Variational Transition State Theory
Truhlar, Donald G. [Univ. of Minnesota, Minneapolis, MN (United States)
2016-09-29
This is the final report on a project involving the development and applications of variational transition state theory. This project involved the development of variational transition state theory for gas-phase reactions, including optimized multidimensional tunneling contributions and the application of this theory to gas-phase reactions with a special emphasis on developing reaction rate theory in directions that are important for applications to combustion. The development of variational transition state theory with optimized multidimensional tunneling as a useful computational tool for combustion kinetics involved eight objectives.
Variational transition state theory
Truhlar, D.G.
1986-01-01
This project is concerned with the development and applications of generalized transition state theory and multidimensional tunneling approximations to chemical reaction rates. They have developed and implemented several practical versions of variational transition state theory (VTST), namely canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (μVT). They have also developed and implemented several accurate multidimensional semiclassical tunneling approximations, the most accurate of which are the small-curvature semiclassical adiabatic (SCSA), large-curvature version-3 (LC3), and least-action (LA) approximations. They have applied the methods to thermal rate constants, using transmission coefficients based on ground-state tunneling, and they have also presented and applied adiabatic and diabatic extensions to calculated rate constants for vibrationally excited reactants. Their general goal is to develop accurate methods for calculating chemical reaction rate constants that remain practical even for reasonably complicated molecules. The approximations mentioned above yield rate constants for systems whose potential energy surface is known or assumed. Thus a second, equally important aspect of their work is the determination or modeling, semi-empirically and/or from electronic structure calculations, of potential energy surfaces
Variational transition-state theory
Truhlar, D.G.; Garrett, B.C.
1980-01-01
A general introduction to and some results from studies of a procedure called variational transition-state theory are presented. A fundamental assumption of this theory is that the net rate of forward reaction at equilibrium equals the equilibrium flux in the product direction through the transition state where the transition state is a surface in phase space dividing reactants from products. Classical generalized-transition-state-theory calculations for nine collinear systems are compared to classical trajectory calculations. This new technique should provide useful insight into the successes and failures of the conventional theory and useful quantitative estimates of possible errors on the predictions of conventional transition-state theory. This should also contribute to a more accurate theory now available for the practical calculations of chemical reaction rates and thermochemical and structural interpretations of rate processes
Berezhkovskii, Alexander M.; Frishman, Anatoli M.; Pollak, Eli
1994-09-01
Variational transition state theory (VTST) is applied to the study of the activated escape of a particle trapped in a multidimensional potential well and coupled to a heat bath. Special attention is given to the dependence of the rate constant on the friction coefficients in the case of anisotropic friction. It is demonstrated explicitly that both the traditional as well as the nontraditional scenarios for the particle escape are recovered uniformly within the framework of VTST. Effects such as saddle point avoidance and friction dependence of the activation energy are derived from VTST using optimized planar dividing surfaces.
Variational transition-state theory. Progress report, February 1981-January 1983
Truhlar, D.G.
1983-01-01
During the past two years we have extended the variational transition-state theory in several ways. Especially notable is that we have developed several new methods for calculating tunneling probabilities, including two general techniques applicable to systems with small and large reaction-path curvature. We have tested these methods successfully against accurate quantal calculations, and we have applied them to real systems in three dimensions. We have also developed general algorithms for variational transition state theory calculations on polyatomic systems and we have applied these to the combustion reaction OH + H 2 → H 2 O + H. We have developed and successfully applied a statistical-diabatic theory for state-selected rates. We made a totally ab initio prediction of an absolute chemical reaction rate, for the reaction Mu + H 2 → MuH + H, using an accurate potential energy surface and ethods that we had demonstrated to be reliable by tests against accurate quantal collinear results. This prediction has now been confirmed by unpublished experiments; I believe that this is the first reliable ab initio prediction of a chemical rection rate prior to its measurement. In the rest of this technical progress report we give further details of these and other studies we have carried out in the last two years under this contract
Bao, Junwei Lucas; Zheng, Jingjing; Truhlar, Donald G
2016-03-02
Pressure-dependent reactions are ubiquitous in combustion and atmospheric chemistry. We employ a new calibration procedure for quantum Rice-Ramsperger-Kassel (QRRK) unimolecular rate theory within a chemical activation mechanism to calculate the pressure-falloff effect of a radical association with an aromatic ring. The new theoretical framework is applied to the reaction of H with toluene, which is a prototypical reaction in the combustion chemistry of aromatic hydrocarbons present in most fuels. Both the hydrogen abstraction reactions and the hydrogen addition reactions are calculated. Our system-specific (SS) QRRK approach is adjusted with SS parameters to agree with multistructural canonical variational transition state theory with multidimensional tunneling (MS-CVT/SCT) at the high-pressure limit. The new method avoids the need for the usual empirical estimations of the QRRK parameters, and it eliminates the need for variational transition state theory calculations as a function of energy, although in this first application we do validate the falloff curves by comparing SS-QRRK results without tunneling to multistructural microcanonical variational transition state theory (MS-μVT) rate constants without tunneling. At low temperatures, the two approaches agree well with each other, but at high temperatures, SS-QRRK tends to overestimate falloff slightly. We also show that the variational effect is important in computing the energy-resolved rate constants. Multiple-structure anharmonicity, torsional-potential anharmonicity, and high-frequency-mode vibrational anharmonicity are all included in the rate computations, and torsional anharmonicity effects on the density of states are investigated. Branching fractions, which are both temperature- and pressure-dependent (and for which only limited data is available from experiment), are predicted as a function of pressure.
Tejero, Ismael; Gonzalez-García, Núria; Gonzalez-Lafont, Angels; Lluch, José M
2007-05-09
The catechol functionality present in the catechins is responsible for the protective effects exerted by green tea against a wide range of human diseases. High-level electronic structure calculations and canonical variational transition-state theory including multidimensional tunneling corrections have allowed us to understand the key factors of the antioxidant effectiveness of the catechol group. This catechol group forms two hydrogen bonds with the two oxygen atoms of the lipid peroxyl radical, leading to a very compact reactant complex. This fact produces an extremely narrow adiabatic potential-energy profile corresponding to the hydrogen abstraction by the peroxyl radical, which makes it possible for a huge tunneling contribution to take place. So, quantum-mechanical tunneling highly increases the corresponding rate constant value, in such a way that catechins become able to trap the lipid peroxyl radicals in a dominant competition with the very damaging free-radical chain-lipid peroxidation reaction.
Bao, Junwei Lucas; Zhang, Xin
2016-01-01
Bond dissociation is a fundamental chemical reaction, and the first principles modeling of the kinetics of dissociation reactions with a monotonically increasing potential energy along the dissociation coordinate presents a challenge not only for modern electronic structure methods but also for kinetics theory. In this work, we use multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) to compute the high-pressure limit dissociation rate constant of tetrafluoroethylene (C2F4), in which the potential energies are computed by direct dynamics with the M08-HX exchange correlation functional. To treat the pressure dependence of the unimolecular rate constants, we use the recently developed system-specific quantum Rice–Ramsperger–Kassel theory. The calculations are carried out by direct dynamics using an exchange correlation functional validated against calculations that go beyond coupled-cluster theory with single, double, and triple excitations. Our computed dissociation rate constants agree well with the recent experimental measurements. PMID:27834727
Ramírez-Anguita, Juan M; González-Lafont, Àngels; Lluch, José M
2011-07-30
The chemical tropospheric dimethyl sulfide (DMS, CH3SCH3) degradation involves several steps highly dependent on the environmental conditions. So, intensive efforts have been devoted during the last years to enhance the understanding of the DMS oxidation mechanism under different conditions. The reaction of DMS with OH is considered to be the most relevant process that initiates the whole oxidation process. The experimental observations have been explained by a two-channel mechanism consisting of a H-abstraction process leading to CH3S(O)CH3 and HO2 and an addition reaction leading to the DMS·OH adduct. In the presence of O2, the DMS·OH adduct is competitively scavenged increasing the contribution of the addition channel to the overall DMS oxidation. Recent experimental measurements have determined from a global fit that the rate constant of this scavenging process is independent of pressure and temperature but this rate constant cannot be directly measured. In this article, a variational transition-state theory calculation of the low- and high-pressure rate constants for the reaction between DMS·OH and O2 has been carried out as a function of temperature. Our proposal is that the slight temperature dependence of the scavenging rate constant can only be explained if the H-abstraction bottleneck is preceded by a dynamical bottleneck corresponding to the association process between the DMS·OH adduct and the O2 molecule. The agreement between the low-pressure and high-pressure rate constants confirms the experimental observations. Copyright © 2011 Wiley Periodicals, Inc.
Transition state theory for enzyme kinetics
Truhlar, Donald G.
2015-01-01
This article is an essay that discusses the concepts underlying the application of modern transition state theory to reactions in enzymes. Issues covered include the potential of mean force, the quantization of vibrations, the free energy of activation, and transmission coefficients to account for nonequilibrium effect, recrossing, and tunneling. PMID:26008760
Zhang, Hui; Zhang, Xin; Truhlar, Donald G; Xu, Xuefei
2017-11-30
The reaction between H and benzene is a prototype for reactions of radicals with aromatic hydrocarbons. Here we report calculations of the reaction rate constants and the branching ratios of the two channels of the reaction (H addition and H abstraction) over a wide temperature and pressure range. Our calculations, obtained with an accurate potential energy surface, are based on variational transition-state theory for the high-pressure limit of the addition reaction and for the abstraction reaction and on system-specific quantum Rice-Ramsperger-Kassel theory calibrated by variational transition-state theory for pressure effects on the addition reaction. The latter is a very convenient way to include variational effects, corner-cutting tunneling, and anharmonicity in falloff calculations. Our results are in very good agreement with the limited experimental data and show the importance of including pressure effects in the temperature interval where the mechanism changes from addition to abstraction. We found a negative temperature effect of the total reaction rate constants at 1 atm pressure in the temperature region where experimental data are missing and accurate theoretical data were previously missing as well. We also calculated the H + C 6 H 6 /C 6 D 6 and D + C 6 H 6 /C 6 D 6 kinetic isotope effects, and we compared our H + C 6 H 6 results to previous theoretical data for H + toluene. We report a very novel nonmonotonic dependence of the kinetic isotope effect on temperature. A particularly striking effect is the prediction of a negative temperature dependence of the total rate constant over 300-500 K wide temperature ranges, depending on the pressure but generally in the range from 600 to 1700 K, which includes the temperature range of ignition in gasoline engines, which is important because aromatics are important components of common fuels.
Vibrational nonadiabaticity and tunneling effects in transition state theory
Marcus, R.A.
1979-01-01
The usual quantum mechanical derivation of transition state theory is a statistical one (a quasi-equilibrium is assumed) or dynamical. The typical dynamical one defines a set of internal states and assumes vibrational adiabaticity. Effects of nonadiabaticity before and after the transition state are included in the present derivation, assuming a classical treatment of the reaction coordinate. The relation to a dynamical derivation of classical mechanical transition state theory is described, and tunneling effects are considered
A Quantum Version of Wigner's Transition State Theory
Schubert, R.; Waalkens, H.; Wiggins, S.
A quantum version of a recent realization of Wigner's transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in (h) over bar. This leads to an explicit
A Quantum Version of Wigner’s Transition State Theory
Schubert, R.; Waalkens, H.; Wiggins, S.
2009-01-01
A quantum version of a recent realization of Wigner’s transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in ħ. This leads to an explicit algorithm to
Quantifying the limits of transition state theory in enzymatic catalysis.
Zinovjev, Kirill; Tuñón, Iñaki
2017-11-21
While being one of the most popular reaction rate theories, the applicability of transition state theory to the study of enzymatic reactions has been often challenged. The complex dynamic nature of the protein environment raised the question about the validity of the nonrecrossing hypothesis, a cornerstone in this theory. We present a computational strategy to quantify the error associated to transition state theory from the number of recrossings observed at the equicommittor, which is the best possible dividing surface. Application of a direct multidimensional transition state optimization to the hydride transfer step in human dihydrofolate reductase shows that both the participation of the protein degrees of freedom in the reaction coordinate and the error associated to the nonrecrossing hypothesis are small. Thus, the use of transition state theory, even with simplified reaction coordinates, provides a good theoretical framework for the study of enzymatic catalysis. Copyright © 2017 the Author(s). Published by PNAS.
Transition-state theory predicts clogging at the microscale
Laar, T. Van De; Klooster, S. Ten; Schroën, K.; Sprakel, J.
2016-06-01
Clogging is one of the main failure mechanisms encountered in industrial processes such as membrane filtration. Our understanding of the factors that govern the build-up of fouling layers and the emergence of clogs is largely incomplete, so that prevention of clogging remains an immense and costly challenge. In this paper we use a microfluidic model combined with quantitative real-time imaging to explore the influence of pore geometry and particle interactions on suspension clogging in constrictions, two crucial factors which remain relatively unexplored. We find a distinct dependence of the clogging rate on the entrance angle to a membrane pore which we explain quantitatively by deriving a model, based on transition-state theory, which describes the effect of viscous forces on the rate with which particles accumulate at the channel walls. With the same model we can also predict the effect of the particle interaction potential on the clogging rate. In both cases we find excellent agreement between our experimental data and theory. A better understanding of these clogging mechanisms and the influence of design parameters could form a stepping stone to delay or prevent clogging by rational membrane design.
Garrett, B.C.; Truhlar, D.G.
1979-01-01
Canonical variational transition state theory, microcanonical variational transition state theory, and Miller's unified statistical theory were used in an attempt to correct two major deficiencies of the conventional transition state theory. These are: (1) the necessity of extra assumptions to include quantum mechanical tunneling effects and (2) the fundamental assumption that trajectories crossing a dividing surface in phase space proceed directly to products. The accuracy of these approximate methods were tested by performing calculations for several collinear reactions of hydrogen, deuterium, chlorine, or iodine, with five isotopes of hydrogen molecules and comparison of these results with those from accurate quantitative calculations of the reaction probabilities as functions of energy and of the thermal rate constants as functions of temperature. 49 references, 28 figures, 17 tables
Garrett, B.C.; Truhlar, D.G.; Grev, R.S.
1981-01-01
Accurate classical dynamical fixed-energy reaction probabilities and fixed-temperature rate constants are calculated for the collinear reaction H + FH on a low-barrier model potential energy surface. The calculations cover energies from 0.1 to 100 kcal/mol above threshold and temperatures of 100 to 10,000 K. The accurate results are used to test five approximate theories: conventional transition-state theory (TST), canonical variational theory (CVT), improved canonical variational theory (ICVT), microcanonical variational theory (μVT), and the unified statistical model (US). The first four of these theories involve a single dividing surface in phase space, and the US theory involves three dividing surfaces. The tests are particularly interesting because the potential energy surface has two identical saddle points. At temperatures from 100 to 2000 K, the μVt is the most accurate theory, with errors in the range 11 to 14%; for temperatures from 2000 to 10,000 K, the US theory is the most successful, with errors in the range 3 to 14%. Over the whole range, a factor of 100 in temperature, both theories have errors of 35% or less. Even TST has errors of 47% or less over the whole factor-of-100 temperature range. Although the US model should become exact at threshold for this system, it already underestimates the reaction probability by a factor of 0.64 at 0.1 kcal/mol above threshold. TST and μVT agree with each other within 12% up to an energy 13 kcal/mol above the saddle point energy. 3 figures, 2 tables
Jain, Amber; Herman, Michael F; Ouyang, Wenjun; Subotnik, Joseph E
2015-10-07
We provide an in-depth investigation of transmission coefficients as computed using the augmented-fewest switches surface hopping algorithm in the low energy regime. Empirically, microscopic reversibility is shown to hold approximately. Furthermore, we show that, in some circumstances, including decoherence on top of surface hopping calculations can help recover (as opposed to destroy) oscillations in the transmission coefficient as a function of energy; these oscillations can be studied analytically with semiclassical scattering theory. Finally, in the spirit of transition state theory, we also show that transmission coefficients can be calculated rather accurately starting from the curve crossing point and running trajectories forwards and backwards.
Comparison of 3D Classical Trajectory and Transition-State Theory Reaction Cross Sections
Koeppl, G. W.; Karplus, Martin
1970-10-01
Although there is excellent agreement for a system such as H+H{sub 2} --> H{sub 2}+H, in which both the potential and the particle masses are symmetric, significant deviations occur for more asymmetric reactions. A detailed analysis show that the calculated differences are from the violation of two assumptions of transition-state theory.
Wigner's dynamical transition state theory in phase space : classical and quantum
Waalkens, Holger; Schubert, Roman; Wiggins, Stephen
We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs
Thermal isomerization of azobenzenes: on the performance of Eyring transition state theory
Rietze, Clemens; Titov, Evgenii; Lindner, Steven; Saalfrank, Peter
2017-08-01
The thermal Z\\to E (back-)isomerization of azobenzenes is a prototypical reaction occurring in molecular switches. It has been studied for decades, yet its kinetics is not fully understood. In this paper, quantum chemical calculations are performed to model the kinetics of an experimental benchmark system, where a modified azobenzene (AzoBiPyB) is embedded in a metal-organic framework (MOF). The molecule can be switched thermally from cis to trans, under solvent-free conditions. We critically test the validity of Eyring transition state theory for this reaction. As previously found for other azobenzenes (albeit in solution), good agreement between theory and experiment emerges for activation energies and activation free energies, already at a comparatively simple level of theory, B3LYP/6-31G* including dispersion corrections. However, theoretical Arrhenius prefactors and activation entropies are in qualitiative disagreement with experiment. Several factors are discussed that may have an influence on activation entropies, among them dynamical and geometric constraints (imposed by the MOF). For a simpler model—Z\\to E isomerization in azobenzene—a systematic test of quantum chemical methods from both density functional theory and wavefunction theory is carried out in the context of Eyring theory. Also, the effect of anharmonicities on activation entropies is discussed for this model system. Our work highlights capabilities and shortcomings of Eyring transition state theory and quantum chemical methods, when applied for the Z\\to E (back-)isomerization of azobenzenes under solvent-free conditions.
Transition state theory approach to polymer escape from a one dimensional potential well.
Mökkönen, Harri; Ikonen, Timo; Ala-Nissila, Tapio; Jónsson, Hannes
2015-06-14
The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.
Experimental and theoretical examples of the value and limitations of transition state theory
Golden, D.M.
1979-01-01
Value and limitations of transition-state theory (TST) are reviewed. TST analyses of the temperature dependence of the ''direct'' reactions CH 3 + CH 3 CHO → CH 4 + CH 3 CO (1) and O + CH 4 → OH + CH 3 (2) are presented in detail, and other examples of TST usefulness are recalled. Limitations are discussed for bimolecular processes in terms of ''complex'' vs ''direct'' mechanisms. The reaction OH + CO → CO 2 + H is discussed in this context. Limitations for unimolecular processes seem to arise only for simple bond fission processes, and recent advances are noted. 2 figures, 5 tables
Experimental and theoretical examples of the value and limitations of transition state theory
Golden, D. M.
1979-01-01
Value and limitations of transition-state theory (TST) are reviewed. TST analyses of the temperature dependence of the 'direct' reactions CH3 + CH3CHO yields CH4 + CH3CO(1) and O + CH4 yields OH + CH3(2) are presented in detail, and other examples of TST usefulness are recalled. Limitations are discussed for bimolecular processes in terms of 'complex' vs. 'direct' mechanisms. The reaction OH + CO yields CO2 + H is discussed in this context. Limitations for unimolecular processes seem to arise only for simple bond fission processes, and recent advances are noted.
Jain, Amber; Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu [Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pennsylvania 19104 (United States)
2015-10-07
We investigate a simple approach to compute a non-adiabatic thermal rate constant using the fewest switches surface hopping (FSSH) dynamics. We study the effects of both decoherence (using our augmented-FSSH (A-FSSH) algorithm) and forbidden hops over a large range of parameters, including high and low friction regimes, and weak and strong electronic coupling regimes. Furthermore, when possible, we benchmark our results against exact hierarchy equations of motion results, where we usually find a maximum error of roughly a factor of two (at reasonably large temperatures). In agreement with Hammes-Schiffer and Tully, we find that a merger of transition state theory and surface hopping can be both accurate and efficient when performed correctly. We further show that detailed balance is followed approximately by A-FSSH dynamics.
Can quantum transition state theory be defined as an exact t = 0+ limit?
Jang, Seogjoo; Voth, Gregory A.
2016-02-01
The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown
Greene, Samuel M., E-mail: samuel.greene@chem.ox.ac.uk; Shan, Xiao, E-mail: xiao.shan@chem.ox.ac.uk; Clary, David C., E-mail: david.clary@chem.ox.ac.u [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)
2016-06-28
Semiclassical Transition State Theory (SCTST), a method for calculating rate constants of chemical reactions, offers gains in computational efficiency relative to more accurate quantum scattering methods. In full-dimensional (FD) SCTST, reaction probabilities are calculated from third and fourth potential derivatives along all vibrational degrees of freedom. However, the computational cost of FD SCTST scales unfavorably with system size, which prohibits its application to larger systems. In this study, the accuracy and efficiency of 1-D SCTST, in which only third and fourth derivatives along the reaction mode are used, are investigated in comparison to those of FD SCTST. Potential derivatives are obtained from numerical ab initio Hessian matrix calculations at the MP2/cc-pVTZ level of theory, and Richardson extrapolation is applied to improve the accuracy of these derivatives. Reaction barriers are calculated at the CCSD(T)/cc-pVTZ level. Results from FD SCTST agree with results from previous theoretical and experimental studies when Richardson extrapolation is applied. Results from our implementation of 1-D SCTST, which uses only 4 single-point MP2/cc-pVTZ energy calculations in addition to those for conventional TST, agree with FD results to within a factor of 5 at 250 K. This degree of agreement and the efficiency of the 1-D method suggest its potential as a means of approximating rate constants for systems too large for existing quantum scattering methods.
A harmonic transition state theory model for defect initiation in crystals
Delph, T J; Cao, P; Park, H S; Zimmerman, J A
2013-01-01
We outline here a model for the initiation of defects in crystals based upon harmonic transition state theory (hTST). This model combines a previously developed model for zero-temperature defect initiation with a multi-dimensional hTST model that is capable of accurately predicting the effects of temperature and loading rate upon defect initiation. The model has several features that set it apart from previous efforts along these lines, most notably a straightforward method of determining the energy barrier between adjacent equilibrium states that does not depend upon a priori information concerning the nature of the defect. We apply the model to two examples, triaxial stretching of a perfect fcc crystal and nanoindentation of a gold substrate. Very good agreement is found between the predictions of the model and independent molecular dynamics (MD) simulations. Among other things, the model predicts a strong dependence of the defect initiation behavior upon the loading parameter. A very attractive feature of this model is that it is valid for arbitrarily slow loading rates, in particular loading rates achievable in the laboratory, and suffers from none of the limitations in this regard inherent in MD simulations. (paper)
Wigner's dynamical transition state theory in phase space: classical and quantum
Waalkens, Holger; Schubert, Roman; Wiggins, Stephen
2008-01-01
We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated
Phillips, M A; Kaplan, A P; Rutter, W J; Bartlett, P A
1992-02-04
A new strategy of potentially broad application for probing transition-state (TS) analogy in enzymatic systems is described in this paper. The degree to which a series of phosphonate inhibitors act as TS analogues of rat carboxypeptidase A1 has been determined for the wild-type enzyme, for the R127K, R127M, and R127A mutants, and for the R127A mutant in the presence of 0.5 M guanidine hydrochloride. The impact that the mutations have on the inverse second-order rate constants (Km/kcat) for substrate hydrolysis is mirrored by the effect on the inhibition constants (Ki) for the corresponding phosphonate inhibitors. These results demonstrate that the phosphonate moiety mimics some of the electronic as well as the geometric characteristics of the TS. A similar but distinctly separate correlation is observed for tripeptide analogues in comparison to analogues of the dipeptide Cbz-Gly-Phe, reflecting an anomalous mode of binding for the latter system. The selective rate increases and corresponding enhancement in inhibitor binding observed on addition of 0.5 M guanidine hydrochloride to the R127A mutant indicate that the exogenous cation can assume the role played by Arg-127 in stabilizing the TS and in providing substrate selectivity at the P2 position.
Greene, Samuel M; Shan, Xiao; Clary, David C
2016-02-28
We investigate which terms in Reduced-Dimensionality Semiclassical Transition State Theory (RD SCTST) contribute most significantly in rate constant calculations of hydrogen extraction and exchange reactions of hydrocarbons. We also investigate the importance of deep tunneling corrections to the theory. In addition, we introduce a novel formulation of the theory in Jacobi coordinates. For the reactions of H atoms with methane, ethane, and cyclopropane, we find that a one-dimensional (1-D) version of the theory without deep tunneling corrections compares well with 2-D SCTST results and accurate quantum scattering results. For the "heavy-light-heavy" H atom exchange reaction between CH3 and CH4, deep tunneling corrections are needed to yield 1-D results that compare well with 2-D results. The finding that accurate rate constants can be obtained from derivatives of the potential along only one dimension further validates RD SCTST as a computationally efficient yet accurate rate constant theory.
Vaz, L.C.; Alexander, J.M.
1983-01-01
Fission angular distributions have been studied for years and have been treated as classic examples of transition-state theory. Early work involving composite nuclei of relatively low excitation energy Esup(*) ( 2 0 (K 2 0 = Psub(eff)T/(h/2π) 2 ) are presented along with comparissons of Psub(eff) to moments of inertia for saddle-point nuclei from the rotating liquid drop model. This model gives an excellent guide for the intermediate spin zone (30 < or approx. I < or approx. 65), while strong shell and/or pairing effects are evident for excitations less than < or approx. 35 MeV. Observations of strong anisotropies for very high-spin systems signal the demise of certain approximations commonly made in the theory, and suggestions are made toward this end. (orig.)
Greene, Samuel M; Shan, Xiao; Clary, David C
2015-12-17
Quantum mechanical methods for calculating rate constants are often intractable for reactions involving many atoms. Semiclassical transition state theory (SCTST) offers computational advantages over these methods but nonetheless scales exponentially with the number of degrees of freedom (DOFs) of the system. Here we present a method with more favorable scaling, reduced-dimensionality SCTST (RD SCTST), that treats only a subset of DOFs of the system explicitly. We apply it to three H abstraction and exchange reactions for which two-dimensional potential energy surfaces (PESs) have previously been constructed and evaluated using RD quantum scattering calculations. We differentiated these PESs to calculate harmonic frequencies and anharmonic constants, which were then used to calculate cumulative reaction probabilities and rate constants by RD SCTST. This method yielded rate constants in good agreement with quantum scattering results. Notably, it performed well for a heavy-light-heavy reaction, even though it does not explicitly account for corner-cutting effects. Recent extensions to SCTST that improve its treatment of deep tunneling were also evaluated within the reduced-dimensionality framework. The success of RD SCTST in this study suggests its potential applicability to larger systems.
Jang, Seogjoo; Voth, Gregory A
2017-05-07
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
Lu, Dahong; Maurice, D.; Truhlar, D.G.
1990-01-01
Variational Transition state theory calculations with semiclassical transmission coefficients have been carried out for a prototype case of α-deuterium secondary kinetic isotope effects (KIEs) in a reaction involving the transformation of an sp 3 carbon to sp 2 , in particular for the reactions of CH 4 and CD 3 H with H and D. The authors also study the KIE for the reverse direction and for the reactions of CH 4 and CD 3 H with D. They find that the variational transition states lead to significantly different nontunneling KIEs than the conventional ones, e.g., 1.22 vs. 1.07, and the inclusion of multidimensional tunneling effects increases the discrepancy even more. The origins of these variations and tunneling effects are examined in detail in terms of structures, vibrational frequencies, and the curvature of the reaction path. The conclusions have wide implications for the validity of conventional treatments of kinetic isotope effects. They predict some particularly large secondary KIEs at low temperature, and these predictions can be tested by future experiments
Variation and Linguistic Theory.
Bailey, Charles-James N.
This volume presents principles and models for describing language variation, and introduces a time-based, dynamic framework for linguistic description. The book first summarizes some of the problems of grammatical description encountered from Saussure through the present and then outlines possibilities for new descriptions of language which take…
Vereecken, Luc; Peeters, Jozef
2003-09-01
The rigorous implementation of transition state theory (TST) for a reaction system with multiple reactant rotamers and multiple transition state conformers is discussed by way of a statistical rate analysis of the 1,5-H-shift in 1-butoxy radicals, a prototype reaction for the important class of H-shift reactions in atmospheric chemistry. Several approaches for deriving a multirotamer TST expression are treated: oscillator versus (hindered) internal rotor models; distinguishable versus indistinguishable atoms; and direct count methods versus degeneracy factors calculated by (simplified) direct count methods or from symmetry numbers and number of enantiomers, where applicable. It is shown that the various treatments are fully consistent, even if the TST expressions themselves appear different. The 1-butoxy H-shift reaction is characterized quantum chemically using B3LYP-DFT; the performance of this level of theory is compared to other methods. Rigorous application of the multirotamer TST methodology in an harmonic oscillator approximation based on this data yields a rate coefficient of k(298 K,1 atm)=1.4×105 s-1, and an Arrhenius expression k(T,1 atm)=1.43×1011 exp(-8.17 kcal mol-1/RT) s-1, which both closely match the experimental recommendations in the literature. The T-dependence is substantially influenced by the multirotamer treatment, as well as by the tunneling and fall-off corrections. The present results are compared to those of simplified TST calculations based solely on the properties of the lowest energy 1-butoxy rotamer.
Ng, Maggie; Mok, Daniel K W; Lee, Edmond P F; Dyke, John M
2013-03-15
The minimum energy path (MEP) of the reaction, CF(3)CHFCF(3) + H → transition state (TS) → CF(3)CFCF(3) + H(2), has been computed at different ab initio levels and with density functional theory (DFT) using different functionals. The computed B3LYP/6-31++G**, BH&HLYP/cc-pVDZ, BMK/6-31++G**, M05/6-31+G**, M05-2X/6-31+G**, UMP2/6-31++G**, PUMP2/6-31++G**//UMP2/6-31++G**, RCCSD(T)/aug-cc-pVDZ//UMP2/6-31++G**, RCCSD(T)/aug-cc-pVTZ(spd,sp)//UMP2//6-31++G**, RCCSD(T)/CBS//M05/6-31+G**, and RCCSD(T)/CBS//UMP2/6-31++G** MEPs, and associated gradients and Hessians, were used in reaction rate coefficient calculations based on the transition state theory (TST). Reaction rate coefficients were computed between 300 and 1500 K at various levels of TST, which include conventional TST, canonical variational TST (CVT) and improved CVT (ICVT), and with different tunneling corrections, namely, Wigner, zero-curvature, and small-curvature (SCT). The computed rate coefficients obtained at different ab initio, DFT and TST levels are compared with experimental values available in the 1000-1200 K temperature range. Based on the rate coefficients computed at the ICVT/SCT level, the highest TST level used in this study, the BH&HLYP functional performs best among all the functionals used, while the RCCSD(T)/CBS//MP2/6-31++G** level is the best among all the ab initio levels used. Comparing computed reaction rate coefficients obtained at different levels of theory shows that, the computed barrier height has the strongest effect on the computed reaction rate coefficients as expected. Variational effects on the computed rate coefficients are found to be negligibly small. Although tunneling effects are relatively small at high temperatures (~1500 K), SCT corrections are significant at low temperatures (~300 K), and both barrier heights and the magnitudes of the imaginary frequencies affect SCT corrections. Copyright © 2012 Wiley Periodicals, Inc.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Periodic-orbit formula for quantum reactions through transition states
Schubert, Roman; Waalkens, Holger; Goussev, Arseni; Wiggins, Stephen
2010-01-01
Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient
Fixed point theory, variational analysis, and optimization
Al-Mezel, Saleh Abdullah R; Ansari, Qamrul Hasan
2015-01-01
""There is a real need for this book. It is useful for people who work in areas of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics.""-Nan-Jing Huang, Sichuan University, Chengdu, People's Republic of China
Variational approach in transport theory
Panta Pazos, R.; Tullio de Vilhena, M.
2004-01-01
In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of a slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method. (authors)
Variational approach in transport theory
Panta Pazos, R. [Nucler Engineering Department, UFRGS, Porto-Alegre (Brazil); Tullio de Vilhena, M. [Institute of Mathematics, UFRGS, Porto-Alegre (Brazil)
2004-07-01
In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of a slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method. (authors)
Gauge theory and variational principles
Bleecker, David
2005-01-01
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field
Variational continuum multiphase poroelasticity theory and applications
Serpieri, Roberto
2017-01-01
This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the...
Ouk, Chanda-Malis; Zvereva-Loëte, Natalia; Scribano, Yohann; Bussery-Honvault, Béatrice
2012-10-30
Multireference single and double configuration interaction (MRCI) calculations including Davidson (+Q) or Pople (+P) corrections have been conducted in this work for the reactants, products, and extrema of the doublet ground state potential energy surface involved in the N((2)D) + CH(4) reaction. Such highly correlated ab initio calculations are then compared with previous PMP4, CCSD(T), W1, and DFT/B3LYP studies. Large relative differences are observed in particular for the transition state in the entrance channel resolving the disagreement between previous ab initio calculations. We confirm the existence of a small but positive potential barrier (3.86 ± 0.84 kJ mol(-1) (MR-AQCC) and 3.89 kJ mol(-1) (MRCI+P)) in the entrance channel of the title reaction. The correlation is seen to change significantly the energetic position of the two minima and five saddle points of this system together with the dissociation channels but not their relative order. The influence of the electronic correlation into the energetic of the system is clearly demonstrated by the thermal rate constant evaluation and it temperature dependance by means of the transition state theory. Indeed, only MRCI values are able to reproduce the experimental rate constant of the title reaction and its behavior with temperature. Similarly, product branching ratios, evaluated by means of unimolecular RRKM theory, confirm the NH production of Umemoto et al., whereas previous works based on less accurate ab initio calculations failed. We confirm the previous findings that the N((2)D) + CH(4) reaction proceeds via an insertion-dissociation mechanism and that the dominant product channels are CH(2)NH + H and CH(3) + NH. Copyright © 2012 Wiley Periodicals, Inc.
Transition state structures in solution
Bertran, J.; Lluch, J. M.; Gonzalez-Lafont, A.; Dillet, V.; Perez, V.
1995-01-01
In the present paper the location of transition state structures for reactions in solution has been studied. Continuum model calculations have been carried out on the Friedel-Crafts alkylation reaction and a proton transfer through a water molecule between two oxygen atoms in formic acid. In this model the separation between the chemical system and the solvent has been introduced. On the other hand, the discrete Monte Carlo methodology has also been used to simulate the solvent effect on dissociative electron transfer processes. In this model, the hypothesis of separability is not assumed. Finally, the validity of both approaches is discussed
Learning through the Variation Theory: A Case Study
Cheng, Eddie W. L.
2016-01-01
The variation theory stems from the concept of phenomenography. Although some applications of the theory can be found, the theory is not well known in the field of education, especially with respect to the teaching of business and management subjects. The aim of this paper is to explore the use of the variation theory for teaching management…
Variational formulation of two scalar-tetradic theories of gravitation
Saez, D.
1983-01-01
In this paper we obtain two scalar-tetradic theories of gravitation (theories A and B) from a variational principle. In these theories the gravitational energy is localized and the principle of equivalence holds. They combine some aspects of Moller theory and the Brans-Dicke theory. The first-order approximations and an introduction to the study of both theories in the static spherically symmetric case are presented
Variational theory of nuclear and neutron matter
Pandharipande, V.R.; Wiringa, R.B.
1989-06-01
In these lectures we will discuss attempts to solve the A = 3 to ∞ nuclear many-body problems with the variational method. We choose the form of a variational wave function Χ v (1, 2 hor-ellipsis A) to describe the ground state. The Χ v and the ground-state energy E v are obtained by minimizing E v = left-angle Χ v |H|Χ v right-angle/left-angle Χ v |Χ v right-angle with respect to variations in Χ v . If the form of the variational wave function is chosen properly we can expect Χ v ∼ Χ 0 and E v ∼ E 0 where Χ 0 and E 0 are the exact ground-state wave function and energy. In general E v ≥ E 0 in variational calculations. 63 refs., 11 figs
Bifurcations of transition states: Morse bifurcations
MacKay, R S; Strub, D C
2014-01-01
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)
Variational theory of nuclear and neutron matter
Pandharipande, V.R.; Wiringa, R.B. (Illinois Univ., Urbana, IL (USA). Dept. of Physics; Argonne National Lab., IL (USA))
1989-06-01
In these lectures we will discuss attempts to solve the A = 3 to {infinity} nuclear many-body problems with the variational method. We choose the form of a variational wave function {Chi}{sub v}(1, 2{hor ellipsis}A) to describe the ground state. The {Chi}{sub v} and the ground-state energy E{sub v} are obtained by minimizing E{sub v} = {l angle}{Chi}{sub v}{vert bar}H{vert bar}{Chi}{sub v}{r angle}/{l angle}{Chi}{sub v}{vert bar}{Chi}{sub v}{r angle} with respect to variations in {Chi}{sub v}. If the form of the variational wave function is chosen properly we can expect {Chi}{sub v} {approx} {Chi}{sub 0} and E{sub v} {approx} E{sub 0} where {Chi}{sub 0} and E{sub 0} are the exact ground-state wave function and energy. In general E{sub v} {ge} E{sub 0} in variational calculations. 63 refs., 11 figs.
