
Historical Hamiltonian Dynamics: symplectic and covariant
Lachieze-Rey, M
2016-01-01
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field theories on space-time. It is based on the notion of (Hamiltonian) histories, which are sections of the (extended) phase space bundle. It is developed in the space of sections, in contradistinction with the usual formalism which works in the bundle manifold. In field theories, the formalism remains covariant and does not require a spitting of space-time. It considers space-time exactly in the same manner than time in usual dynamics, both being particular cases of the evolution domain. It applies without modification when the histories (the fields) are forms rather than scalar functions, like in electromagnetism or in tetrad general relativity. We develop a differential calculus in the infinite dimensional space of histories. It admits a (generalized) symplectic form which d...
Dirac Hamiltonian with superstrong Coulomb field
Voronov, B L; Tyutin, I V
2006-01-01
We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist for charge values exceeding the so-called critical charge with Z=137 based on the fact that the standard expression for energy eigenvalues yields complex values at overcritical charges. We show that from the mathematical standpoint, there is no problem in defining a self-adjoint Hamiltonian for any value of charge. What is more, the transition through the critical charge does not lead to any qualitative changes in the mathematical description of the system. A specific feature of overcritical charges is the nonuniqueness of the self-adjoint Hamiltonian, but this nonuniqueness is also characteristic for charge values less than the critical one (and larger than the subcritical charge with Z=118). We present the spectra and (generalized) eigenfunctions for all self-adjoint Hamilt...
A Hamiltonian Five-Field Gyrofluid Model
Keramidas Charidakos, Ioannis; Waelbroeck, Francois; Morrison, Philip
2015-11-01
Reduced fluid models constitute versatile tools for the study of multi-scale phenomena. Examples include magnetic islands, edge localized modes, resonant magnetic perturbations, and fishbone and Alfven modes. Gyrofluid models improve over Braginskii-type models by accounting for the nonlocal response due to particle orbits. A desirable property for all models is that they not only have a conserved energy, but also that they be Hamiltonian in the ideal limit. Here, 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 electron and ion densities, the parallel component of ion and electron velocities and ion temperature. Quasineutrality and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to 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. This work was funded by U.S. DOE Contract No. DE-FG02-04ER-54742.
Cluster Monte Carlo methods for the FePt Hamiltonian
Lyberatos, A., E-mail: lyb@materials.uoc.gr [Materials Science and Technology Department, P.O. Box 2208, 71003 Heraklion (Greece); Parker, G.J. [HGST, A Western Digital Company, 3403 Yerba Buena Road, San Jose, CA 95135 (United States)
2016-02-15
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen–Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L1{sub 0}-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium. - Highlights: • A new cluster Monte Carlo algorithm was applied to FePt nanoparticles. • Magnetic anisotropy imposes a restriction on cluster moves. • Inclusion of Metropolis steps is required to satisfy ergodicity. • In the critical region a percolating cluster occurs for any grain size. • Critical slowing down is not solved by the new cluster algorithms.
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
Györgyi, G.
2001-02-01
In this article we review the framework for spontaneous replica symmetry breaking. Subsequently that is applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron, i.e., simple perceptron. It is shown that in the neuron problem, the general formula that is at the core of all problems admitting Parisi's replica symmetry breaking ansatz with a one-component order parameter appears. The details of Parisi's method are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and the Green function technique is introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The Green function of the Fokker-Planck equation due to Sompolinsky turns out to play the role of the statistical mechanical Green function in the graph rules for replica correlators. The subsequently obtained graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x( q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them is one similar to the Parisi phase in long-range interaction spin glasses. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the
New relativistic Hamiltonian: the angular magnetoelectric coupling
Paillard, Charles; Mondal, Ritwik; Berritta, Marco; Dkhil, Brahim; Singh, Surendra; Oppeneer, Peter M.; Bellaiche, Laurent
2016-10-01
Spin-Orbit Coupling (SOC) is a ubiquitous phenomenon in the spintronics area, as it plays a major role in allowing for enhancing many well-known phenomena, such as the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, the Rashba effect, etc. However, the usual expression of the SOC interaction ħ/4m2c2 [E×p] • σ (1) where p is the momentum operator, E the electric field, σ the vector of Pauli matrices, breaks the gauge invariance required by the electronic Hamiltonian. On the other hand, very recently, a new phenomenological interaction, coupling the angular momentum of light and magnetic moments, has been proposed based on symmetry arguments: ξ/2 [r × (E × B)] M, (2) with M the magnetization, r the position, and ξ the interaction strength constant. This interaction has been demonstrated to contribute and/or give rise, in a straightforward way, to various magnetoelectric phenomena,such as the anomalous Hall effect (AHE), the anisotropic magnetoresistance (AMR), the planar Hall effect and Rashba-like effects, or the spin-current model in multiferroics. This last model is known to be the origin of the cycloidal spin arrangement in bismuth ferrite for instance. However, the coupling of the angular momentum of light with magnetic moments lacked a fundamental theoretical basis. Starting from the Dirac equation, we derive a relativistic interaction Hamiltonian which linearly couples the angular momentum density of the electromagnetic (EM) field and the electrons spin. We name this coupling the Angular MagnetoElectric (AME) coupling. We show that in the limit of uniform magnetic field, the AME coupling yields an interaction exactly of the form of Eq. (2), thereby giving a firm theoretical basis to earlier works. The AME coupling can be expressed as: ξ [E × A] • σ (3) with A being the vector potential. Interestingly, the AME coupling was shown to be complementary to the traditional SOC, and together they restore the gauge invariance of the
Symmetry and reduction in implicit generalized Hamiltonian systems
Blankenstein, G.; Schaft, van der A.J.
