Nonperturbative Case Research Articles

Analysis of Gas Turbine Combustor Exhaust Emissions: Effects of Transient Inlet Air Pressure

Gas turbine combustors are often subjected to combustion instabilities because of variability of operating conditions, affecting components, and altering exhaust emissions. Herein, the analysis focuses on simulating numerically the non‐premixed combustion as unsteady flamelet combustion and detailed kinetic mechanism. The goal is analyzing exhaust gases under unsteady inlet airflow conditions to define operation guidelines. The numerical approach is validated using data from the literature for nonperturbed cases. Three periodical perturbations of different amplitude show differences with the nonperturbed case. Besides emission of exhaust gases, the temperature field is sensitive to airflow inlet conditions. According to the simulation results, a strong dependence of temperature and pressure in primary and dilution zones of combustor exists on the inlet air pressure condition. Emissions of flue gases like CO and NOx respond to combustor thermal behavior showing high sensitivity to inlet air pressure as well. Results indicate that moderate pressure oscillations may derive into flashback effects.

General quantum theory of Thomson scattering

It is well known that the interaction of radiation with matter can be described using classical or quantum physics in relation to three systems: incoming radiation, matter, and scattered radiation. Currently, there is no general non-perturbative theory of electromagnetic wave scattering by free electrons, which describes the scattering process using quantum physics. In this paper, such a non-relativistic theory is presented, where statistics and the number of incoming photons is taken into account, and in scattering, statistics with the number of scattered photons is obtained. This theory is completely analytical, considering an arbitrary number of electrons in the system and, in a particular case, goes over into the previously known theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons. This theory has good prospects for application in quantum optics, since it fully takes into account the quantum nature of the incident and scattered radiation when interacting with an arbitrary number of free electrons, including in the non-perturbative case.

Quantum Theory of Scattering of Nonclassical Fields by Free Electrons

At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and the number of scattered photons. This theory is completely analytical for an arbitrary number of electrons in the system and, in a particular case, is equivalent to the previous theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons.

Perturbative and Non-Pertrubative Trace Anomalies

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.

Dynamical evolution of a young planetary system: stellar flybys in co-planar orbital configuration

Stellar flybys in star clusters may perturb the evolution of young planetary systems in terms of disk truncation, planetary migration and planetary mass accretion. We investigate the feedback of a young planetary system during a single close stellar encounter in a typical open young stellar cluster. We consider 5 masses for the stellar perturbers: 0.5, 0.8, 1, 3 and 8 M$_{Sun}$, in coplanar, prograde and retrograde orbits respect to the planetary disk, varying the pertruber-host star orbital periastron from 100 AU to 500 AU. We have made 3D modelizations with the smooth particle hydrodynamics code GaSPH of a system composed by a solar type star surrounded by a low density disk where a giant planet is embedded in. We focus on the dynamical evolution of global parameters characterizing the disk and the planet, like the Lagrangian radius containing the $63.2\%$ of the mass of the disk, the distance of the planet to its host star, the planet orbital eccentricity and the planetary mass accretion. We find that the most part of the simulated systems show a significant disk truncation after a single close encounter, a final orbital distance of the Jovian, from the central star, lower than the unperturbed case and, finally, the perturbed systems show a final mass accretion of the Jovian planet larger than the non-perturbed case. Therefore, stellar flybys significantly perturb the dynamics of a young planetary system, regardless the orbital configuration of the stellar perturber. In such experiments, the final disk radius and the orbital parameters of the Jovian planet are considerably affected by the stellar close encounter.

Randomly Weighted $d$-Complexes: Minimal Spanning Acycles and Persistence Diagrams

A weighted $d$-complex is a simplicial complex of dimension $d$ in which each face is assigned a real-valued weight. We derive three key results here concerning persistence diagrams and minimal spanning acycles (MSAs) of such complexes. First, we establish an equivalence between the MSA face-weights and death times in the persistence diagram. Next, we show a novel stability result for the MSA face-weights which, due to our first result, also holds true for the death and birth times, separately. Our final result concerns a perturbation of a mean-field model of randomly weighted $d$-complexes. The $d$-face weights here are perturbations of some i.i.d. distribution while all the lower-dimensional faces have a weight of $0$. If the perturbations decay sufficiently quickly, we show that suitably scaled extremal nearest face-weights, face-weights of the $d$-MSA, and the associated death times converge to an inhomogeneous Poisson point process. This result completely characterizes the extremal points of persistence diagrams and MSAs. The point process convergence and the asymptotic equivalence of three point processes are new for any weighted random complex model, including even the non-perturbed case. Lastly, as a consequence of our stability result, we show that Frieze's $\zeta(3)$ limit for random minimal spanning trees and the recent extension to random MSAs by Hino and Kanazawa also hold in suitable noisy settings.