Variational Approach in the Theory of Liquid-Crystal State
Gevorkyan, E. V.
2018-03-01
The variational calculus by Leonhard Euler is the basis for modern mathematics and theoretical physics. The efficiency of variational approach in statistical theory of liquid-crystal state and in general case in condensed state theory is shown. The developed approach in particular allows us to introduce correctly effective pair interactions and optimize the simple models of liquid crystals with help of realistic intermolecular potentials.
Variational analysis of regular mappings theory and applications
Ioffe, Alexander D
2017-01-01
This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, whic...
Variational principle for a prototype Rastall theory of gravitation
Smalley, L.L.
1984-01-01
A prototype of Rastall's theory of gravity, in which the divergence of the energy-momentum tensor is proportional to the gradient of the scalar curvature, is shown to be derivable from a variational principle. Both the proportionality factor and the unrenormalized gravitational constant are found to be covariantly constant, but not necessarily constant. The prototype theory is, therefore, a gravitational theory with variable gravitational constant
Discovering Unique, Low-Energy Transition States Using Evolutionary Molecular Memetic Computing
Ellabaan, Mostafa M Hashim; Ong, Y.S.; Handoko, S.D.
2013-01-01
In the last few decades, identification of transition states has experienced significant growth in research interests from various scientific communities. As per the transition states theory, reaction paths and landscape analysis as well as many thermodynamic properties of biochemical systems can...... be accurately identified through the transition states. Transition states describe the paths of molecular systems in transiting across stable states. In this article, we present the discovery of unique, low-energy transition states and showcase the efficacy of their identification using the memetic computing...... paradigm under a Molecular Memetic Computing (MMC) framework. In essence, the MMC is equipped with the tree-based representation of non-cyclic molecules and the covalent-bond-driven evolutionary operators, in addition to the typical backbone of memetic algorithms. Herein, we employ genetic algorithm...
Calculus of variations and optimal control theory a concise introduction
Liberzon, Daniel
2011-01-01
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the h...
A variational principle for Newton-Cartan theory
Goenner, H.F.M.
1984-01-01
In the framework of a space-time theory of gravitation a variational principle is set up for the gravitational field equations and the equations of motion of matter. The general framework leads to Newton's equations of motion with an unspecified force term and, for irrotational motion, to a restriction on the propagation of the shear tensor along the streamlines of matter. The field equations obtained from the variation are weaker than the standard field equations of Newton-Cartan theory. An application to fluids with shear and bulk viscosity is given. (author)
On time variation of fundamental constants in superstring theories
Maeda, K.I.
1988-01-01
Assuming the action from the string theory and taking into account the dynamical freedom of a dilaton and its coupling to matter fluid, the authors show that fundamental 'constants' in string theories are independent of the 'radius' of the internal space. Since the scalar related to the 'constants' is coupled to the 4-dimensional gravity and matter fluid in the same way as in the Jordan-Brans Dicke theory with ω = -1, it must be massive and can get a mass easily through some symmetry breaking mechanism (e.g. the SUSY breaking due to a gluino condensation). Consequently, time variation of fundamental constants is too small to be observed
A Variational Statistical-Field Theory for Polar Liquid Mixtures
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Variational analysis and generalized differentiation I basic theory
Mordukhovich, Boris S
2006-01-01
Contains a study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces. This title presents many applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, and more.
Bussey, Thomas J.; Orgill, MaryKay; Crippen, Kent J.
2013-01-01
Instructors are constantly baffled by the fact that two students who are sitting in the same class, who have access to the same materials, can come to understand a particular chemistry concept differently. Variation theory offers a theoretical framework from which to explore possible variations in experience and the resulting differences in…
Hamiltonian lattice field theory: Computer calculations using variational methods
Zako, R.L.
1991-01-01
I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems
Hamiltonian lattice field theory: Computer calculations using variational methods
Zako, R.L.
1991-01-01
A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems
Theories of Population Variation in Genes and Genomes
Christiansen, Freddy
This textbook provides an authoritative introduction to both classical and coalescent approaches to population genetics. Written for graduate students and advanced undergraduates by one of the world’s leading authorities in the field, the book focuses on the theoretical background of population...... genetics, while emphasizing the close interplay between theory and empiricism. Traditional topics such as genetic and phenotypic variation, mutation, migration, and linkage are covered and advanced by contemporary coalescent theory, which describes the genealogy of genes in a population, ultimately...... connecting them to a single common ancestor. Effects of selection, particularly genomic effects, are discussed with reference to molecular genetic variation. The book is designed for students of population genetics, bioinformatics, evolutionary biology, molecular evolution, and theoretical biology—as well...
Efficient Computation of Transition State Resonances and Reaction Rates from a Quantum Normal Form
Schubert, Roman; Waalkens, Holger; Wiggins, Stephen
2006-01-01
A quantum version of a recent formulation of transition state theory in phase space is presented. The theory developed provides an algorithm to compute quantum reaction rates and the associated Gamov-Siegert resonances with very high accuracy. The algorithm is especially efficient for
Gauge-invariant variational methods for Hamiltonian lattice gauge theories
Horn, D.; Weinstein, M.
1982-01-01
This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum
Probing the transition state for nucleic acid hybridization using phi-value analysis.
Kim, Jandi; Shin, Jong-Shik
2010-04-27
Genetic regulation by noncoding RNA elements such as microRNA and small interfering RNA (siRNA) involves hybridization of a short single-stranded RNA with a complementary segment in a target mRNA. The physical basis of the hybridization process between the structured nucleic acids is not well understood primarily because of the lack of information about the transition-state structure. Here we use transition-state theory, inspired by phi-value analysis in protein folding studies, to provide quantitative analysis of the relationship between changes in the secondary structure stability and the activation free energy. Time course monitoring of the hybridization reaction was performed under pseudo-steady-state conditions using a single fluorophore. The phi-value analysis indicates that the native secondary structure remains intact in the transition state. The nativelike transition state was confirmed via examination of the salt dependence of the hybridization kinetics, indicating that the number of sodium ions associated with the transition state was not substantially affected by changes in the native secondary structure. These results propose that hybridization between structured nucleic acids undergoes a transition state leading to formation of a nucleation complex and then is followed by sequential displacement of preexisting base pairings involving successive small energy barriers. The proposed mechanism might provide new insight into physical processes during small RNA-mediated gene silencing, which is essential to selection of a target mRNA segment for siRNA design.
Variational cluster perturbation theory for Bose-Hubbard models
Koller, W; Dupuis, N
2006-01-01
We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator-to-superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum-free of spurious gaps-despite the fact that it formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimensional dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed
Variational formulation of covariant eikonal theory for vector waves
Kaufman, A.N.; Ye, H.; Hui, Y.
1986-10-01
The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D/sup μν/(k,x). The eikonal expansion yields, to lowest order, the Hamiltonian ray equations, which define the Lagrangian manifold k(x), and the wave-action conservation law, which determines the wave-amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities
Variational principle for the Bloch unified reaction theory
MacDonald, W.; Rapheal, R.
1975-01-01
The unified reaction theory formulated by Claude Bloch uses a boundary value operator to write the Schroedinger equation for a scattering state as an inhomogeneous equation over the interaction region. As suggested by Lane and Robson, this equation can be solved by using a matrix representation on any set which is complete over the interaction volume. Lane and Robson have proposed, however, that a variational form of the Bloch equation can be used to obtain a ''best'' value for the S-matrix when a finite subset of this basis is used. The variational principle suggested by Lane and Robson, which gives a many-channel S-matrix different from the matrix solution on a finite basis, is considered first, and it is shown that the difference results from the fact that their variational principle is not, in fact, equivalent to the Bloch equation. Then a variational principle is presented which is fully equivalent to the Bloch form of the Schroedinger equation, and it is shown that the resulting S-matrix is the same as that obtained from the matrix solution of this equation. (U.S.)
Variation Theory and the Reception of Chinese Literature in the English-speaking World
Cao, Shunqing
2015-01-01
In his article "Variation Theory and Reception of Chinese Literature in the English-Speaking World" Shunqing Cao introduces "variation theory" he developed and suggests that the framework can be applied in studying the dissemination and reception of Chinese literature in the English-speaking world. Cao argues that cultural and literary differences produce variations in literary exchanges among different cultures and variation theory concentrates on these variations. With unique perspectives o...
Variational methods in electron-atom scattering theory
Nesbet, Robert K
1980-01-01
The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Cha...
The Variable Transition State in Polar Additions to Pi Bonds
Weiss, Hilton M.
2010-01-01
A vast majority of polar additions of Bronsted acids to alkynes involve a termolecular transition state. With strong acids, considerable positive charge is developed on carbon and Markovnikov addition predominates. In less acidic solutions, however, the reaction is much slower and the transition state more closely resembles the olefinic product.…
Variational estimates for the mass gap of SU(2) Euclidean lattice gauge theory
Hari Dass, N.D.
1984-10-01
The purpose of this letter is to report on the progress made in our understanding of series expansions for the masses in lattice gauge theories by the application of variational techniques to the Euclidean SU(2) lattice gauge theory. (Auth.)
José Enrique Barquera-Lozada
2017-09-01
Full Text Available It has been proposed that elemanes are biogenetically formed from germacranes by Cope sigmatropic rearrangements. Normally, this reaction proceeds through a transition state with a chair conformation. However, the transformation of schkuhriolide (germacrane into elemanschkuhriolide (elemane may occur through a boat transition state due to the final configuration of the elemanschkuhriolide, but this transition state is questionable due to its high energy. The possible mechanisms of this transformation were studied in the density functional theory frame. The mechanistic differences between the transformation of (Z,E-germacranes and (E,E-germacranes were also studied. We found that (Z,E-germacranolides are significantly more stable than (E,E-germacranolides and elemanolides. In the specific case of schkuhriolide, even when the boat transition state is not energetically favored, a previous hemiacetalization lowers enough the energetic barrier to allow the formation of a very stable elemanolide that is even more stable than its (Z,E-germacrane.
The variation of G and the quantum theory
Dirac, P.A.M.
1982-01-01
The Einstein theory of gravitation has had enormous success. Various tests have been made and every time the Einstein theory has been confirmed and rival theories have been knocked out. The author discusses the Large Numbers Hypothesis within the framework of the Einstein theory. (Auth.)
A Brief Study of Variation Theory in Quality Management
Mostafa Farah Bakhsh
2016-06-01
Full Text Available Variation is part of everyday life and exists all the time. Variation is the product of differences. Difference in nature of processes results in different products during the time. Proper diagnosis of variation patterns in minimizing the loss is necessary. Continuous quality improvement is regarded as successive reduction of performance variation for delivering high quality products to the customers. In Deming viewpoint, quality deviation is classified to two groups of common and special causes. Variation is not a new word, but understanding and concerns about it are modern. First step in performance variation management is acceptance and belief of variation. For proper management of variations, appropriate tools should be used for detection and display of them. Control are useful tools in recognition, analysis and removing process performance variations.
Variational theory of cyclotron emission from nonuniformly magnetized plasmas
Shvets, V.F.; Swanson, D.G.
1992-01-01
Whereas direct calculations of emission from a source model in both homogeneous and weakly inhomogeneous media have been previously executed, there are no previous theories of the source distribution function from nonuniformly magnetized plasmas where mode conversion phenomena must be taken into account. Whenever the emitting layer is localized due to gradients of the external magnetic field, mode conversion leads to the Generalized Kirchhoff's Law (GKL) E 1 /A 1 = E 2 /A 2 = E 3 /A 3 , where A j represents the absorbed fraction on the j-th wave branch and E j is the corresponding emitted energy along j-th branch. Recently integral expressions for A j and E j in terms of arbitrary localized sink and source distributions have been obtained. The GKL relating absorption to emission along each branch of coexisting in the inhomogeneous mode conversion layer affects the shape of source distribution through a functional of the emissivity. Moreover, E j /A j ≡ I bb , where I bb is a black body radiated power. Accordingly, the distributed emission source function should be an extremal of the emissivity functional. The authors have developed the corresponding variational analysis with nontrivial GKL constraints. As a result they have discovered the correct representation of the ratio of source and sink distributions in the form of an expansion in linearly independent adjoint wave solutions of the absorption problem. Finally, unknown coefficients have been found numerically by further maximization taking account of both source boundedness and the GKL constraints. Calculations performed for a broad variety of plasma parameters will be presented
Quantum catalysis : the modelling of catalytic transition states
Hall, M.B.; Margl, P.; Naray-Szabo, G.; Schramm, Vern; Truhlar, D.G.; Santen, van R.A.; Warshel, A.; Whitten, J.L.; Truhlar, D.G.; Morokuma, K.
1999-01-01
A review with 101 refs.; we present an introduction to the computational modeling of transition states for catalytic reactions. We consider both homogeneous catalysis and heterogeneous catalysis, including organometallic catalysts, enzymes, zeolites and metal oxides, and metal surfaces. We summarize
Variational principles are a powerful tool also for formulating field theories
Dell'Isola , Francesco; Placidi , Luca
2012-01-01
Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories
Constrained variational calculus for higher order classical field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Constrained variational calculus for higher order classical field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn
2010-01-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Variational divergence in wave scattering theory with Kirchhoffean trial functions
Bird, J. F.
1986-01-01
In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.
A variational theory of immiscible mixtures with mechanic constraints
Carmo, E.G.D. do.
1982-02-01
A variational formulation for immiscible mixtures with mechanical restrictions is put forward and the arbitrary parts of the interactional force and stress tensor of the constituents are determined. (Author) [pt
Variational, projection methods and Pade approximants in scattering theory
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
General fluid theories, variational principles and self-organization
Mahajan, S.M.
2002-01-01
This paper reports two distinct but related advances: (1) The development and application of fluid theories that transcend conventional magnetohydrodynamics (MHD), in particular, theories that are valid in the long-mean-free-path limit and in which pressure anisotropy, heat flow, and arbitrarily strong sheared flows are treated consistently. (2) The discovery of new pressure-confining plasma configurations that are self-organized relaxed states. (author)
New variations on two old themes - String Theory and Baryonium
Chan Hong-Mo.
1989-07-01
A trace factor introduced twenty years ago to incorporate internal symmetry into String Theory is generalised to include also string dynamics, while some new spectroscopic data are examined in relation to a ten year old model of exotic qq-q-barq-bar mesons. (author)
Monge Palacios, Manuel
2018-01-22
Reactions of hydroxyl (OH) and hydroperoxyl (HO2) are important for governing the reactivity of combustion systems. We performed post-CCSD(T) ab initio calculations at the W3X-L//CCSD = FC/cc-pVTZ level to explore the triplet ground-state and singlet excited-state potential energy surfaces of the OH + HO2 → H2O + O2(3Σg−)/O2(1Δg) reactions. Using microcanonical and multistructural canonical transition state theories, we calculated the rate constant for the triplet and singlet channels over the temperature range 200–2500 K, represented by k(T) = 3.08 × 1012T0.07 exp(1151/RT) + 8.00 × 1012T0.32 exp(−6896/RT) and k(T) = 2.14 × 106T1.65 exp(−2180/RT) in cm3 mol−1 s−1, respectively. The branching ratios show that the yield of singlet excited oxygen is small (<0.5% below 1000 K). To ascertain the importance of singlet oxygen channel, our new kinetic information was implemented into the kinetic model for hydrogen combustion recently updated by Konnov (Combust. Flame, 2015, 162, 3755–3772). The updated kinetic model was used to perform H2O2 thermal decomposition simulations for comparison against shock tube experiments performed by Hong et al. (Proc. Combust. Inst., 2013, 34, 565–571), and to estimate flame speeds and ignition delay times in H2 mixtures. The simulation predicted a larger amount of O2(1Δg) in H2O2 decomposition than that predicted by Konnov\\'s original model. These differences in the O2(1Δg) yield are due to the use of a higher ab initio level and a more sophisticated methodology to compute the rate constant than those used in previous studies, thereby predicting a significantly larger rate constant. No effect was observed on the rate of the H2O2 decomposition and on the flame speeds and ignition delay times of different H2–oxidizer mixtures. However, if the oxidizer is seeded with O3, small differences appear in the flame speed. Given that O2(1Δg) is much more reactive than O2(3Σg−), we do not preclude an effect of the
Muldowney, Patrick
2012-01-01
A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...
Variational configuration interaction methods and comparison with perturbation theory
Pople, J.A.; Seeger, R.; Krishnan, R.
1977-01-01
A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory
A primer on the calculus of variations and optimal control theory
Mesterton-Gibbons, Mike
2009-01-01
The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical softwa...
Cachera, M.; Ernande, B.; Villanueva, M. C.; Lefebvre, S.
2017-02-01
Individual diet variation (i.e. diet variation among individuals) impacts intra- and inter-specific interactions. Investigating its sources and relationship with species trophic niche organization is important for understanding community structure and dynamics. Individual diet variation may increase with intra-specific phenotypic (or "individual state") variation and habitat variability, according to Optimal Foraging Theory (OFT), and with species trophic niche width, according to the Niche Variation Hypothesis (NVH). OFT proposes "proximate sources" of individual diet variation such as variations in habitat or size whereas NVH relies on "ultimate sources" related to the competitive balance between intra- and inter-specific competitions. The latter implies as a corollary that species trophic niche overlap, taken as inter-specific competition measure, decreases as species niche width and individual niche variation increase. We tested the complementary predictions of OFT and NVH in a marine fish assemblage using stomach content data and associated trophic niche metrics. The NVH predictions were tested between species of the assemblage and decomposed into a between- and a within-functional group component to assess the potential influence of species' ecological function. For most species, individual diet variation and niche overlap were consistently larger than expected. Individual diet variation increased with intra-specific variability in individual state and habitat, as expected from OFT. It also increased with species niche width but in compliance with the null expectation, thus not supporting the NVH. In contrast, species niche overlap increased significantly less than null expectation with both species niche width and individual diet variation, supporting NVH corollary. The between- and within-functional group components of the NVH relationships were consistent with those between species at the assemblage level. Changing the number of prey categories used to
Calculus of variations in rate of reactions tax using the general pertubation theory
Silva, F.C. da.
1981-02-01
A perturbation expression to calculate the variations in the rates of integral parameters (such as reaction rates) of a reactor using a Time-Independent Generalized Perturbation Theory, was developed. This theory makes use of the concepts of neutron generation and neutron importance with respect to a given process occurring in a system. The application of Time-Dependent Generalized Perturbation Theory to the calculation of Burnup, by using the expressions derived by A. Gandini, along with the perturbation expression derived in the Time Independent Generalized Perturbation Theory, is done. (Author) [pt
Communication: Electronic flux induced by crossing the transition state
Jia, Dongming; Manz, Jörn; Yang, Yonggang
2018-01-01
We present a new effect of chemical reactions, e.g., isomerizations, that occurs when the reactants pass along the transition state, on the way to products. It is based on the well-known fact that at the transition state, the electronic structure of one isomer changes to the other. We discover that this switch of electronic structure causes a strong electronic flux that is well distinguishable from the usual flux of electrons that travel with the nuclei. As a simple but clear example, the effect is demonstrated here for bond length isomerization of Na2 (21Σu+), with adiabatic crossing the barrier between the inner and outer wells of the double minimum potential that support different "Rydberg" and "ionic" type electronic structures, respectively.
Black, Joshua A.; Knowles, Peter J.
2018-06-01
The performance of quasi-variational coupled-cluster (QV) theory applied to the calculation of activation and reaction energies has been investigated. A statistical analysis of results obtained for six different sets of reactions has been carried out, and the results have been compared to those from standard single-reference methods. In general, the QV methods lead to increased activation energies and larger absolute reaction energies compared to those obtained with traditional coupled-cluster theory.
Apramian, Tavis; Watling, Christopher; Lingard, Lorelei; Cristancho, Sayra
2015-10-01
Surgical research struggles to describe the relationship between procedural variations in daily practice and traditional conceptualizations of evidence. The problem has resisted simple solutions, in part, because we lack a solid understanding of how surgeons conceptualize and interact around variation, adaptation, innovation, and evidence in daily practice. This grounded theory study aims to describe the social processes that influence how procedural variation is conceptualized in the surgical workplace. Using the constructivist grounded theory methodology, semi-structured interviews with surgeons (n = 19) from four North American academic centres were collected and analysed. Purposive sampling targeted surgeons with experiential knowledge of the role of variations in the workplace. Theoretical sampling was conducted until a theoretical framework representing key processes was conceptually saturated. Surgical procedural variation was influenced by three key processes. Seeking improvement was shaped by having unsolved procedural problems, adapting in the moment, and pursuing personal opportunities. Orienting self and others to variations consisted of sharing stories of variations with others, taking stock of how a variation promoted personal interests, and placing trust in peers. Acting under cultural and material conditions was characterized by being wary, positioning personal image, showing the logic of a variation, and making use of academic resources to do so. Our findings include social processes that influence how adaptations are incubated in surgical practice and mature into innovations. This study offers a language for conceptualizing the sociocultural influences on procedural variations in surgery. Interventions to change how surgeons interact with variations on a day-to-day basis should consider these social processes in their design. © 2015 John Wiley & Sons, Ltd.
Mery, P.
1977-01-01
The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed
Variational methods for problems from plasticity theory and for generalized Newtonian fluids
Fuchs, Martin
2000-01-01
Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
New variational formulation of Maxwell-Vlasov and guiding center theories
Pfirsch, D.
1983-07-01
A new variational formulation of Maxwell-Vlasov and related theories is given in terms of a common Lagrangian density for both the 'Vlasov particles' and the Maxwell fields. This formulation is used to derive in a consistent way, on the one hand, correct charge and current densities and, on the other, corresponding energy and energy flux densities. All of these densities generally show in addition to particle like contributions electric polarization and magnetization terms. By some limiting procedure collisionless guiding center theories with polarization drifts included are also treated. In this way local energy conservation laws are formulated for such theories, which has not been possible up to now. (orig.)
On the inverse problem of the calculus of variations in field theory
Henneaux, M.
1984-01-01
The inverse problem of the calculus of variations is investigated in the case of field theory. Uniqueness of the action principle is demonstrated for the vector Laplace equation in a non-decomposable Riemannian space, as well as for the harmonic map equation. (author)
Toward convergence of the variational mass expansion in asymptotically free theories
Kneur, J L
2001-01-01
We re-examine a modification of perturbative expansions, valid for asymptotically free theories, producing "variationally improved" expansions of physical quantities relevant to dynamical (chiral) symmetry breaking. The large order behaviour of this expansion is shown to be drastically improved, for reasons analogous to the convergence properties of the delta-expansion of the anharmonic oscillator.
Variational second-order Moller-Plesset theory based on the Luttinger-Ward functional
Dahlen, NE; von Barth, U
2004-01-01
In recent years there have been some rather successful applications of a new variational technique for calculating the total energies of electronic systems. The new method is based on many-body perturbation theory and uses the one-electron Green function as the basic "variable" rather than the wave
Variational approach to gravity field theories from Newton to Einstein and beyond
Vecchiato, Alberto
2017-01-01
This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughout the text, solved exercis...
Transitional states of central serotonin receptors in Parkinson's disease
Kienzl, E.; Riederer, P.; Jellinger, K.; Wesemann, W.; Marburg Univ.
1981-01-01
Crude membrane preparations from the frontal cortex of controls and pakinsonian patients were used to demonstrate affinity changes of the specific 3 H-5-hydroxytryptamine (5-HT) binding sites. Two such sites were noteable in controls, a finding consistent with earlier observations. In Parkinson's disease, both high- and low-affinity sites are significantly decreased. Additional experiments either with prolonged incubation times or pre-incubation with N-ethylmaleimide change the two affinities to a single high-affinity or low-affinity constant. The concept of transitional states of 5-HT receptors is discussed and seems to have important implications in the treatment of parkinsonism. (author)
Transitional states of central serotonin receptors in Parkinson's disease
Kienzl, E; Riederer, P; Jellinger, K; Wesemann, W [Krankenhaus der Stadt Wien-Lainz (Austria). Ludwig Boltzmann Inst. fuer Neurobiologie; Marburg Univ. (Germany, F.R.). Inst. fuer Physiologie II, Abt. fuer Neurochemie)
1981-01-01
Crude membrane preparations from the frontal cortex of controls and pakinsonian patients were used to demonstrate affinity changes of the specific /sup 3/H-5-hydroxytryptamine (5-HT) binding sites. Two such sites were noteable in controls, a finding consistent with earlier observations. In Parkinson's disease, both high- and low-affinity sites are significantly decreased. Additional experiments either with prolonged incubation times or pre-incubation with N-ethylmaleimide change the two affinities to a single high-affinity or low-affinity constant. The concept of transitional states of 5-HT receptors is discussed and seems to have important implications in the treatment of parkinsonism.
Klimes, JirI; Michaelides, Angelos; Bowler, David R
2010-01-01
The performance of a variety of techniques for locating transition states on potential energy surfaces is evaluated within the density functional theory framework. Diffusion of a water molecule across NaCl(001) and HCl bond breaking on the same surface are treated as general test cases; the former is an example of a low barrier diffusion process and the latter an example of a relatively high barrier covalent bond rupture event. The methods considered include the nudged elastic band (NEB), Dewar, Healy and Stewart (DHS), dimer, constrained optimization (CO), activation-relaxation technique (ART) and one-side growing string (OGS) as well as novel combinations of the DHS with growing string (DHS + GS) and DHS plus climbing image (CI-DHS). A key conclusion to come from this study is that the NEB method is relatively fast, especially when just a single (climbing) image is used. Indeed, using more images represents an unnecessary computational burden for our set of processes. The dimer method exhibits variable performance; being poor for the water diffusion processes, which have small activation energies, but much more efficient for the HCl bond breaking process which has a higher barrier. When only a poor initial guess of the transition state geometry is available, the CI-DHS scheme is one of the most efficient techniques considered. And as a means to quickly establish an approximate minimum energy pathway the DHS + GS scheme offers some potential.
Variational study of mass generation and deconfinement in Yang-Mills theory
Comitini, Giorgio; Siringo, Fabio
2018-03-01
A very simple variational approach to pure SU (N ) Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at Tc≈250 MeV for N =3 ) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.
Nonperturbative calculations in the framework of variational perturbation theory in QCD
Solovtsova, O. P.
2017-07-01
We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. We apply this method to investigate the Borel representation of the light Adler function constructed from the τ data and to determine the residual condensates. It is shown that within the method suggested the optimal values of these lower dimension condensates are close to zero.
Musilová Jana
2016-12-01
Full Text Available As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \\true trajectories" of the physical systems represent stationary points of the corresponding functionals.
Jing, Ting Jing; Tarmizi, Rohani Ahmad; Bakar, Kamariah Abu; Aralas, Dalia
2017-01-01
This study investigates the effect of utilizing Variation Theory Based Strategy on students' algebraic achievement and motivation in learning algebra. The study used quasi-experimental non-equivalent control group research design and involved 56 Form Two (Secondary Two) students in two classes (28 in experimental group, 28 in control group) in Malaysia The first class of students went through algebra class taught with Variation Theory Based Strategy (VTBS) while the second class of students experienced conventional teaching strategy. The instruments used for the study were a 24-item Algebra Test and 36-item Instructional Materials Motivation Survey. Result from analysis of Covariance indicated that experimental group students achieved significantly better test scores than control group. Result of Multivariate Analysis of Variance also shows evidences of significant effect of VTBS on experimental students' overall motivation in all the five subscales; attention, relevance, confidence, and satisfaction. These results suggested the utilization of VTBS would improve students' learning in algebra.
Probing the transition state region in catalytic CO oxidation on Ru
Ostrom, H. [Stockholm Univ. (Sweden); Oberg, H. [Stockholm Univ. (Sweden); Xin, H. [SLAC National Accelerator Lab., Menlo Park, CA (United States); LaRue, J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., Stanford, CA (United States); Beye, M. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Helmholtz Zentrum Berlin fur Materialien und Energie GmbH, Berlin (Germany); Dell' Angela, M. [Univ. of Hamburg and Center for Free Electron Laser Science, Hamburg (Germany); Gladh, J. [Stockholm Univ. (Sweden); Ng, M. L. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Sellberg, J. A. [Stockholm Univ. (Sweden); SLAC National Accelerator Lab., Menlo Park, CA (United States); Kaya, S. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mercurio, G. [Univ. of Hamburg and Center for Free Electron Laser Science, Hamburg (Germany); Nordlund, D. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Hantschmann, M. [Helmholtz Zentrum Berlin fur Materialien und Energie GmbH, Berlin (Germany); Hieke, F. [Univ. of Hamburg and Center for Free Electron Laser Science, Hamburg (Germany); Kuhn, D. [Helmholtz Zentrum Berlin fur Materialien und Energie GmbH, Berlin (Germany); Schlotter, W. F. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Dakovski, G. L. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Turner, J. J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Minitti, M. P. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mitra, A. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Moeller, S. P. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Fohlisch, A. [Helmholtz Zentrum Berlin fur Materialien und Energie GmbH, Berlin (Germany); Univ. Potsdam, Potsdam (Germany); Wolf, M. [Fritz-Haber Institute of the Max-Planck-Society, Berlin (Germany); Wurth, W. [Univ. of Hamburg and Center for Free Electron Laser Science, Hamburg (Germany); DESY Photon Science, Hamburg (Germany); Persson, M. [The Univ. of Liverpool, Liverpool (United Kingdom); Norskov, J. K. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., Stanford, CA (United States); Abild-Pedersen, F. [Stanford Univ., Stanford, CA (United States); Ogasawara, H. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Pettersson, L. G. M. [Stockholm Univ. (Sweden); Nilsson, A. [Stockholm Univ. (Sweden); SLAC National Accelerator Lab., Menlo Park, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-02-12
Femtosecond x-ray laser pulses are used to probe the CO oxidation reaction on ruthenium (Ru) initiated by an optical laser pulse. On a time scale of a few hundred femtoseconds, the optical laser pulse excites motions of CO and O on the surface, allowing the reactants to collide, and, with a transient close to a picosecond (ps), new electronic states appear in the O K-edge x-ray absorption spectrum. Density functional theory calculations indicate that these result from changes in the adsorption site and bond formation between CO and O with a distribution of OC–O bond lengths close to the transition state (TS). After 1 ps, 10% of the CO populate the TS region, which is consistent with predictions based on a quantum oscillator model.
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Zhengde Tan
2013-01-01
Full Text Available In comparison with the Q-e scheme, the Revised Patterns Scheme: the U, V Version (the U-V scheme has greatly improved both its accessibility and its accuracy in interpreting and predicting the reactivity of a monomer in free-radical copolymerizations. Quantitative structure-activity relationship (QSAR models were developed to predict the reactivity parameters u and v of the U-V scheme, by applying genetic algorithm (GA and support vector machine (SVM techniques. Quantum chemical descriptors used for QSAR models were calculated from transition state species with structures C¹H3 - C²HR³• or •C¹H2 - C²H2R³ (formed from vinyl monomers C¹H²=C²HR³ + H•, using density functional theory (DFT, at the UB3LYP level of theory with 6-31G(d basis set. The optimum support vector regression (SVR model of the reactivity parameter u based on Gaussian radial basis function (RBF kernel (C = 10, ε = 10- 5 and γ = 1.0 produced root-mean-square (rms errors for the training, validation and prediction sets being 0.220, 0.326 and 0.345, respectively. The optimal SVR model for v with the RBF kernel (C = 20, ε = 10- 4 and γ = 1.2 produced rms errors for the training set of 0.123, the validation set of 0.206 and the prediction set of 0.238. The feasibility of applying the transition state quantum chemical descriptors to develop SVM models for reactivity parameters u and v in the U-V scheme has been demonstrated.
MEANINGFUL VARIABILITY: A SOCIOLINGUISTICALLY-GROUNDED APPROACH TO VARIATION IN OPTIMALITY THEORY
Juan Antonio Cutillas Espinosa
2004-12-01
Full Text Available Most approaches to variability in Optimality Theory have attempted to make variation possible within the OT framework, i.e. to reformulate constraints and rankings to accommodate variable and gradient linguistic facts. Sociolinguists have attempted to apply these theoretical advances to the study of language variation, with an emphasis on language-interna1 variables (Auger 2001, Cardoso 2001. Little attention has been paid to the array of externa1 factors that influence the patterning of variation. In this paper, we argue that some variation pattems-specially those that are socially meaningful- are actually the result of a three-grarnmar system. G, is the standard grammar, which has to be available to the speaker to obtain these variation patterns. G; is the vernacular grammar, which the speaker is likely to have acquired in his local community. Finally, G, is an intergrammar, which is used by the speaker as his 'default' constraint set. G is a continuous ranking (Boersma & Hayes 2001 and domination relations are consciously altered by the speakers to shape the appropriate and variable linguistic output. We illustrate this model with analyses of English and Spanish.
Cant, Michael A; Llop, Justine B; Field, Jeremy
2006-06-01
Recent theory suggests that much of the wide variation in individual behavior that exists within cooperative animal societies can be explained by variation in the future direct component of fitness, or the probability of inheritance. Here we develop two models to explore the effect of variation in future fitness on social aggression. The models predict that rates of aggression will be highest toward the front of the queue to inherit and will be higher in larger, more productive groups. A third prediction is that, in seasonal animals, aggression will increase as the time available to inherit the breeding position runs out. We tested these predictions using a model social species, the paper wasp Polistes dominulus. We found that rates of both aggressive "displays" (aimed at individuals of lower rank) and aggressive "tests" (aimed at individuals of higher rank) decreased down the hierarchy, as predicted by our models. The only other significant factor affecting aggression rates was date, with more aggression observed later in the season, also as predicted. Variation in future fitness due to inheritance rank is the hidden factor accounting for much of the variation in aggressiveness among apparently equivalent individuals in this species.
General variational many-body theory with complete self-consistency for trapped bosonic systems
Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2006-01-01
In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states
Edegger, B.
2007-01-01
We consider the theory of high temperature superconductivity from the viewpoint of a strongly correlated electron system. In particular, we discuss Gutzwiller projected wave functions, which incorporate strong correlations by prohibiting double occupancy in orbitals with strong on-site repulsion. After a general overview on high temperature superconductivity, we discuss Anderson's resonating valence bond (RVB) picture and its implementation by renormalized mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. In the following, we present a detailed review on RMFT and VMC results with emphasis on our recent contributions. Especially, we are interested in spectral features of Gutzwiller-Bogolyubov quasiparticles obtained by extending VMC and RMFT techniques to excited states. We explicitly illustrate this method to determine the quasiparticle weight and provide a comparison with angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). We conclude by summarizing recent successes and by discussing open questions, which must be solved for a thorough understanding of high temperature superconductivity by Gutzwiller projected wave functions. (orig.)
Edegger, B.
2007-08-10
We consider the theory of high temperature superconductivity from the viewpoint of a strongly correlated electron system. In particular, we discuss Gutzwiller projected wave functions, which incorporate strong correlations by prohibiting double occupancy in orbitals with strong on-site repulsion. After a general overview on high temperature superconductivity, we discuss Anderson's resonating valence bond (RVB) picture and its implementation by renormalized mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. In the following, we present a detailed review on RMFT and VMC results with emphasis on our recent contributions. Especially, we are interested in spectral features of Gutzwiller-Bogolyubov quasiparticles obtained by extending VMC and RMFT techniques to excited states. We explicitly illustrate this method to determine the quasiparticle weight and provide a comparison with angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). We conclude by summarizing recent successes and by discussing open questions, which must be solved for a thorough understanding of high temperature superconductivity by Gutzwiller projected wave functions. (orig.)
Migórski, Stanisław; Sofonea, Mircea
2015-01-01
Highlighting recent advances in variational and hemivariational inequalities with an emphasis on theory, numerical analysis and applications, this volume serves as an indispensable resource to graduate students and researchers interested in the latest results from recognized scholars in this relatively young and rapidly-growing field. Particularly, readers will find that the volume’s results and analysis present valuable insights into the fields of pure and applied mathematics, as well as civil, aeronautical, and mechanical engineering. Researchers and students will find new results on well posedness to stationary and evolutionary inequalities and their rigorous proofs. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Finally, the applications presented illustrate the use of these results in the study of miscellaneous mathematical models which describe the contact between deformable bodies and a...
A Duality Theory for Non-convex Problems in the Calculus of Variations
Bouchitté, Guy; Fragalà, Ilaria
2018-02-01
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).
Skorobogatiy, Maksim; Jacobs, Steven; Johnson, Steven; Fink, Yoel
2002-10-21
Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electro-magnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fail when applied to the problem of shifted material boundaries. In this paper we developed a novel coupled mode and perturbation theory formulations for treating generic non-uniform (varying along the direction of propagation) perturbations of a waveguide cross-section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate and rapidly converges to an exact result when used in a coupled mode theory framework even for the high index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of induced PMD due to a generic distortion of a waveguide profile, analysis of mode filters, mode converters and other optical elements such as strong Bragg gratings, tapers, bends etc., and arbitrary combinations of thereof. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary non-uniform profile variations in high index-contrast waveguides.
GLAG theory for superconducting property variations with A15 composition in Nb3Sn wires.