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this a
Symmetry and Reduction in Implicit Generalized Hamiltonian Systems
Blankenstein, G.; Schaft, A.J. van der
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding conserved quantities. Main features
Non-self-adjoint hamiltonians defined by Riesz bases
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.
HAMILTONIAN DECOMPOSITION OF COMPLETE BIPARTITE r-HYPERGRAPHS
吉日木图; 王建方
2001-01-01
In [1] the concepts of paths and cycles of a hypergraph were introduced. In this paper, we give the concepts for bipartite hypergraph and Hamiltonian paths and cycles of a hypergraph,and prove that the complete bipartite 3-hypergraph with q vertices in each part is Hamiltonian decomposable where q is a prime.
A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION
丰建文; 陈士华
2001-01-01
This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.
THE HAMILTONIAN SYSTEMS OF THE LCZ HIERARCHY BY NONLINEARIZATION
Li Lu
2000-01-01
In this paper, we first search for the Hamiltonian structure of LCZ hierarchy by use of a trace identity. Then we determine a higher-order constraint condition between the potentials and the eigenfunctions of the LCZ spectral problem, and under this constraint condition, the Lax pairs of LCZ hierarchy are all nonlinearized into the finite-dimensional integrable Hamiltonian systems in Liouville sense.
Integrability and Non-integrability of Hamiltonian Normal Forms
Verhulst, Ferdinand
2015-01-01
This paper summarizes the present state of integrability of Hamiltonian normal forms and it aims at characterizing non-integrable behaviour in higher-dimensional systems. Non-generic behaviour in Hamiltonian systems can be a sign of integrability, but it is not a conclusive indication. We will discu
A SUFFICIENT CONDITION FOR HAMILTONIAN CYCLES IN BIPARTITE TOURNAMENTS
无
2007-01-01
In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W(n - 3), then T is Hamiltonian, except for four exceptional graphs. This result is shown to be best possible in a sense.
Bifurcations in Hamiltonian systems with a reflecting symmetry
Bosschaert, M.; Hanssmann, H.
2011-01-01
A reflecting symmetry q 7→ −q of a Hamiltonian system does not leave the symplectic structure dq∧dp invariant and is therefore usually asso- ciated with a reversible Hamiltonian system. However, if q 7→ −q leads to H 7→ −H, then the equations of motion are invariant under the re- flection. This impo
Quantum System Identification: Hamiltonian Estimation using Spectral and Bayesian Analysis
Schirmer, S G
2009-01-01
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available.
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.
Distributed port-Hamiltonian formulation of infinite dimensional systems
Macchelli, Alessandro; Schaft, van der Arjan J.; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-va
Distributed Port-Hamiltonian Formulation of Innite Dimensional Systems
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-va
Port controlled Hamiltonian representation of distributed parameter systems
Maschke, B.M.; van der Schaft, Arjan
2000-01-01
A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. This port controlled
Port-Hamiltonian approach to deployment on a line
Vos, Ewoud; Scherpen, Jacquelien M.A.; van der Schaft, Abraham
2012-01-01
In this talk we present a port-Hamiltonian approach to the deployment on a line of a robotic sensor network (see e.g. [3] for related work). Using the port-Hamiltonian modelling framework has some clear benefits. Including physical interpretation of the model, insight in the system’s energy and
On the minimization of Hamiltonians over pure Gaussian states
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Port-Hamiltonian approach to deployment on a line
Vos, Ewoud; Scherpen, Jacquelien M.A.; van der Schaft, Abraham
2012-01-01
In this talk we present a port-Hamiltonian approach to the deployment on a line of a robotic sensor network (see e.g. [3] for related work). Using the port-Hamiltonian modelling framework has some clear benefits. Including physical interpretation of the model, insight in the system’s energy and stru
The Group of Hamiltonian Automorphisms of a Star Product
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.