Barabási–Albert random graph with multiple type edges and perturbation

We introduce the perturbed version of the Barabasi–Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic degree distribution depends on the almost sure limit of the proportion of edges of different types. However, if there is perturbation, then the resulting degree distribution will be deterministic, which is a major difference compared to the non-perturbed case.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Fisher information approach to nonequilibrium phase transitions in a quantum XXZ spin chain with boundary noise

We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behaviour due to a phase transition, since all the interaction terms are extensive. Perturbatively in the noise strength, we found superextensive Fisher information at anisotropy $|\Delta|\leqslant1$ and irrational $\frac{\arccos\Delta}{\pi}$ irrespective of the order of two non-commuting limits, i.e. the thermodynamic limit and the limit of sending $\frac{\arccos\Delta}{\pi}$ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a non-equilibrium quantum phase transition with a critical phase $|\Delta|\leqslant1$. From the non-superextensivity of the Fisher information of reduced states, we infer that this non-equilibrium quantum phase transition does not have local order parameters but has non-local ones, at least at $|\Delta|=1$. In the non-perturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full state Fisher information, and is superextensive only at $|\Delta|=1$. Form the latter result, we derived local order parameters at $|\Delta|=1$ in the non-perturbative case. The existence of critical behaviour witnessed by the Fisher information in the phase $|\Delta|<1$ is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy $\Delta$, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.

A Perturbative-Based Generalized Series Expansion in Terms of Non-Orthogonal Component Functions

In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.

Perturbative and Non-perturbative Aspects of the Chern-Simons-Witten Theory

We investigate a relation between non-perturbative and perturbative cases in the 2+1 dimensional Chern-Simons-Witten (CSW) theory for G = E6 gauge group. In the perturbative case, we calculate the vacuum expectation value (VEV) of an unknotted Wilson loop operator up to order 1/k3 (k is a coupling constant). The result above is proved to be identical to the polynomial invariant E0 (ρ) in the non-perturbative case at the same order of expansion.

Perturbativity and nonperturbativity in large-Z effects for hydrogen-like atoms

The effects induced by the interaction ΔUAMM of the anomalous component of the electron magnetic moment with the Coulomb field of a nucleus at Zα > 1 are examined for the lower levels of a hydrogen-like atom within purely perturbative and essentially nonperturbative in α/π approaches. Owing to the specific features of the ΔUAMM operator for a point-like Coulomb source, the distribution of the charge over the volume of the nucleus is set in the nonperturbative case at the quark structure level using valence (constituent) u and d quarks. It is demonstrated that such nonperturbative analysis turns out to be nontrivial as well as the manner in which its results are altered in the transition from the central problem with spherical symmetry to the inclusion of the peripheral contribution. It is also demonstrated that these methods yield matching (with an accuracy no worse than 0.1%) results for the shift of levels 1s1/2 and 2p1/2 due to ΔUAMM at all values of Z through to critical ones. Thus, it is confirmed that the perturbation theory in α/π provides correct results for superheavy atoms if the complete dependence of the wave function on Zα is taken into account from the beginning.

Fluctuations of energy losses of charged particles colliding with an oscillator

Fluctuations of energy losses of fast charged particles colliding with an oscillator have been considered in the dipole approximation. In this approximation, the problem has been solved exactly, and fluctuations of energy losses of the oscillator from the initial state |m〉 = |0〉 have been found in the form of the sum of single integrals. It has been shown that the Bohr formulas for fluctuations can be obtained in the passage to the classical limit, whereas analogs of the Fano formula in perturbation theory and the Titeica formula in the nonperturbative case can be obtained when the velocities of an ion are much higher than atomic velocities.

Strongly-coupled unquenchedQED4propagators using Schwinger-Dyson equations

We study unquenched QED in four dimensions using renormalised Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kizilersu-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime and is free of kinematic singularities. We find that the KP vertex performs very well as expected specially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalised inverse photon propagator having zero crossing.