Li, Yingxu; Gao, Yuanwen
2017-04-25
We present a model for the variation of the upper critical field H c2 with Sn content in A15-type Nb-Sn wires, within the Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) theory frame. H c2 at the vicinity of the critical temperature T c is related quantitatively to the electrical resistivity ρ, specific heat capacity coefficient γ and T c . H c2 versus tin content is theoretically formulated within the GLAG theory, and generally reproduces the experiment results. As Sn content gradually approaches the stoichiometry, A15-type Nb-Sn undergoes a transition from the dirty limit to clean limit, split by the phase transformation boundary. The H-T phase boundary and pinning force show different behaviors in the cubic and tetragonal phase. We dipict the dependence of the composition gradient on the superconducting properties variation in the A15 layer, as well as the curved tail at vicinity of H c2 in the Kramer plot of the Nb 3 Sn wire. This helps understanding of the inhomogeneous-composition inducing discrepancy between the results by the state-of-art scaling laws and experiments.
Life-history variation of a neotropical thrush challenges food limitation theory
Ferretti, V.; Llambias, P.E.; Martin, T.E.
2005-01-01
Since David Lack first proposed that birds rear as many young as they can nourish, food limitation has been accepted as the primary explanation for variation in clutch size and other life-history traits in birds. The importance of food limitation in life-history variation, however, was recently questioned on theoretical grounds. Here, we show that clutch size differences between two populations of a neotropical thrush were contrary to expectations under Lack's food limitation hypothesis. Larger clutch sizes were found in a population with higher nestling starvation rate (i.e. greater food limitation). We experimentally equalized clutches between populations to verify this difference in food limitation. Our experiment confirmed greater food limitation in the population with larger mean clutch size. In addition, incubation bout length and nestling growth rate were also contrary to predictions of food limitation theory. Our results demonstrate the inability of food limitation to explain differences in several life-history traits: clutch size, incubation behaviour, parental feeding rate and nestling growth rate. These life-history traits were better explained by inter-population differences in nest predation rates. Food limitation may be less important to life history evolution in birds than suggested by traditional theory. ?? 2005 The Royal Society.
Atkins, Louise; Hunkeler, Enid M; Jensen, Christopher D; Michie, Susan; Lee, Jeffrey K; Doubeni, Chyke A; Zauber, Ann G; Levin, Theodore R; Quinn, Virginia P; Corley, Douglas A
2016-03-01
Interventions to improve physician adenoma detection rates for colonoscopy have generally not been successful, and there are little data on the factors contributing to variation that may be appropriate targets for intervention. We sought to identify factors that may influence variation in detection rates by using theory-based tools for understanding behavior. We separately studied gastroenterologists and endoscopy nurses at 3 Kaiser Permanente Northern California medical centers to identify potentially modifiable factors relevant to physician adenoma detection rate variability by using structured group interviews (focus groups) and theory-based tools for understanding behavior and eliciting behavior change: the Capability, Opportunity, and Motivation behavior model; the Theoretical Domains Framework; and the Behavior Change Wheel. Nine factors potentially associated with adenoma detection rate variability were identified, including 6 related to capability (uncertainty about which types of polyps to remove, style of endoscopy team leadership, compromised ability to focus during an examination due to distractions, examination technique during withdrawal, difficulty detecting certain types of adenomas, and examiner fatigue and pain), 2 related to opportunity (perceived pressure due to the number of examinations expected per shift and social pressure to finish examinations before scheduled breaks or the end of a shift), and 1 related to motivation (valuing a meticulous examination as the top priority). Examples of potential intervention strategies are provided. By using theory-based tools, this study identified several novel and potentially modifiable factors relating to capability, opportunity, and motivation that may contribute to adenoma detection rate variability and be appropriate targets for future intervention trials. Copyright © 2016 American Society for Gastrointestinal Endoscopy. Published by Elsevier Inc. All rights reserved.
Schwinger variational principle in the nuclear two-body problem and multichannel theory
Zubarev, A.L.; Podkopaev, A.P.
1978-01-01
The aim of the investigation is to study the Schwinger variational principle in the nuclear two-body problem and the multichannel theory. An approach is proposed to problems of the potential scattering based on the substitution of the exact potential operator V by the finite rank operator Vsup((n)) with which the dynamic equations are solved exactly. The functionals obtained for observed values coincide with corresponding expressions derived by the Schwinger variational principle with the set of test functions. The determination of the Schwinger variational principle is given. The method is given for finding amplitude of the double-particle scattering with the potential Vsup((n)). The corresponding amplitudes are constructed within the framework of the multichannel potential model. Interpolation formula for determining amplitude, which describes with high accuracy a process of elastic scattering for any energies, is obtained. On the basis of the above method high-energy amplitude may be obtained within the range of small and large scattering angles
Heys, D.W.; Stump, D.R.
1987-01-01
Variational calculations are described that use multi-parameter trial wave functions for the U(1) lattice gauge theory in two space dimensions, and for the XY model. The trial functions are constructed as the exponential of a linear combination of states from the strong-coupling basis of the model, with the coefficients treated as variational parameters. The expectation of the hamiltonian is computed by the Monte Carlo method, using a reweighting technique to evaluate expectation values in finite patches of the parameter space. The trial function for the U(1) gauge theory involves six variational parameters, and its weak-coupling behaviour is in reasonable agreement with theoretical expectations. (orig.)
Monitoring Mars LOD Variations from a High Altitude Circular Equatorial Orbit: Theory and Simulation
Barriot, J.; Dehant, V.; Duron, J.
2003-12-01
We compute the perturbations of a high altitude circular equatorial orbit of a martian probe under the influence of an annual variation of the martian lenght of day. For this purpose, we use the first order perturbations of the newtonian equations of motion, where the small parameter is given from the hourglass model of Chao and Rubincam, which allow a simple computation of CO2 exchanges during the martian year. We are able to demonstrate that the perturbations contains two components: the first one is a sine/cosine modulation at the orbit frequency, the second one is composed of terms of the form exp(t)*sin(t), so the orbit may not stable in the long term (several martian years), with perturbations growing exponentially. We give the full theory and numbers.
Perturbation theory corrections to the two-particle reduced density matrix variational method.
Juhasz, Tamas; Mazziotti, David A
2004-07-15
In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.
Brandow, B. H.
1986-01-01
A variational study of ground states of the orbitally nondegenerate Anderson lattice model, using a wave function with one variational parameter per Bloch state k, has been extended to deal with essentially metallic systems having a nonintegral number of electrons per site. Quasiparticle excitations are obtained by direct appeal to Landau's original definition for interacting Fermi liquids, scrEqp(k,σ)=δEtotal/δn qp(k,σ). This approach provides a simple and explicit realization of the Luttinger picture of a periodic Fermi liquid. A close correspondence is maintained between the ``interacting'' (U=∞) system and the corresponding ``noninteracting'' (U=0) case, i.e., ordinary band theory; the result can be described as a renormalized band or renormalized hybridization theory. The occupation-number distribution for the conduction orbitals displays a finite discontinuity at the Fermi surface. If the d-f hybridization is nonzero throughout the Brillouin zone, the quasiparticle spectrum will always exhibit a gap, although this gap becomes exponentially small (i.e., of order TK) in the Kondo-lattice regime. In the ``ionic'' case with precisely two electrons per site, such a system may therefore exhibit an insulating (semiconducting) gap. The quasiparticle state density exhibits a prominent spike on each side of the spectral gap, just as in the elementary hybridization model (the U=0 case). For the metallic case, with a nonintegral number of electrons per site, the Fermi level falls within one of the two sharp density peaks. The effective mass at the Fermi surface tends to be very large; enhancements by a factor >~102 are quite feasible. The foregoing variational theory has also been refined by means of a trial wave function having two variational parameters per Bloch state k. The above qualitative features are all retained, with some quantitative differences, but there are also some qualitatively new features. The most interesting of these is the appearance, within
Heys, D.W.; Stump, D.R.
1984-01-01
The variational principle is used to estimate the ground state of the Kogut-Susskind Hamiltonian of the SU(2) lattice gauge theory, with a trial wave function for which the magnetic fields on different plaquettes are uncorrelated. This trial function describes a disordered state. The energy expectation value is evaluated by a Monte Carlo method. The variational results are compared to similar results for a related Abelian gauge theory. Also, the expectation value of the Wilson loop operator is computed for the trial state, and the resulting estimate of the string tension is compared to the prediction of asymptotic freedom
El-Nabulsi, Ahmad Rami
2009-01-01
Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.
Pratihar, Subha; Ma, Xinyou; Xie, Jing; Scott, Rebecca; Gao, Eric; Ruscic, Branko; Aquino, Adelia J. A.; Setser, Donald W.; Hase, William L.
2017-10-01
Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH3CN → HF + CH2CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. The experiments were performed at 300 K, and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F⋯HCH2CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH2CN and then trapping in the CH2CN⋯HF post-reaction potential energy well of ˜10 kcal/mol with respect to the HF + CH2CN products. In contrast to this IRC, five different trajectory types were observed: the majority proceeded by direct H-atom transfer and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH2CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. Simulations with an anharmonic zero-point energy constraint gave product distributions for relative translation, HF rotation, HF vibration, CH2CN rotation, and CH2CN vibration as 5%, 11%, 60%, 7%, and 16%, respectively. In contrast, the experimental energy partitioning percentages to HF rotation and vibration are 6% and 41%. Comparisons are made between the current simulation and those for other F + H-atom abstraction reactions. The simulation product energy partitioning and HF vibrational population for F + CH3CN → HF + CH2CN
Pratihar, Subha; Ma, Xinyou; Xie, Jing; Scott, Rebecca; Gao, Eric; Ruscic, Branko; Aquino, Adelia J A; Setser, Donald W; Hase, William L
2017-10-14
Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH 3 CN → HF + CH 2 CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. The experiments were performed at 300 K, and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F⋯HCH 2 CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH 2 CN and then trapping in the CH 2 CN⋯HF post-reaction potential energy well of ∼10 kcal/mol with respect to the HF + CH 2 CN products. In contrast to this IRC, five different trajectory types were observed: the majority proceeded by direct H-atom transfer and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH 2 CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. Simulations with an anharmonic zero-point energy constraint gave product distributions for relative translation, HF rotation, HF vibration, CH 2 CN rotation, and CH 2 CN vibration as 5%, 11%, 60%, 7%, and 16%, respectively. In contrast, the experimental energy partitioning percentages to HF rotation and vibration are 6% and 41%. Comparisons are made between the current simulation and those for other F + H-atom abstraction reactions. The simulation product energy partitioning and HF vibrational population for F + CH 3 CN
Isomorph theory prediction for the dielectric loss variation along an isochrone
Xiao, Wence; Tofteskov, Jon; Dyre, J. C.
2015-01-01
This paper derives a prediction for the variation of the amplitude of the dielectric loss from isomorph theory, and presents an experimental test of the prediction performed by measuring the dielectric relaxation behavior of the van der Waals liquid 5-phenyl-4-ether (5PPE). The liquid is studied...... isomorph-invariant terms, one of which is used in analyzing our data. It is the frequency-dependent term χe(f)ργ − 1, with electric susceptibility χe, density ρ, and density-scaling factor γ. Due to the unique design of our experimental setup, we obtain dielectric loss data where the amplitude...... is reproducible ± 0.1 %. We moreover find that the empty capacitance of the capacitor cell is stable within ± 0.3 % in our measuring range and can be assumed to be constant. Using this we predict for two isomorph states there is C2″(f) = C1″(f)(ρ1/ρ2)γ−1 to scale the imaginary capacitance, where C1...
Transitional states in marine fisheries: adapting to predicted global change.
MacNeil, M Aaron; Graham, Nicholas A J; Cinner, Joshua E; Dulvy, Nicholas K; Loring, Philip A; Jennings, Simon; Polunin, Nicholas V C; Fisk, Aaron T; McClanahan, Tim R
2010-11-27
Global climate change has the potential to substantially alter the production and community structure of marine fisheries and modify the ongoing impacts of fishing. Fish community composition is already changing in some tropical, temperate and polar ecosystems, where local combinations of warming trends and higher environmental variation anticipate the changes likely to occur more widely over coming decades. Using case studies from the Western Indian Ocean, the North Sea and the Bering Sea, we contextualize the direct and indirect effects of climate change on production and biodiversity and, in turn, on the social and economic aspects of marine fisheries. Climate warming is expected to lead to (i) yield and species losses in tropical reef fisheries, driven primarily by habitat loss; (ii) community turnover in temperate fisheries, owing to the arrival and increasing dominance of warm-water species as well as the reduced dominance and departure of cold-water species; and (iii) increased diversity and yield in Arctic fisheries, arising from invasions of southern species and increased primary production resulting from ice-free summer conditions. How societies deal with such changes will depend largely on their capacity to adapt--to plan and implement effective responses to change--a process heavily influenced by social, economic, political and cultural conditions.
Variational derivatives in locally Lagrangian field theories and Noether-Bessel-Hagen currents
Cattafi, Francesco; Palese, Marcella; Winterroth, Ekkehart
2016-01-01
The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application, we determine the condition for a
Morgenstern Horing, Norman J
2017-01-01
This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...
Lithuanian health care in transitional state: ethical problems
Žekas Romualdas
2005-11-01
Full Text Available Abstract Background Throughout the economic and political reforms in post-communist countries, significant changes have also occurred in public morality. One of the tasks of the Lithuanian health policy is to create mechanisms for strengthening the significance of ethical considerations in the decision-making processes concerning health care of individuals and groups of individuals, as well as considering the positions of physicians and the health care system itself in a general way. Thus, health care ethics could be analyzed at two levels: the micro level (the ethics of doctor-patient relationships and the macro level (the ethics of health policy-making, which can be realized by applying the principles of equal access, reasonable quality, affordable care and shared responsibilities. To date, the first level remains dominant, but the need arises for our attention to refocus now from the micro level to the patterns of managing and delivering care, managing the health care resources, and conducting business practices. Discussion In attempting to increase the efficiency of health services in Lithuania, a common strategy has been in place for the last fifteen years. Decentralization and privatization have been implemented as part of its policy to achieve greater efficiency. Although decentralization in theory is supposed to improve efficiency, in practice the reform of decentralization has still to be completely implemented in Lithuania. Debates on health policy in Lithuania also include the issue of private versus public health care. Although the approach of private health care is changing in a positive way, it is obvious that reduced access to health services is the most vulnerable aspect. In the Lithuanian Health Program adopted in July 1998, the target of equity was stressed, stating that by 2010, differences in health and health care between various socio-economic groups should be reduced by 25%. Summary The restructuring of health care system
Lithuanian health care in transitional state: ethical problems.
Jakusovaite, Irayda; Darulis, Zilvinas; Zekas, Romualdas
2005-11-09
Throughout the economic and political reforms in post-communist countries, significant changes have also occurred in public morality. One of the tasks of the Lithuanian health policy is to create mechanisms for strengthening the significance of ethical considerations in the decision-making processes concerning health care of individuals and groups of individuals, as well as considering the positions of physicians and the health care system itself in a general way. Thus, health care ethics could be analyzed at two levels: the micro level (the ethics of doctor-patient relationships) and the macro level (the ethics of health policy-making, which can be realized by applying the principles of equal access, reasonable quality, affordable care and shared responsibilities). To date, the first level remains dominant, but the need arises for our attention to refocus now from the micro level to the patterns of managing and delivering care, managing the health care resources, and conducting business practices. In attempting to increase the efficiency of health services in Lithuania, a common strategy has been in place for the last fifteen years. Decentralization and privatization have been implemented as part of its policy to achieve greater efficiency. Although decentralization in theory is supposed to improve efficiency, in practice the reform of decentralization has still to be completely implemented in Lithuania. Debates on health policy in Lithuania also include the issue of private versus public health care. Although the approach of private health care is changing in a positive way, it is obvious that reduced access to health services is the most vulnerable aspect. In the Lithuanian Health Program adopted in July 1998, the target of equity was stressed, stating that by 2010, differences in health and health care between various socio-economic groups should be reduced by 25%. The restructuring of health care system in Lithuania should be based on a balance between
Pathak, Nidhi; Kaur, Sukhdeep; Singh, Sukhmander
2018-05-01
In this paper, self-focusing/defocusing effects have been studied by taking into account the combined effect of ponder-motive and relativistic non linearity during the laser plasma interaction with density variation. The formulation is based on the numerical analysis of second order nonlinear differential equation for appropriate set of laser and plasma parameters by employing moment theory approach. We found that self-focusing increases with increasing the laser intensity and density variation. The results obtained are valuable in high harmonic generation, inertial confinement fusion and charge particle acceleration.
Visualization of the Differential Transition State Stabilization within the Active Site Environment
Jerzy Leszczynski
2004-05-01
Full Text Available Abstract: Increasing interest in the enzymatic reaction mechanisms and in the nature of catalytic effects in enzymes causes the need of appropriate visualization methods. A new interactive method to investigate catalytic effects using differential transition state stabilization approach (DTSS [1, 2] is presented. The catalytic properties of the active site of cytidine deaminase (E.C. 3.5.4.5 is visualized in the form of differential electrostatic properties. The visualization was implemented using scripting interface of VMD [3]. Cumulative Atomic Multipole Moments (CAMM [4,5,6] were utilized for efficient yet accurate evaluation of the electrostatic properties. The implementation is efficient enough for interactive presentation of catalytic effects in the active site of the enzyme due to transition state or substrate movement. This system of visualization of DTTS approach can be potentially used to validate hypotheses regarding the catalytic mechanism or to study binding properties of transition state analogues.
Kvaal, Simen; Helgaker, Trygve
2015-11-14
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
Anomalous singularities in the complex Kohn variational principle of quantum scattering theory
Lucchese, R.R.
1989-01-01
Variational principles for symmetric complex scattering matrices (e.g., the S matrix or the T matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied
Kinetic Analysis for Macrocyclizations Involving Anionic Template at the Transition State
Vicente Martí-Centelles
2012-01-01
competitive oligomerization/polymerization processes yielding undesired oligomeric/polymeric byproducts. The effect of anions has also been included in the kinetic models, as they can act as catalytic templates in the transition state reducing and stabilizing the transition state. The corresponding differential equation systems for each kinetic model can be solved numerically. Through a comprehensive analysis of these results, it is possible to obtain a better understanding of the different parameters that are involved in the macrocyclization reaction mechanism and to develop strategies for the optimization of the desired processes.
Pratihar, Subha [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA; Ma, Xinyou [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA; Xie, Jing [Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA; Scott, Rebecca [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA; Gao, Eric [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA; Ruscic, Branko [Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA and Computation Institute, University of Chicago, Chicago, Illinois 60637, USA; Aquino, Adelia J. A. [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA; School of Pharmaceutical Science and Technology, Tianjin University, Tianjin 300072, People’s Republic of China; Institute for Soil Research University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria; Setser, Donald W. [Institute for Soil Research University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria; Hase, William L. [Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA
2017-10-14
Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH_{3}CN → HF + CH_{2}CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. In accord with experiment and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F-HCH_{2}CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST for the simulation. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH_{2}CN and then trapping in the CH_{2}CN-HF post-reaction potential energy well of ~10 kcal/mol with respect to the HF + CH_{2}CN products. In contrast to this IRC, five different trajectory types were observed, with the majority involving direct dissociation and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH_{2}CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. From the simulations and with an anharmonic zero-point energy constraint, the percentage partitioning of the product energy to relative translation, HF rotation, HF vibration, CH_{2}CN rotation and CH_{2}CN vibration is 5, 11, 60, 7, and 16%, respectively. In contrast the experimental energy partitioning percentages to HF rotation and vibration are 6 and 41%. Comparisons are made between the current simulation and those for other F + H
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Patel, Ashay; Vella, Joseph R; Ma, Zhi-Xiong; Hsung, R P; Houk, K N
2015-12-04
Hsung et al. have reported a series of torquoselective electrocyclizations of chiral 1-azahexa-1E,3Z,5E-trienes that yield functionalized dihydropyridines. To understand the origins of the torquoselectivities of these azaelectrocyclizations, we modeled these electrocyclic ring closures using the M06-2X density functional. A new stereochemical model that rationalizes the observed 1,2 stereoinduction emerges from these computations. This model is an improvement and generalization of the "inside-alkoxy" model used to rationalize stereoselectivities of the 1,3-dipolar cycloaddition of chiral allyl ethers and emphasizes a stabilizing hyperconjugative effect, which we have termed a transition state gauche effect. This stereoelectronic effect controls the conformational preferences at the electrocyclization transition states, and only in one of the allowed disrotatory electrocyclization transition states is the ideal stereoelectronic arrangement achieved without the introduction of a steric clash. Computational experiments confirm the role of this effect as a stereodeterminant since substrates with electropositive groups and electronegative groups have different conformational preferences at the transition state and undergo ring closure with divergent stereochemical outcomes. This predicted reversal of stereoselectivity for the ring closures of several silyl substituted azatrienes have been demonstrated experimentally.
Molecular dynamics simulations from putative transition states of alpha-spectrin SH3 domain
Periole, Xavier; Vendruscolo, Michele; Mark, Alan E.
2007-01-01
A series of molecular dynamics simulations in explicit solvent were started from nine structural models of the transition state of the SH3 domain of alpha-spectrin, which were generated by Lindorff Larsen et al. (Nat Struct Mol Biol 2004;11:443-449) using molecular dynamics simulations in which
Schatz, G.C.; Walch, S.P.; Wagner, A.F.
1980-01-01
We present ab initio (GVB--POL--CI) calculations for enough of the region about the abstraction and exchange saddle points for H(T)+CH 4 (CD 4 ) to perform a full normal mode analysis of the transition states. The resulting normal mode frequencies are compared to four other published surfaces: an ab initio UHF--SCF calculation by Carsky and Zahradnik, a semiempirical surface by Raff, and two semiempirical surfaces by Kurylo, Hollinden, and Timmons. Significant quantitative and qualitative differences exist between the POL--CI results and those of the other surfaces. Transition state theory rate constants and vibrationally adiabatic reaction threshold energies were computed for all surfaces and compared to available experimental values. For abstraction, the POL--CI rates are in good agreement with experimental rates and in better agreement than are the rates of any of the other surfaces. For exchange, uncertainties in the experimental values and in the importance of vibrationally nonadiabatic effects cloud the comparison of theory to experiment. Tentative conclusions are that the POL--CI barrier is too low by several kcal. Unless vibrationaly nonadiabatic effects are severe, the POL--CI surface is still in better agreement with experiment than are the other surfaces. The rates for a simple 3-atom transition state theory model (where CH 3 is treated as an atom) are compared to the rates for the full 6-atom model. The kinetic energy coupling of reaction coordinate modes to methyl group modes is identified as being of primary importance in determining the accuracy of the 3-atom model for this system. Substantial coupling in abstraction, but not exchange, causes the model to fail for abstraction but succeed for exchange
Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory
Huntington, L. M.; Demel, Ondřej; Nooijen, M.
2016-01-01
Roč. 12, č. 1 (2016), s. 114-132 ISSN 1549-9618 R&D Projects: GA ČR GJ15-00058Y Institutional support: RVO:61388955 Keywords : MR-EOM * Benchmark applications * variations Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.245, year: 2016
Vladimirov, Yu.S.; Kislov, V.V.
1982-01-01
Basic equations of the united five-dimensional theory of gravity, electromagnetism and scalar field are given. Discussed is one of the given theory consequences - dependence of electric charge ratio to the e/m test, particle mass on fundamental scalar field value in the specified point. The latter is determined by the solution of the Einstein, Maxwell and Klein-Fock equations system. In particular, this field varies in the Sun-Earth system for an observer bound to the Earth owing to orbit ellipticity of the Earth. The formula describing the e/m variation is given. Data on measuring Josephson frequency revealing the tendency of season dependence (Earth-Sun distances) which raises the problem of performing direct experiments for controlling e/m ratio stability are reproduced
Zhekova, Hristina R; Seth, Michael; Ziegler, Tom
2011-11-14
We have recently developed a methodology for the calculation of exchange coupling constants J in weakly interacting polynuclear metal clusters. The method is based on unrestricted and restricted second order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) and is here applied to eight binuclear copper systems. Comparison of the SF-CV(2)-DFT results with experiment and with results obtained from other DFT and wave function based methods has been made. Restricted SF-CV(2)-DFT with the BH&HLYP functional yields consistently J values in excellent agreement with experiment. The results acquired from this scheme are comparable in quality to those obtained by accurate multi-reference wave function methodologies such as difference dedicated configuration interaction and the complete active space with second-order perturbation theory. © 2011 American Institute of Physics
Miehe, C; Teichtmeister, S; Aldakheel, F
2016-04-28
This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic-plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. © 2016 The Author(s).
Dopamine Receptor D4 Gene Variation Predicts Preschoolers' Developing Theory of Mind
Lackner, Christine; Sabbagh, Mark A.; Hallinan, Elizabeth; Liu, Xudong; Holden, Jeanette J. A.
2012-01-01
Individual differences in preschoolers' understanding that human action is caused by internal mental states, or representational theory of mind (RTM), are heritable, as are developmental disorders such as autism in which RTM is particularly impaired. We investigated whether polymorphisms of genes affecting dopamine (DA) utilization and metabolism…
On choice of trial functions in integro-differential variational principles of transport theory
Loyalka, S.K.; Cipolla, J.W. Jr.
1988-01-01
In several problems of particle transport, quantities of macroscopic interest can be related to stationary values of variational functionals based on general integro-differential equations and boundary conditions. Within the context of the jump (Milne's) problem, it is shown how highly accurate results can be obtained by using trial functions based on the eigenfunctions of the relevant integrodifferential equations. Such choices of trial functions should apply equally effectively to problems in curved geometries, both internal and external
A new variational formulation of kinetic plasma theory and the application of moving finite elements
Glasser, A.H.
1991-01-01
A new variational formulation has been developed for the system of equations governing kinetic plasmas and electromagnetic fields. It is used to apply the method of Moving Finite Elements to the electromagnetic fields. The fields are expanded in a basis of linear finite elements on a movable, unstructured grid of triangles in 2D or tetrahedra in 3D, while the plasma distribution function is expanded in a basis of super particles. Minimization of the variational with respect to the time derivatives of the field quantities yields a coupled system of equations for simultaneously advancing the amplitudes and node positions, resulting in adaptive grid motion. The adaptivity of the grid may save a large factor in the size of the grid and the number of particles required in many problems. Minimization of the variational with respect to the time derivatives of the particle positions and velocities gives the equations of motion, providing consistent prescriptions for assigning particles to the grid and fields to the particles. Orthogonality conditions on the particles are derived as conditions for keeping their equations of motion independent. Collisions can be included in a natural way. The relationship between PIC methods and alternative methods of discretizing phase space is clarified
Theory in Highly Cited Studies of Sexual Minority Parent Families: Variations and Implications.
Farr, Rachel H; Tasker, Fiona; Goldberg, Abbie E
2017-01-01
This article includes a systematic review and citation analysis of the literature regarding sexual minority parent families, particularly attending to what theories have been used, and how. We consider the importance of theoretical frameworks for future research and implications for policy, practice, and law related to sexual minority parent families. Our review targets 30 highly cited studies located through Google Scholar (as an interdisciplinary search engine) and published within a specific timeframe (2005-2010). We highlight the dominant theoretical models employed across disciplines studying sexual minority parent families. Although the majority of studies reviewed referred to theoretical models or perspectives, explicit theoretical grounding was frequently lacking. Instead, the empirical work reviewed appeared to have a predominantly applied focus in addressing public debates on sexual minority parent families. We provide recommendations for how theory might be more fully integrated into the social science literature on sexual minority parents and their children.
Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications
Shi, Tao; Demler, Eugene; Ignacio Cirac, J.
2018-03-01
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieffer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.
Low-frequency variation of a zonally localized jet stream: Observation and theory
Cai, M.
1994-01-01
The climatological mean circulation in the extratropics of the Northern Hemisphere is characterized by two zonally localized jet streams over the east coasts of the two major continents. The zonal inhomogeneity of the climatological mean circulation is believed to be a primary factor determining the geographical locations of the maximum activity centers of the atmospheric transients, such as storm tracks over the east coasts of the two major continents and frequent blocking episodes occurring over the central regions of the two oceans. The impact of the transients on the zonally localized jet streams is studied mostly in the linear dynamics framework in terms of so-called open-quotes feedbackclose quotes diagnosis. This study investigates nonlinear instability of a zonally localized jet stream. The emphasis is on the nonlinear adjustment of a zonally localized jet stream associated with the development of the transients via local instability. The adjustment of a zonally localized jet stream would naturally consists of two parts: One is the time-invariant part and the other is the transient part (temporal variation of the adjustment). In conjunction with the observation, the time-mean adjustment is part of the climatological mean flow and hence is open-quotes invisible.close quotes The transient part of the adjustment is evidenced by the changes of the jet streams in terms of both location and intensity. In this study, we tend to relate the transient part of the adjustment of the jet stream to the maximum activity centers of low-frequency variability. The underlying mechanisms that are responsible for the temporal variation of the adjustment will be investigated. The time-mean adjustment will be also studied to better understand the temporal variation of the adjustment
Variational calculations in gauge theories with approximate projection on gauge invariant states
Heinemann, C.; Martin, C.; Vautherin, D.; Iancu, E.
1999-01-01
Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. The minimization with respect to the kernel and center of the Gaussian leads to a gap type equation which is free of the difficulties generally encountered with negative modes. We show that the divergences in the expectation value of the energy density are only logarithmic and can be removed by a renormalization of the coupling constant. The renormalized energy density has a minimum which corresponds to a vanishing background magnetic field. We obtain an estimate for the gluon condensate. (authors)
Calculus of variations an introduction to the one-dimensional theory with examples and exercises
Kielhöfer, Hansjörg
2018-01-01
This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous th...
Quantum theory of anharmonic oscillators - a variational and systematic general approximation method
Yamazaki, K.; Kyoto Univ.
1984-01-01
The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)
Seifert, Wolfgang [Institute of Physics, Martin Luther University, Halle-Wittenberg (Germany); Zabrocki, Knud; Mueller, Eckhard [Institute of Materials Research, German Aerospace Center (DLR), 51170 Koeln (Germany); Snyder, G.J. [California Institute of Technology, Pasadena, California 91125 (United States)
2010-03-15
The compatibility approach introduced by Snyder and Ursell opens a new pathway for the improvement of thermoelectric (TE) device performance. It has been shown that sufficient compatibility is - besides an increase of the averaged figure of merit Z - essential for efficient operation of a TE device, and that compatibility will facilitate rational materials selection, device design, and the engineering of functionally graded materials (FGMs). In this paper, the authors give an overview of the fundamental results and present a new approach from the perspective of variational calculus. A particular focus is on the role of ideal self-compatibility, i.e., adjusting compatibility locally at any position along a TE leg. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data
Schikorra, Armin
2018-02-01
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.
Parallel algorithm of real-time infrared image restoration based on total variation theory
Zhu, Ran; Li, Miao; Long, Yunli; Zeng, Yaoyuan; An, Wei
2015-10-01
Image restoration is a necessary preprocessing step for infrared remote sensing applications. Traditional methods allow us to remove the noise but penalize too much the gradients corresponding to edges. Image restoration techniques based on variational approaches can solve this over-smoothing problem for the merits of their well-defined mathematical modeling of the restore procedure. The total variation (TV) of infrared image is introduced as a L1 regularization term added to the objective energy functional. It converts the restoration process to an optimization problem of functional involving a fidelity term to the image data plus a regularization term. Infrared image restoration technology with TV-L1 model exploits the remote sensing data obtained sufficiently and preserves information at edges caused by clouds. Numerical implementation algorithm is presented in detail. Analysis indicates that the structure of this algorithm can be easily implemented in parallelization. Therefore a parallel implementation of the TV-L1 filter based on multicore architecture with shared memory is proposed for infrared real-time remote sensing systems. Massive computation of image data is performed in parallel by cooperating threads running simultaneously on multiple cores. Several groups of synthetic infrared image data are used to validate the feasibility and effectiveness of the proposed parallel algorithm. Quantitative analysis of measuring the restored image quality compared to input image is presented. Experiment results show that the TV-L1 filter can restore the varying background image reasonably, and that its performance can achieve the requirement of real-time image processing.
Minimum current principle and variational method in theory of space charge limited flow
Rokhlenko, A. [Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019 (United States)
2015-10-21
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system, its reaction is such that it modifies its state to “agree” with the perturbation by “minimal” change of its initial state. In particular, the electron field emission should produce the minimum current consistent with boundary conditions. It can be found theoretically by solving corresponding equations using different techniques. We apply here the variational method for the current calculation, which can be quite effective even when involving a short set of trial functions. The approach to a better result can be monitored by the total current that should decrease when we on the right track. Here, we present only an illustration for simple geometries of devices with the electron flow. The development of these methods can be useful when the emitter and/or anode shapes make difficult the use of standard approaches. Though direct numerical calculations including particle-in-cell technique are very effective, but theoretical calculations can provide an important insight for understanding general features of flow formation and even sometimes be realized by simpler routines.
Hazarika, Bhaskar Jyoti; Choudhury, D.K.
2015-01-01
We use variationally improved perturbation theory (VIPT) for calculating the elastic form factors and charge radii of D, D s , B, B s and B c mesons in a quantum chromodynamics (QCD)-inspired potential model. For that, we use linear-cum-Coulombic potential and opt the Coulombic part first as parent and then the linear part as parent. The results show that charge radii and form factors are quite small for the Coulombic parent compared to the linear parent. Also, the analysis leads to a lower as well as upper bounds on the four-momentum transfer Q 2 , hinting at a workable range of Q 2 within this approach, which may be useful in future experimental analyses. Comparison of both the options shows that the linear parent is the better option. (author)
Yildiz, C.
1998-01-01
The critical slab problem is studied in one-speed neutron transport theory using a linearly anisotropic kernel which combines forward and backward scattering. It is shown that, the recently observed non-monotonic variation of the thickness also exists in this strongly anisotropic case. In addition, the influence of the linear anisotropy on the critical thickness is analysed in detail. Numerical analysis for the critical thickness are performed using the spherical harmonics method and results are tabulated for selected illustrative cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with those already obtained by other methods, the agreement is satisfactory. The spherical harmonic method gives generally accurate results in one dimensional geometry, and it is very suitable for the numerical solution of the neutron transport equation with linearly anisotropic scattering
Study of radicals, clusters and transition state species by anion photoelectron spectroscopy
Arnold, Don Wesley [Univ. of California, Berkeley, CA (United States)
1994-08-01
Free radicals, elemental and van der Waals clusters and transition state species for bimolecular chemical reactions are investigated using anion photoelectron spectroscopy. Several low-lying electronic states of ozone have been identified via photoelectron spectroscopy of O_{3}^{-}. A characterization of these states is important to models for atmospheric ozone reaction kinetics. The fluoroformyloxyl radical, FCO_{2}, has been investigated, providing vibrational frequencies and energies for two electronic states. The technique has also been employed to make the first direct observation and characterization of the NNO_{2} molecule. Several electronic states are observed for this species which is believed to play a role as a reactive intermediate in the N + NO_{2} reaction. The experimental results for all three of these radicals are supplemented by ab initio investigations of their molecular properties. The clusters investigations include studies of elemental carbon clusters (C_{2}^{-} - C_{11}^{-}), and van der Waals clusters (X^{-}(CO_{2})_{n}, X = I, Br, Cl; n {le} 13 and I^{-} (N_{2}O)_{n=1--11}). Primarily linear clusters are observed for the smaller carbon clusters, while the spectra of the larger clusters contain contribution from cyclic anion photodetachment. Very interesting ion-solvent interactions are observed in the X^{-}(CO_{2})n clusters. The transition state regions for several bimolecular chemical reactions have also been investigated by photodetachment of a negative ion precursor possessing a geometry similar to that of the transition state species. These spectra show features which are assigned to motions of the unstable neutral complex existing between reactants and products.
Four Generations of Transition State Analogues for Human Purine Nucleoside Phosphorylase
Ho, M.; Shi, W; Rinaldo-Mathis, A; Tyler, P; Evans, G; Almo, S; Schramm, V
2010-01-01
Inhibition of human purine nucleoside phosphorylase (PNP) stops growth of activated T-cells and the formation of 6-oxypurine bases, making it a target for leukemia, autoimmune disorders, and gout. Four generations of ribocation transition-state mimics bound to PNP are structurally characterized. Immucillin-H (K*{sub i} = 58 pM, first-generation) contains an iminoribitol cation with four asymmetric carbons. DADMe-Immucillin-H (K*{sub i} = 9 pM, second-generation), uses a methylene-bridged dihydroxypyrrolidine cation with two asymmetric centers. DATMe-Immucillin-H (K*{sub i} = 9 pM, third-generation) contains an open-chain amino alcohol cation with two asymmetric carbons. SerMe-ImmH (K*{sub i} = 5 pM, fourth-generation) uses achiral dihydroxyaminoalcohol seramide as the ribocation mimic. Crystal structures of PNPs establish features of tight binding to be; (1) ion-pair formation between bound phosphate (or its mimic) and inhibitor cation, (2) leaving-group interactions to N1, O6, and N7 of 9-deazahypoxanthine, (3) interaction between phosphate and inhibitor hydroxyl groups, and (4) His257 interacting with the 5{prime}-hydroxyl group. The first generation analogue is an imperfect fit to the catalytic site with a long ion pair distance between the iminoribitol and bound phosphate and weaker interactions to the leaving group. Increasing the ribocation to leaving-group distance in the second- to fourth-generation analogues provides powerful binding interactions and a facile synthetic route to powerful inhibitors. Despite chemical diversity in the four generations of transition-state analogues, the catalytic site geometry is almost the same for all analogues. Multiple solutions in transition-state analogue design are available to convert the energy of catalytic rate enhancement to binding energy in human PNP.