A Quantum Algorithm for the Hamiltonian NAND Tree
Farhi, E; Gutmann, S
2007-01-01
We give a quantum algorithm for the NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt(N)*sqrt(logN). We also show a lower bound of sqrt(N) for the NAND tree problem in the Hamiltonian oracle model.
Nonperturbative light-front Hamiltonian methods
Hiller, J R
2016-01-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, $\\phi^4$ theory, ordinary Yukawa theory, supersymmetric Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations...
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.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Using Hamiltonian control to desynchronize Kuramoto oscillators
Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo
2017-02-01
Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.
Hamiltonian description of composite fermions: Magnetoexciton dispersions
Murthy, Ganpathy
1999-11-01
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in fractional quantum hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the ν=13, 25, and 37 gapped fractions, and find approximate agreement with numerical results. I also analyze the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 25 and 37, and it is shown that the spin-polarized 25 state, in contrast to the spin-polarized 13 state, cannot be described as a simple quantum ferromagnet.
Hamiltonian formalism and path entropy maximization
Davis, Sergio; González, Diego
2015-10-01
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.
Weak Hamiltonian, CP Violation and Rare Decays
Buras, Andrzej J
1998-01-01
These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dimensions of operators and anomalous dimension matrices. We elaborate on the renormalzation scheme and renormalization scale dependences and their cancellations in physical amplitudes. In particular we discuss the issue of gamma-5 in D-dimensions and the role of evanescent operators in the calculation of two-loop anomalous dimensions. We present an explicit calculation of the 6 times 6 one-loop anomalous dimension matrix involving current-current and QCD-penguin operators and we give some hints how to properly calculate two-loop anomalous dimensions of these operators. In the phenonomenological part of these lectures we discuss in detail: CKM matrix, the unitarity triangle and its determination, two-body non-leptonic...
Geometric solitons of Hamiltonian flows on manifolds
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.
Nonperturbative light-front Hamiltonian methods
Hiller, J. R.
2016-09-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
Boundary Liouville Theory: Hamiltonian Description and Quantization
Harald Dorn
2007-01-01
Full Text Available The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator $e^varphi$ in terms of free field exponentials is constructed in the hyperbolic sector.
Entanglement Concentration with Quantum Non Demolition Hamiltonians
Tatham, Richard
2011-01-01
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
Mixing properties of stochastic quantum Hamiltonians
Onorati, E; Kliesch, M; Brown, W; Werner, A H; Eisert, J
2016-01-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathema...
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Action and Index Spectra and Periodic Orbits in Hamiltonian Dynamics
Ginzburg, Viktor L
2008-01-01
The main theme of this paper is the connection between the existence of infinitely many periodic orbits for a Hamiltonian system and the behavior of its action or index spectrum under iterations. We use the action and index spectra to show that any Hamiltonian diffeomorphism of a closed, rational manifold with zero first Chern class has infinitely many periodic orbits and that, for a general rational manifold, the number of geometrically distinct periodic orbits is bounded from below by the ratio of the minimal Chern number and half of the dimension. These generalizations of the Conley conjecture follow from another result proved here asserting that a Hamiltonian diffeomorphism with a symplectically degenerate maximum on a closed rational manifold has infinitely many periodic orbits. We also show that for a broad class of manifolds and/or Hamiltonian diffeomorphisms the minimal action--index gap remains bounded for some infinite sequence of iterations and, as a consequence, whenever a Hamiltonian diffeomorphi...
Remarks on the Lagrangian representation of bi-Hamiltonian equations
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David
2015-01-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradski ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David; Noui, Karim
2016-07-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian $H_s$, which is a matrix written in a basis that depend on the scale (or size) parameter $s$. The effective Hamiltonians $H_s$ and the (regularized) canonical Hamiltonian $H_{0}$ are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
How could the replica method improve accuracy of performance assessment of channel coding?
Kabashima, Yoshiyuki
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.
Beyond Storage Capacity in a Single Model Neuron: Continuous Replica Symmetry Breaking
Györgyi, G.; Reimann, P.
2000-10-01
A single McCulloch-Pitts neuron, that is, the simple perceptron is studied, with focus on the region beyond storage capacity. It is shown that Parisi's hierarchical ansatz for the overlap matrix of the synaptic couplings with so called continuous replica symmetry breaking is a solution, and as we propose it is the exact one, to the equilibrium problem. We describe some of the most salient features of the theory and give results about the low temperature region. In particular, the basics of the Parisi technique and the way to calculate thermodynamical expectation values is explained. We have numerically extremized the replica free energy functional for some parameter settings, and thus obtained the order parameter function, i.e., the probability distribution of overlaps. That enabled us to evaluate the probability density of the local stability parameter. We also performed a simulation and found a local stability density closer to the theoretical curve than previous numerical results were.
