Truncation Scheme Research Articles

Error bounds in the gap metric for dissipative balanced approximations

We derive an error bound in the gap metric for positive real balanced truncation and positive real singular perturbation approximation. We prove these results by working in the context of dissipative driving-variable systems, as in behavioral and state/signal systems theory. In such a framework no prior distinction is made between inputs and outputs. Dissipativity preserving balanced truncation of dissipative driving-variable systems is addressed and a gap metric error bound is obtained. Bounded real and positive real input–state–output systems are manifestations of a dissipative driving-variable system through particular decompositions of the signal space. Under such decompositions the existing bounded real and positive real balanced truncation schemes can be seen as special cases of dissipative balanced truncation and the new positive real error bounds follow.

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

In the past years, many applications of historymatching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a historymatching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields

Similarity transformed coupled cluster response (ST-CCR) theory - A time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

On the functional renormalization group approach for Yang-Mills fields

We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of $S$-matrix.

Baryon and meson screening masses

In a strongly coupled quark-gluon plasma, collective excitations of gluons and quarks should dominate over the excitation of individual quasifree gluon and quark modes. To explore this possibility, we computed screening masses for ground-state light-quark mesons and baryons at leading order in a symmetry-preserving truncation scheme for the Dyson-Schwinger equations using a confining formulation of a contact interaction at nonzero temperature. Meson screening masses are obtained from Bethe-Salpeter equations, and baryon analogues from a novel construction of the Faddeev equation, which employs an improved quark-exchange approximation in the kernel. Our treatment implements a deconfinement transition that is coincident with chiral symmetry restoration in the chiral limit, when both transitions are second order. Despite deconfinement, in all $T=0$ bound-state channels, strong correlations persist above the critical temperature, $T>{T}_{c}$; and, in the spectrum defined by the associated screening masses, degeneracy between parity-partner correlations is apparent for $T\ensuremath{\gtrsim}1.3{T}_{c}$. Notwithstanding these results, there are reasons (including Golberger-Treiman relations) to suppose that the inertial masses of light-quark bound states, when they may be defined, vanish at the deconfinement temperature, and that this is a signal of bound-state dissolution. Where a sensible comparison is possible, our predictions are consistent with results from contemporary numerical simulations of lattice-regularized QCD.

Fuzzy Meshless Local Petrov-Galerkin Method for Analysis of Imprecisely Defined Systems

Many engineering systems contain uncertainties that cannot be described by either deterministic or probabilistic approaches. For example, the geometry, material properties, external actions (loads), and boundary conditions may be imprecise in a practical mechanical or structural system. The uncertainties present may be associated with parameters that are vague, imprecise, or linguistic. A fuzzy meshless local Petrov-Galerkin approach is developed in this work for the analysis of imprecisely defined systems. Starting from the basic concepts of fuzzy sets, fuzzy arithmetic, and fuzzy calculus (differentiation and integration) the various steps of the meshless local Petrov-Galerkin approach involved in the derivation of the equations are redefined using fuzzy concepts. The resulting fuzzy equations are derived using a fuzzy version of Gaussian elimination procedure coupled with truncation. A one-dimensional heat-transfer problem involving conduction, convection, and radiation with vaguely defined thermal properties of the material and boundary conditions and two stress-analysis problems (a beam and a plate with a hole) with vaguely defined material properties and external loads are considered to demonstrate the methodology. A truncation scheme is used to overcome the difficulty of overestimating the width of the response characteristics of the system due to repeated fuzzy arithmetic operations in the solution of the fuzzy equations. A simple sequential linearization scheme is used to handle the nonlinear boundary-value problem associated with the radiation boundary condition in the heat-transfer problem. The present approach represents a unique methodology that enables the handling of certain types of imprecisely known data more realistically compared to the existing procedures.

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

Extended coupled cluster through nth perturbation order for molecular response properties: A comparative study

In this paper, we have presented and analyzed the extended coupled cluster (ECC) energy functional, truncated up to nth perturbation order in which expansion is limit to operators of the single and double excitations. The expression for the first order energy derivatives based on the above truncation schemes has been derived and numerically analyzed. We have done a comparative study for dipole moment in various perturbative ECC (n) methods (2⩽n⩽5) for three systems (HF, H2O and BH) at equilibrium geometry. We have particularly studied two variants of ECC (4) and ECC (5∗) method for stretched geometry. We have analyzed the contribution of important terms present in ECC functional based on perturbative argument. We have compared our results with standard coupled cluster (CCSD) as well as cubic truncated ECC and also benchmarked with the full CI results wherever available.

Improved approximate methods for calculating frequency response function matrix and response of MDOF systems with viscoelastic hereditary terms

As we know, it is difficult and unnecessary to obtain all the eigenpairs of a large-scaled viscoelastic (nonviscous or hysteretic) damping systems, which means that the mode truncation scheme is generally used and the mode-truncated error is therefore introduced. This study is aimed at eliminating the influence of the unavailable modes on the dynamic response of MDOF systems with viscoelastic hereditary terms. The energy dissipation terms of the system depend on the past history of motion via convolution integrals over some kernel functions. Therefore, the system is a nonviscously damped system, which has been considered as the most generalized damping model within the scope of a linear mechanical analysis. To approximate frequency response function (FRF) matrix and response without using the unavailable modes, we suggest two methods, which attempt to approximate the influence of the unavailable modes in terms of the lower modes and system matrices by using the first one or two terms of Neumann expansion of the contribution of the unavailable modes. In contrast with the FRF matrix approximated in terms of the first two terms of Neumann expansion, these procedures cannot be extended to further high order terms since all of them will be affected by the frequency-dependent variation of damping matrix from previous terms. Finally, an example is shown that the two presented methods can make the mode-truncated error reduce and may be used to approximate the influence of nonviscous modes contributed to FRF matrix due to the fact that the nonviscous modes are difficult to be obtained accurately even if a small scaled model is used for some eigensolution methods.

Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions

Recently, efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized sinc functions. This paper studies the error of the reconstructed non-bandlimited signal when an adaptive truncation scheme is employed. Further, when there are noises present in the samples, estimation on the expectation and variance of the error pertinent to the reconstructed signal is also given. Finally discussed are the reproducing properties and the Sobolev smoothness of functions in the space of non-bandlimited signals that admits such a sampling formula.

Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover

We derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, chemical potential and Fermi momentum. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger-Dyson equation for the fermion propagator, and compute the perturbative contact on the BCS and BEC sides within this framework. A Functional Renormalization Group approach is then put forward, which allows to determine the contact over the whole crossover and, in particular, for the Unitary Fermi gas. We present numerical results from an implementation of the Renormalization Group equations within a basic truncation scheme.

A contrast source inversion method in the wavelet domain

We present a contrast source inversion (CSI) algorithm using truncated wavelet representations. Specifically, we represent the unknown contrast sources and the contrast function in terms of the wavelet basis functions. In order to reduce the number of wavelet coefficients for these unknowns, we apply a progressive multiscale truncation scheme based on the reconstructed contrast function. This approach increases the robustness of the CSI algorithm for noisy or limited data, and decreases the computation time as well as the memory usage. We tested the wavelet-domain CSI method using both synthetic and experimental data. The numerical experiments show that similar results with the regular spatial-domain CSI method are obtained when the number of (independent) measurement data points is comparable to the number of the unknowns in the contrast function. The advantages of the wavelet-domain CSI method become apparent as we deal with cases where the number of measurement data points is smaller than the number of unknowns in the contrast function.

Stochastic dynamics of dengue epidemics

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.

Towards a self-consistent solution of the Landau gauge quark-gluon vertex Dyson-Schwinger equation

The quark-gluon vertex in Landau gauge QCD is investigated in the Dyson-Schwinger approach. The aim is to obtain a fully self-consistent solution of the quark propagator and the quark-gluon vertex Dyson-Schwinger equation (DSE) in the vacuum using the gluon propagator as input from other calculations. The truncation scheme used in an earlier study is systematically improved and the rst decisive step towards a full solution is presented. First results for the quark propagator with a fully dressed quarkgluon vertex in a truncation that incorporates all twelve vertex tensorstructures are shown.

Effective-average-action-based approach to correlation functions at finite momenta

We present a truncation scheme of the effective-average-action approach of the nonperturbative renormalization group that allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion that includes both all local correlations and two-point and four-point irreducible correlations to all orders in the derivatives. We discuss schemes for both the symmetric and the symmetry broken phase of the O(N) model and present results for D=3. All approximations are done directly in the effective average action rather than in the flow equations of irreducible vertices. The approach is numerically relatively easy to implement and yields good results for all N both for the critical exponents and for the momentum dependence of the two-point function.

Stochastic analysis of complex reaction networks using binomial moment equations

The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.

Generalized seniority with realistic interactions in open-shell nuclei

Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.Communicated by B M Schwenk

Research on Retrofit Schemes for Reheat Steam Underheating and Excessive Desuperheater Spray for a 600 MW Tangentially Coal-Fired Boiler

Reheat steam underheating, excessive desuperheater water, and temperature deviation at the furnace outlet are common problems of the large scale tangentially coal-fired boilers both in China and abroad. It is thus very important to develop an effective retrofit scheme to settle the problems. Truncation of partition platen superheater (PPS) is found to be one of the most promising schemes, based on qualitative analysis and calculation. Detailed analyses of the truncation schemes are done in this work for Unit 1 boiler of Wangtan Power Plant (WPP) suffering all the aforementioned problems. Effects are thoroughly analyzed for 1 m, 2 m, and 3 m truncations of PPS at boiler operation loads of 600 MW, 450 MW, and 300 MW. Effects of different truncation schemes on the gas flow field in the boiler are also simulated at both cold and hot conditions. The 2 m PPS truncation scheme is found capable to solve the problems properly, and it is recommended for implementation. After retrofitted, the temperature of reheat steam has been increased to the designed value, the desuperheater spray has been reduced by an average of about 30 t/h, and steam temperature deviation at the furnace outlet has also been alleviated.

SFT on separated D-branes and D-brane translation

We discuss novel properties of the string field and the Open String Field Theory action arising in a system with multiple D-branes, then use the level truncation scheme to study marginal deformations and tachyon condensation in a system with two parallel but separated branes. We find string fields corresponding to D-brane decay combined with a finite change in the distance between the two D-branes. Using D-brane separation as a yardstick, we are able to continuously control the spacetime displacement of the D-branes and find that our solutions exist only for a finite range of this displacement. Thus, at least in level truncation, Open String Field Theory seems unable to describe the entire CFT moduli space.

A STUDY OF THE INFLUENCE OF THE GAUGE GROUP ON THE DYSON–SCHWINGER EQUATIONS FOR SCALAR-YANG–MILLS SYSTEMS

The particular choice of the gauge group for Yang–Mills theory plays an important role when it comes to the influence of matter fields. In particular, both the chosen gauge group and the representation of the matter fields yield structural differences in the quenched case. Especially, the qualitative behavior of the Wilson potential is strongly dependent on this selection. Though the algebraic reasons for this observation is clear, it is far from obvious how this behavior can be described besides using numerical simulations. Herein, it is investigated how the group structure appears in the Dyson–Schwinger equations, which as a hierarchy of equations for the correlation functions have to be satisfied. It is found that there are differences depending on both the gauge group and the representation of the matter fields. This provides insight into possible truncation schemes for practical calculations using these equations.