Study of radicals, clusters and transition state species by anion photoelectron spectroscopy
Arnold, D.W.
1994-08-01
Free radicals, elemental and van der Waals clusters and transition state species for bimolecular chemical reactions are investigated using anion photoelectron spectroscopy. Several low-lying electronic states of ozone have been identified via photoelectron spectroscopy of O 3 - . A characterization of these states is important to models for atmospheric ozone reaction kinetics. The fluoroformyloxyl radical, FCO 2 , has been investigated, providing vibrational frequencies and energies for two electronic states. The technique has also been employed to make the first direct observation and characterization of the NNO 2 molecule. Several electronic states are observed for this species which is believed to play a role as a reactive intermediate in the N + NO 2 reaction. The experimental results for all three of these radicals are supplemented by ab initio investigations of their molecular properties. The clusters investigations include studies of elemental carbon clusters (C 2 - - C 11 - ), and van der Waals clusters (X - (CO 2 ) n , X = I, Br, Cl; n ≤ 13 and I - (N 2 O) n=1--11 ). Primarily linear clusters are observed for the smaller carbon clusters, while the spectra of the larger clusters contain contribution from cyclic anion photodetachment. Very interesting ion-solvent interactions are observed in the X - (CO 2 )n clusters. The transition state regions for several bimolecular chemical reactions have also been investigated by photodetachment of a negative ion precursor possessing a geometry similar to that of the transition state species. These spectra show features which are assigned to motions of the unstable neutral complex existing between reactants and products
Robinson H.; Mage, M.; Dolan, M.; Wang, R.; Boyd, L.; Revilleza, M.; Natarajan, K.; Myers, N.; Hansen, T.; Margulies, D.
2012-05-01
MHC class I (MHC-I) proteins of the adaptive immune system require antigenic peptides for maintenance of mature conformation and immune function via specific recognition by MHC-I-restricted CD8(+) T lymphocytes. New MHC-I molecules in the endoplasmic reticulum are held by chaperones in a peptide-receptive (PR) transition state pending release by tightly binding peptides. In this study, we show, by crystallographic, docking, and molecular dynamics methods, dramatic movement of a hinged unit containing a conserved 3(10) helix that flips from an exposed 'open' position in the PR transition state to a 'closed' position with buried hydrophobic side chains in the peptide-loaded mature molecule. Crystallography of hinged unit residues 46-53 of murine H-2L(d) MHC-I H chain, complexed with mAb 64-3-7, demonstrates solvent exposure of these residues in the PR conformation. Docking and molecular dynamics predict how this segment moves to help form the A and B pockets crucial for the tight peptide binding needed for stability of the mature peptide-loaded conformation, chaperone dissociation, and Ag presentation.
State-to-State Mode Specificity: Energy Sequestration and Flow Gated by Transition State.
Zhao, Bin; Sun, Zhigang; Guo, Hua
2015-12-23
Energy flow and sequestration at the state-to-state level are investigated for a prototypical four-atom reaction, H2 + OH → H + H2O, using a transition-state wave packet (TSWP) method. The product state distribution is found to depend strongly on the reactant vibrational excitation, indicating mode specificity at the state-to-state level. From a local-mode perspective, it is shown that the vibrational excitation of the H2O product derives from two different sources, one attributable to the energy flow along the reaction coordinate into the newly formed OH bond and the other due to the sequestration of the vibrational energy in the OH spectator moiety during the reaction. The analysis provided a unified interpretation of some seemingly contradicting experimental observations. It is further shown that the transfer of vibrational energy from the OH reactant to H2O product is gated by the transition state, accomplished coherently by multiple TSWPs with the corresponding OH vibrational excitation.
McMichael, K.D.; Korver, G.L.
1979-01-01
Kinetic experiments were carried out simultaneously on separate methyl salicylate solutions of allyl phenyl ether and its deuterated phenyl analogues at 170 to 195 0 C. Gas chromatographic analysis for allyl phenyl ether using an internal standard (anisole) and mechanical integration produced concentration/time data which were fitted to the exponential form of the first-order rate equation by a standard and nonlinear least-square program. At least 15 points were obtained for each run, covering 10 to 85% reaction. The derived isotope effects show no temperature dependence. Averages for 6 runs with each compound are k/sub H//k/sub α-D 2 / = 1.18 and K/sub H//k/sub γ-D 2 / = 0.95. An equilibrium α effect of 1.30 and a γ effect of 0.87 may be calculated for both deuterium atoms at 185 0 C. These results show that the C--H vibration frequencies are approximately (1.18 - 1)/(1.27 - 1) or 57 to 77% of the way from those of allyl phenyl ether to those of the cyclohexadiene intermediate. The C--H frequencies of the γ carbon in the transition state are about (0.95 - 1)/(0.88 - 1) or 22 to 62% of the way to those of the intermediate. The structure of the transition state, as far as these bonding frequencies are concerned, is consistent with the Claisen rearrangement
Harding, L.B.; Wagner, A.F.; Bowman, J.M.; Schatz, G.C.; Christoffel, K.
1982-01-01
GVB-POL-CI ab initio calculations of the geometries, energetics, and normal mode frequencies of C 2 H 2 , C 2 H 3 , and the transition state for the addition reaction of H + C 2 H 2 are presented. In addition, normal mode frequencies for the isotopic variants D + C 2 D 2 , D + C 2 H 2 , and H + C 2 D 2 are preented. These results are compared to experimental values for C 2 H 2 and to ab initio values of Hagase and Kern, and semiempirical values of Keil, Lynch, Cowfer, and Michael. The results are also used to calculate the apparent bimolecular addition rate constant using conventional RRKM theory for chemical activation. The calculated rate constants and their isotopic variants are compared as a function of temperature and pressure to available experimental information. The agreement is little different from that obtained by Keil et al. with a similar calculation using semiempirical values for acetylene, transition-state, and vinyl radical properties. In particular, the calculated high-pressure limit of the rate constant appears to be at least 1 order of magnitude higher than the experimental limit. Several possible reasons for this discrepancy are discussed
Serpieri , Roberto; Travascio , Francesco
2016-01-01
A macroscopic continuum theory of two-phase saturated porous media is derived by a purely variational deduction based on the least Action principle. The proposed theory proceeds from the consideration of a minimal set of kinematic descriptors and keeps a specific focus on the derivation of most general medium-independent governing equations, which have a form independent from the particular constitutive relations and thermodynamic constraints characterizing a specific medium. The kinematics o...
Eisenberg, Bob; Hyon, YunKyong; Liu, Chun
2010-01-01
Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton’s least action and Rayleigh’s dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an “extra layer” of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler–Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components
Eisenberg, Bob; Hyon, Yunkyong; Liu, Chun
2010-09-14
Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new
Eisenberg, Bob; Hyon, YunKyong; Liu, Chun
2010-09-01
Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new
Insights from the structure of a smallpox virus topoisomerase-DNA transition state mimic
Perry, Kay; Hwang, Young; Bushman, Frederic D.; Van Duyne, Gregory D.
2010-01-01
Summary Poxviruses encode their own type IB topoisomerases (TopIBs) which release superhelical tension generated by replication and transcription of their genomes. To investigate the reaction catalyzed viral TopIBs, we have determined the structure of a variola virus topoisomerase-DNA complex trapped as a vanadate transition state mimic. The structure reveals how the viral TopIB enzymes are likely to position the DNA duplex for ligation following relaxation of supercoils and identifies the sources of friction observed in single molecule experiments that argue against free rotation. The structure also identifies a conformational change in the leaving group sugar that must occur prior to cleavage and reveals a mechanism for promoting ligation following relaxation of supercoils that involves a novel Asp-minor groove interaction. Overall, the new structural data support a common catalytic mechanism for the TopIB superfamily but indicate distinct methods for controlling duplex rotation in the small vs. large enzyme subfamilies. PMID:20152159
Dynamics of SARS-coronavirus HR2 domain in the prefusion and transition states
McReynolds, Susanna; Jiang, Shaokai; Rong, Lijun; Caffrey, Michael
2009-12-01
The envelope glycoproteins S1 and S2 of severe acute respiratory syndrome coronavirus (SARS-CoV) mediate viral entry by conformational change from a prefusion state to a postfusion state that enables fusion of the viral and target membranes. In this work we present the characterization of the dynamic properties of the SARS-CoV S2-HR2 domain (residues 1141-1193 of S) in the prefusion and newly discovered transition states by NMR 15N relaxation studies. The dynamic properties of the different states, which are stabilized under different experimental conditions, extend the current model of viral membrane fusion and give insight into the design of structure-based antagonists of SARS-CoV in particular, as well as other enveloped viruses such as HIV.
Rinaldo-Matthis,A.; Wing, C.; Ghanem, M.; Deng, H.; Wu, P.; Gupta, A.; Tyler, P.; Evans, G.; Furneaux, R.; et al.
2007-01-01
Trichomonas vaginalis is a parasitic protozoan purine auxotroph possessing a unique purine salvage pathway consisting of a bacterial type purine nucleoside phosphorylase (PNP) and a purine nucleoside kinase. Thus, T. vaginalis PNP (TvPNP) functions in the reverse direction relative to the PNPs in other organisms. Immucillin-A (ImmA) and DADMe-Immucillin-A (DADMe-ImmA) are transition stte mimics of adenosine with geometric and electrostatic features that resemble early and late transition states of adenosine at the transition state stabilized by TvPNP. ImmA demonstrates slow-onset tight-binding inhibition with TvPNP, to give an equilibrium dissociation constant of 87 pM, an inhibitor release half-time of 17.2 min, and a K{sub m}/K{sub d} ratio of 70,100. DADMe-ImmA resembles a late ribooxacarbenium ion transition state for TvPNP to give a dissociation constant of 30 pM, an inhibitor release half-time of 64 min, and a K{sub m}/K{sub d} ratio of 203,300. The tight binding of DADMe-ImmA supports a late S{sub N}1 transition state. Despite their tight binding to TvPNP, ImmA and DADMe-ImmA are weak inhibitors of human and P. falciparum PNPs. The crystal structures of the TvPNP-ImmA{center_dot}PO{sub 4} and TvPNP{center_dot}DADMe-ImmA{center_dot}PO{sub 4} ternary complexes differ from previous structures with substrate anologues. The tight binding with DADMe-ImmA is in part due to a 2.7 {angstrom} ionic interaction between a PO{sub 4} oxygen and the N1 cation of the hydroxypyrrolidine and is weaker in the TvPNP{center_dot}ImmA{center_dot}PO{sub 4} structure at 3.5 {angstrom}. However, the TvPNP{center_dot}ImmA{center_dot}PO{sub 4} structure includes hydrogen bonds between the 2'-hydroxyl and the protein that are not present in TvPNP{center_dot}DADMe-ImmA{center_dot}PO{sub 4}. These structures explain why DADMe-ImmA binds tighter than ImmA. Immucillin-H is a 12 nM inhibitor of TvPNP but a 56 pM inhibitor of human PNP. And this difference is explained by isotope
Gisdon, Florian J; Culka, Martin; Ullmann, G Matthias
2016-10-01
Conjugate peak refinement (CPR) is a powerful and robust method to search transition states on a molecular potential energy surface. Nevertheless, the method was to the best of our knowledge so far only implemented in CHARMM. In this paper, we present PyCPR, a new Python-based implementation of the CPR algorithm within the pDynamo framework. We provide a detailed description of the theory underlying our implementation and discuss the different parts of the implementation. The method is applied to two different problems. First, we illustrate the method by analyzing the gauche to anti-periplanar transition of butane using a semiempirical QM method. Second, we reanalyze the mechanism of a glycyl-radical enzyme, namely of 4-hydroxyphenylacetate decarboxylase (HPD) using QM/MM calculations. In the end, we suggest a strategy how to use our implementation of the CPR algorithm. The integration of PyCPR into the framework pDynamo allows the combination of CPR with the large variety of methods implemented in pDynamo. PyCPR can be used in combination with quantum mechanical and molecular mechanical methods (and hybrid methods) implemented directly in pDynamo, but also in combination with external programs such as ORCA using pDynamo as interface. PyCPR is distributed as free, open source software and can be downloaded from http://www.bisb.uni-bayreuth.de/index.php?page=downloads . Graphical Abstract PyCPR is a search tool for finding saddle points on the potential energy landscape of a molecular system.
Williams, Stefanie L; French, David P
2014-02-05
Longitudinal studies have shown that objectively measured walking behaviour is subject to seasonal variation, with people walking more in summer compared to winter. Seasonality therefore may have the potential to bias the results of randomised controlled trials if there are not adequate statistical or design controls. Despite this there are no studies that assess the impact of seasonality on walking behaviour in a randomised controlled trial, to quantify the extent of such bias. Further there have been no studies assessing how season impacts on the psychological predictors of walking behaviour to date. The aim of the present study was to assess seasonal differences in a) objective walking behaviour and b) Theory of Planned Behaviour (TPB) variables during a randomised controlled trial of an intervention to promote walking. 315 patients were recruited to a two-arm cluster randomised controlled trial of an intervention to promote walking in primary care. A series of repeated measures ANCOVAs were conducted to examine the effect of season on pedometer measures of walking behaviour and TPB measures, assessed immediately post-intervention and six months later. Hierarchical regression analyses were conducted to assess whether season moderated the prediction of intention and behaviour by TPB measures. There were no significant differences in time spent walking in spring/summer compared to autumn/winter. There was no significant seasonal variation in most TPB variables, although the belief that there will be good weather was significantly higher in spring/summer (F = 19.46, p behaviour, or moderate the effects of TPB variables on intention or behaviour. Seasonality does not influence objectively measured walking behaviour or psychological variables during a randomised controlled trial. Consequently physical activity behaviour outcomes in trials will not be biased by the season in which they are measured. Previous studies may have overestimated the extent of
Yang, Xue-Min; Li, Jin-Yan; Zhang, Meng; Chai, Guo-Min; Zhang, Jian
2014-12-01
A thermodynamic model for predicting sulfide capacity of CaO-FeO-Fe2O3-Al2O3-P2O5 slags in a large variation range of oxygen potential corresponding to mass percentage of FetO from 1.88 to 55.50 pct, i.e., IMCT- model, has been developed by coupling with the deduced desulfurization mechanism of the slags based on the ion and molecule coexistence theory (IMCT). The developed IMCT- model has been verified through comparing the determined sulfide capacity after Ban-ya et al.[20] with the calculated by the developed IMCT- model and the calculated by the reported sulfide capacity models such as the KTH model. Mass percentage of FetO as 6.75 pct corresponding to the mass action concentration of FetO as 0.0637 or oxygen partial as 2.27 × 10-6 Pa is the criterion for distinguishing reducing and oxidizing zones for the slags. Sulfide capacity of the slags in reducing zone is controlled by reaction ability of CaO regardless of slag oxidization ability. However, sulfide capacity of the slags in oxidizing zone shows an obvious increase tendency with the increasing of slag oxidization ability. Sulfide capacity of the slags in reducing zone keeps almost constant with variation of the simplified complex basicity (pct CaO)/((pct Al2O3) + (pct P2O5)), or optical basicity, or the mass action concentration ratios of N FeO/ N CaO, , , and . Sulfide capacity of the slags in oxidizing zone shows an obvious increase with the increasing of the simplified complex basicity (pct CaO)/((pct Al2O3) + (pct P2O5)) or optical basicity, or the aforementioned mass action concentration ratios. Thus, the aforementioned mass action concentration ratios and the corresponding mass percentage ratios of various iron oxides to basic oxide CaO are recommended to represent the comprehensive effect of various iron oxides and basic oxide CaO on sulfide capacity of the slags.
Abad, J.; Esteve, J.G.; Pacheco, A.F.
1985-01-01
An approximation technique to construct the low-lying energy eigenstates of any bosonic field theory on the lattice is proposed. It is based on the SLAC blocking method, after performing a finite-spin approximation to the individual degrees of freedom of the problem. General expressions for any polynomial self-interacting theory are given. Numerical results for phi 2 and phi 4 theories in 1+1 dimensions are offered; they exhibit a fast convergence rate. The complete low-lying energy spectrum of the phi 4 theory in 1+1 dimensions is calculated
Wong, Kin-Yiu; Gao, Jiali
2008-09-09
In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property
Ensemble of Transition State Structures for the Cis-Trans Isomerization of N-Methylacetamide
Mantz, Yves A. [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States); Branduardi, Davide [Italian Inst. of Technology, Genoa (Italy); Bussi, Giovanni [Univ. of Modena and Reggio Emilia and INFM-CNR (Italy); Parrinello, Michele [ETH Zurich, Lugano (Switzerland). Dept. of Chemistry and Applied Biosciences
2009-09-17
The cis-trans isomerization of N-methylacetamide (NMA), a model peptidic fragment, is studied theoretically in vacuo and in explicit water solvent at 300 K using the metadynamics technique. The computed cis-trans free energy difference is very similar for NMA(g) and NMA(aq), in agreement with experimental measurements of population ratios and theoretical studies at 0 K. By exploiting the flexibility in the definition of a pair of recently introduced collective variables (Branduardi, D.; Gervasio, F. L.; Parrinello, M. J. Chem. Phys. 2007, 126, 054103), an ensemble of transition state structures is generated at finite temperature for both NMA(g) and NMA(aq), as verified by computing committor distribution functions. Ensemble members of NMA(g) are shown to have correlated values of the backbone dihedral angle and a second dihedral angle involving the amide hydrogen atom. The dynamical character of these structures is preserved in the presence of solvent, whose influence on the committor functions can be modeled using effective friction/noise terms.
Geierhaas, Christian D; Salvatella, Xavier; Clarke, Jane; Vendruscolo, Michele
2008-03-01
It has been suggested that Phi-values, which allow structural information about transition states (TSs) for protein folding to be obtained, are most reliably interpreted when divided into three classes (high, medium and low). High Phi-values indicate almost completely folded regions in the TS, intermediate Phi-values regions with a detectable amount of structure and low Phi-values indicate mostly unstructured regions. To explore the extent to which this classification can be used to characterise in detail the structure of TSs for protein folding, we used Phi-values divided into these classes as restraints in molecular dynamics simulations. This type of procedure is related to that used in NMR spectroscopy to define the structure of native proteins from the measurement of inter-proton distances derived from nuclear Overhauser effects. We illustrate this approach by determining the TS ensembles of five proteins and by showing that the results are similar to those obtained by using as restraints the actual numerical Phi-values measured experimentally. Our results indicate that the simultaneous consideration of a set of low-resolution Phi-values can provide sufficient information for characterising the architecture of a TS for folding of a protein.
Role of Chemical Reactivity and Transition State Modeling for Virtual Screening.
Karthikeyan, Muthukumarasamy; Vyas, Renu; Tambe, Sanjeev S; Radhamohan, Deepthi; Kulkarni, Bhaskar D
2015-01-01
Every drug discovery research program involves synthesis of a novel and potential drug molecule utilizing atom efficient, economical and environment friendly synthetic strategies. The current work focuses on the role of the reactivity based fingerprints of compounds as filters for virtual screening using a tool ChemScore. A reactant-like (RLS) and a product- like (PLS) score can be predicted for a given compound using the binary fingerprints derived from the numerous known organic reactions which capture the molecule-molecule interactions in the form of addition, substitution, rearrangement, elimination and isomerization reactions. The reaction fingerprints were applied to large databases in biology and chemistry, namely ChEMBL, KEGG, HMDB, DSSTox, and the Drug Bank database. A large network of 1113 synthetic reactions was constructed to visualize and ascertain the reactant product mappings in the chemical reaction space. The cumulative reaction fingerprints were computed for 4000 molecules belonging to 29 therapeutic classes of compounds, and these were found capable of discriminating between the cognition disorder related and anti-allergy compounds with reasonable accuracy of 75% and AUC 0.8. In this study, the transition state based fingerprints were also developed and used effectively for virtual screening in drug related databases. The methodology presented here provides an efficient handle for the rapid scoring of molecular libraries for virtual screening.
An automated method to find transition states using chemical dynamics simulations.
Martínez-Núñez, Emilio
2015-02-05
A procedure to automatically find the transition states (TSs) of a molecular system (MS) is proposed. It has two components: high-energy chemical dynamics simulations (CDS), and an algorithm that analyzes the geometries along the trajectories to find reactive pathways. Two levels of electronic structure calculations are involved: a low level (LL) is used to integrate the trajectories and also to optimize the TSs, and a higher level (HL) is used to reoptimize the structures. The method has been tested in three MSs: formaldehyde, formic acid (FA), and vinyl cyanide (VC), using MOPAC2012 and Gaussian09 to run the LL and HL calculations, respectively. Both the efficacy and efficiency of the method are very good, with around 15 TS structures optimized every 10 trajectories, which gives a total of 7, 12, and 83 TSs for formaldehyde, FA, and VC, respectively. The use of CDS makes it a powerful tool to unveil possible nonstatistical behavior of the system under study. © 2014 Wiley Periodicals, Inc.
Sikorski, R.S.; Malany, S.; Seravalli, J.; Quinn, D.M.
2002-01-01
Secondary isotope effects for carbonyl addition reactions of methyl thioacetate, acetone and acetaldehyde have been calculated by ab initio quantum mechanical methods in an effect to interpret measured β-deuterium isotope effects on acetylcholinesterase-catalysed hydrolysis of acetylthiocholine. The calculated β-deuterium isotope effect for equilibrium addition of methanol to methyl thioacetate is D3 K eq = 0.965, and the corresponding effect for addition of methoxide ion to methyl thioacetate wherein three waters are hydrogen bonded to the carbonyl oxyanion is D3 K eq = 1.086. Neither of these calculated isotope effects is an inverse as the experimental β-deuterium isotope effect for acetylcholinesterase-catalysed hydrolysis of acetylthiocholine, D3 K eq = 0.90±0.03. Structural comparisons show that the water-solvated methoxide adduct of methyl thioacetate is more expanded than is the natural methanol addition adduct, and suggest that the degree of which the isotope effect is inverse (i.e. less than) is inversely correlated to the degree of expansion of the adduct. A similar correlation of α-deuterium and β-deuterium secondary isotope effects with the degree of expansion of the adducts is found for equilibrium additions of methanol and methoxide ion to acetylaldehyde. These computational results suggest that the markedly inverse β-deuterium isotope effect for the acetylcholinesterase reaction arises from enzymatic compression of the transition state. (author)
Formoso, Elena; Matxain, Jon M; Lopez, Xabier; York, Darrin M
2010-06-03
The mechanisms of enzymes are intimately connected with their overall structure and dynamics in solution. Experimentally, it is considerably challenging to provide detailed atomic level information about the conformational events that occur at different stages along the chemical reaction path. Here, theoretical tools may offer new potential insights that complement those obtained from experiments that may not yield an unambiguous mechanistic interpretation. In this study, we apply molecular dynamics simulations of bovine pancreatic ribonuclease A, an archetype ribonuclease, to study the conformational dynamics, structural relaxation, and differential solvation that occur at discrete stages of the transesterification and cleavage reaction. Simulations were performed with explicit solvation with rigorous electrostatics and utilize recently developed molecular mechanical force field parameters for transphosphorylation and hydrolysis transition state analogues. Herein, we present results for the enzyme complexed with the dinucleotide substrate cytidilyl-3',5'-adenosine (CpA) in the reactant, and transphosphorylation and hydrolysis transition states. A detailed analysis of active site structures and hydrogen-bond patterns is presented and compared. The integrity of the overall backbone structure is preserved in the simulations and supports a mechanism whereby His12 stabilizes accumulating negative charge at the transition states through hydrogen-bond donation to the nonbridge oxygens. Lys41 is shown to be highly versatile along the reaction coordinate and can aid in the stabilization of the dianionic transition state, while being poised to act as a general acid catalyst in the hydrolysis step.
Wang, Hui-Fang; Liu, Zhi-Pan
2008-08-20
Ethanol oxidation on Pt is a typical multistep and multiselectivity heterogeneous catalytic process. A comprehensive understanding of this fundamental reaction would greatly benefit design of catalysts for use in direct ethanol fuel cells and the degradation of biomass-derived oxygenates. In this work, the reaction network of ethanol oxidation on different Pt surfaces, including close-packed Pt{111}, stepped Pt{211}, and open Pt{100}, is explored thoroughly with an efficient reaction path searching method, which integrates our new transition-state searching technique with periodic density functional theory calculations. Our new technique enables the location of the transition state and saddle points for most surface reactions simply and efficiently by optimization of local minima. We show that the selectivity of ethanol oxidation on Pt depends markedly on the surface structure, which can be attributed to the structure-sensitivity of two key reaction steps: (i) the initial dehydrogenation of ethanol and (ii) the oxidation of acetyl (CH3CO). On open surface sites, ethanol prefers C-C bond cleavage via strongly adsorbed intermediates (CH2CO or CHCO), which leads to complete oxidation to CO2. However, only partial oxidizations to CH3CHO and CH3COOH occur on Pt{111}. Our mechanism points out that the open surface Pt{100} is the best facet to fully oxidize ethanol at low coverages, which sheds light on the origin of the remarkable catalytic performance of Pt tetrahexahedra nanocrystals found recently. The physical origin of the structure-selectivity is rationalized in terms of both thermodynamics and kinetics. Two fundamental quantities that dictate the selectivity of ethanol oxidation are identified: (i) the ability of surface metal atoms to bond with unsaturated C-containing fragments and (ii) the relative stability of hydroxyl at surface atop sites with respect to other sites.
Teilum, Kaare; Thormann, Thorsten; Caterer, Nigel R; Poulsen, Heidi I; Jensen, Peter H; Knudsen, Jens; Kragelund, Birthe B; Poulsen, Flemming M
2005-04-01
Comparison of the folding processes for homologue proteins can provide valuable information about details in the interactions leading to the formation of the folding transition state. Here the folding kinetics of 18 variants of yACBP and 3 variants of bACBP have been studied by Phi-value analysis. In combination with Phi-values from previous work, detailed insight into the transition states for folding of both yACBP and bACBP has been obtained. Of the 16 sequence positions that have been studied in both yACBP and bACBP, 5 (V12, I/L27, Y73, V77, and L80) have high Phi-values and appear to be important for the transition state formation in both homologues. Y31, A34, and A69 have high Phi-values only in yACBP, while F5, A9, and I74 have high Phi-values only in bACBP. Thus, additional interactions between helices A2 and A4 appear to be important for the transition state of yACBP, whereas additional interactions between helices A1 and A4 appear to be important for the transition state of bACBP. To examine whether these differences could be assigned to different packing of the residues in the native state, a solution structure of yACBP was determined by NMR. Small changes in the packing of the hydrophobic side-chains, which strengthen the interactions between helices A2 and A4, are observed in yACBP relative to bACBP. It is suggested that different structure elements serve as scaffolds for the folding of the 2 ACBP homologues. (c) 2005 Wiley-Liss, Inc.
Nakatsuji, H.; Hirao, K.
1978-01-01
The symmetry-adapted-cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry-adapted excited configurations having the symmetry under consideration, and includes their higher-order effect and self-consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open-shell systems as well as closed-shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher-order effect and the self-consistency effect. We have expressed some existing open-shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo-orbital theory which is an extension of open-shell orbital theory in the SAC expansion formula
Contribution of cutinase serine 42 side chain to the stabilization of the oxyanion transition state.
Nicolas, A; Egmond, M; Verrips, C T; de Vlieg, J; Longhi, S; Cambillau, C; Martinez, C
1996-01-16
Cutinase from the fungus Fusarium solani pisi is a lipolytic enzyme able to hydrolyze both aggregated and soluble substrates. It therefore provides a powerful tool for probing the mechanisms underlying lipid hydrolysis. Lipolytic enzymes have a catalytic machinery similar to those present in serine proteinases. It is characterized by the triad Ser, His, and Asp (Glu) residues, by an oxyanion binding site that stabilizes the transition state via hydrogen bonds with two main chain amide groups, and possibly by other determinants. It has been suggested on the basis of a covalently bond inhibitor that the cutinase oxyanion hole may consist not only of two main chain amide groups but also of the Ser42 O gamma side chain. Among the esterases and the serine and the cysteine proteases, only Streptomyces scabies esterase, subtilisin, and papain, respectively, have a side chain residue which is involved in the oxyanion hole formation. The position of the cutinase Ser42 side chain is structurally conserved in Rhizomucor miehei lipase with Ser82 O gamma, in Rhizopus delemar lipase with Thr83 O gamma 1, and in Candida antartica B lipase with Thr40 O gamma 1. To evaluate the increase in the tetrahedral intermediate stability provided by Ser42 O gamma, we mutated Ser42 into Ala. Furthermore, since the proper orientation of Ser42 O gamma is directed by Asn84, we mutated Asn84 into Ala, Leu, Asp, and Trp, respectively, to investigate the contribution of this indirect interaction to the stabilization of the oxyanion hole. The S42A mutation resulted in a drastic decrease in the activity (450-fold) without significantly perturbing the three-dimensional structure. The N84A and N84L mutations had milder kinetic effects and did not disrupt the structure of the active site, whereas the N84W and N84D mutations abolished the enzymatic activity due to drastic steric and electrostatic effects, respectively.
Lipi Thukral
2011-09-01
Full Text Available Small globular proteins and peptides commonly exhibit two-state folding kinetics in which the rate limiting step of folding is the surmounting of a single free energy barrier at the transition state (TS separating the folded and the unfolded states. An intriguing question is whether the polypeptide chain reaches, and leaves, the TS by completely random fluctuations, or whether there is a directed, stepwise process. Here, the folding TS of a 15-residue β-hairpin peptide, Peptide 1, is characterized using independent 2.5 μs-long unbiased atomistic molecular dynamics (MD simulations (a total of 15 μs. The trajectories were started from fully unfolded structures. Multiple (spontaneous folding events to the NMR-derived conformation are observed, allowing both structural and dynamical characterization of the folding TS. A common loop-like topology is observed in all the TS structures with native end-to-end and turn contacts, while the central segments of the strands are not in contact. Non-native sidechain contacts are present in the TS between the only tryptophan (W11 and the turn region (P7-G9. Prior to the TS the turn is found to be already locked by the W11 sidechain, while the ends are apart. Once the ends have also come into contact, the TS is reached. Finally, along the reactive folding paths the cooperative loss of the W11 non-native contacts and the formation of the central inter-strand native contacts lead to the peptide rapidly proceeding from the TS to the native state. The present results indicate a directed stepwise process to folding the peptide.
High Pressure ZZ-Exchange NMR Reveals Key Features of Protein Folding Transition States.
Zhang, Yi; Kitazawa, Soichiro; Peran, Ivan; Stenzoski, Natalie; McCallum, Scott A; Raleigh, Daniel P; Royer, Catherine A
2016-11-23
Understanding protein folding mechanisms and their sequence dependence requires the determination of residue-specific apparent kinetic rate constants for the folding and unfolding reactions. Conventional two-dimensional NMR, such as HSQC experiments, can provide residue-specific information for proteins. However, folding is generally too fast for such experiments. ZZ-exchange NMR spectroscopy allows determination of folding and unfolding rates on much faster time scales, yet even this regime is not fast enough for many protein folding reactions. The application of high hydrostatic pressure slows folding by orders of magnitude due to positive activation volumes for the folding reaction. We combined high pressure perturbation with ZZ-exchange spectroscopy on two autonomously folding protein domains derived from the ribosomal protein, L9. We obtained residue-specific apparent rates at 2500 bar for the N-terminal domain of L9 (NTL9), and rates at atmospheric pressure for a mutant of the C-terminal domain (CTL9) from pressure dependent ZZ-exchange measurements. Our results revealed that NTL9 folding is almost perfectly two-state, while small deviations from two-state behavior were observed for CTL9. Both domains exhibited large positive activation volumes for folding. The volumetric properties of these domains reveal that their transition states contain most of the internal solvent excluded voids that are found in the hydrophobic cores of the respective native states. These results demonstrate that by coupling it with high pressure, ZZ-exchange can be extended to investigate a large number of protein conformational transitions.
2018-01-02
SECURITY CLASSIFICATION OF: 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES 12. DISTRIBUTION AVAILIBILITY STATEMENT 6...redox reactions. The existence of mercury either in elemental (Hg0) or in oxidized divalent Hg2+ forms affects mercury availability and mobility within...halides formation in presence of water molecules (as water is present in upper atmosphere). Although we could locate the low barrier for the Hg—Br
Perez-Benito, Joaquin F.
2017-01-01
The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…
Takayoshi Kobayashi
2013-02-01
Full Text Available Chemical bond breaking and formation during chemical reactions can be observed using “transition state spectroscopy”. Comparing the measurement result of the transition state spectroscopy with the simulation result of single direct-dynamics trajectory, we have elucidated the reaction dynamics of Claisen rearrangement of allyl vinyl ether. Observed the reaction of the neat sample liquid, we have estimated the time constants of transformation from straight-chain structure to aromatic-like six-membered ring structure forming the C1-C6 bond. The result clarifies that the reaction proceeds via three steps taking longer time than expected from the gas phase calculation. This finding provides new hypothesis and discussions, helping the development of the field of reaction mechanism analysis.
Palenik, Mark C; Rodriguez, Jorge H
2014-07-07
Understanding mechanisms of (+)-anti-BPDE detoxification is crucial for combating its mutagenic and potent carcinogenic action. However, energetic-structural correlations of reaction intermediates and transition states during detoxification via hydrolysis are poorly understood. To gain mechanistic insight we have computationally characterized intermediate and transition species associated with spontaneous and general-acid catalyzed hydrolysis of (+)-anti-BPDE. We studied the role of cacodylic acid as a proton donor in the rate limiting step. The computed activation energy (ΔG‡) is in agreement with the experimental value for hydrolysis in a sodium cacodylate buffer. Both types of, spontaneous and acid catalyzed, BPDE hydrolysis can proceed through low-entropy hydrogen bonded intermediates prior to formation of transition states whose energies determine reaction activation barriers and rates.
Origin of the Hawaiian rainforest and its transition states in long-term primary succession
Mueller-Dombois, D.; Boehmer, H. J.
2013-07-01
This paper addresses the question of transition states in the Hawaiian rainforest ecosystem with emphasis on their initial developments. Born among volcanoes in the north central Pacific about 4 million years ago, the Hawaiian rainforest became assembled from spores of algae, fungi, lichens, bryophytes, ferns and from seeds of about 275 flowering plants that over the millennia evolved into ca. 1000 endemic species. Outstanding among the forest builders were the tree ferns (Cibotium spp.) and the 'ōhi'a lehua trees (Metrosideros spp.), which still dominate the Hawaiian rainforest ecosystem today. The structure of this forest is simple. The canopy in closed mature rainforests is dominated by cohorts of Metrosideros polymorpha and the undergrowth by tree fern species of Cibotium. When a new lava flow cuts through this forest, kipuka are formed, i.e., islands of remnant vegetation. On the new volcanic substrate, the assemblage of plant life forms is similar to the assemblage during the evolution of this system. In open juvenile forests, a mat-forming fern, the uluhe fern (Dicranopteris linearis), becomes established. It inhibits further regeneration of the dominant 'ōhi'a tree, thereby reinforcing the cohort structure of the canopy guild. In the later part of its life cycle, the canopy guild breaks down often in synchrony. The trigger is hypothesized to be a climatic perturbation. After the disturbance, the forest becomes reestablished in about 30-40 yr. As the volcanic surfaces age, they go from a mesotrophic to a eutrophic phase, reaching a biophilic nutrient climax by about 1-25 K yr. Thereafter, a regressive oligotrophic phase follows; the soils become exhausted of nutrients. The shield volcanoes break down. Marginally, forest habitats change into bogs and stream ecosystems. The broader 'ōhi'a rainforest redeveloping in the more dissected landscapes of the older islands loses stature, often forming large gaps that are invaded by the aluminum tolerant uluhe fern
Origin of the Hawaiian rainforest and its transition states in long-term primary succession
D. Mueller-Dombois
2013-07-01
Full Text Available This paper addresses the question of transition states in the Hawaiian rainforest ecosystem with emphasis on their initial developments. Born among volcanoes in the north central Pacific about 4 million years ago, the Hawaiian rainforest became assembled from spores of algae, fungi, lichens, bryophytes, ferns and from seeds of about 275 flowering plants that over the millennia evolved into ca. 1000 endemic species. Outstanding among the forest builders were the tree ferns (Cibotium spp. and the 'ōhi'a lehua trees (Metrosideros spp., which still dominate the Hawaiian rainforest ecosystem today. The structure of this forest is simple. The canopy in closed mature rainforests is dominated by cohorts of Metrosideros polymorpha and the undergrowth by tree fern species of Cibotium. When a new lava flow cuts through this forest, kipuka are formed, i.e., islands of remnant vegetation. On the new volcanic substrate, the assemblage of plant life forms is similar to the assemblage during the evolution of this system. In open juvenile forests, a mat-forming fern, the uluhe fern (Dicranopteris linearis, becomes established. It inhibits further regeneration of the dominant 'ōhi'a tree, thereby reinforcing the cohort structure of the canopy guild. In the later part of its life cycle, the canopy guild breaks down often in synchrony. The trigger is hypothesized to be a climatic perturbation. After the disturbance, the forest becomes reestablished in about 30–40 yr. As the volcanic surfaces age, they go from a mesotrophic to a eutrophic phase, reaching a biophilic nutrient climax by about 1–25 K yr. Thereafter, a regressive oligotrophic phase follows; the soils become exhausted of nutrients. The shield volcanoes break down. Marginally, forest habitats change into bogs and stream ecosystems. The broader 'ōhi'a rainforest redeveloping in the more dissected landscapes of the older islands loses stature, often forming large gaps that are invaded by the aluminum
Gao, Daquan; Zhan, Chang-Guo
2006-01-01
Molecular dynamics (MD) simulations and quantum mechanical/molecular mechanical (QM/MM) calculations were performed on the prereactive enzyme-substrate complex, transition states, intermediates, and product involved in the process of human butyrylcholinesterase (BChE)-catalyzed hydrolysis of (−)-cocaine. The computational results consistently reveal a unique role of the oxyanion hole (consisting of G116, G117, and A199) in BChE-catalyzed hydrolysis of cocaine, as compared to acetylcholinester...