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.
Kaivarainen, A
2001-01-01
The original mechanism of bivacuum mediated Mind-Matter and Mind-Mind interaction, proposed here, is based on the following stages of long term efforts: New dynamic models of bivacuum, sub-elementary particles and corpuscle-wave [C-W] duality, as a background of Superunification; New Hierarchic theory of liquids and solids; New Hierarchic model of elementary act of consciousness; Virtual Replica (VR)of matter, including living organisms, in bivacuum; The distant resonant [Mind-Bivacuum-Matter] and [Mind-Bivacuum-Mind] interaction, mediated by Bivacuum oscillation (BvO, accompanied by virtual particles/antiparticles pressure oscillation. The latter factor is related to oscillation of vacuum permittivity and permeability. The virtual replica (VR) of condensed matter (living organisms in private case), may influence the properties of virtual pressure of bivacuum in following manner: 1) changing the amplitude of virtual pressure waves (VPW) in-phase with Bivacuum oscillations (BvO). This factor is dependent on fr...
Wu-hwan Jong
2013-11-01
Full Text Available We proved a parameterized KAM theorem in Hamiltonian system which has differentiable Hamiltonian without action-angle coordinates. It is a generalization of the result of [20] that deals with real analytic Hamiltonians.
Quantum control by means of hamiltonian structure manipulation.
Donovan, A; Beltrani, V; Rabitz, H
2011-04-28
A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians
Patel, Apoorva; Priyadarsini, Anjani
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.
PHYSICAL DISABILITY, STIGMA, AND PHYSICAL ACTIVITY IN CHILDREN: A REPLICA STUDY
Gebhardt, Markus; MORA Julio G.; SCHWAB Susanne
2016-01-01
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 w...
Impact of Channel Estimation Errors on Multiuser Detection via the Replica Method
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.
Karakaya, S; Sengun, A; Ozer, F
2005-06-01
This study was aimed at investigating the internal adaptation of a ceramic (Ceramco II) and two composite resin inlay materials (SureFil and 3M Filtek Z 250) using silicon replica technique as an indicator. Forty-five standard mesial-occlusal-distal (MOD) cavities were prepared into brass moulds by using computer numerically controlled system. Inlays were prepared according to manufacturers' instructions with indirect methods. Replicas of the prepared cavities and inlays were produced with a polyvinyl siloxane material (Elite H-D). The spaces between inlays and cavities were filled by different coloured light-body polyvinyl siloxane material. Two parallel slices (mesio-distally) were obtained from the replicas with a sharp blade. Different coloured polyvinyl siloxane material thickness between cavity and inlay was measured at seven points (mesial, occlusal and distal). The data were evaluated with anova and Tukey's honestly significantly different (HSD) statistical tests. In the SureFil and Ceramco II groups, the sizes of the contraction gaps at mesial and distal gingival floors were greater than that of the occlusal marginal walls. In comparison of gap formation at occlusal regions, while the 3M composite group showed highest gap values (204.33 +/- 75.45 microm), the Ceramco II group revealed the lowest (141.17 +/- 23.66 microm) (P 0.05). In conclusion, our results showed that ceramic inlays did not confer any big advantage for internal adaptation over the composite inlays.
Recent advances in fabrication of monolayer colloidal crystals and their inverse replicas
YE XiaoZhou; QI LiMin
2014-01-01
Monolayer colloidal crystals（MCCs）are two-dimensional（2D）colloidal crystals consisting of a monolayer of monodisperse colloidal particles arrayed with a 2D periodic order.In recent years,MCCs have attracted intensive interest because they can act as 2D photonic crystals and be used as versatile templates for fabrication of various 2D nanostructure arrays.In this review,we provide an overview of the recent progress in the controllable fabrication of MCCs and their inverse replicas.First,some newly-developed methods for the self-assembly of MCCs based on different strategies including interfacial assembly and convective assembly are introduced.Second,some representative novel methods regarding the fabrication of various functional2D inverse replicas of MCCs,such as 2D arrays of nanobowls,nanocaps,and hollow spheres,as well as 2D monolayer inverse opals（MIOs）,are described.In addition,the potential applications of MCCs and their inverse replicas are discussed.
Characterization of Nb SRF cavity materials by white light interferometry and replica techniques
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).
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.
Tabrizi, Shadan Ghassemi; Arbuznikov, Alexei V; Kaupp, Martin
2016-05-10
A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.
An effective Hamiltonian approach to quantum random walk
Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti
2017-03-01
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 Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.
Unconstrained Hamiltonian formulation of low energy QCD
Pavel Hans-Peter
2014-04-01
Full Text Available Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case. The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons, and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate
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