Holographic models and the QCD trace anomaly

Five dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and non-perturbative beta-functions are studied. It is shown that in the perturbative case, where the beta-function is the QCD one at leading order, the resulting space is not asymptotically AdS. In the non-perturbative case, the model considered presents confinement of static quarks and leads to a non-vanishing gluon condensate, although it does not correspond to an asymptotically free theory. In both cases analyses based on the trace anomaly and on Wilson loops are carried out.

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

SUMMARY Weakly inhomogeneous time-harmonic plane waves propagating in homogeneous anisotropic, weakly dissipative media are studied using the perturbation method. Only dissipation mechanisms, which can be described within the framework of linear viscoelasticity, are considered. As a reference (non-perturbed) case, plane waves with a real-valued slowness vector propagating in perfectly elastic anisotropic media are used. Simple approximate expressions for the complex-valued slowness and polarization vectors of weakly inhomogeneous plane waves propagating in anisotropic, weakly dissipative media are derived. Special attention is devoted to the imaginary part of the slowness vector, known as the attenuation vector, which is responsible for the amplitude attenuation of a plane wave. The derived approximate expression for the attenuation vector depends on the material (intrinsic) dissipation parameters as well as on the inhomogeneity of the plane wave. Its scalar product with the energy‐velocity vector yields, however, the intrinsic attenuation factor, which does not depend on the inhomogeneity of the wave, and which thus represents a very suitable measure of the material dissipation. The derived expression for the intrinsic attenuation factor is valid for media of unrestricted anisotropy and weak dissipation and for homogeneous as well as weakly inhomogeneous plane waves. The intrinsic attenuation factor is inversely proportional to the scalar quantity, which, in isotropic viscoelastic media, corresponds to the well-known quality factor Q. Its generalization to anisotropic weakly viscoelastic media is directionally dependent. Numerical examples are presented, in which the accuracy of the approximate formulae based on the perturbation method is studied. The results indicate that the presented perturbation results are sufficiently accurate to be used in practical applications. Strong directivity of the intrinsic attenuation factor shows its great potential in solving inverse problems.

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system–bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system–bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system–bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system–bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system–bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.

The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences

Under the mild trace-norm assumptions, we show that the eigenvalues of an arbitrary (non-Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function 2 cos t on [ 0 , π ] which characterizes the nonperturbed case. In this way the real interval [ - 2 , 2 ] is still a cluster for the asymptotic joint spectrum and, moreover, [ - 2 , 2 ] still attracts strongly (with infinite order) the perturbed matrix sequence. The results follow in a straightforward way from more general facts that we prove in an asymptotic linear algebra framework and are plainly generalized to the case of matrix-valued symbols, which arises when dealing with orthogonal polynomials with asymptotically periodic recurrence coefficients.

H+2 ionization by ultra-short electromagnetic pulses investigated through a non-perturbative Coulomb–Volkov approach

The sudden Coulomb–Volkov theoretical approximation has been shown to well describe atomic ionization by intense and ultra-short electromagnetic pulses, such as pulses generated by very fast highly-charged ions. This approach is extended here to investigate single ionization of homonuclear diatomic molecules by such pulses in the framework of one-active electron. Under particular conditions, a Young-like interference formula can approximately be factored out. Present calculations show interference effects originating from the molecular two-centre structure. Fivefold differential angular distributions of the ejected electron are studied as a function of the molecular orientation and internuclear distance. Both non-perturbative and perturbative regimes are examined. In the non-perturbative case, an interference pattern is visible but a main lobe, opposite to the electric field polarization direction, dominates the angular distribution. In contrast, in perturbation conditions the structure of interferences shows analogies to the Young-like interference pattern obtained in ionization of molecules by fast electron impacts. Finally, the strong dependence of these Young-like angular distributions on the internuclear distance is addressed.

Spectral features of the wall-pressure fluctuations in turbulent wall flows with and without perturbations using LES

The statistical properties of the fluctuating wall-pressure field are studied using a numerical database generated by large eddy simulation of incompressible turbulent flow in a plane channelOResa 640U. Emphasis is given on the study of spectral features in the wavevector space and as a function of frequency, particularly in the region of low wavenumbers that are of major concern in submarine applications. A correction procedure is used to cancel the artificial pseudo-acoustic eAect due to periodic boundary conditions. The influence of superimposed perturbations on one wall of the channel is considered afterwards in comparison with the non-perturbed case. ” 2001 Elsevier Science Inc. All rights reserved.