Ting, Jing Jing; Tarmizi, Rohani Tarmizi; Bakar, Kamariah Abu; Aralas, Dalia
2017-01-01
Introduction: Analysis of lessons held in East Asia regions that perform well in Trends in International Mathematics and Science Studies such as; South Korea, Hong Kong and Japan, demonstrated teachers in mathematics classroom enacted features of the content systematically with consideration of variation within students' capabilities. Recent…
Salau Tajudeen A.O.
2014-01-01
Full Text Available This study reported a simulation approach to the understanding of the interactions between a buried pipe and the soil system by computing the bending stress variation of harmonically-excited buried pipes. The established principles of linear dynamics theory and simple beam theory were utilised in the analysis of the problem of buried pipe bending stress accumulation and its dynamics. With regards to the parameters that influence the bending stress variations, the most important are the isolation factor, uniform external load, and the corresponding limiting conditions. The simulated mathematical expressions, containing static and dynamic parameters of the buried pipe and earth, were coded in Fortran programming language and applied in the simulation experiment. The results obtained showed that harmonically-excited buried thick-walled pipe became stable and effective when the ratio of the natural frequency of vibration to the forced frequency is greater than 2.0, whenever the damped factor is used as the control parameter for the maximum bending stress. The mirror image of the stress variation produces variation in the location of the maximum bending stress in quantitative terms. The acceptable pipe materials for the simulated cases must have yield strength in bending greater than or equal to 13.95 MPa. The results obtained in this work fill a gap in the literature and will be useful to pipeline engineers and designers, as well as to environmental scientists in initialising and controlling environmental issues and policy formulation concerning the influence of buried pipe on the soil and water in the environment.
Eric P. Baumer
2008-11-01
Full Text Available One of the most influential statements in the anomie theory tradition has been Merton’s argument that the volume of instrumental property crime should be higher where there is a greater imbalance between the degree of commitment to monetary success goals and the degree of commitment to legitimate means of pursuing such goals. Contemporary anomie theories stimulated by Merton’s perspective, most notably Messner and Rosenfeld’s institutional anomie theory, have expanded the scope conditions by emphasizing lethal criminal violence as an outcome to which anomie theory is highly relevant, and virtually all contemporary empirical studies have focused on applying the perspective to explaining spatial variation in homicide rates. In the present paper, we argue that current explications of Merton’s theory and IAT have not adequately conveyed the relevance of the core features of the anomie perspective to lethal violence. We propose an expanded anomie model in which an unbalanced pecuniary value system – the core causal variable in Merton’s theory and IAT – translates into higher levels of homicide primarily in indirect ways by increasing levels of firearm prevalence, drug market activity, and property crime, and by enhancing the degree to which these factors stimulate lethal outcomes. Using aggregate-level data collected during the mid-to-late 1970s for a sample of relatively large social aggregates within the U.S., we find a significant effect on homicide rates of an interaction term reflecting high levels of commitment to monetary success goals and low levels of commitment to legitimate means. Virtually all of this effect is accounted for by higher levels of property crime and drug market activity that occur in areas with an unbalanced pecuniary value system. Our analysis also reveals that property crime is more apt to lead to homicide under conditions of high levels of structural disadvantage. These and other findings underscore the
Zahavi, Arielle Y; Sabbagh, Mark A; Washburn, Dustin; Mazurka, Raegan; Bagby, R Michael; Strauss, John; Kennedy, James L; Ravindran, Arun; Harkness, Kate L
2016-01-01
Theory of mind-the ability to decode and reason about others' mental states-is a universal human skill and forms the basis of social cognition. Theory of mind accuracy is impaired in clinical conditions evidencing social impairment, including major depressive disorder. The current study is a preliminary investigation of the association of polymorphisms of the serotonin transporter (SLC6A4), dopamine transporter (DAT1), dopamine receptor D4 (DRD4), and catechol-O-methyl transferase (COMT) genes with theory of mind decoding in a sample of adults with major depression. Ninety-six young adults (38 depressed, 58 non-depressed) completed the 'Reading the Mind in the Eyes task' and a non-mentalistic control task. Genetic associations were only found for the depressed group. Specifically, superior accuracy in decoding mental states of a positive valence was seen in those homozygous for the long allele of the serotonin transporter gene, 9-allele carriers of DAT1, and long-allele carriers of DRD4. In contrast, superior accuracy in decoding mental states of a negative valence was seen in short-allele carriers of the serotonin transporter gene and 10/10 homozygotes of DAT1. Results are discussed in terms of their implications for integrating social cognitive and neurobiological models of etiology in major depression.
Arielle Y Zahavi
Full Text Available Theory of mind-the ability to decode and reason about others' mental states-is a universal human skill and forms the basis of social cognition. Theory of mind accuracy is impaired in clinical conditions evidencing social impairment, including major depressive disorder. The current study is a preliminary investigation of the association of polymorphisms of the serotonin transporter (SLC6A4, dopamine transporter (DAT1, dopamine receptor D4 (DRD4, and catechol-O-methyl transferase (COMT genes with theory of mind decoding in a sample of adults with major depression. Ninety-six young adults (38 depressed, 58 non-depressed completed the 'Reading the Mind in the Eyes task' and a non-mentalistic control task. Genetic associations were only found for the depressed group. Specifically, superior accuracy in decoding mental states of a positive valence was seen in those homozygous for the long allele of the serotonin transporter gene, 9-allele carriers of DAT1, and long-allele carriers of DRD4. In contrast, superior accuracy in decoding mental states of a negative valence was seen in short-allele carriers of the serotonin transporter gene and 10/10 homozygotes of DAT1. Results are discussed in terms of their implications for integrating social cognitive and neurobiological models of etiology in major depression.
Sharma, C.S.; Rebelo, I.
1975-01-01
It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banch spaces. It is shown that this result makes the calculus largely inapplicable to the solution od variational problems of quantum mechanics. A new concept of differentiability called semidifferentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-value functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (J. Phys. A; 2:413 (1969)) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus in banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear function as particular cases. (author)
Variation and Mathematics Pedagogy
Leung, Allen
2012-01-01
This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…
Gao Fei; Weber, W J; Corrales, L R; Jonsson, H
2003-01-01
Energetic primary recoil atoms from ion implantation or fast neutron irradiation produce isolated point defects and clusters of both vacancies and interstitials. The migration energies and mechanisms for these defects are crucial to successful multiscale modeling of microstructural evolution during ion-implantation, thermal annealing, or under irradiation over long periods of time. The dimer method is employed to search for possible transition states of interstitials and small interstitial clusters in SiC and alpha-Fe. The method uses only the first derivatives of the potential energy to find saddle points without knowledge of the final state of the transition. In SiC, the possible migration pathway for the C interstitial is found to consist of the first neighbor jump via a Si site or second neighbor jump, but the relative probability for the second neighbor jump is very low. In alpha-Fe, the possible transition states are studied as a function of interstitial cluster size, and the lowest energy barriers corr...
Xu, Guoyan G; Zhang, Yan; Mercedes-Camacho, Ana Y; Etzkorn, Felicia A
2011-11-08
The mechanism of the cell cycle regulatory peptidyl prolyl isomerase (PPIase), Pin1, was investigated using reduced-amide inhibitors designed to mimic the twisted-amide transition state. Inhibitors, R-pSer-Ψ[CH(2)N]-Pro-2-(indol-3-yl)ethylamine, 1 [R = fluorenylmethoxycarbonyl (Fmoc)] and 2 (R = Ac), of Pin1 were synthesized and bioassayed. Inhibitor 1 had an IC(50) value of 6.3 μM, which is 4.5-fold better for Pin1 than our comparable ground-state analogue, a cis-amide alkene isostere-containing inhibitor. The change of Fmoc to Ac in 2 improved aqueous solubility for structural determination and resulted in an IC(50) value of 12 μM. The X-ray structure of the complex of 2 bound to Pin1 was determined to 1.76 Å resolution. The structure revealed that the reduced amide adopted a conformation similar to the proposed twisted-amide transition state of Pin1, with a trans-pyrrolidine conformation of the prolyl ring. A similar conformation of substrate would be destabilized relative to the planar amide conformation. Three additional reduced amides, with Thr replacing Ser and l- or d-pipecolate (Pip) replacing Pro, were slightly weaker inhibitors of Pin1.
Seidu, Issaka; Zhekova, Hristina R; Seth, Michael; Ziegler, Tom
2012-03-08
The performance of the second-order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) for the calculation of the exchange coupling constant (J) is assessed by application to a series of triply bridged Cu(II) dinuclear complexes. A comparison of the J values based on SF-CV(2)-DFT with those obtained by the broken symmetry (BS) DFT method and experiment is provided. It is demonstrated that our methodology constitutes a viable alternative to the BS-DFT method. The strong dependence of the calculated exchange coupling constants on the applied functionals is demonstrated. Both SF-CV(2)-DFT and BS-DFT affords the best agreement with experiment for hybrid functionals.
Moiseiwitsch, B L
2004-01-01
This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mecha
Variational principles for locally variational forms
Brajercik, J.; Krupka, D.
2005-01-01
We present the theory of higher order local variational principles in fibered manifolds, in which the fundamental global concept is a locally variational dynamical form. Any two Lepage forms, defining a local variational principle for this form, differ on intersection of their domains, by a variationally trivial form. In this sense, but in a different geometric setting, the local variational principles satisfy analogous properties as the variational functionals of the Chern-Simons type. The resulting theory of extremals and symmetries extends the first order theories of the Lagrange-Souriau form, presented by Grigore and Popp, and closed equivalents of the first order Euler-Lagrange forms of Hakova and Krupkova. Conceptually, our approach differs from Prieto, who uses the Poincare-Cartan forms, which do not have higher order global analogues
Bhattacherjee, Aditi, E-mail: abhattacherjee@berkeley.edu, E-mail: andrewattar@berkeley.edu; Attar, Andrew R., E-mail: abhattacherjee@berkeley.edu, E-mail: andrewattar@berkeley.edu [Department of Chemistry, University of California, Berkeley, California 94720 (United States); Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Leone, Stephen R., E-mail: srl@berkeley.edu [Department of Chemistry, University of California, Berkeley, California 94720 (United States); Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Department of Physics, University of California, Berkeley, California 94720 (United States)
2016-03-28
Femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy based on a high-harmonic generation source is used to study the 266 nm induced A-band photodissociation dynamics of allyl iodide (CH{sub 2} =CHCH{sub 2}I). The photolysis of the C—I bond at this wavelength produces iodine atoms both in the ground ({sup 2}P{sub 3/2}, I) and spin-orbit excited ({sup 2}P{sub 1/2}, I*) states, with the latter as the predominant channel. Using XUV absorption at the iodine N{sub 4/5} edge (45–60 eV), the experiments constitute a direct probe of not only the long-lived atomic iodine reaction products but also the fleeting transition state region of the repulsive n{sub I}σ{sup ∗}{sub C—I} excited states. Specifically, three distinct features are identified in the XUV transient absorption spectrum at 45.3 eV, 47.4 eV, and 48.4 eV (denoted transients A, B, and C, respectively), which arise from the repulsive valence-excited nσ{sup ∗} states and project onto the high-lying core-excited states of the dissociating molecule via excitation of 4d(I) core electrons. Transients A and B originate from 4d(I) → n(I) core-to-valence transitions, whereas transient C is best assigned to a 4d(I) →σ{sup ∗}(C—I) transition. The measured differential absorbance of these new features along with the I/I* branching ratios known from the literature is used to suggest a more definitive assignment, albeit provisional, of the transients to specific dissociative states within the A-band manifold. The transients are found to peak around 55 fs–65 fs and decay completely by 145 fs–185 fs, demonstrating the ability of XUV spectroscopy to map the evolution of reactants into products in real time. The similarity in the energies of transients A and B with analogous features observed in methyl iodide [Attar et al. J. Phys. Chem. Lett. 6, 5072, (2015)] together with the new observation of transient C in the present work provides a more complete picture of the valence electronic
Lagana, Antonio; Faginas Lago, Noelia; Rampino, Sergio [Dipartimento di Chimica, Universita di Perugia, 06123 Perugia (Italy); Huarte-Larranaga, FermIn [Computer Simulation and Modeling Lab (CoSMoLab), Parc CientIfic de Barcelona, 08028 Barcelona (Spain); GarcIa, Ernesto [Departamento de Quimica Fisica, Universidad del PaIs Vasco, 01006 Vitoria (Spain)], E-mail: lagana05@gmail.com, E-mail: fhuarte@pcb.ub.es, E-mail: e.garcia@ehu.es
2008-10-15
Zero total angular momentum exact quantum calculations of the probabilities of the N+N{sub 2} reaction have been performed on the L3 potential energy surface having a bent transition state. This has allowed us to work out J-shifting estimates of the thermal rate coefficient based on the calculation of either detailed (state-to-state) or cumulative (multiconfiguration) probabilities. The results obtained are used to compare the numerical outcomes and the concurrent computational machineries of both quantum and semiclassical approaches as well as to exploit the potentialities of the J-shifting model. The implications of moving the barrier to reaction from the previously proposed collinear geometry of the LEPS to the bent one of L3 are also investigated by comparing the related detailed reactive probabilities.
Gao, Daquan; Zhan, Chang-Guo
2006-01-01
Molecular dynamics (MD) simulations and quantum mechanical/molecular mechanical (QM/MM) calculations were performed on the prereactive enzyme-substrate complex, transition states, intermediates, and product involved in the process of human butyrylcholinesterase (BChE)-catalyzed hydrolysis of (-)-cocaine. The computational results consistently reveal a unique role of the oxyanion hole (consisting of G116, G117, and A199) in BChE-catalyzed hydrolysis of cocaine, compared to acetylcholinesterase (AChE)-catalyzed hydrolysis of acetylcholine. During BChE-catalyzed hydrolysis of cocaine, only G117 has a hydrogen bond with the carbonyl oxygen (O31) of the cocaine benzoyl ester in the prereactive BChE-cocaine complex, and the NH groups of G117 and A199 are hydrogen-bonded with O31 of cocaine in all of the transition states and intermediates. Surprisingly, the NH hydrogen of G116 forms an unexpected hydrogen bond with the carboxyl group of E197 side chain and, therefore, is not available to form a hydrogen bond with O31 of cocaine in the acylation. The NH hydrogen of G116 is only partially available to form a weak hydrogen bond with O31 of cocaine in some structures involved in the deacylation. The change of the estimated hydrogen-bonding energy between the oxyanion hole and O31 of cocaine during the reaction process demonstrates how the protein environment can affect the energy barrier for each step of the BChE-catalyzed hydrolysis of cocaine. These insights concerning the effects of the oxyanion hole on the energy barriers provide valuable clues on how to rationally design BChE mutants with a higher catalytic activity for the hydrolysis of (-)-cocaine. 2005 Wiley-Liss, Inc.
Eccles Martin
2007-09-01
Full Text Available Abstract Background For people with dementia, patient-centred care should involve timely explanation of the diagnosis and its implications. However, this is not routine. Theoretical models of behaviour change offer a generalisable framework for understanding professional practice and identifying modifiable factors to target with an intervention. Theoretical models and empirical work indicate that behavioural intention represents a modifiable predictor of actual professional behaviour. We identified factors that predict the intentions of members of older people's mental health teams (MHTs to perform key behaviours involved in the disclosure of dementia. Design Postal questionnaire survey. Participants Professionals from MHTs in the English National Health Service. Methods We selected three behaviours: Determining what patients already know or suspect about their diagnosis; using explicit terminology when talking to patients; and exploring what the diagnosis means to patients. The questionnaire was based upon the Theory of Planned Behaviour (TPB, Social Cognitive Theory (SCT, and exploratory team variables. Main outcomes Behavioural intentions. Results Out of 1,269 professionals working in 85 MHTs, 399 (31.4% returned completed questionnaires. Overall, the TPB best explained behavioural intention. For determining what patients already know, the TPB variables of subjective norm, perceived behavioural control and attitude explained 29.4% of the variance in intention. For the use of explicit terminology, the same variables explained 53.7% of intention. For exploring what the diagnosis means to patients, subjective norm and perceived behavioural control explained 48.6% of intention. Conclusion These psychological models can explain up to half of the variation in intention to perform key disclosure behaviours. This provides an empirically-supported, theoretical basis for the design of interventions to improve disclosure practice by targeting relevant
Essa, K.S.M.; Embaby, M.; Marrouf, A.A.; Koza, A.M.; Abd El-Monsef, M.E.
2007-01-01
It is well known that the wind energy potential is proportional to both air density and the third power of the wind speed average over a suitable time period. The wind speed and air density have random variables depending on both time and location. The main objective of this work is to derive the most general wind energy potential of the wind formulation putting into consideration the time variable in both wind speed and air density. The correction factor is derived explicitly in terms of the cross-correlation and the coefficients of variation.The application is performed for environmental and wind speed measurements at the Cairo Airport, Kosseir and Hurguada, Egypt. Comparisons are made between Weibull, Rayleigh, and actual data distributions of wind speed and wind power of one year 2005. A Weibull distribution is the best match to the actual probability distribution of wind speed data for most stations. The maximum wind energy potential was 373 W/m 2 in June at Hurguada (Red Sea coast) where the annual mean value was 207 W/m 2 . By Using Rough Set Theory, We Find That the Wind Power Depends on the Wind Speed with greater than air density
Bailey, Johnathan O; Singleton, Daniel A
2017-11-08
Our previous work found that canonical forms of transition state theory incorrectly predict the regioselectivity of the hydroboration of propene with BH 3 in solution. In response, it has been suggested that alternative statistical and nonstatistical rate theories can adequately account for the selectivity. This paper uses a combination of experimental and theoretical studies to critically evaluate the ability of these rate theories, as well as dynamic trajectories and newly developed localized statistical models, to predict quantitative selectivities and qualitative trends in hydroborations on a broader scale. The hydroboration of a series of terminally substituted alkenes with BH 3 was examined experimentally, and a classically unexpected trend is that the selectivity increases as the alkyl chain is lengthened far from the reactive centers. Conventional and variational transition state theories can predict neither the selectivities nor the trends. The canonical competitive nonstatistical model makes somewhat better predictions for some alkenes but fails to predict trends, and it performs poorly with an alkene chosen to test a specific prediction of the model. Added nonstatistical corrections to this model make the predictions worse. Parametrized Rice-Ramsperger-Kassel-Marcus (RRKM)-master equation calculations correctly predict the direction of the trend in selectivity versus alkene size but overpredict its magnitude, and the selectivity with large alkenes remains unpredictable with any parametrization. Trajectory studies in explicit solvent can predict selectivities without parametrization but are impractical for predicting small changes in selectivity. From a lifetime and energy analysis of the trajectories, "localized RRKM-ME" and "competitive localized noncanonical" rate models are suggested as steps toward a general model. These provide the best predictions of the experimental observations and insight into the selectivities.
Nguyen, Trong-Nghia [Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan (China); Department of Physical Chemistry, Hanoi University of Science and Technology, Hanoi (Viet Nam); Putikam, Raghunath; Lin, M. C., E-mail: chemmcl@emory.edu [Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan (China)
2015-03-28
We have discovered a new and highly competitive product channel in the unimolecular decay process for small Criegee intermediates, CH{sub 2}OO and anti/syn-CH{sub 3}C(H)OO, occurring by intramolecular insertion reactions via a roaming-like transition state (TS) based on quantum-chemical calculations. Our results show that in the decomposition of CH{sub 2}OO and anti-CH{sub 3}C(H)OO, the predominant paths directly produce cis-HC(O)OH and syn-CH{sub 3}C(O)OH acids with >110 kcal/mol exothermicities via loose roaming-like insertion TSs involving the terminal O atom and the neighboring C–H bonds. For syn-CH{sub 3}C(H)OO, the major decomposition channel occurs by abstraction of a H atom from the CH{sub 3} group by the terminal O atom producing CH{sub 2}C(H)O–OH. At 298 K, the intramolecular insertion process in CH{sub 2}OO was found to be 600 times faster than the commonly assumed ring-closing reaction.
Nguyen, Trong-Nghia; Putikam, Raghunath; Lin, M. C.
2015-01-01
We have discovered a new and highly competitive product channel in the unimolecular decay process for small Criegee intermediates, CH 2 OO and anti/syn-CH 3 C(H)OO, occurring by intramolecular insertion reactions via a roaming-like transition state (TS) based on quantum-chemical calculations. Our results show that in the decomposition of CH 2 OO and anti-CH 3 C(H)OO, the predominant paths directly produce cis-HC(O)OH and syn-CH 3 C(O)OH acids with >110 kcal/mol exothermicities via loose roaming-like insertion TSs involving the terminal O atom and the neighboring C–H bonds. For syn-CH 3 C(H)OO, the major decomposition channel occurs by abstraction of a H atom from the CH 3 group by the terminal O atom producing CH 2 C(H)O–OH. At 298 K, the intramolecular insertion process in CH 2 OO was found to be 600 times faster than the commonly assumed ring-closing reaction
The Role of Backbone Hydrogen Bonds in the Transition State for Protein Folding of a PDZ Domain.
Søren W. Pedersen
Full Text Available Backbone hydrogen bonds are important for the structure and stability of proteins. However, since conventional site-directed mutagenesis cannot be applied to perturb the backbone, the contribution of these hydrogen bonds in protein folding and stability has been assessed only for a very limited set of small proteins. We have here investigated effects of five amide-to-ester mutations in the backbone of a PDZ domain, a 90-residue globular protein domain, to probe the influence of hydrogen bonds in a β-sheet for folding and stability. The amide-to-ester mutation removes NH-mediated hydrogen bonds and destabilizes hydrogen bonds formed by the carbonyl oxygen. The overall stability of the PDZ domain generally decreased for all amide-to-ester mutants due to an increase in the unfolding rate constant. For this particular region of the PDZ domain, it is therefore clear that native hydrogen bonds are formed after crossing of the rate-limiting barrier for folding. Moreover, three of the five amide-to-ester mutants displayed an increase in the folding rate constant suggesting that the hydrogen bonds are involved in non-native interactions in the transition state for folding.
Hanzlik, R.P.; Schaefer, A.R.; Moon, J.B.; Judson, C.M.
1987-01-01
As a chemical model for benzylic hydroxylation effects by cytochrome P-450 enzymes, the chlorination of PhCH 3 , PhCH 2 D, PhCHD 2 , and PhCD 3 in a two-phase system of hypochlorite/CH 2 Cl 2 with a phase-transfer catalyst has been investigated. On the basis of the deuterium content of the product benzyl chlorides, relative rate constants were deduced for all possible H- and D-abstractions with these substrates. From this the primary (P) and secondary (S) KDIEs were found to be 5.90 +/- 0.41 and 1.03 +/- 0.02, respectively, and the rule of the geometric mean was found to be closely obeyed. For the analogous bromination of toluene by N-bromosuccinimide in CCl 4 , P and S were 6.37 +/- 0.43 and 1.05 +/- 0.01. The transition states of these processes must therefore involve extensive C-H bond breaking but relatively little rehybridization toward planarity at the reacting carbon
Norrby, Per-Ola; Brandt, Peter; Rein, Tobias
1999-01-01
A new method for creating a transition-state force field, based on quantum chemical normal-mode analysis, is described. The force field was used to rationalize the experimentally observed product selectivities in asymmetric Horner-Wadsworth-Emmons reactions between some chiral phosphonates and ch...
Rate Coefficient for the (4)Heμ + CH4 Reaction at 500 K: Comparison between Theory and Experiment.
Arseneau, Donald J; Fleming, Donald G; Li, Yongle; Li, Jun; Suleimanov, Yury V; Guo, Hua
2016-03-03
The rate constant for the H atom abstraction reaction from methane by the muonic helium atom, Heμ + CH4 → HeμH + CH3, is reported at 500 K and compared with theory, providing an important test of both the potential energy surface (PES) and reaction rate theory for the prototypical polyatomic CH5 reaction system. The theory used to characterize this reaction includes both variational transition-state (CVT/μOMT) theory (VTST) and ring polymer molecular dynamics (RPMD) calculations on a recently developed PES, which are compared as well with earlier calculations on different PESs for the H, D, and Mu + CH4 reactions, the latter, in particular, providing for a variation in atomic mass by a factor of 36. Though rigorous quantum calculations have been carried out for the H + CH4 reaction, these have not yet been extended to the isotopologues of this reaction (in contrast to H3), so it is important to provide tests of less rigorous theories in comparison with kinetic isotope effects measured by experiment. In this regard, the agreement between the VTST and RPMD calculations and experiment for the rate constant of the Heμ + CH4 reaction at 500 K is excellent, within 10% in both cases, which overlaps with experimental error.
Ouzon-Shubeita, Hala; Lee, Seongmin
2014-01-01
N7-Methyl-2′-deoxyguanosine (m7dG) is the predominant lesion formed by methylating agents. A systematic investigation on the effect of m7dG on DNA replication has been difficult due to the chemical instability of m7dG. To gain insights into the m7dG effect, we employed a 2′-fluorine-mediated transition-state destabilzation strategy. Specifically, we determined kinetic parameters for dCTP insertion opposite a chemically stable m7dG analogue, 2′-fluoro-m7dG (Fm7dG), by human DNA polymerase β (polβ) and solved three X-ray structures of polβ in complex with the templating Fm7dG paired with incoming dCTP or dTTP analogues. The kinetic studies reveal that the templating Fm7dG slows polβ catalysis ∼300-fold, suggesting that m7dG in genomic DNA may impede replication by some DNA polymerases. The structural analysis reveals that Fm7dG forms a canonical Watson–Crick base pair with dCTP, but metal ion coordination is suboptimal for catalysis in the polβ-Fm7dG:dCTP complex, which partially explains the slow insertion of dCTP opposite Fm7dG by polβ. In addition, the polβ-Fm7dG:dTTP structure shows open protein conformations and staggered base pair conformations, indicating that N7-methylation of dG does not promote a promutagenic replication. Overall, the first systematic studies on the effect of m7dG on DNA replication reveal that polβ catalysis across m7dG is slow, yet highly accurate. PMID:24966350
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Kedziora David J.
2011-10-01
Full Text Available Collisions of actinide nuclei form, during very short times of few zs (10−21 s, the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric ﬁelds by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay predicted by the quantum electrodynamics (QED theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasiﬁssion mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF code tdhf3d is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions from TDHF transfer probabilities, on the one hand, and using the BalianVeneroni variational principle, on the other hand. A ﬁrst application to test QED is discussed. Collision times in 238U+238U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of ~ 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are suﬃcient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasiﬁssion mechanism associated to a speciﬁc orientation of the nuclei is proposed to
Nagar, Mitesh; Bearne, Stephen L
2015-11-10
Mandelate racemase (MR) catalyzes the interconversion of the enantiomers of mandelate and serves as a paradigm for understanding the enzyme-catalyzed abstraction of an α-proton from a carbon acid substrate with a high pKa. The enzyme utilizes a two-base mechanism with Lys 166 and His 297 acting as Brønsted acid and base catalysts, respectively, in the R → S reaction direction. In the S → R reaction direction, their roles are reversed. Using isothermal titration calorimetry (ITC), MR is shown to bind the intermediate/transition state (TS) analogue inhibitor benzohydroxamate (BzH) in an entropy-driven process with a value of ΔCp equal to -358 ± 3 cal mol(-1) K(-1), consistent with an increased number of hydrophobic interactions. However, MR binds BzH with an affinity that is ∼2 orders of magnitude greater than that predicted solely on the basis of hydrophobic interactions [St. Maurice, M., and Bearne, S. L. (2004) Biochemistry 43, 2524], suggesting that additional specific interactions contribute to binding. To test the hypothesis that cation-π/NH-π interactions between the side chains of Lys 166 and His 297 and the aromatic ring and/or the hydroxamate/hydroximate moiety of BzH contribute to the binding of BzH, site-directed mutagenesis was used to generate the MR variants K166M, K166C, H297N, and K166M/H297N and their binding affinity for various ligands determined using ITC. Comparison of the binding affinities of these MR variants with the intermediate/TS analogues BzH and cyclohexanecarbohydroxamate revealed that cation-π/NH-π interactions between His 297 and the hydroxamate/hydroximate moiety and the phenyl ring of BzH contribute approximately 0.26 and 0.91 kcal/mol to binding, respectively, while interactions with Lys 166 contribute approximately 1.74 and 1.74 kcal/mol, respectively. Similarly, comparison of the binding affinities of these mutants with substrate analogues revealed that Lys 166 contributes >2.93 kcal/mol to the binding of (R
Mandal, Debasish; Mallick, Dibyendu; Shaik, Sason
2018-01-16
This Account outlines interplay of theory and experiment in the quest to identify the reactive-spin-state in chemical reactions that possess a few spin-dependent routes. Metalloenzymes and synthetic models have forged in recent decades an area of increasing appeal, in which oxometal species bring about functionalization of hydrocarbons under mild conditions and via intriguing mechanisms that provide a glimpse of Nature's designs to harness these reactions. Prominent among these are oxoiron(IV) complexes, which are potent H-abstractors. One of the key properties of oxoirons is the presence of close-lying spin-states, which can mediate H-abstractions. As such, these complexes form a fascinating chapter of spin-state chemistry, in which chemical reactivity involves spin-state interchange, so-called two-state reactivity (TSR) and multistate reactivity (MSR). TSR and MSR pose mechanistic challenges. How can one determine the structure of the reactive transition state (TS) and its spin state for these mechanisms? Calculations can do it for us, but the challenge is to find experimental probes. There are, however, no clear kinetic signatures for the reactive-spin-state in such reactions. This is the paucity that our group has been trying to fill for sometime. Hence, it is timely to demonstrate how theory joins experiment in realizing this quest. This Account uses a set of the H-abstraction reactions of 24 synthetic oxoiron(IV) complexes and 11 hydrocarbons, together undergoing H-abstraction reactions with TSR/MSR options, which provide experimentally determined kinetic isotope effect (KIE exp ) data. For this set, we demonstrate that comparing KIE exp results with calculated tunneling-augmented KIE (KIE TC ) data leads to a clear identification of the reactive spin-state during H-abstraction reactions. In addition, generating KIE exp data for a reaction of interest, and comparing these to KIE TC values, provides the mechanistic chemist with a powerful capability to
Parkin, D.W.; Mentch, F.; Banks, G.A.; Horenstein, B.A.; Schramm, V.L.
1991-01-01
The transition state of the V max mutant of AMP nucleosidase from Azotobacter vinelandii has been characterized by heavy-atom kinetic isotope effects in the presence and absence of MgATP, the allosteric activator. The enzyme catalyzes hydrolysis of the N-glycosidic bond of AMP at approximately 2% of the rate of the normal enzyme with only minor changes in the K m for substrate, the activation constant for MgATP, and the K i for formycin 5'-phosphate, a tight-binding competitive inhibitor. Isotope effects were measured as a function of the allosteric activator concentration that increases the turnover number of the enzyme from 0.006 s -1 . The kinetic isotope effects were measured with the substrates [1'- 3 H]AMP, [2'- 2 H]AMP, [9- 15 N]AMP, and [1',9- 14 C, 15 N]AMP. All substrates gave significant kinetic isotope effects in a pattern that establishes that the reaction expresses intrinsic kinetic isotope effects in the presence or absence of MgATP. Transition-state analysis using bond-energy and bond-order vibrational analysis indicated that the transition state for the mutant enzyme has a similar position in the reaction coordinate compared to that for the normal enzyme. The mutant enzyme is less effective in stabilizing the carbocation-like intermediate and in the ability to protonate N7 of adenine to create a better leaving group. This altered transition-state structure was confirmed by an altered substrate specificity for the mutant protein
Harel, M.; Silman, I. [Weizmann Inst. of Science, Rehovot (Israel); Quinn, D.M.; Nair, H.K. [Univ. of Iowa, Iowa City, IA (United States); Sussman, J.L. [Weizmann Inst. of Science, Rehovot (Israel)]|[Brookhaven National Lab., Upton, NY (United States)
1996-03-13
The structure of a complex of Torpedo californica acetylcholinesterase with the transition state analog inhibitor m-(N, N,N-trimethylammonio)-2,2,2-trifluoroacetophenone has been solved by X-ray crystallographic methods to 2.8 A resolution. Since the inhibitor binds to the enzyme about 10{sup 10}-fold more tightly than the substrate acetylcholine, this complex provides a visual accounting of the enzyme-ligand interactions that provide the molecular basis for the catalytic power of acetylcholinesterase. The acetyl ester hydrolytic specificity of the enzyme is revealed by the interaction of the CF{sub 3} function of the transition state analog with a concave binding site comprised of the residues G119, W233, F288, F290, and F331. The highly geometrically convergent array of enzyme-ligand interactions visualized in the complex described herein envelopes the acylation transition state and sequesters it from solvent, this being consistent with the location of the active site at the bottom of a deep and narrow gorge. 82 refs., 5 figs.
The chemical reaction mechanism of NO addition to two β and δ isoprene hydroxy–peroxy radical isomers is examined in detail using density functional theory, coupled cluster methods, and the energy resolved master equation formalism to provide estimates of rate co...
Pyrolysis of 3-carene: Experiment, Theory and Modeling
which is used as a rocket fuel has been well studied.2–5. 3-carene, a .... lated using frequencies obtained at MP2/6-31G* level ..... Figure 5. Transition state structures for intermediate reaction steps originating from 3-carene optimized at G3 level of theory (except for TS1, optimized at B3LYP/6-311+G(d,p) level of theory.
Lindström, Ida; Dogan, Jakob
2017-08-15
A significant fraction of the eukaryotic proteome consists of proteins that are either partially or completely disordered under native-like conditions. Intrinsically disordered proteins (IDPs) are common in protein-protein interactions and are involved in numerous cellular processes. Although many proteins have been identified as disordered, much less is known about the binding mechanisms of the coupled binding and folding reactions involving IDPs. Here we have analyzed the rate-limiting transition state for binding between the TAZ1 domain of CREB binding protein and the intrinsically disordered transactivation domain of STAT2 (TAD-STAT2) by site-directed mutagenesis and kinetic experiments (Φ-value analysis) and found that the native protein-protein binding interface is not formed at the transition state for binding. Instead, native hydrophobic binding interactions form late, after the rate-limiting barrier has been crossed. The association rate constant in the absence of electrostatic enhancement was determined to be rather high. This is consistent with the Φ-value analysis, which showed that there are few or no obligatory native contacts. Also, linear free energy relationships clearly demonstrate that native interactions are cooperatively formed, a scenario that has usually been observed for proteins that fold according to the so-called nucleation-condensation mechanism. Thus, native hydrophobic binding interactions at the rate-limiting transition state for association between TAD-STAT2 and TAZ1 are not a requirement, which is generally in agreement with previous findings on other IDP systems and might be a common mechanism for IDPs.
Chojnowski, Grzegorz; Breer, Katarzyna; Narczyk, Marta; Wielgus-Kutrowska, Beata; Czapinska, Honorata; Hashimoto, Mariko; Hikishima, Sadao; Yokomatsu, Tsutomu; Bochtler, Matthias; Girstun, Agnieszka; Staron, Krzysztof; Bzowska, Agnieszka
2010-01-01
Low molecular mass purine nucleoside phosphorylases (PNPs, E.C. 2.4.2.1) are homotrimeric enzymes that are tightly inhibited by immucillins. Due to the positive charge on the ribose like part (iminoribitol moiety) and protonation of the N7 atom of the purine ring, immucillins are believed to act as transition state analogues. Over a wide range of concentrations, immucillins bind with strong negative cooperativity to PNPs, so that only every third binding site of the enzyme is occupied (third-of-the-sites binding). 9-(5',5'-difluoro-5'-phosphonopentyl)-9-deazaguanine (DFPP-DG) shares with immucillins the protonation of the N7, but not the positive charge on the ribose like part of the molecule. We have previously shown that DFPP-DG interacts with PNPs with subnanomolar inhibition constant. Here, we report additional biochemical experiments to demonstrate that the inhibitor can be bound with the same K d (∼190 pM) to all three substrate binding sites of the trimeric PNP, and a crystal structure of PNP in complex with DFPP-DG at 1.45 A resolution, the highest resolution published for PNPs so far. The crystals contain the full PNP homotrimer in the asymmetric unit. DFPP-DG molecules are bound in superimposable manner and with full occupancies to all three PNP subunits. Thus the postulated third-of-the-sites binding of immucillins should be rather attribute to the second feature of the transition state, ribooxocarbenium ion character of the ligand or to the coexistence of both features characteristic for the transition state. The DFPP-DG/PNP complex structure confirms the earlier observations, that the loop from Pro57 to Gly66 covering the phosphate-binding site cannot be stabilized by phosphonate analogues. The loop from Glu250 to Gln266 covering the base-binding site is organized by the interactions of Asn243 with the Hoogsteen edge of the purine base of analogues bearing one feature of the postulated transition state (protonated N7 position).
Variational submanifolds of Euclidean spaces
Krupka, D.; Urban, Z.; Volná, J.
2018-03-01
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.
Cosmological constants and variations
Barrow, John D
2005-01-01
We review properties of theories for the variation of the gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that is consistent with time-variation in the fine structure 'constant' since a redshift of 3.5. The behaviour of a simple class of varying alpha cosmologies is outlined in the light of all the observational constraints. We also discuss some of the consequences of varying 'constants' for oscillating universes and show by means of exact solutions that they appear to evolve monotonically in time even though the scale factor of the universe oscillates
Welsh, K.M.; Creighton, D.J.; Klinman, J.P.
1980-01-01
Solvent and alpha-secondary isotope effects have been measured in the yeast alcohol dehydrogenase reaction, under conditions of a rate-limiting transfer of hydrogen between coenzyme and substrate. Determination of catalytic constants in H20 and D20 as a function of pH(D) has allowed the separation of solvent effects on pKa from kcat. The small effect of D20 on pKa is tentatively assigned to ionization of an active-site ZnOH 2 . The near absence of an isotope effect on kcat in the direction of alcohol oxidation rules out a mechanism involving concerted catalysis by an active-site base of hydride transfer. The near identity of kinetic and equilibrium alpha-secondary isotope effects in the direction of alcohol oxidation implicates a transition-state structure which resembles aldehyde with regard to bond hybridization properties. The result contrasts sharply with previously reported structure - reactivity correlations, which implicate a transition-state structure resembling alcohol with regard to charge properties. The significance of these findings to the mechanism of NAD(P)H-dependent redox reactions is discussed
Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen
2014-09-09
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
On exterior variational calculus
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt
La Guardia, J G; Ryan, R M; Couchman, C E; Deci, E L
2000-09-01
Attachment research has traditionally focused on individual differences in global patterns of attachment to important others. The current research instead focuses primarily on within-person variability in attachments across relational partners. It was predicted that within-person variability would be substantial, even among primary attachment figures of mother, father, romantic partner, and best friend. The prediction was supported in three studies. Furthermore, in line with self-determination theory, multilevel modeling and regression analyses showed that, at the relationship level, individuals' experience of fulfillment of the basic needs for autonomy, competence, and relatedness positively predicted overall attachment security, model of self, and model of other. Relations of both attachment and need satisfaction to well-being were also explored.
Ouk, Chanda-Malis; Zvereva-Loëte, Natalia; Bussery-Honvault, Béatrice
2011-10-01
The N( 2D) + CH 4 reaction appears to be a key reaction for the chemistry of Titan's atmosphere, opening the door to nitrile formation as recently observed by the Cassini-Huygens mission. Faced to the controversy concerning the existence or not of a potential barrier for this reaction, we have carried out accurate ab initio calculations by means of multi-state multi-reference configuration interaction (MS-MR-SDCI) method. These calculations have been partially corrected for the size-consistency errors (SCE) by Davidson, Pople or AQCC corrections. We suggest a barrier height of 3.86 ± 0.84 kJ/mol, including ZPE, for the entrance transition state, in good agreement with the experimental value. Its implication in Titan's atmopsheric chemistry is discussed.
Mario César Sánchez Villa
2017-05-01
Full Text Available The triumph of the reason as the only way of natural knowledge was the most remarkable result of the paradigm shift occurred during the so-called Scientific Revolution, which reaches from the Renaissance to the Enlightenment, and in which dogmatic reasoning lost progressively its role as the principal form of knowledge. Nevertheless, during the following centuries, a large part of the men of science were willing to favour the conversion of dogma into an agent of rational thought. This paper, tries to offer a point of reflection on the influence that the biblical account maintained in the construction of the modern scientific theories that, somehow, tried to explain relevant issues such as the origin of physical and moral differences between humans. The broader objective is to demonstrate that, as a form of cultural expression, the dogmatic-religious thought continued to play a transcendental role in the legitimation of a part of the modern rational scientific discourse, committed to defending the civilizing role and the physical and moral superiority of Western states, far beyond what the simple use of reason permitted.
Vegge, Tejs
2004-01-01
The dissociation of molecular hydrogen on a Mgs0001d surface and the subsequent diffusion of atomic hydrogen into the magnesium substrate is investigated using Density Functional Theory (DFT) calculations and rate theory. The minimum energy path and corresponding transition states are located usi...... to be rate-limiting for the ab- and desorption of hydrogen, respectively. Zero-point energy contributions are found to be substantial for the diffusion of atomic hydrogen, but classical rates are still found to be within an order of magnitude at room temperature.......The dissociation of molecular hydrogen on a Mgs0001d surface and the subsequent diffusion of atomic hydrogen into the magnesium substrate is investigated using Density Functional Theory (DFT) calculations and rate theory. The minimum energy path and corresponding transition states are located using...
Harvey, Gill; Jas, Pauline; Walshe, Kieran
2015-01-01
Organisational context is frequently cited as an important consideration when implementing and evaluating quality improvement interventions in healthcare, but limited guidance is available on which aspects of context are most influential or modifiable. This paper examines how internal and external contextual factors mediate organisational-level performance improvement through applying the knowledge-based theory of absorptive capacity (AC). Three healthcare case studies are presented. Each case is a UK National Health Service organisation that had been identified as having performance problems. Qualitative data were collected through semi-structured interviews with general and clinical managers within the organisation and members of external teams supporting or overseeing performance improvement (n=22). Interview data were analysed using an existing AC framework from the literature. The organisation with the highest AC showed the quickest and most comprehensive performance improvement. Internal characteristics including strategic priorities, processes for managing information, communication and orientation to learning and development impacted on the organisation's ability to engage successfully with external stakeholders and make use of available knowledge. This enabled the organisation to thrive despite the challenging external environment. Lower levels of AC appeared to delay or limit the improvement trajectory. Developing a more detailed and nuanced understanding of how context influences improvement is an important step towards achieving more effective and sustainable quality improvement programmes in healthcare. AC, with its focus on knowledge and organisational learning, provides a useful way to explore the relationship between context and quality improvement and represents a potentially valuable area for future research and development. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go
Zhao, Bin; Guo, Hua; Sun, Zhigang
2015-01-01
Quantum state-to-state dynamics of a prototypical four-atom reaction, namely, Cl + H 2 O → HCl + OH, is investigated for the first time in full dimensionality using a transition-state wave packet method. The state-to-state reactivity and its dependence on the reactant internal excitations are analyzed and found to share many similarities both energetically and dynamically with the H + H 2 O → H 2 + OH reaction. The strong enhancement of reactivity by the H 2 O stretching vibrational excitations in both reactions is attributed to the favorable energy flow into the reaction coordinate near the transition state. On the other hand, the insensitivity of the product state distributions with regard to reactant internal excitation stems apparently from the transition-state control of product energy disposal
Zhao, Bin; Sun, Zhigang; Guo, Hua
2015-06-28
Quantum state-to-state dynamics of a prototypical four-atom reaction, namely, Cl + H2O → HCl + OH, is investigated for the first time in full dimensionality using a transition-state wave packet method. The state-to-state reactivity and its dependence on the reactant internal excitations are analyzed and found to share many similarities both energetically and dynamically with the H + H2O → H2 + OH reaction. The strong enhancement of reactivity by the H2O stretching vibrational excitations in both reactions is attributed to the favorable energy flow into the reaction coordinate near the transition state. On the other hand, the insensitivity of the product state distributions with regard to reactant internal excitation stems apparently from the transition-state control of product energy disposal.
On the theory of time dilation in chemical kinetics
Baig, Mirza Wasif
2017-10-01
The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying basic theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasi-equilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius equation, of the collision frequency and of the Eyring and Marcus equations renders the rate of reaction to be Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate, the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction to complete. Lorentz transformation of the half-life equation explains time dilation of the half-life period of chemical reactions and proves special theory of relativity and presents theory in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine into Bismuth are considered as numerical examples.
Splines and variational methods
Prenter, P M
2008-01-01
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimension
Cavalier, Michael C.; Kim, Song-Gun; Neau, David; Lee, Yong-Hwan
2012-01-01
The molecular basis of fructose-2,6-bisphosphatase (F-2,6-P 2 ase) of 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFKFB) was investigated using the crystal structures of the human inducible form (PFKFB3) in a phospho-enzyme intermediate state (PFKFB3-P · F-6-P), in a transition state-analogous complex (PFKFB3 · AlF 4 ), and in a complex with pyrophosphate (PFKFB3 · PP i ) at resolutions of 2.45, 2.2, and 2.3 (angstrom), respectively. Trapping the PFKFB3-P · F-6-P intermediate was achieved by flash cooling the crystal during the reaction, and the PFKFB3 · AlF 4 and PFKFB3 · PP i complexes were obtained by soaking. The PFKFB3 · AlF 4 and PFKFB3 · PP i complexes resulted in removing F-6-P from the catalytic pocket. With these structures, the structures of the Michaelis complex and the transition state were extrapolated. For both the PFKFB3-P formation and break down, the phosphoryl donor and the acceptor are located within ∼5.1 (angstrom), and the pivotal point 2-P is on the same line, suggesting an 'in-line' transfer with a direct inversion of phosphate configuration. The geometry suggests that NE2 of His253 undergoes a nucleophilic attack to form a covalent N-P bond, breaking the 2O-P bond in the substrate. The resulting high reactivity of the leaving group, 2O of F-6-P, is neutralized by a proton donated by Glu322. Negative charges on the equatorial oxygen of the transient bipyramidal phosphorane formed during the transfer are stabilized by Arg252, His387, and Asn259. The C-terminal domain (residues 440-446) was rearranged in PFKFB3 · PP i , implying that this domain plays a critical role in binding of substrate to and release of product from the F-2,6-P 2 ase catalytic pocket. These findings provide a new insight into the understanding of the phosphoryl transfer reaction.
Negele, J.W.
1977-01-01
Recent advances in variational and perturbative theories are surveyed which offer genuine promise that nuclear matter will soon become a viable tool for investigating nuclear interactions. The basic elements of the hypernetted chain expansion for Jastrow variational functions are briefly reviewed, and comparisons of variational and perturbative results for a series of increasingly complicated systems are presented. Prospects for investigating realistic forces are assessed and the unresolved, open problems are summarized
Acheson, S.A.; Bell, J.B.; Jones, M.E.; Wolfenden, R. (Univ. of North Carolina School of Medicine, Chapel Hill (USA))
1990-04-03
The enzymatic decarboxylation of orotidine 5'-monophosphate may proceed by an addition-elimination mechanism involving a covalently bound intermediate or by elimination of CO2 to generate a nitrogen ylide. In an attempt to distinguish between these two alternatives, 1-(phosphoribosyl)barbituric acid was synthesized with 13C at the 5-position. Interaction of this potential transition-state analogue inhibitor with yeast orotidine-5'-monophosphate decarboxylase resulted in a small (0.6 ppm) downfield displacement of the C-5 resonance, indicating no rehybridization of the kind that might have been expected to accompany 5,6-addition of an enzyme nucleophile. When the substrate orotidine 5'-monophosphate was synthesized with deuterium at C-5, no significant change in kcat (H/D = 0.99 +/- 0.06) or kcat/KM (H/D = 1.00 +/- 0.06) was found to result, suggesting that C-5 does not undergo significant changes in geometry before or during the step that determines the rate of the catalytic process. These results are consistent with a nitrogen ylide mechanism and offer no support for the intervention of covalently bound intermediates in the catalytic process.
Hou, Gao-Lei [Physical; Wang, Xue-Bin [Physical; McCoy, Anne B. [Department; Borden, Weston Thatcher [Department
2017-10-05
The transition-state (TS) region of the simplest heavy-light-heavy type of reaction, F• + H-F F-H + F•, is investigated in this work by a joint experimental and theoretical approach. Photodetaching the bifluride anion, [F…H…F]–, generates a negative ion photoelectron (NIPE) spectrum with three partially resolved bands in the electron binding energy (eBE) range of 5.4 – 7.0 eV. These bands correspond to the transition from the ground state of the anion to the electronic ground state of [F-H-F]• neutral, with associated vibrational excitations. The significant increase of eBE of the bifluride anion, relative to that of F-, reflects a hydrogen bond energy between F- and HF of 46 kcal/mol. Theoretical modeling reveals that the antisymmetric motion of H between the two F atoms, near the TS on the neutral [F-H-F]• surface, dominates the observed three bands, while the F-H-F bending, F—F symmetric stretching modes, and the couplings between them is calculated to account for the breadth of the observed spectrum. From the NIPE spectrum, a lower limit on the activation enthalpy for F• + H-F F-H + F can be estimated to be H‡ = 12 ± 2 kcal/mol, a value below that of H‡ = 14.9 kcal/mol, given by our G4 calculations.
Li, Hou-Kuan; Tsai, Po-Yu; Hung, Kai-Chan; Kasai, Toshio; Lin, King-Chuen
2015-01-01
Following photodissociation of acetaldehyde (CH3CHO) at 308 nm, the CO(v = 1-4) fragment is acquired using time-resolved Fourier-transform infrared emission spectroscopy. The CO(v = 1) rotational distribution shows a bimodal feature; the low- and high-J components result from H-roaming around CH3CO core and CH3-roaming around CHO radical, respectively, in consistency with a recent assignment by Kable and co-workers (Lee et al., Chem. Sci. 5, 4633 (2014)). The H-roaming pathway disappears at the CO(v ≥ 2) states, because of insufficient available energy following bond-breaking of H + CH3CO. By analyzing the CH4 emission spectrum, we obtained a bimodal vibrational distribution; the low-energy component is ascribed to the transition state (TS) pathway, consistent with prediction by quasiclassical trajectory calculations, while the high-energy component results from H- and CH3-roamings. A branching fraction of H-roaming/CH3-roaming/TS contribution is evaluated to be (8% ± 3%)/(68% ± 10%)/(25% ± 5%), in which the TS pathway was observed for the first time. The three pathways proceed concomitantly along the electronic ground state surface.
A survey of variational principles
Lewins, J.D.
1993-01-01
In this article survey of variational principles has been given. Variational principles play a significant role in mathematical theory with emphasis on the physical aspects. There are two principals used i.e. to represent the equation of the system in a succinct way and to enable a particular computation in the system to be carried out with greater accuracy. The survey of variational principles has ranged widely from its starting point in the Lagrange multiplier to optimisation principles. In an age of digital computation, these classic methods can be adapted to improve such calculations. We emphasize particularly the advantage of basic finite element methods on variational principles. (A.B.)
Electromagnetic scattering theory
Bird, J. F.; Farrell, R. A.
1986-01-01
Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.
Rotzinger, François P
2016-12-19
The water exchange reaction on Co(NH 3 ) 5 OH 2 3+ was investigated with various density functionals and basis sets. A Gibbs activation energy (ΔG ⧧ ) agreeing with experiment was obtained with the long-range-corrected functionals ωB97X-D3 and LC-BOP-LRD, SMD hydration, and modified Karlsruhe def2-TZVP basis sets. This computational technique was then applied to the reaction of NO + with Co(NH 3 ) 5 N 3 2+ . All of the possible pathways were investigated, NO + attack at the terminal N of Co(NH 3 ) 5 N 3 2+ via the E and the Z isomers of the transition states, and NO + attack at the bound N of azide, also via both isomers. The most favorable pathway proceeds via the attack at the bound N via the Z isomer. This leads to the intermediate with an oxatetrazole ligand bound to Co(III) at the N in the 3-position, Co(NH 3 ) 5 (cycl-N 4 O) 3+ , which undergoes N 2 elimination to yield the Co(NH 3 ) 5 N 2 O 3+ intermediate. The subsequent substitution of N 2 O by water follows the I d mechanism with retention of the configuration. No evidence for the existence of the square-pyramidal pentacoordinated intermediate Co(NH 3 ) 5 3+ was found. All of the investigated intermediates, Co(NH 3 ) 5 N 2 3+ , Co(NH 3 ) 5 [E-N(N 2 )(NO)] 3+ , Co(NH 3 ) 5 (E-ON 4 ) 3+ , Co(NH 3 ) 5 ON 2 3+ , Co(NH 3 ) 5 (cycl-N 4 O) 3+ , and Co(NH 3 ) 5 N 2 O 3+ , exhibit short lifetimes of less than ∼60 μs and react via the I d mechanism.
Masato Kiyoshi
Full Text Available The optimization of antibodies is a desirable goal towards the development of better therapeutic strategies. The antibody 11K2 was previously developed as a therapeutic tool for inflammatory diseases, and displays very high affinity (4.6 pM for its antigen the chemokine MCP-1 (monocyte chemo-attractant protein-1. We have employed a virtual library of mutations of 11K2 to identify antibody variants of potentially higher affinity, and to establish benchmarks in the engineering of a mature therapeutic antibody. The most promising candidates identified in the virtual screening were examined by surface plasmon resonance to validate the computational predictions, and to characterize their binding affinity and key thermodynamic properties in detail. Only mutations in the light-chain of the antibody are effective at enhancing its affinity for the antigen in vitro, suggesting that the interaction surface of the heavy-chain (dominated by the hot-spot residue Phe101 is not amenable to optimization. The single-mutation with the highest affinity is L-N31R (4.6-fold higher affinity than wild-type antibody. Importantly, all the single-mutations showing increase affinity incorporate a charged residue (Arg, Asp, or Glu. The characterization of the relevant thermodynamic parameters clarifies the energetic mechanism. Essentially, the formation of new electrostatic interactions early in the binding reaction coordinate (transition state or earlier benefits the durability of the antibody-antigen complex. The combination of in silico calculations and thermodynamic analysis is an effective strategy to improve the affinity of a matured therapeutic antibody.
Solid mechanics a variational approach
Dym, Clive L
2013-01-01
Solid Mechanics: A Variational Approach, Augmented Edition presents a lucid and thoroughly developed approach to solid mechanics for students engaged in the study of elastic structures not seen in other texts currently on the market. This work offers a clear and carefully prepared exposition of variational techniques as they are applied to solid mechanics. Unlike other books in this field, Dym and Shames treat all the necessary theory needed for the study of solid mechanics and include extensive applications. Of particular note is the variational approach used in developing consistent structural theories and in obtaining exact and approximate solutions for many problems. Based on both semester and year-long courses taught to undergraduate seniors and graduate students, this text is geared for programs in aeronautical, civil, and mechanical engineering, and in engineering science. The authors’ objective is two-fold: first, to introduce the student to the theory of structures (one- and two-dimensional) as ...
Variational methods in molecular modeling
2017-01-01
This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical unders...
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive...
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality...
Yao, Jianzhuang; Wang, Xia; Luo, Haixia; Gu, Pengfei
2017-11-16
Shikimate kinase (SK) is the fifth bacterial enzyme involved in the shikimate pathway for biosynthesis of life-indispensable components, such as aromatic amino acids. The absence of the shikimate pathway in humans makes SK an attractive target for the rational design of drugs aimed at pathogenesis bacteria, such as Mycobacterium tuberculosis and Helicobacter pylori. However, an effective inhibitor of SK (e.g., a transition-state analogue) is still not available on the market due, at least in part, to a lack of knowledge on the catalytic mechanism and the nature of the rate-limiting transition state. Herein, quantum mechanical/molecular mechanical (QM/MM) reaction coordinate, molecular dynamics (MD), and free-energy simulations have been performed to answer these questions. The results presented herein demonstrate that the phosphoryl-transfer process, which is the rate-limiting step of SK-catalyzed phosphorylation of shikimic acid (SKM), is a concerted one-step reaction proceeding through a loose transition state. The computational results agree well with those of experimental studies, specifically NMR results, X-ray crystal structure observation, and activation free-energy barrier. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Kuang, Zhen-Bang
2014-01-01
Theory of Electroelasticity analyzes the stress, strain, electric field and electric displacement in electroelastic structures such as sensors, actuators and other smart materials and structures. This book also describes new theories such as the physical variational principle and the inertial entropy theory. It differs from the traditional method by using the physical variational principle to derive the governing equations of the piezoelectric material, whereas the Maxwell stress is obtained automatically. By using the inertial entropy theory, the temperature wave equation is obtained very easily. The book is intended for scientists, researchers and engineers in the areas of mechanics, physics, smart material and control engineering as well as mechanical, aeronautical and civil engineering, etc. Zhen-Bang Kuang is a professor at Shanghai Jiao Tong University.
A theory of piezoelectric laminates
Giangreco, E.
1997-01-01
A theory of piezoelectric laminates is rationally derived from the three-dimensional Voigt theory of piezoelectricity. The present theory is a generalization to piezoelectric laminates of the Reissner-Mindlin-type layer-wise theory of elastic laminates. Both a differential formulation and a variational formulation of the piezoelectric laminate problem are presented. The proposed theory is adopted in the analysis of simple problems, in order to verify its effectiveness. The results it provides turn out to be in good agreement with the results supplied by the Voigt theory of piezoelectricity
Pernot, Dominique
2014-01-01
Les derniers romans de Gabriel Josipovici offrent beaucoup de variété, allant de la parodie, de la fiction comique légère, dans Only Joking et Making Mistakes, à des sujets plus graves, plus personnels, ontologiques. Dans un court roman, Everything Passes, et dans un roman majeur, Goldberg: Variations, le lecteur est amené à se poser des questions sur la nature mystérieuse de la réalité, qui est, trop souvent, acceptée sans conteste par de nombreux roma...
Bork, Nicolai Christian; Kurten, T.; Enghoff, Martin Andreas Bødker
2011-01-01
Based on density functional theory calculations we present a study of the gaseous oxidation of SO2 to SO3 by an anionic O3−(H2On cluster, n=0–5. The configurations of the most relevant reactants, transition states, and products are discussed and compared to previous findings. Two different classes......, the most energetically favorable class of transition states vary with the number of water molecules attached. A kinetic model is utilized, taking into account the most likely outcomes of the initial SO2O3−(H2O)n collision complexes. This model shows that the reaction takes place at collision rates...
On quadratic variation of martingales
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Linking numbers and variational method
Oda, I.; Yahikozawa, S.
1989-09-01
The ordinary and generalized linking numbers for two surfaces of dimension p and n-p-1 in an n dimensional manifold are derived. We use a variational method based on the properties of topological quantum field theory in order to derive them. (author). 13 refs, 2 figs
Distinguishing the rates of gene activation from phenotypic variations.
Chen, Ye; Lv, Cheng; Li, Fangting; Li, Tiejun
2015-06-18
Stochastic genetic switching driven by intrinsic noise is an important process in gene expression. When the rates of gene activation/inactivation are relatively slow, fast, or medium compared with the synthesis/degradation rates of mRNAs and proteins, the variability of protein and mRNA levels may exhibit very different dynamical patterns. It is desirable to provide a systematic approach to identify their key dynamical features in different regimes, aiming at distinguishing which regime a considered gene regulatory network is in from their phenotypic variations. We studied a gene expression model with positive feedbacks when genetic switching rates vary over a wide range. With the goal of providing a method to distinguish the regime of the switching rates, we first focus on understanding the essential dynamics of gene expression system in different cases. In the regime of slow switching rates, we found that the effective dynamics can be reduced to independent evolutions on two separate layers corresponding to gene activation and inactivation states, and the transitions between two layers are rare events, after which the system goes mainly along deterministic ODE trajectories on a particular layer to reach new steady states. The energy landscape in this regime can be well approximated by using Gaussian mixture model. In the regime of intermediate switching rates, we analyzed the mean switching time to investigate the stability of the system in different parameter ranges. We also discussed the case of fast switching rates from the viewpoint of transition state theory. Based on the obtained results, we made a proposal to distinguish these three regimes in a simulation experiment. We identified the intermediate regime from the fact that the strength of cellular memory is lower than the other two cases, and the fast and slow regimes can be distinguished by their different perturbation-response behavior with respect to the switching rates perturbations. We proposed a
Variational integrators in plasma physics
Kraus, Michael
2013-07-01
To a large extent, research in plasma physics is concerned with the description and analysis of energy and momentum transfer between different scales and different kinds of waves. In the numerical modelling of such phenomena it appears to be crucial to describe the transfer processes preserving the underlying conservation laws in order to prevent physically spurious solutions. In this work, special numerical methods, so called variational integrators, are developed for several models of plasma physics. Special attention is given to conservation properties like conservation of energy and momentum. By design, variational integrators are applicable to all systems that have a Lagrangian formulation. Usually, equations of motion are derived by Hamilton's action principle and then discretised. In the application of the variational integrator theory, the order of these steps is reversed. At first, the Lagrangian and the accompanying variational principle are discretised, such that discrete equations of motion can be obtained directly by applying the discrete variational principle to the discrete Lagrangian. The advantage of this approach is that the resulting discretisation automatically retains the conservation properties of the continuous system. Following an overview of the geometric formulation of classical mechanics and field theory, which forms the basis of the variational integrator theory, variational integrators are introduced in a framework adapted to problems from plasma physics. The applicability of variational integrators is explored for several important models of plasma physics: particle dynamics (guiding centre dynamics), kinetic theory (the Vlasov-Poisson system) and fluid theory (magnetohydrodynamics). These systems, with the exception of guiding centre dynamics, do not possess a Lagrangian formulation to which the variational integrator methodology is directly applicable. Therefore the theory is extended by linking it to Ibragimov's theory of
Variational integrators in plasma physics
Kraus, Michael
2013-01-01
To a large extent, research in plasma physics is concerned with the description and analysis of energy and momentum transfer between different scales and different kinds of waves. In the numerical modelling of such phenomena it appears to be crucial to describe the transfer processes preserving the underlying conservation laws in order to prevent physically spurious solutions. In this work, special numerical methods, so called variational integrators, are developed for several models of plasma physics. Special attention is given to conservation properties like conservation of energy and momentum. By design, variational integrators are applicable to all systems that have a Lagrangian formulation. Usually, equations of motion are derived by Hamilton's action principle and then discretised. In the application of the variational integrator theory, the order of these steps is reversed. At first, the Lagrangian and the accompanying variational principle are discretised, such that discrete equations of motion can be obtained directly by applying the discrete variational principle to the discrete Lagrangian. The advantage of this approach is that the resulting discretisation automatically retains the conservation properties of the continuous system. Following an overview of the geometric formulation of classical mechanics and field theory, which forms the basis of the variational integrator theory, variational integrators are introduced in a framework adapted to problems from plasma physics. The applicability of variational integrators is explored for several important models of plasma physics: particle dynamics (guiding centre dynamics), kinetic theory (the Vlasov-Poisson system) and fluid theory (magnetohydrodynamics). These systems, with the exception of guiding centre dynamics, do not possess a Lagrangian formulation to which the variational integrator methodology is directly applicable. Therefore the theory is extended by linking it to Ibragimov's theory of
Wæver, Ole
2009-01-01
-empiricism and anti-positivism of his position. Followers and critics alike have treated Waltzian neorealism as if it was at bottom a formal proposition about cause-effect relations. The extreme case of Waltz being so victorious in the discipline, and yet being consistently mis-interpreted on the question of theory......, shows the power of a dominant philosophy of science in US IR, and thus the challenge facing any ambitious theorising. The article suggests a possible movement of fronts away from the ‘fourth debate' between rationalism and reflectivism towards one of theory against empiricism. To help this new agenda...
Variational inequalities and flow in porous media
Chipot, M.
1984-01-01
This book is concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most interesting applications of variational inequalities with an obstacle
Solutions to variational inequalities of parabolic type
Zhu, Yuanguo
2006-09-01
The existence of strong solutions to a kind of variational inequality of parabolic type is investigated by the theory of semigroups of linear operators. As an application, an abstract semi permeable media problem is studied.
Knudsen, Thorbjørn
2003-01-01
principles of variation, continuity and selection, it is argued that economic selection theory should mimic the causal structure of neo-Darwinian theory. Two of the most influential explanations of economic evolution, Alchian's and Nelson and Winter's, are used to illustrate how this could be achieved.......The present article provides a minimal description of the causal structure of economic selection theory and outlines how the internal selection dynamics of business organisations can be reconciled with selection in competitive markets. In addition to generic similarity in terms of the Darwinian...
Kobayashi, Sofie; Berge, Maria; Grout, Brian William Wilson
2017-01-01
This study contributes towards a better understanding of learning dynamics in doctoral supervision by analysing how learning opportunities are created in the interaction between supervisors and PhD students, using the notion of experiencing variation as a key to learning. Empirically, we have based...... the study on four video-recorded sessions, with four different PhD students and their supervisors, all from life sciences. Our analysis revealed that learning opportunities in the supervision sessions concerned either the content matter of research (for instance, understanding soil structure......), or the research methods— more specifically how to produce valid results. Our results illustrate how supervisors and PhD students create a space of learning together in their particular discipline by varying critical aspects of their research in their discussions. Situations where more openended research issues...
Harcourt, R.D.
1987-01-01
Bohr orbit theory is used to calculate energies for the 1S, 2P, 3D, 4F and 5G states of the helium muonic atom, when the muon is excited. These energies are close to those which have been calculated variationally by Huang (1977, Phys. Rev. A 15 1832-8). (author)
Multiconfigurational self-consistent reaction field theory for nonequilibrium solvation
Mikkelsen, Kurt V.; Cesar, Amary; Ågren, Hans
1995-01-01
electronic structure whereas the inertial polarization vector is not necessarily in equilibrium with the actual electronic structure. The electronic structure of the compound is described by a correlated electronic wave function - a multiconfigurational self-consistent field (MCSCF) wave function. This wave......, open-shell, excited, and transition states. We demonstrate the theory by computing solvatochromatic shifts in optical/UV spectra of some small molecules and electron ionization and electron detachment energies of the benzene molecule. It is shown that the dependency of the solvent induced affinity...
Jara, Pascual; Torrecillas, Blas
1988-01-01
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
Hendricks, Vincent F.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
Variational form for a viscous plasma
Ishida, A.; Steinhauer, L.C.; Berk, H.L.
1991-01-01
The variational formulation for a fluid plasma including the parallel and gyroviscosities is developed using the basic approach of Berk et al. [Phys. Fluids 24, 2245 (1981)]. The equivalence of the variational problem to the original viscous fluid equations of motion is shown. The theory is developed for an axisymmetric plasma with no magnetic field in the azimuthal direction and therefore applies to field-reversed configurations and axisymmetric mirrors. This theory offers the advantage of describing both parallel and transverse ion kinetic effects within the simplicity afforded by a variational fluid model
A survey of variational principles
Lewins, J.D.
1993-01-01
The survey of variational principles has ranged widely from its starting point in the Lagrange multiplier to optimisation principles. In an age of digital computation, these classic methods can be adapted to improve such calculations. We emphasize particularly the advantage of basing finite element methods on variational principles, especially if, as maximum and minimum principles, these can provide bounds and hence estimates of accuracy. The non-symmetric (and hence stationary rather than extremum principles) are seen however to play a significant role in optimisation theory. (Orig./A.B.)
Supersymmetric and supergravity theories
Pernici, M.
1986-01-01
The author addressed problems in Kaluza-Klein supergravity, in supersymmetric theories and in string theories. They constructed the following supergravity theories in higher dimensions: the maximal gauged supergravities in five and seven dimensions, both related to the respective ungauged theory, though the latter cannot be obtained by putting the coupling constant of the gauged version to zero (gauge discontinuity); the ten-dimensional N = 2 non-chiral and the six-dimensional N = 4 supergravities, through trivial dimensional reduction of higher dimensional theories. They studied the Kaluza-Klein compactifications of the seven-dimensional supergravity theories and of the ten-dimensional, N = 2 non-chiral supergravity. They obtained the non-compact gaugings and the critical points of the potential of the maximal gauged supergravity in seven dimensions. They computed the non-abelian chiral anomaly in super Yang-Mills theories, using a variation of the Fujikawa method. The covariant action of the SU(2) spinning string is obtained together with its extension to non-linear sigma models. A covariant action for the free open spinning string field theory is constructed by analyzing the BRST transformations
Chan Hongmo.
1987-10-01
The paper traces the development of the String Theory, and was presented at Professor Sir Rudolf Peierls' 80sup(th) Birthday Symposium. The String theory is discussed with respect to the interaction of strings, the inclusion of both gauge theory and gravitation, inconsistencies in the theory, and the role of space-time. The physical principles underlying string theory are also outlined. (U.K.)
String theory or field theory?
Marshakov, A.V.
2002-01-01
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments, which are our concern in this review [ru
Matter tensor from the Hilbert variational principle
Pandres, D. Jr.
1976-01-01
We consider the Hilbert variational principle which is conventionally used to derive Einstein's equations for the source-free gravitational field. We show that at least one version of the equivalence principle suggests an alternative way of performing the variation, resulting in a different set of Einstein equations with sources automatically present. This illustrates a technique which may be applied to any theory that is derived from a variational principle and that admits a gauge group. The essential point is that, if one first imposes a gauge condition and then performs the variation, one obtains field equations with source terms which do not appear if one first performs the variation and then imposes the gauge condition. A second illustration is provided by the variational principle conventionally used to derive Maxwell's equations for the source-free electromagnetic field. If one first imposes the Lorentz gauge condition and then performs the variation, one obtains Maxwell's equations with sources present
Variational Perturbation Treatment of the Confined Hydrogen Atom
Montgomery, H. E., Jr.
2011-01-01
The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…
Freed, Karl F
2014-10-14
A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.
Freed, Karl F., E-mail: freed@uchicago.edu [James Franck Institute and Department of Chemistry, University of Chicago, 929 East 57 Street, Chicago, Illinois 60637 (United States)
2014-10-14
A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition” [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.
Accumulating Project Management Knowledge Using Process Theory
Niederman, Fred; March, Salvatore T.; Mueller, Benjamin
2016-01-01
Process theory has become an important mechanism for the accumulation of knowledge in a number of disciplines. In contrast with variance theory, which focuses on co-variation of dependent and independent variables, process theory focuses on sequences of activities, their duration and the intervals
Transport perturbation theory in nuclear reactor analysis
Nishigori, Takeo; Takeda, Toshikazu; Selvi, S.
1985-01-01
Perturbation theory is formulated on the basis of transport theory to obtain a formula for the reactivity changes due to possible variations of cross sections. Useful applications to cell homogenization are presented for the whole core calculation in transport and in diffusion theories. (author)
Uehara, S.
1985-01-01
Of all supergravity theories, the maximal, i.e., N = 8 in 4-dimension or N = 1 in 11-dimension, theory should perform the unification since it owns the highest degree of symmetry. As to the N = 1 in d = 11 theory, it has been investigated how to compactify to the d = 4 theories. From the phenomenological point of view, local SUSY GUTs, i.e., N = 1 SUSY GUTs with soft breaking terms, have been studied from various angles. The structures of extended supergravity theories are less understood than those of N = 1 supergravity theories, and matter couplings in N = 2 extended supergravity theories are under investigation. The harmonic superspace was recently proposed which may be useful to investigate the quantum effects of extended supersymmetry and supergravity theories. As to the so-called Kaluza-Klein supergravity, there is another possibility. (Mori, K.)
Johnstone, PT
2014-01-01
Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, other subjects. 1977 edition.
A Theoretical Analysis of the Reaction Between Ethyl and Molecular Oxygen
Miller, James A; Klippenstein, Stephen J; Robertson, Struan H
2000-01-01
Using a combination of electronic-structure theory, variational transition-state theory, and solutions to the time-dependent master equation, we have studied the kinetics of the reaction between ethyl...
Dorogovtsev, A Ya; Skorokhod, A V; Silvestrov, D S; Skorokhod, A V
1997-01-01
This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.
Lee, B.W.
1976-01-01
Some introductory remarks to Yang-Mills fields are given and the problem of the Coulomb gauge is considered. The perturbation expansion for quantized gauge theories is discussed and a survey of renormalization schemes is made. The role of Ward-Takahashi identities in gauge theories is discussed. The author then discusses the renormalization of pure gauge theories and theories with spontaneously broken symmetry. (B.R.H.)
Unified theory of dislocation motion including thermal activation and inertial effects
Isaac, R.D.; Granato, A.V.
1979-01-01
Transition-state rate theory has generally been used to explain the temperature dependence of the flow stress of a crystal. However, the existence of a change in the flow stress during the superconducting transition indicates the presence of inertial effects in which dislocations overcome obstacles mechanically rather than thermally. It is shown here that the thermally activated and the inertial overcoming of obstacles are not unrelated but can both be derived from principles of stochastic motion. This leads to a theory of dislocation motion that includes both thermal activation and inertial effects. It is also shown that a distribution of activation energies must be considered to account for the experimental data
Ermakov, A. I.; Mashutin, V. Y.; Vishnjakov, A. V.
With the help of the results of semiempirical (parametric method 3) and ab initio (second-order Møller-Plesset [MP2] unrestricted Hartree-Fock [UHF] 6-31G**, unrestricted density functional theory [UDFT] 6-31G** Becke's three-parameter exchange functional and the gradient-corrected functional of Lee, Yang, and Paar [B3LYP] and UDFT LANL2DZ B3LYP) quantum-chemical calculations has been studied the complexation CO and NO with molecular hydroxide of copper(I). The influence of charge defects has been simulated by the calculations of anionic, neutral, and cationic systems. It is shown that CO and NO are mainly coordinated by nonoxygen atom on an atom of copper(I) hydroxide as one- and two-center forms. These forms are suitable for appearance of prereactionary complexes of catalytic oxidation CO by molecular oxygen and decomposition NO into atoms of nitrogen and oxygen. The corresponding prereactionary complexes for systems with participation of copper(II) hydroxide and copper(III) hydroxide are not revealed. The calculations predict inhibiting impact of copper(II) and copper(III) of the observed reactions. Computed stability of complexes CO and NO with copper(I) hydroxide and activation energy of catalytic conversion of monooxides essentially depend on an excessive charge of the system. Introduction of electron-donating additives into copper(I) hydroxide promotes rise of catalytic activity of copper(I) compound.
Loring, FH
2014-01-01
Summarising the most novel facts and theories which were coming into prominence at the time, particularly those which had not yet been incorporated into standard textbooks, this important work was first published in 1921. The subjects treated cover a wide range of research that was being conducted into the atom, and include Quantum Theory, the Bohr Theory, the Sommerfield extension of Bohr's work, the Octet Theory and Isotopes, as well as Ionisation Potentials and Solar Phenomena. Because much of the material of Atomic Theories lies on the boundary between experimentally verified fact and spec
Harris, Tina
2015-04-29
Grounded theory is a popular research approach in health care and the social sciences. This article provides a description of grounded theory methodology and its key components, using examples from published studies to demonstrate practical application. It aims to demystify grounded theory for novice nurse researchers, by explaining what it is, when to use it, why they would want to use it and how to use it. It should enable nurse researchers to decide if grounded theory is an appropriate approach for their research, and to determine the quality of any grounded theory research they read.
Number theory via Representation theory
2014-11-09
Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.
Schwarz, J.H.
1985-01-01
Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(eta) or Sp(2eta) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D=10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N=4, D=4 super Yang-Mills theory and SST II reduces to N=8, D=4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions
String theory or field theory?
Marshakov, Andrei V
2002-01-01
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review. (reviews of topical problems)
Dependence theory via game theory
Grossi, D.; Turrini, P.
2011-01-01
In the multi-agent systems community, dependence theory and game theory are often presented as two alternative perspectives on the analysis of social interaction. Up till now no research has been done relating these two approaches. The unification presented provides dependence theory with the sort
Vitullo, V.P.; Grabowski, J.; Sridharan, S.
1980-01-01
Rates and α-D isotope effects have been determined for the following substrates and nucleophiles: p-methoxybenzyl bromide (Et 3 N, SCN - , N 3 - , OH - , S 2 O 3 2- ), benzyl bromide (Et 3 N, SCN - , N 3 - , OH - , S 2 O 3 2- ), and p-nitrobenzyl bromide (Et 3 N, SCN - , N 3 - , S 2 O 3 2- ). In nearly all cases the second-order rate constant for each nucleophile goes through a minimum for the unsubstituted compound while the α-D isotope increases monotonically in the squence p-NO 2 > p-H > p-OCH 3 . These results are consistent with an increasing looseness of the S/sub N/2 transition state as the substituent on the aromatic ring becomes more electron donating. 4 figures, 3 tables
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Moon, Ji Hyun; Kim, Min Young; Han, So Yeop; Um, Ik Hwan
2015-01-01
Second-order rate constants (math formula) for alkaline hydrolysis of 2,4-dinitrophenyl X-substituted benzenesulfonates (1a–1f) and Y-substituted phenyl 4-nitrobezenesulfonates (2a–2g) have been measured spectrophotometrically. Comparison of math formula with the math formula values reported previously for the corresponding reactions with math formula has revealed that OH [BOND] is only 10"3-fold more reactive than math formula, although the former is 11 pK _a units more basic than the latter. The Yukawa–Tsuno plot for the reactions of 1a–1f results in an excellent linear correlation with ρ_X = 2.09 and r = 0.41. The Brønsted-type plot for the reactions of 2a–2g is linear with β_l_g = −0.51, which is typical for reactions reported to proceed through a concerted mechanism. The Yukawa–Tsuno plot for the reactions of 2a–2g exhibits excellent linearity with ρ_Y = 1.85 and r = 0.25, indicating that a partial negative charge develops on the O atom of the leaving group in the transition state. Thus, the alkaline hydrolysis of 1a–1f and 2a–2g has been concluded to proceed through a concerted mechanism. Comparison of the ρ_X and β_l_g values for the reactions with math formula ions suggests that the reactions with hydroxide ion proceed through a tighter transition-state structure than those with azide ion
Multiple integrals in the calculus of variations
Morrey, Charles B
1966-01-01
From the reviews: "…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book." M. R. Hestenes in Journal of Optimization Theory and Applications "The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems." L. Schmetterer in Monatshefte für Mathematik "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book...
Chang, CC
2012-01-01
Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods - including classification theory and nonstandard analysis - the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Sko
Aubin, Jean-Pierre; Saint-Pierre, Patrick
2011-01-01
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explai
On a class of general variational inequalities
Siddiqi, A.H.
1990-06-01
The study of variational inequalities was initiated by the Italian Mathematician, Guido Stampacchia in the early 60's. Besides several other important problems of Physics and Engineering this theory has been applied to solve the problem of Elasticity with unilateral constraints. In this paper we introduce a new class of variational inequalities and study the existence and uniqueness of its solution. Error estimates, convergence of approximate solution and the penalty method are also discussed. (author). 25 refs
Introduction to the calculus of variations
Sagan, Hans
1992-01-01
Excellent text provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares readers for the study of modern optimal control theory. Treatment limited to extensive coverage of single integral problems in one and more unknown functions. Carefully chosen variational problems and over 400 exercises. ""Should find wide acceptance as a text and reference.""-American Mathematical Monthly. 1969 edition. Bibliography.
Cox, David A
2012-01-01
Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"—Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galo
Dufwenberg, Martin
2011-03-01
Game theory is a toolkit for examining situations where decision makers influence each other. I discuss the nature of game-theoretic analysis, the history of game theory, why game theory is useful for understanding human psychology, and why game theory has played a key role in the recent explosion of interest in the field of behavioral economics. WIREs Cogni Sci 2011 2 167-173 DOI: 10.1002/wcs.119 For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Hashiguchi, Koichi
2009-01-01
This book details the mathematics and continuum mechanics necessary as a foundation of elastoplasticity theory. It explains physical backgrounds with illustrations and provides descriptions of detailed derivation processes..
About Applications of the Fixed Point Theory
Bucur Amelia
2017-06-01
Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
Elsgolc, L E; Stark, M
1961-01-01
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
R. Veenhoven (Ruut)
2014-01-01
markdownabstract__Abstract__ Need theory of happiness is linked to affect theory, which holds that happiness is a reflection of how well we feel generally. In this view, we do not "calculate" happiness but rather "infer" it, the typical heuristic being "I feel good most of the time, hence
Bouwkamp, C.J.
1954-01-01
A critical review is presented of recent progress in classical diffraction theory. Both scalar and electromagnetic problems are discussed. The report may serve as an introduction to general diffraction theory although the main emphasis is on diffraction by plane obstacles. Various modifications of
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal...
Bjerg, Ole; Presskorn-Thygesen, Thomas
2017-01-01
The paper is a contribution to current debates about conspiracy theories within philosophy and cultural studies. Wittgenstein’s understanding of language is invoked to analyse the epistemological effects of designating particular questions and explanations as a ‘conspiracy theory......’. It is demonstrated how such a designation relegates these questions and explanations beyond the realm of meaningful discourse. In addition, Agamben’s concept of sovereignty is applied to explore the political effects of using the concept of conspiracy theory. The exceptional epistemological status assigned...... to alleged conspiracy theories within our prevalent paradigms of knowledge and truth is compared to the exceptional legal status assigned to individuals accused of terrorism under the War on Terror. The paper concludes by discussing the relation between conspiracy theory and ‘the paranoid style...
1999-11-08
In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.
Liu, Baoding
2015-01-01
When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, c...
Hjørland, Birger
2009-01-01
Concept theory is an extremely broad, interdisciplinary and complex field of research related to many deep fields with very long historical traditions without much consensus. However, information science and knowledge organization cannot avoid relating to theories of concepts. Knowledge...... organizing systems (e.g. classification systems, thesauri and ontologies) should be understood as systems basically organizing concepts and their semantic relations. The same is the case with information retrieval systems. Different theories of concepts have different implications for how to construe......, evaluate and use such systems. Based on "a post-Kuhnian view" of paradigms this paper put forward arguments that the best understanding and classification of theories of concepts is to view and classify them in accordance with epistemological theories (empiricism, rationalism, historicism and pragmatism...
Variationally Optimized Free-Energy Flooding for Rate Calculation
McCarty, James; Valsson, Omar; Tiwary, Pratyush; Parrinello, Michele
2015-08-01
We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways.
Theoretical physics. Field theory
Landau, L.; Lifchitz, E.
2004-01-01
This book is the fifth French edition of the famous course written by Landau/Lifchitz and devoted to both the theory of electromagnetic fields and the gravity theory. The talk of the theory of electromagnetic fields is based on special relativity and relates to only the electrodynamics in vacuum and that of pointwise electric charges. On the basis of the fundamental notions of the principle of relativity and of relativistic mechanics, and by using variational principles, the authors develop the fundamental equations of the electromagnetic field, the wave equation and the processes of emission and propagation of light. The theory of gravitational fields, i.e. the general theory of relativity, is exposed in the last five chapters. The fundamentals of the tensor calculus and all that is related to it are progressively introduced just when needed (electromagnetic field tensor, energy-impulse tensor, or curve tensor...). The worldwide reputation of this book is generally allotted to clearness, to the simplicity and the rigorous logic of the demonstrations. (A.C.)
Variational principles for dissipative waves
Dodin, I. Y.; Ruiz, D. E.
2016-10-01
Variational methods are a powerful tool in plasma theory. However, their applications are typically restricted to conservative systems or require doubling of variables, which often contradicts the purpose of the variational approach altogether. We show that these restrictions can be relaxed for some classes of dynamical systems that are of practical interest in plasma physics, particularly including dissipative plasma waves. Applications will be discussed to calculating dispersion relations and modulational dynamics of individual plasma waves and wave ensembles. The work was supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.
Hong, Kiryong; Kim, Tae Kyu
2012-01-01
We investigate the doublet and quartet potential energy surfaces associated with the gas-phase reaction between Ti + and CF 3 COCH 3 for two plausible reaction pathways, TiF 2 + and TiO + formation pathways by using the density functional theory (DFT) method. The molecular structures of intermediates and transition states involved in these reaction pathways are optimized at the DFT level by using the PBE0 functional. All transition states are identified by using the intrinsic reaction coordinate (IRC) method, and the resulting reaction coordinates describe how Ti + activates CF 3 COCH 3 and produces TiF 2 + and TiO + as products. On the basis of presented results, we propose the most favorable reaction pathway in the reaction between Ti + and CF 3 COCH 3
Gauge theories of the weak interactions
Quinn, H.
1978-01-01
Lectures are given on the Weinberg--Salam or Weinberg--Salam--Glashow--Iliopoulos--Maiani gauge theory. The way it is put together and some possible variations in the literature are discussed. 53 references
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Schmidli, Hanspeter
2017-01-01
This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.
Smith, Shelley
This paper came about within the context of a 13-month research project, Focus Area 1 - Method and Theory, at the Center for Public Space Research at the Royal Academy of the Arts School of Architecture in Copenhagen, Denmark. This project has been funded by RealDania. The goals of the research...... project, Focus Area 1 - Method and Theory, which forms the framework for this working paper, are: * To provide a basis from which to discuss the concept of public space in a contemporary architectural and urban context - specifically relating to theory and method * To broaden the discussion of the concept...
Lubliner, Jacob
2008-01-01
The aim of Plasticity Theory is to provide a comprehensive introduction to the contemporary state of knowledge in basic plasticity theory and to its applications. It treats several areas not commonly found between the covers of a single book: the physics of plasticity, constitutive theory, dynamic plasticity, large-deformation plasticity, and numerical methods, in addition to a representative survey of problems treated by classical methods, such as elastic-plastic problems, plane plastic flow, and limit analysis; the problem discussed come from areas of interest to mechanical, structural, and
Linder, Stefan; Foss, Nicolai Juul
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting and informational conditions, the theory addresses problems of ex...... ante (“hidden characteristics”) as well as ex post information asymmetry (“hidden action”), and examines conditions under which various kinds of incentive instruments and monitoring arrangements can be deployed to minimize the welfare loss. Its clear predictions and broad applicability have allowed...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism....
Linder, Stefan; Foss, Nicolai Juul
2015-01-01
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting, and informational conditions, the theory addresses problems of ex...... ante (‘hidden characteristics’) as well as ex post information asymmetry (‘hidden action’), and examines conditions under which various kinds of incentive instruments and monitoring arrangements can be deployed to minimize the welfare loss. Its clear predictions and broad applicability have allowed...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism....
Chen, Yue; Sakaki, Shigeyoshi
2017-04-03
The recently reported high reactivity of the Mo-Mo quintuple bond of Mo 2 (N ∧ N) 2 (1) {N ∧ N = μ-κ 2 -CH[N(2,6-iPr 2 C 6 H 3 )] 2 } in the H-H σ-bond cleavage was investigated. DFT calculations disclosed that the H-H σ-bond cleavage by 1 occurs with nearly no barrier to afford the cis-dihydride species followed by cis-trans isomerization to form the trans-dihydride product, which is consistent with the experimental result. The O-H and C-H bond cleavages by 1 were computationally predicted to occur with moderate (ΔG° ⧧ = 9.0 kcal/mol) and acceptable activation energies (ΔG° ⧧ = 22.5 kcal/mol), respectively, suggesting that the Mo-Mo quintuple bond can be applied to various σ-bond cleavages. In these σ-bond cleavage reactions, the charge-transfer (CT Mo→XH ) from the Mo-Mo quintuple bond to the X-H (X = H, C, or O) bond and that (CT XH→Mo ) from the X-H bond to the Mo-Mo bond play crucial roles. Though the HOMO (dδ-MO) of 1 is at lower energy and the LUMO + 2 (dδ*-MO) of 1 is at higher energy than those of RhCl(PMe 3 ) 2 (LUMO and LUMO + 1 of 1 are not frontier MO), the H-H σ-bond cleavage by 1 more easily occurs than that by the Rh complex. Hence, the frontier MO energies are not the reason for the high reactivity of 1. The high reactivity of 1 arises from the polarization of dδ-type MOs of the Mo-Mo quintuple bond in the transition state. Such a polarized electronic structure enhances the bonding overlap between the dδ-MO of the Mo-Mo bond and the σ*-antibonding MO of the X-H bond to facilitate the CT Mo→XH and reduce the exchange repulsion between the Mo-Mo bond and the X-H bond. This polarized electronic structure of the transition state is similar to that of a frustrated Lewis pair. The easy polarization of the dδ-type MOs is one of the advantages of the metal-metal multiple bond, because such polarization is impossible in the mononuclear metal complex.
Statistical theory of electron densities
Pratt, L.R.; Hoffman, G.G.; Harris, R.A.
1988-01-01
An optimized Thomas--Fermi theory is proposed which retains the simplicity of the original theory and is a suitable reference theory for Monte Carlo density functional treatments of condensed materials. The key ingredient of the optimized theory is a neighborhood sampled potential which contains effects of the inhomogeneities in the one-electron potential. In contrast to the traditional Thomas--Fermi approach, the optimized theory predicts a finite electron density in the vicinity of a nucleus. Consideration of the example of an ideal electron gas subject to a central Coulomb field indicates that implementation of the approach is straightforward. The optimized theory is found to fail completely when a classically forbidden region is approached. However, these circumstances are not of primary interest for calculations of interatomic forces. It is shown how the energy functional of the density may be constructed by integration of a generalized Hellmann--Feynman relation. This generalized Hellmann--Feynman relation proves to be equivalent to the variational principle of density functional quantum mechanics, and, therefore, the present density theory can be viewed as a variational consequence of the constructed energy functional
Elsgolc, Lev D
2007-01-01
This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems.Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features nu
M theory on deformed superspace
Faizal, Mir
2011-11-01
In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in N=1 superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.
Equivariance, Variational Principles, and the Feynman Integral
George Svetlichny
2008-03-01
Full Text Available We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman's integral.
Partial differential equations and calculus of variations
Leis, Rolf
1988-01-01
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Optimal control and the calculus of variations
Pinch, Enid R
1993-01-01
This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.
Fundamental quadratic variational principle underlying general relativity
Atkins, W.K.
1983-01-01
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed
Elements of magnetohydrodynamic stability theory
Spies, G.O.
1976-11-01
The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes
Nel, Louis
2016-01-01
This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject's classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, especially those that contribute to ...
Hodges, Wilfrid
1993-01-01
An up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians.
Lunardi, Alessandra
2018-01-01
This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
1989-06-01
This report discusses concepts in nuclear theory such as: neutrino nucleosynthesis; double beta decay; neutrino oscillations; chiral symmetry breaking; T invariance; quark propagator; cold fusion; and other related topics
R. Veenhoven (Ruut)
2014-01-01
markdownabstract__Abstract__ Assumptions Livability theory involves the following six key assumptions: 1. Like all animals, humans have innate needs, such as for food, safety, and companionship. 2. Gratification of needs manifests in hedonic experience. 3. Hedonic experience determines how
SAIDANI Lassaad
2015-01-01
The nokton theory is an attempt to construct a theory adapted to every physical phenomenon. Space and time have been discretized. Its laws are iterative and precise. Probability plays an important role here. At first I defined the notion of image function and its mathematical framework. The notion of nokton and its state are the basis of several definitions. I later defined the canonical image function and the canonical contribution. Two constants have been necessary to define the dynam...
SAIDANI Lassaad
2017-01-01
The nokton theory is an attempt to construct a theory adapted to every physical phenomenon. Space and time have been discretized. Its laws are iterative and precise. Probability plays an important role here. At first I defined the notion of image function and its mathematical framework. The notion of nokton and its state are the basis of several definitions. I later defined the canonical image function and the canonical contribution. Two constants have been necessary to define the dynam...
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Transition States from Empirical Force Fields
Jensen, Frank; Norrby, Per-Ola
2003-01-01
This is an overview of the use of empirical force fields in the study of reaction mechanisms. EVB-type methods (including RFF and MCMM) produce full reaction surfaces by mixing, in the simplest case, known force fields describing reactants and products. The SEAM method instead locates approximate...
Malinowska , Agnieszka B.; Torres , Delfim
2014-01-01
International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...
Bilateral renal artery variation
Üçerler, Hülya; Üzüm, Yusuf; İkiz, Z. Aslı Aktan
2014-01-01
Each kidney is supplied by a single renal artery, although renal artery variations are common. Variations of the renal arteryhave become important with the increasing number of renal transplantations. Numerous studies describe variations in renalartery anatomy. Especially the left renal artery is among the most critical arterial variations, because it is the referred side forresecting the donor kidney. During routine dissection in a formalin fixed male cadaver, we have found a bilateral renal...
Koehler, H.S.
1979-01-01
A short review of the early developments due largely to K. A Brueckner is given. Special emphasis is given to insertions in hole and particle lines, dispersion-effects and healings, and how the quantitative effects of these are related to the nature of the force. The importance of higher-order insertions in hole and particle lines and its relation to the force is also emphasized. This is important in a quantitative comparison of BBG theory with variational theory. The inceased healing-distance due to the tensor force is also pointed out. This gives convergence problems. Experiment may leave room for a nuclear force with weaker tensor force than mostly used. (Auth.)
Perturbation theory with instantons
Carruthers, P.; Pinsky, S.S.; Zachariasen, F.
1977-05-01
''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...
John R. Jones; Norbert V. DeByle
1985-01-01
The broad genotypic variability in quaking aspen (Populus tremuloides Michx.), that results in equally broad phenotypic variability among clones is important to the ecology and management of this species. This chapter considers principles of aspen genetics and variation, variation in aspen over its range, and local variation among clones. For a more...
Janssen, B.; van Kranenburg, P.
2014-01-01
Variation in music can be caused by different phenomena: conscious, creative manipulation of musical ideas; but also unconscious variation during music recall. It is the latter phenomenon that we wish to study: variation which occurs in oral transmission, in which a melody is taught without the help
Target Selection Models with Preference Variation Between Offenders
Townsley, Michael; Birks, Daniel; Ruiter, Stijn; Bernasco, Wim; White, Gentry
2016-01-01
Objectives: This study explores preference variation in location choice strategies of residential burglars. Applying a model of offender target selection that is grounded in assertions of the routine activity approach, rational choice perspective, crime pattern and social disorganization theories,
Quantum field theory and link invariants
Cotta-Ramusino, P.; Guadagnini, E.; Mintchev, M.; Martellini, M.
1990-01-01
A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established. (orig.)
Variational principles for Ginzburg-Landau equation by He's semi-inverse method
Liu, W.Y.; Yu, Y.J.; Chen, L.D.
2007-01-01
Via the semi-inverse method of establishing variational principles proposed by He, a generalized variational principle is established for Ginzburg-Landau equation. The present theory provides a quite straightforward tool to the search for various variational principles for physical problems. This paper aims at providing a more complete theoretical basis for applications using finite element and other direct variational methods
Discrete variational Hamiltonian mechanics
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Kodaira, Kunihiko
2017-01-01
This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.
Kenyon, I.R.
1986-01-01
Modern theories of the interactions between fundamental particles are all gauge theories. In the case of gravitation, application of this principle to space-time leads to Einstein's theory of general relativity. All the other interactions involve the application of the gauge principle to internal spaces. Electromagnetism serves to introduce the idea of a gauge field, in this case the electromagnetic field. The next example, the strong force, shows unique features at long and short range which have their origin in the self-coupling of the gauge fields. Finally the unification of the description of the superficially dissimilar electromagnetic and weak nuclear forces completes the picture of successes of the gauge principle. (author)
Higher-dimensional analogues of Donaldson-Witten theory
Acharya, B.S.; Spence, B.
1997-01-01
We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of G 2 holonomy, respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher-dimensional analogue of the fact that Donaldson-Witten field theory on hyper-Kaehler 4-manifolds is topological without twisting. Higher-dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. (orig.)
Stewart, Ian
2003-01-01
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the g
Sitenko, A.
1991-01-01
This book emerged out of graduate lectures given by the author at the University of Kiev and is intended as a graduate text. The fundamentals of non-relativistic quantum scattering theory are covered, including some topics, such as the phase-function formalism, separable potentials, and inverse scattering, which are not always coverded in textbooks on scattering theory. Criticisms of the text are minor, but the reviewer feels an inadequate index is provided and the citing of references in the Russian language is a hindrance in a graduate text
Simulating Variation in Order to Learn Classroom Management
Ragnemalm, Eva L.; Samuelsson, Marcus
2016-01-01
Classroom management is an important part of learning to be a teacher. The variation theory of learning provides the insight that it is important to vary the critical aspects of any task or subject that is to be learned. Simulation technology is useful in order to provide a controlled environment for that variation, and text as a medium gives the…
Adult sex ratio variation : Implications for breeding system evolution
Szekely, T.; Weissing, F. J.; Komdeur, J.
Adult sex ratio (ASR) exhibits immense variation in nature, although neither the causes nor the implications of this variation are fully understood. According to theory, the ASR is expected to influence sex roles and breeding systems, as the rarer sex in the population has more potential partners to
Problems of phenomenological simulation of the Dst variation
Gul'el'mi, A.V.
1988-01-01
Stochastic generalization of RBM model, describing the D st -variation is suggested. The corresponding Fokker-Planck equation contains a new phenomenological parameter enabling to obtain the interval estimation of D st forecast. The structure of sources and sinks forming the D st -variation is considered from the viewpoint of critical phenomenon theory
Sferra, Bobbie A.; Paddock, Susan C.
This booklet describes various theoretical aspects of leadership, including the proper exercise of authority, effective delegation, goal setting, exercise of control, assignment of responsibility, performance evaluation, and group process facilitation. It begins by describing the evolution of general theories of leadership from historic concepts…
Hall, Marshall
2011-01-01
Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
Toso, Robert B.
2000-01-01
Inspired by William Glasser's Reality Therapy ideas, Control Theory (CT) is a disciplinary approach that stresses people's ability to control only their own behavior, based on internal motivations to satisfy five basic needs. At one North Dakota high school, CT-trained teachers are the program's best recruiters. (MLH)
de Vreese, C.H.; Lecheler, S.; Mazzoleni, G.; Barnhurst, K.G.; Ikeda, K.; Maia, R.C.M.; Wessler, H.
2016-01-01
Political issues can be viewed from different perspectives and they can be defined differently in the news media by emphasizing some aspects and leaving others aside. This is at the core of news framing theory. Framing originates within sociology and psychology and has become one of the most used
Gong, Ha Soung
2006-12-01
The text book composed of five parts, which are summary of this book, arrangement of electricity theory including electricity nad magnetism, a direct current, and alternating current. It has two dictionary electricity terms for a synonym. The last is an appendix. It is for preparing for test of officer, electricity engineer and fire fighting engineer.
Monthoux, Pierre Guillet de; Statler, Matt
2014-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer’s Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specifically...
Guillet de Monthoux, Pierre; Statler, Matt
2017-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer's Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specifically...
Tang, W.M.
2001-01-01
This is a summary of the advances in magnetic fusion energy theory research presented at the 17th International Atomic Energy Agency Fusion Energy Conference from 19 24 October, 1998 in Yokohama, Japan. Theory and simulation results from this conference provided encouraging evidence of significant progress in understanding the physics of thermonuclear plasmas. Indeed, the grand challenge for this field is to acquire the basic understanding that can readily enable the innovations which would make fusion energy practical. In this sense, research in fusion energy is increasingly able to be categorized as fitting well the 'Pasteur's Quadrant' paradigm, where the research strongly couples basic science ('Bohr's Quadrant') to technological impact ('Edison's Quadrant'). As supported by some of the work presented at this conference, this trend will be further enhanced by advanced simulations. Eventually, realistic three-dimensional modeling capabilities, when properly combined with rapid and complete data interpretation of results from both experiments and simulations, can contribute to a greatly enhanced cycle of understanding and innovation. Plasma science theory and simulation have provided reliable foundations for this improved modeling capability, and the exciting advances in high-performance computational resources have further accelerated progress. There were 68 papers presented at this conference in the area of magnetic fusion energy theory
Penland, Patrick R.
Three papers are presented which delineate the foundation of theory and principles which underlie the research and instructional approach to communications at the Graduate School of Library and Information Science, University of Pittsburgh. Cybernetic principles provide the integration, and validation is based in part on a situation-producing…
Lee, William H K.
2016-01-01
A complex system consists of many interacting parts, generates new collective behavior through self organization, and adaptively evolves through time. Many theories have been developed to study complex systems, including chaos, fractals, cellular automata, self organization, stochastic processes, turbulence, and genetic algorithms.
Plummer, MD
1986-01-01
This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.
Bertelsen, Olav Wedege; Bødker, Susanne
2003-01-01
the young HCI research tradition. But HCI was already facing problems: lack of consideration for other aspects of human behavior, for interaction with other people, for culture. Cognitive science-based theories lacked means to address several issues that came out of the empirical projects....
On the variation of the gravitational constant G
De Sabbata, V.
1980-01-01
We consider the variation of the gravitational constant G starting from Dirac's large number hypothesis. After a brief description of the various gravitational theories which, other than General Relativity, incorporate the variation of G, we consider the geophysical and astrophysical consequences of the variation of G and the present status of the performed experiments. Finally, a short account on strong gravity is given which seems to provide a basis for Dirac's large number hypothesis. (author)
Stein, Irene F.; Stelter, Reinhard
2011-01-01
Communication theory covers a wide variety of theories related to the communication process (Littlejohn, 1999). Communication is not simply an exchange of information, in which we have a sender and a receiver. This very technical concept of communication is clearly outdated; a human being...... is not a data processing device. In this chapter, communication is understood as a process of shared meaning-making (Bruner, 1990). Human beings interpret their environment, other people, and themselves on the basis of their dynamic interaction with the surrounding world. Meaning is essential because people...... ascribe specific meanings to their experiences, their actions in life or work, and their interactions. Meaning is reshaped, adapted, and transformed in every communication encounter. Furthermore, meaning is cocreated in dialogues or in communities of practice, such as in teams at a workplace or in school...
2015-01-01
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Helms, Lester L
2014-01-01
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In ...
Jensen, Klaus Bruhn
2016-01-01
This article revisits the place of normative and other practical issues in the wider conceptual architecture of communication theory, building on the tradition of philosophical pragmatism. The article first characterizes everyday concepts of communication as the accumulated outcome of natural...... evolution and history: practical resources for human existence and social coexistence. Such practical concepts have served as the point of departure for diverse theoretical conceptions of what communication is. The second part of the article highlights the past neglect and current potential of normative...... communication theories that ask, in addition, what communication ought to be, and what it could be, taking the relationship between communication and justice as a case in point. The final section returns to empirical conceptualizations of different institutions, practices and discourses of communication...
Jarlskog, C.
An introduction to the unified gauge theories of weak and electromagnetic interactions is given. The ingredients of gauge theories and symmetries and conservation laws lead to discussion of local gauge invariance and QED, followed by weak interactions and quantum flavor dynamics. The construction of the standard SU(2)xU(1) model precedes discussion of the unification of weak and electromagnetic interactions and weak neutral current couplings in this model. Presentation of spontaneous symmetry breaking and spontaneous breaking of a local symmetry leads to a spontaneous breaking scheme for the standard SU(2)xU(1) model. Consideration of quarks, leptons, masses and the Cabibbo angles, of the four quark and six quark models and CP violation lead finally to grand unification, followed by discussion of mixing angles in the Georgi-Glashow model, the Higgses of the SU(5) model and proton/ neutron decay in SU(5). (JIW)
Perjes, Z.
1982-01-01
Particle models in twistor theory are reviewed, starting with an introduction into the kinematical-twistor formalism which describes massive particles in Minkowski space-time. The internal transformations of constituent twistors are then discussed. The quantization rules available from a study of twistor scattering situations are used to construct quantum models of fundamental particles. The theory allows the introduction of an internal space with a Kaehlerian metric where hadron structure is described by spherical states of bound constituents. It is conjectured that the spectrum of successive families of hadrons might approach an accumulation point in energy. Above this threshold energy, the Kaehlerian analog of ionization could occur wherein the zero-mass constituents (twistors) of the particle break free. (Auth.)
Carroll, Joseph; Clasen, Mathias; Jonsson, Emelie
2017-01-01
Biocultural theory is an integrative research program designed to investigate the causal interactions between biological adaptations and cultural constructions. From the biocultural perspective, cultural processes are rooted in the biological necessities of the human life cycle: specifically human...... of research as contributions to a coherent, collective research program. This article argues that a mature biocultural paradigm needs to be informed by at least 7 major research clusters: (a) gene-culture coevolution; (b) human life history theory; (c) evolutionary social psychology; (d) anthropological...... forms of birth, growth, survival, mating, parenting, and sociality. Conversely, from the biocultural perspective, human biological processes are constrained, organized, and developed by culture, which includes technology, culturally specific socioeconomic and political structures, religious...
Weber, Rebecca
2012-01-01
What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including re...
Hashiguchi, Koichi
2014-01-01
This book was written to serve as the standard textbook of elastoplasticity for students, engineers and researchers in the field of applied mechanics. The present second edition is improved thoroughly from the first edition by selecting the standard theories from various formulations and models, which are required to study the essentials of elastoplasticity steadily and effectively and will remain universally in the history of elastoplasticity. It opens with an explanation of vector-tensor analysis and continuum mechanics as a foundation to study elastoplasticity theory, extending over various strain and stress tensors and their rates. Subsequently, constitutive equations of elastoplastic and viscoplastic deformations for monotonic, cyclic and non-proportional loading behavior in a general rate and their applications to metals and soils are described in detail, and constitutive equations of friction behavior between solids and its application to the prediction of stick-slip phenomena are delineated. In additi...
Weinstock, Robert
1975-01-01
Basic introduction covering isoperimetric problems, theory of elasticity, quantum mechanics, electrostatics, geometrical optics, particle dynamics, more. Exercises throughout. "A very useful book." - J. L. Synge, American Mathematical Monthly.
Veenhoven, Ruut
2014-01-01
markdownabstract__Abstract__ Assumptions Livability theory involves the following six key assumptions: 1. Like all animals, humans have innate needs, such as for food, safety, and companionship. 2. Gratification of needs manifests in hedonic experience. 3. Hedonic experience determines how much we like the life we live (happiness). Hence, happiness depends on need gratification. 4.Need gratification depends on both external living conditions and inner abilities to use these. Hence, bad living...
Casten, R F
2015-01-01
This paper discusses some simple issues that arise in testing models, with a focus on models for low energy nuclear structure. By way of simplified examples, we illustrate some dangers in blind statistical assessments, pointing out especially the need to include theoretical uncertainties, the danger of over-weighting precise or physically redundant experimental results, the need to assess competing theories with independent and physically sensitive observables, and the value of statistical tests properly evaluated. (paper)
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Friedrich, Harald
2016-01-01
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...
An introduction to the calculus of variations
Pars, LA
2009-01-01
This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abstract theory to its use in concrete problems. It offers a working knowledge of relevant techniques, plus an impetus for further study.Starting with an overview of fundamental problems and theories, the text advances to illustrative examples and examinations of variable end-points and the fundamental sufficiency theorem. Subsequent chapters explore the isoperimetrical problem, curves in space, the p
Stability in quadratic torsion theories
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Optimal control theory an introduction
Kirk, Donald E
2004-01-01
Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization.Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin's minimum principle are the subjects of chapters 4 and 5, and chapter
Stability in quadratic torsion theories
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado
2017-01-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Variational identities and Hamiltonian structures
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Equilibrium models and variational inequalities
Konnov, Igor
2007-01-01
The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models- Covers the basics of theory and solution methods both for the complementarity and variational inequality probl...
Verb Movement Variation in Germanic and Optimality Theory
Vikner, Sten
2001-01-01
This habilitation dissertation falls into two parts. In the first part, "Establishing the typology: Verb Movement in the Germanic VO- and OV-languages", I continue the work in Vikner (1995a, 1997) on the movement of finite verbs across the Germanic languages. Chapter 1 argues that rich finite inf...... data are treated: constructions with auxiliaries, negation and/or do-insertion, and chapter 7 accounts for the differences in distribution between the V2 word order and the non-V2 word order between the languages.......This habilitation dissertation falls into two parts. In the first part, "Establishing the typology: Verb Movement in the Germanic VO- and OV-languages", I continue the work in Vikner (1995a, 1997) on the movement of finite verbs across the Germanic languages. Chapter 1 argues that rich finite...... inflection triggers V°-to-I° movement in the Germanic (and Romance) VO-languages, chapter 2 supports the claim that Yiddish is an OV-language, and chapter 3 defends the view that all Germanic OV-languages except Yiddish do not have V°-to-I° movement. Where Part I tries to establish facts and arguments which...
Variational techniques in non-perturbative QCD
Kovner, Alex; Kovner, Alex
2004-01-01
We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.
Boltzmann, Darwin and Directionality theory
Demetrius, Lloyd A., E-mail: ldemetr@oeb.harvard.edu
2013-09-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Boltzmann, Darwin and Directionality theory
Demetrius, Lloyd A.
2013-01-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Heshmat, Mojgan; Privalov, Timofei
2017-07-06
By using transition-state (TS) calculations, we examined how Lewis acid (LA) complexation activates carbonyl compounds in the context of hydrogenation of carbonyl compounds by H 2 in Lewis basic (ethereal) solvents containing borane LAs of the type (C 6 F 5 ) 3 B. According to our calculations, LA complexation does not activate a ketone sufficiently enough for the direct addition of H 2 to the O=C unsaturated bond; but, calculations indicate a possibly facile heterolytic cleavage of H 2 at the activated and thus sufficiently Lewis acidic carbonyl carbon atom with the assistance of the Lewis basic solvent (i.e., 1,4-dioxane or THF). For the solvent-assisted H 2 splitting at the carbonyl carbon atom of (C 6 F 5 ) 3 B adducts with different ketones, a number of TSs are computed and the obtained results are related to insights from experiment. By using the Born-Oppenheimer molecular dynamics with the DFT for electronic structure calculations, the evolution of the (C 6 F 5 ) 3 B-alkoxide ionic intermediate and the proton transfer to the alkoxide oxygen atom were investigated. The results indicate a plausible hydrogenation mechanism with a LA, that is, (C 6 F 5 ) 3 B, as a catalyst, namely, 1) the step of H 2 cleavage that involves a Lewis basic solvent molecule plus the carbonyl carbon atom of thermodynamically stable and experimentally identifiable (C 6 F 5 ) 3 B-ketone adducts in which (C 6 F 5 ) 3 B is the "Lewis acid promoter", 2) the transfer of the solvent-bound proton to the oxygen atom of the (C 6 F 5 ) 3 B-alkoxide intermediate giving the (C 6 F 5 ) 3 B-alcohol adduct, and 3) the S N 2-style displacement of the alcohol by a ketone or a Lewis basic solvent molecule. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Goldie, Charles M
1991-01-01
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
2009-01-01
This book deals with the basic subjects of design theory. It begins with balanced incomplete block designs, various constructions of which are described in ample detail. In particular, finite projective and affine planes, difference sets and Hadamard matrices, as tools to construct balanced incomplete block designs, are included. Orthogonal latin squares are also treated in detail. Zhu's simpler proof of the falsity of Euler's conjecture is included. The construction of some classes of balanced incomplete block designs, such as Steiner triple systems and Kirkman triple systems, are also given.
Optimal Control of Evolution Mixed Variational Inclusions
Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx [Universidad Nacional Autónoma de México, Departamento de Recursos Naturales, Instituto de Geofísica (Mexico)
2013-12-15
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
Optimal Control of Evolution Mixed Variational Inclusions
Alduncin, Gonzalo
2013-01-01
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory
A variational synthesis nodal discrete ordinates method
Favorite, J.A.; Stacey, W.M.
1999-01-01
A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems
Bruschetta, M.; Saccon, A.; Picci, G.
2014-01-01
The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in
Marin-Garcia Pablo
2010-05-01
Full Text Available Abstract Background The maturing field of genomics is rapidly increasing the number of sequenced genomes and producing more information from those previously sequenced. Much of this additional information is variation data derived from sampling multiple individuals of a given species with the goal of discovering new variants and characterising the population frequencies of the variants that are already known. These data have immense value for many studies, including those designed to understand evolution and connect genotype to phenotype. Maximising the utility of the data requires that it be stored in an accessible manner that facilitates the integration of variation data with other genome resources such as gene annotation and comparative genomics. Description The Ensembl project provides comprehensive and integrated variation resources for a wide variety of chordate genomes. This paper provides a detailed description of the sources of data and the methods for creating the Ensembl variation databases. It also explores the utility of the information by explaining the range of query options available, from using interactive web displays, to online data mining tools and connecting directly to the data servers programmatically. It gives a good overview of the variation resources and future plans for expanding the variation data within Ensembl. Conclusions Variation data is an important key to understanding the functional and phenotypic differences between individuals. The development of new sequencing and genotyping technologies is greatly increasing the amount of variation data known for almost all genomes. The Ensembl variation resources are integrated into the Ensembl genome browser and provide a comprehensive way to access this data in the context of a widely used genome bioinformatics system. All Ensembl data is freely available at http://www.ensembl.org and from the public MySQL database server at ensembldb.ensembl.org.
International business theory and marketing theory
Soldner, Helmut
1984-01-01
International business theory and marketing theory : elements for internat. marketing theory building. - In: Marketing aspects of international business / Gerald M. Hampton ... (eds.). - Boston u.a. : Kluwer, 1984. - S. 25-57
Markland, J.T.
1992-01-01
Techniques used in conventional project appraisal are mathematically very simple in comparison to those used in reservoir modelling, and in the geosciences. Clearly it would be possible to value assets in mathematically more sophisticated ways if it were meaningful and worthwhile so to do. The DCf approach in common use has recognized limitations; the inability to select a meaningful discount rate being particularly significant. Financial Theory has advanced enormously over the last few years, along with computational techniques, and methods are beginning to appear which may change the way we do project evaluations in practice. The starting point for all of this was a paper by Black and Scholes, which asserts that almost all corporate liabilities can be viewed as options of varying degrees of complexity. Although the financial presentation may be unfamiliar to engineers and geoscientists, some of the concepts used will not be. This paper outlines, in plain English, the basis of option pricing theory for assessing the market value of a project. it also attempts to assess the future role of this type of approach in practical Petroleum Exploration and Engineering economics. Reference is made to relevant published Natural Resource literature
Coupled variations of fundamental couplings and primordial nucleosynthesis
Coc, Alain; Nunes, Nelson J.; Olive, Keith A.; Uzan, Jean-Philippe; Vangioni, Elisabeth
2006-10-01
The effect of variations of the fundamental nuclear parameters on big-bang nucleosynthesis are modeled and discussed in detail taking into account the interrelations between the fundamental parameters arising in unified theories. Considering only 4 He, strong constraints on the variation of the neutron lifetime, neutron-proton mass difference are set. These constraints are then translated into constraints on the time variation of the Yukawa couplings and the fine structure constant. Furthermore, we show that a variation of the deuterium binding energy is able to reconcile the 7 Li abundance deduced from the WMAP analysis with its spectroscopically determined value while maintaining concordance with D and 4 He. (authors)
Chambolle's Projection Algorithm for Total Variation Denoising
Joan Duran
2013-12-01
Full Text Available Denoising is the problem of removing the inherent noise from an image. The standard noise model is additive white Gaussian noise, where the observed image f is related to the underlying true image u by the degradation model f=u+n, and n is supposed to be at each pixel independently and identically distributed as a zero-mean Gaussian random variable. Since this is an ill-posed problem, Rudin, Osher and Fatemi introduced the total variation as a regularizing term. It has proved to be quite efficient for regularizing images without smoothing the boundaries of the objects. This paper focuses on the simple description of the theory and on the implementation of Chambolle's projection algorithm for minimizing the total variation of a grayscale image. Furthermore, we adapt the algorithm to the vectorial total variation for color images. The implementation is described in detail and its parameters are analyzed and varied to come up with a reliable implementation.
A variational principle for the plasma centrifuge
Ludwig, G.O.
1986-09-01
A variational principle is derived which describes the stationary state of the plasma column in a plasma centrifuge. Starting with the fluid equations in a rotating frame the theory is developed using the method of irreversible thermodynamics. This formulation easily leads to an expression for the density distribution of the l-species at sedimentation equilibrium, taking into account the effect of the electric and magnetic forces. Assuming stationary boundary conditions and rigid rotation nonequilibrium states the condition for thermodynamic stability integrated over the volume of the system reduces, under certain restrictions, to the principle of minimum entropy production in the stationary state. This principle yields a variational problem which is equivalent to the original problem posed by the stationary fluid equations. The variational method is useful in achieving approximate solutions that give the electric potential and current distributions in the rotating plasma column consistent with an assumed plasma density profile. (Author) [pt
Malinowska, Agnieszka B
2014-01-01
This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...
Variational Monte Carlo Technique
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 8. Variational Monte Carlo Technique: Ground State Energies of Quantum Mechanical Systems. Sukanta Deb. General Article Volume 19 Issue 8 August 2014 pp 713-739 ...
Variational principles in physics
Basdevant, Jean-Louis
2007-01-01
Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieu’s famous formulation: "In all magistracies, the greatness of the power must be compensated by the brevity of the duration." Astonishingly, natural laws are guided by a similar principle. Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be known as Fermat’s principle, a cornerstone of geometrical optics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted to the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdev...
Conformal tension in string theories and M-theory
Barros, Manuel; Ferrandez, Angel; Lucas, Pascual
2000-01-01
This paper deals with string theories and M-theories on backgrounds of the form AdSxM,M being a compact principal U(1)-bundle. These configurations are the natural settings to study Hopf T-dualities (Duff et al., Nucl. Phys. B 544 (1999) 145), and so to define duality chains connecting different string theories and M-theories. There is an increasing great interest in studying those properties (physical or geometrical) which are preserved along the duality chains. For example, it is known that Hopf T-dualities preserve the black hole entropies (Duff et al., Nucl. Phys. B 544 (1999) 145). In this paper we consider a two-parameter family of actions which constitutes a natural variation of the conformal total tension action (also known as Willmore-Chen functional in differential geometry). Then, we show that the existence of wide families of solutions (in particular compact solutions) for the corresponding motion equations is preserved along those duality chains. In particular, we exhibit ample classes of Willmore-Chen submanifolds with a reasonable degree of symmetry in a wide variety of conformal string theories and conformal M-theories, that in addition are solutions of a second variational problem known as the area-volume isoperimetric problem. These are good reasons to refer those submanifolds as the best worlds one can find in a conformal universe. The method we use to obtain this invariant under Hopf T-dualities is based on the principle of symmetric criticality. However, it is used in a two-fold sense. First to break symmetry and so to reduce variables. Second to gain rigidity in direct approaches to integrate the Euler-Lagrange equations. The existence of generalized elastic curves is also important in the explicit exhibition of those configurations. The relationship between solutions and elasticae can be regarded as a holographic property
General quantum variational calculus
Artur M. C. Brito da Cruz
2018-02-01
Full Text Available We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-calculus.
Generalized quasi variational inequalities
Noor, M.A. [King Saud Univ., Riyadh (Saudi Arabia)
1996-12-31
In this paper, we establish the equivalence between the generalized quasi variational inequalities and the generalized implicit Wiener-Hopf equations using essentially the projection technique. This equivalence is used to suggest and analyze a number of new iterative algorithms for solving generalized quasi variational inequalities and the related complementarity problems. The convergence criteria is also considered. The results proved in this paper represent a significant improvement and refinement of the previously known results.
Sugama, H.
1999-08-01
The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles' dynamics as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell's equations for the electromagnetic fields are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from the Noether's theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequency. (author)
Density functional theory of nuclei
Terasaki, Jun
2008-01-01
The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)
Extreme values, regular variation and point processes
Resnick, Sidney I
1987-01-01
Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records It emphasizes the core primacy of three topics necessary for understanding extremes the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enj...
Boltzmann, Darwin and Directionality theory
Demetrius, Lloyd A.
2013-09-01
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and
Ruttkay, Zsofia
1997-01-01
Discusses an old and quite surprising musical example that provides good challenges in probability theory ranging from practical routine computations to fundamental and philosophical ones, and extended with the engineering design task of generating random numbers. (ASK)
Gong, Ha Seong
2006-02-01
This book explains electric theory which is divided into four chapters. The first chapter includes electricity and material, electric field, capacitance, magnetic field and electromagnetic force, inductance. The second chapter mentions electronic circuit analysis, electric resistance,heating and power, chemical activity on current and battery with electrolysis. The third chapter deals with an alternating current circuit about the basics of an AC circuit, operating of resistance, inductance and capacitance, series circuit and parallel circuit of PLC, an alternating current circuit, Three-phase Alternating current, two terminal pair network and voltage and current of non-linearity circuit. The last explains transient phenomena of RC series circuit, RL series circuit, transient phenomena of an alternating current circuit and transient phenomena of RLC series circuit.
Nobile, G.
1993-07-01
With reference to highly debated sustainable growth strategies to counter pressing interrelated global environmental and socio-economic problems, this paper reviews economic and resource development theories proposed by classical and neoclassical economists. The review evidences the growing debate among public administration decision makers regarding appropriate methods to assess the worth of natural resources and ecosystems. Proposed methods tend to be biased either towards environmental protection or economic development. Two major difficulties in the effective implementation of sustainable growth strategies are also evidenced - the management of such strategies would require appropriate revisions to national accounting systems, and the dynamic flow of energy and materials between an economic system and the environment would generate a sequence of unstable structures evolving in a chaotic and unpredictable way
Variational field theoretic approach to relativistiv meson-nucleon scattering
Alexandrou, C.; Rosenfelder, R.; Schreiber, A.W.; TRIUMF, Vancouver, BC; Adelaide Univ., SA; Adelaide Univ., SA; Univ. Adelaide
1998-01-01
Non-perturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick-Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the s-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results. (orig.)
Noether's theorems applications in mechanics and field theory
Sardanashvily, Gennadi
2016-01-01
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
A Future of Communication Theory: Systems Theory.
Lindsey, Georg N.
Concepts of general systems theory, cybernetics and the like may provide the methodology for communication theory to move from a level of technology to a level of pure science. It was the purpose of this paper to (1) demonstrate the necessity of applying systems theory to the construction of communication theory, (2) review relevant systems…
Salam, Abdus; Wigner, E. P.
2010-03-01
Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.
Hydrodynamics, fields and constants in gravitational theory
Stanyukovich, K.P.; Mel'nikov, V.N.
1983-01-01
Results of original inveatigations into problems of standard gravitation theory and its generalizations are presented. The main attention is paid to the application of methods of continuous media techniques in the gravitation theory; to the specification of the gravitation role in phenomena of macro- and microworld, accurate solutions in the case, when the medium is the matter, assigned by hydrodynamic energy-momentum tensor; and to accurate solutions for the case when the medium is the field. GRT generalizations are analyzed, such as the new cosmologic hypothesis which is based on the gravitation vacuum theory. Investigations are performed into the quantization of cosmological models, effects of spontaneous symmetry violation and particle production in cosmology. Graeity theory with fundamental Higgs field is suggested in the framework of which in the atomic unit number one can explain possible variations of the effective gravitational bonds, and in the gravitation bond, variations of masses of all particles
Parquet theory of finite temperature boson systems
He, H.W.
1992-01-01
In this dissertation, the author uses the parquet summation for the two-body vertex as the framework for a perturbation theory of finite-temperature homogeneous boson systems. The present formalism is a first step toward a full description of the thermodynamic behavior of a finite temperature boson system through parquet summation. The current approximation scheme focuses on a system below the Bose-Einstein condensation temperature and considers only the contribution from Bogoliubov excitations out of a boson condensate. Comparison with the finite temperature variational theory by Campbell et al. shows strong similarities between variational theory and the current theory. Numerical results from a 4 He system and a nuclear system are discussed
Monte Carlo algorithms for lattice gauge theory
Creutz, M.
1987-05-01
Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations
Khandige, Surabhi; Møller-Jensen, Jakob
2016-01-01
Surface fimbriae of pathogenic Escherichia coli facilitate sensing, adhesion and even invasion of host epithelial cells. While it is known that the pathogen has the potential to express a plethora of fimbrial variants susceptible to rapid phase ON/OFF variation, it is an open question if the fimb......Surface fimbriae of pathogenic Escherichia coli facilitate sensing, adhesion and even invasion of host epithelial cells. While it is known that the pathogen has the potential to express a plethora of fimbrial variants susceptible to rapid phase ON/OFF variation, it is an open question...... if the fimbrial diversity seen at the population level is the product of random stochasticity or a concerted effort based on active communication. Here we discuss the possibility of a mechanism alternative to a stochastic fimbrial phase variation model affecting the dynamics of a heterogeneous population....
Variation, structure and norms
Harder, Peter
2014-01-01
in linguistics: those that see linguistic norms as antithetical to a descriptive and variational linguistics. Once such a re-evaluation has taken place, however, the social recontextualization of cognition will enable linguistics (including sociolinguistics as an integral part), to eliminate the cracks...... that an evolutionary account can reintegrate the opposed fragments into a whole picture that puts each of them in their ‘ecological position’ with respect to each other. Empirical usage facts should be seen in the context of operational norms in relation to which actual linguistic choices represent adaptations....... Variational patterns should be seen in the context of structural categories without which there would be only ‘differences’ rather than variation. And emergence, individual choice, and flux should be seen in the context of the individual’s dependence on lineages of community practice sustained by collective...
Maillard, S.; Skorek, R.; Maugis, P.; Dumont, M.
2015-01-01
This chapter presents the basic principles of cluster dynamics as a particular case of mesoscopic rate theory models developed to investigate fuel behaviour under irradiation such as in UO 2 . It is shown that as this method simulates the evolution of the concentration of every type of point or aggregated defect in a grain of material. It produces rich information that sheds light on the mechanisms involved in microstructure evolution and gas behaviour that are not accessible through conventional models but yet can provide for improvements in those models. Cluster dynamics parameters are mainly the energetic values governing the basic evolution mechanisms of the material (diffusion, trapping and thermal resolution). In this sense, the model has a general applicability to very different operational situations (irradiation, ion-beam implantation, annealing) provided that they rely on the same basic mechanisms, without requiring additional data fitting, as is required for more empirical conventional models. This technique, when applied to krypton implanted and annealed samples, yields a precise interpretation of the release curves and helps assess migration mechanisms and the krypton diffusion coefficient, for which data is very difficult to obtain due to the low solubility of the gas. (authors)
Variational principles for particles and fields in Heisenberg matrix mechanics
Klein, A.; Li, C.T.; Vassanji, M.
1980-01-01
For many years we have advocated a form of quantum mechanics based on the application of sum rule methods (completeness) to the equations of motion and to the commutation relations, i.e., to Heisenberg matrix mechanics. Sporadically we have discussed or alluded to a variational foundation for this method. In this paper we present a series of variational principles applicable to a range of systems from one-dimensional quantum mechanics to quantum fields. The common thread is that the stationary quantity is the trace of the Hamiltonian over Hilbert space (or over a subspace of interest in an approximation) expressed as a functional of matrix elements of the elementary operators of the theory. These parameters are constrained by the kinematical relations of the theory introduced by the method of Lagrange multipliers. For the field theories, variational principles in which matrix elements of the density operators are chosen as fundamental are also developed. A qualitative discussion of applications is presented
Ladder variational autoencoders
Sønderby, Casper Kaae; Raiko, Tapani; Maaløe, Lars
2016-01-01
Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder...... Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared...
Ladder Variational Autoencoder
Sønderby, Casper Kaae; Raiko, Tapani; Maaløe, Lars
2016-01-01
Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder...... Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared...
Isaacs, Rufus
1999-01-01
Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.
Resolving Rapid Variation in Energy for Particle Transport
Haut, Terry Scot [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational, and Statistical Sciences Division; Ahrens, Cory Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational, and Statistical Sciences Division; Jonko, Alexandra [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational, and Statistical Sciences Division; Till, Andrew Thomas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational, and Statistical Sciences Division; Lowrie, Robert Byron [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational, and Statistical Sciences Division
2016-08-23
Resolving the rapid variation in energy in neutron and thermal radiation transport is needed for the predictive simulation capability in high-energy density physics applications. Energy variation is difficult to resolve due to rapid variations in cross sections and opacities caused by quantized energy levels in the nuclei and electron clouds. In recent work, we have developed a new technique to simultaneously capture slow and rapid variations in the opacities and the solution using homogenization theory, which is similar to multiband (MB) and to the finite-element with discontiguous support (FEDS) method, but does not require closure information. We demonstrated the accuracy and efficiency of the method for a variety of problems. We are researching how to extend the method to problems with multiple materials and the same material but with different temperatures and densities. In this highlight, we briefly describe homogenization theory and some results.
Dall, Sasha R. X.; Gosling, Samuel; Gordon D.A., Brown,; Dingemanse, Niels; Ido, Erev,; Martin, Kocher,; Laura, Schulz,; Todd, Peter M; Weissing, Franz; Wolf, Max; Hammerstein, Peter; Stevens, Jeffrey R.
2012-01-01
Variation in how organisms allocate their behavior over their lifetimes is key to determining Darwinian fitness., and thus the evolution of human and nonhuman decision making. This chapter explores how decision making varies across biologically and societally significant scales and what role such
Seasonal Variation in Epidemiology
Marrero, Osvaldo
2013-01-01
Seasonality analyses are important in medical research. If the incidence of a disease shows a seasonal pattern, then an environmental factor must be considered in its etiology. We discuss a method for the simultaneous analysis of seasonal variation in multiple groups. The nuts and bolts are explained using simple trigonometry, an elementary…
The variational spiked oscillator
Aguilera-Navarro, V.C.; Ullah, N.
1992-08-01
A variational analysis of the spiked harmonic oscillator Hamiltonian -d 2 / d x 2 + x 2 + δ/ x 5/2 , δ > 0, is reported in this work. A trial function satisfying Dirichlet boundary conditions is suggested. The results are excellent for a large range of values of the coupling parameter. (author)
Appell, Jürgen; Merentes Díaz, Nelson José
2013-01-01
This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations, and boundary value problems. The book is written for non-specialists. Every chapter closes with a list of exercises and open problems.
Power variation for Gaussian processes with stationary increments
Barndorff-Nielsen, Ole Eiler; Corcuera, J.M.; Podolskij, Mark
2009-01-01
We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of the pr......We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path...... a chaos representation....
MACCIA, ELIZABETH S.; AND OTHERS
AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…
The nonholonomic variational principle
Krupkova, Olga [Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc (Czech Republic); Department of Mathematics, La Trobe University, Bundoora, Victoria 3086 (Australia)], E-mail: krupkova@inf.upol.cz
2009-05-08
A variational principle for mechanical systems and fields subject to nonholonomic constraints is found, providing Chetaev-reduced equations as equations for extremals. Investigating nonholonomic variations of the Chetaev type and their properties, we develop foundations of the calculus of variations on constraint manifolds, modelled as fibred submanifolds in jet bundles. This setting is appropriate to study general first-order 'nonlinear nonitegrable constraints' that locally are given by a system of first-order ordinary or partial differential equations. We obtain an invariant constrained first variation formula and constrained Euler-Lagrange equations both in intrinsic and coordinate forms, and show that the equations are the same as Chetaev equations 'without Lagrange multipliers', introduced recently by other methods. We pay attention to two possible settings: first, when the constrained system arises from an unconstrained Lagrangian system defined in a neighbourhood of the constraint, and second, more generally, when an 'internal' constrained system on the constraint manifold is given. In the latter case a corresponding unconstrained system need not be a Lagrangian, nor even exist. We also study in detail an important particular case: nonholonomic constraints that can be alternatively modelled by means of (co)distributions in the total space of the fibred manifold; in nonholonomic mechanics this happens whenever constraints affine in velocities are considered. It becomes clear that (and why) if the distribution is completely integrable (= the constraints are semiholonomic), the principle of virtual displacements holds and can be used to obtain the constrained first variational formula by a more or less standard procedure, traditionally used when unconstrained or holonomic systems are concerned. If, however, the constraint is nonintegrable, no significant simplifications are available. Among others, some properties of nonholonomic
Cui, J.; Galand, M.; Yelle, R. V.; Vuitton, V.; Wahlund, J.-E.; Lavvas, P. P.; Mueller-Wodarg, I. C. F.; Kasprzak, W. T.; Waite, J. H.
2009-04-01
We present our analysis of the diurnal variations of Titan's ionosphere (between 1,000 and 1,400 km) based on a sample of Ion Neutral Mass Spectrometer (INMS) measurements in the Open Source Ion (OSI) mode obtained from 8 close encounters of the Cassini spacecraft with Titan. Though there is an overall ion depletion well beyond the terminator, the ion content on Titan's nightside is still appreciable, with a density plateau of ~700 cm-3 below ~1,300 km. Such a plateau is associated with the combination of distinct diurnal variations of light and heavy ions. Light ions (e.g. CH5+, HCNH+, C2H5+) show strong diurnal variation, with clear bite-outs in their nightside distributions. In contrast, heavy ions (e.g. c-C3H3+, C2H3CNH+, C6H7+) present modest diurnal variation, with significant densities observed on the nightside. We propose that the distinctions between light and heavy ions are associated with their different chemical loss pathways, with the former primarily through "fast" ion-neutral chemistry and the latter through "slow" electron dissociative recombination. The INMS data suggest day-to-night transport as an important source of ions on Titan's nightside, to be distinguished from the conventional scenario of auroral ionization by magnetospheric particles as the only ionizing source on the nightside. This is supported by the strong correlation between the observed night-to-day ion density ratios and the associated ion lifetimes. We construct a time-dependent ion chemistry model to investigate the effects of day-to-night transport on the ionospheric structures of Titan. The predicted diurnal variation has similar general characteristics to those observed, with some apparent discrepancies which could be reconciled by imposing fast horizontal thermal winds in Titan's upper atmosphere.
Introduction to the theory of nonlinear optimization
Jahn, Johannes
2007-01-01
This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba
Band theory of metals the elements
Altmann, Simon L
1970-01-01
Band Theory of Metals: The Elements focuses on the band theory of solids. The book first discusses revision of quantum mechanics. Topics include Heisenberg's uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. The text takes a look at the free-electron theory of metals, including heat capacities, density of states, Fermi energy, core and metal electrons, and eigenfunctions in three dimensions. The book also reviews the effects of crystal fields in one dimension. The eigenfunctions of the translations; symmetry operations of t
On the theory of optimal processes
Goldenberg, P.; Provenzano, V.
1975-01-01
The theory of optimal processes is a recent mathematical formalism that is used to solve an important class of problems in science and in technology, that cannot be solved by classical variational techniques. An example of such processes would be the control of a nuclear reactor. Certain features of the theory of optimal processes are discussed, emphasizing the central contribution of Pontryagin with his formulation of the maximum principle. An application of the theory of optimum control is presented. The example is a time optimum problem applied to a simplified model of a nuclear reactor. It deals with the question of changing the equilibrium power level of the reactor in an optimum time
Müller, Gert; Sacks, Gerald
1990-01-01
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
K-theory and representation theory
Kuku, A.O.
2003-01-01
This contribution includes K-theory of orders, group-rings and modules over EI categories, equivariant higher algebraic K-theory for finite, profinite and compact Lie group actions together with their relative generalisations and applications
Renormalization group theory of critical phenomena
Menon, S.V.G.
1995-01-01
Renormalization group theory is a framework for describing those phenomena that involve a multitude of scales of variations of microscopic quantities. Systems in the vicinity of continuous phase transitions have spatial correlations at all length scales. The renormalization group theory and the pertinent background material are introduced and applied to some important problems in this monograph. The monograph begins with a historical survey of thermal phase transitions. The background material leading to the renormalization group theory is covered in the first three chapters. Then, the basic techniques of the theory are introduced and applied to magnetic critical phenomena in the next four chapters. The momentum space approach as well as the real space techniques are, thus, discussed in detail. Finally, brief outlines of applications of the theory to some of the related areas are presented in the last chapter. (author)
Gravity, general relativity theory and alternative theories
Zel'dovich, Ya.B.; Grishchuk, L.P.; Moskovskij Gosudarstvennyj Univ.
1986-01-01
The main steps in plotting the current gravitation theory and some prospects of its subsequent development are reviewed. The attention is concentrated on a comparison of the relativistic gravitational field with other physical fields. Two equivalent formulations of the general relativity (GR) - geometrical and field-theoretical - are considered in detail. It is shown that some theories of gravity constructed as the field theories at a flat background space-time are in fact just different formulations of GR and not alternative theories
Generalizability theory and item response theory
Glas, Cornelis A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.
2012-01-01
Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a selected-response format. This chapter presents a short overview of how item response theory and generalizability theory were integrated to model such assessments. Further, the precision of the esti...
Conjugation-promoted reaction of open-cage fullerene: A density functional theory study
Guo, Yong
2012-01-20
Density functional theory calculations are performed to study the addition mechanism of e-rich moieties such as triethyl phosphite to a carbonyl group on the rim of a fullerene orifice. Three possible reaction channels have been investigated. The obtained results show that the reaction of a carbonyl group on a fullerene orifice with triethyl phosphite most likely proceeds along the classical Abramov reaction; however, the classical product is not stable and is converted into the experimental product. An attack on a fullerene carbonyl carbon will trigger a rearrangement of the phosphate group to the carbonyl oxygen as the conversion transition state is stabilized by fullerene conjugation. This work provides a new insight on the reactivity of open-cage fullerenes, which may prove helpful in designing new switchable fullerene systems. Not that classical: The reaction of a carbonyl group on the fullerene orifice with triethyl phosphite most likely proceeds following the Abramov reaction to firstly form a classical product. However, this product is not stable and turns into an experimental product as the conversion transition state is stabilized by fullerene conjugation (see picture). Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Self Modeling: Expanding the Theories of Learning
Dowrick, Peter W.
2012-01-01
Self modeling (SM) offers a unique expansion of learning theory. For several decades, a steady trickle of empirical studies has reported consistent evidence for the efficacy of SM as a procedure for positive behavior change across physical, social, educational, and diagnostic variations. SM became accepted as an extreme case of model similarity;…
Gauge theories of the weak interactions
Quinn, H.
1978-08-01
Two lectures are presented on the Weinberg--Salam--Glashow--Iliopoulos--Maiani gauge theory for weak interactions. An attempt is made to give some impressions of the generality of this model, how it was developed, variations found in the literature, and the status of the standard model. 21 references
Classical quantum theory of wobbling modes
Onishi, Naoki
1986-01-01
Wobbling modes are studied extensively in terms of time-dependent variational theory. Quantum states and their energies are determined by the Bohr-Sommerfeld rule of classical quantization. Numerical calculations are performed for states of 166 Er with vertical strokejvertical stroke=30-40 (h/2π). (orig.)
Becker, Katrin; Becker, Melanie; Schwarz, John H.
String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697. Comprehensive coverage of topics from basics of string theory to recent developments Ideal textbook for a one-year course in string theory Includes over 100 exercises with solutions Contains over 200 homework problems with solutions available to lecturers on-line
Miyazawa, T; Kuwabara, S; Fujii, T [Doshisha University, Kyoto (Japan); Nonaka, K [Bando Chemical Industries, Ltd., Kobe (Japan)
1997-10-01
A numerical model was developed to analyze the power transmitting mechanisms for CVT (Continuous Variable Transmissions) using a dry hybrid belt. The model consists of linear springs representing the rigidities of blocks, rubber and cord, and interface elements which identify slippage between pulleys and blocks. By using the present model, forces acting on the belt were calculated not only at steady but also transitional states. Calculated results well coincide with experimental ones. It is revealed that there is a great change of the pulley thrust when the speed ratio is shifting. Little radial slippage occurs when the pulley groove is reduced. 1 ref., 9 figs.
Conformable variational iteration method
Omer Acan
2017-02-01
Full Text Available In this study, we introduce the conformable variational iteration method based on new defined fractional derivative called conformable fractional derivative. This new method is applied two fractional order ordinary differential equations. To see how the solutions of this method, linear homogeneous and non-linear non-homogeneous fractional ordinary differential equations are selected. Obtained results are compared the exact solutions and their graphics are plotted to demonstrate efficiency and accuracy of the method.
Kucherenko, L.
1990-01-01
Full text: 32 varieties of Oryza sativa L. ssp. japonica were used as donors for callus induction from somatic tissues. In some cases, the callus was treated before regeneration with the chemical mutagen MNU. Some of the regenerated plants demonstrated heritable alterations, among them chlorophyll deficiencies, variation in plant height, awness, glume colouring and fertility. Along with these, a number of lines with agronomically valuable alterations concerning maturity time, panicle structure, plant productivity and grain quality were found. The spectrum of variability was very wide. Vivipary was noticed. Superdwarfs with plant height of about 15 cm were found. Plants with no visible distinctions could be variants too, for example, with increased protein content or disease resistance. The rate and the spectrum of the somaclonal variation were not influenced by the culture media but depended on the donor's genotype. On the basis of somaclonal variation a variety 'Bioryza' was developed. It is an early maturing (about 95-100 days), long grain variety, with grain yield up to 8 t/ha. (author)
Luo, Chongliang; Liu, Jin; Dey, Dipak K; Chen, Kun
2016-07-01
In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Gyarmati’s Variational Principle of Dissipative Processes
József Verhás
2014-04-01
Full Text Available Like in mechanics and electrodynamics, the fundamental laws of the thermodynamics of dissipative processes can be compressed into Gyarmati’s variational principle. This variational principle both in its differential (local and in integral (global forms was formulated by Gyarmati in 1965. The consistent application of both the local and the global forms of Gyarmati’s principle provides all the advantages throughout explicating the theory of irreversible thermodynamics that are provided in the study of mechanics and electrodynamics by the corresponding classical variational principles, e.g., Gauss’ differential principle of least constraint or Hamilton’s integral principle.
Dzewaltowski, David A; Noble, John M; Shaw, Jeff M
1990-12-01
Social cognitive theory and the theories of reasoned action and planned behavior were examined in the prediction of 4 weeks of physical activity participation. The theories of reasoned action and planned behavior were supported. Attitude and perceived control predicted intention, and intention predicted physical activity participation. The social cognitive theory variables significantly predicted physical activity participation, with self-efficacy and self-evaluation of the behavior significantly contributing to the prediction. The greater the confidence in participating in physical activity and the greater the satisfaction with present physical activity, the more physical activity performed. Hierarchical regression analyses indicated that perceived control and intentions did not account for any unique variation in physical activity participation over self-efficacy. Therefore the social cognitive theory constructs were better predictors of physical activity than those from the theories of reasoned action and planned behavior.
Variational characterization of generalized Jacobi equations
Casciaro, B.
1995-09-01
A Lagrangian depending on derivatives of the fields up to a generic order is considered, together with a series development around a given section. The problem of extremality and stability of action for this system is then addressed. Higher-order variations in the Lagrangian, the Euler-Lagrange equation, the expansion of the action, the D-invariant decomposition of the Lagrangian, the Jacobi equation, and a unified description of the Euler-Lag range and Jacobi equations are discussed. As a conclusion of the work it is stated that the theory of second variations is worthy to be revisited and a comment on a recent paper by Taub is made. 10 refs
Variational Algorithms for Test Particle Trajectories
Ellison, C. Leland; Finn, John M.; Qin, Hong; Tang, William M.
2015-11-01
The theory of variational integration provides a novel framework for constructing conservative numerical methods for magnetized test particle dynamics. The retention of conservation laws in the numerical time advance captures the correct qualitative behavior of the long time dynamics. For modeling the Lorentz force system, new variational integrators have been developed that are both symplectic and electromagnetically gauge invariant. For guiding center test particle dynamics, discretization of the phase-space action principle yields multistep variational algorithms, in general. Obtaining the desired long-term numerical fidelity requires mitigation of the multistep method's parasitic modes or applying a discretization scheme that possesses a discrete degeneracy to yield a one-step method. Dissipative effects may be modeled using Lagrange-D'Alembert variational principles. Numerical results will be presented using a new numerical platform that interfaces with popular equilibrium codes and utilizes parallel hardware to achieve reduced times to solution. This work was supported by DOE Contract DE-AC02-09CH11466.
On minimizers of causal variational principles
Schiefeneder, Daniela
2011-01-01
Causal variational principles are a class of nonlinear minimization problems which arise in a formulation of relativistic quantum theory referred to as the fermionic projector approach. This thesis is devoted to a numerical and analytic study of the minimizers of a general class of causal variational principles. We begin with a numerical investigation of variational principles for the fermionic projector in discrete space-time. It is shown that for sufficiently many space-time points, the minimizing fermionic projector induces non-trivial causal relations on the space-time points. We then generalize the setting by introducing a class of causal variational principles for measures on a compact manifold. In our main result we prove under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed analysis of the minimizers. (orig.)
Black-Box Search by Unbiased Variation
Lehre, Per Kristian; Witt, Carsten
2012-01-01
The complexity theory for black-box algorithms, introduced by Droste, Jansen, and Wegener (Theory Comput. Syst. 39:525–544, 2006), describes common limits on the efficiency of a broad class of randomised search heuristics. There is an obvious trade-off between the generality of the black-box model...... and the strength of the bounds that can be proven in such a model. In particular, the original black-box model provides for well-known benchmark problems relatively small lower bounds, which seem unrealistic in certain cases and are typically not met by popular search heuristics.In this paper, we introduce a more...... restricted black-box model for optimisation of pseudo-Boolean functions which we claim captures the working principles of many randomised search heuristics including simulated annealing, evolutionary algorithms, randomised local search, and others. The key concept worked out is an unbiased variation operator...
Generalized structural theory of freezing
Yussouff, M.
1980-10-01
The first-principles order parameter theory of freezing, proposed in an earlier work, has been successful in yielding quantitative agreement with known freezing parameters for monoatomic liquids forming solids with one atom per unit cell. A generalization of this theory is presented here to include the effects of a basis set of many atoms per unit cell. The basic equations get modified by the 'density structure factors' fsub(i) which arise from the density variations within the unit cell. Calculations are presented for the important case of monoatomic liquids freezing into hexagonal close packed solids. It is concluded that all freezing transitions can be described by using structural correlations in the liquid instead of the pair potential; and that the three body correlations are important in deciding the type of solid formed after freezing. (author)
Quaternionic Weinberg-Salam theory
Morita, Katsusada
1982-01-01
A quaternionic Weinberg-Salam theory is formulated based on the assumption that fermio ns and Higgs mesons are defined over quaternions. The new formalism, reproducing the left-right symmetric SU(2)sub(L) x SU(2)sub(R) x U(1) Weinberg-Salam theory at the phenomenological level, offers an algebraic explanation for replication of quarks and leptons in flavor doublets, and correlates the spontaneous symmetry breakdown to U(1)sub(em) with the existence of Fock space for gauge singlets but not for quaternionic states. In particular, the quaternionic variational principle introduced to canonically quantize the quaternionic fields in conformity with the gauge-singlet Fock-space formulation and the spontaneous symmetry breakdown. Physical states must be gauge singlets since they belong to the Fock space. (author)
Bergmann, P.G.
1980-01-01
A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion
Boley, Bruno A
1997-01-01
Highly regarded text presents detailed discussion of fundamental aspects of theory, background, problems with detailed solutions. Basics of thermoelasticity, heat transfer theory, thermal stress analysis, more. 1985 edition.
Marciano, W.J.
1984-12-01
The present state of the art in elementary particle theory is reviewed. Topics include quantum electrodynamics, weak interactions, electroweak unification, quantum chromodynamics, and grand unified theories. 113 references
Mathematical methods of electromagnetic theory
Friedrichs, Kurt O
2014-01-01
This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in el
A reconciliation of extinction theories
Sabine, T.M.
1988-01-01
The differences between previous theoretical treatments of extinction based on the Darwin intensity equations arise because of the different functional form chosen for the coupling constant σ. When the same function is used these theories make closely similar predictions. It is shown that a limiting condition on integrated intensity as the crystal size increases puts restrictions on the functions which may be used. A Lorentzian or Fresnellian function can be used for primary extinction while secondary extinction requires a Gaussian, rectangular or triangular function. An analytical expression is given for the variation in the value of the extinction factor with scattering angle. (orig.)
Application of generalized perturbation theory to flux disadvantage factor calculations
Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.
1979-01-01
The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper
GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun
2002-01-01
In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.
Variational multiscale models for charge transport.
Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin
2012-01-01
This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle