Exact Perturbation Research Articles

Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

Mixed and componentwise condition numbers for matrix decompositions

We present normwise and componentwise perturbation bounds for the LU, the Cholesky, the LDLT and the QR decompositions by using a new approach. The explicit expressions of mixed and componentwise condition numbers for these matrix decompositions are derived. The condition numbers improve known results of the normwise and componentwise cases and reveal the characterizations of the structured perturbations. The exact explicit perturbation expressions are derived for the factors L and U of the LU decomposition, and the rigorous normwise and componentwise perturbation bounds are presented for the LU decomposition.

Comment on the spherical quantum dot with interaction effects

A series of studies of the lowest [Formula: see text] state of a model of a two-electron quantum dot, that consists of a finite spherical well [see, for example, Sivakami et al., Int. J. Mod. Phys. B 24, 5561 (2010)], exhibited a range of interesting applications. However, the quantity of central interest, the expectation value of the interelectronic repulsion (that must be nonnegative) was calculated erroneously, yielding negative values. In the present note, this expectation value is evaluated with respect to the exact first-order perturbation theory wavefunction (the scheme considered in the papers cited above) as well as with respect to a minimal basis set Gaussian variational wavefunction. Reasonable agreement between the two schemes is confirmed, both yielding the expected positive values of the expectation value of the interelectronic repulsion, over the whole range of the relevant parameters.

Analyses of sizable ZFS and magnetic tensors of high spin metallocomplexes.

The fictitious spin-1/2 Hamiltonian approach is the putative method to analyze the fine-structure/hyperfine ESR spectra of high spin metallocomplexes having sizable zerofield splitting (ZFS), thus giving salient principal g-values far from around g = 2 without explicitly providing their ZFS parameters in most cases. Indeed, the significant departure of the g-values from g = 2 is indicative of the occurrence of their high spin states, but naturally they never agree with true g-values acquired by quantum chemical calculations such as sophisticated DFT or ab initio MO calculations. In this work, we propose facile approaches to determine the magnetic tensors of high spin metallocomplexes having sizable ZFS, instead of performing advanced high-field/high-frequency ESR spectroscopy. We have revisited analytical expressions for the relationship between effective g-values and true principal g-values for high spins. The useful analytical formulas for the geff-gtrue relationships are given for S's up to 7/2. The genuine Zeeman perturbation formalism gives the exact solutions for S = 3/2, and for higher S's it is much more accurate than the pseudo-Zeeman perturbation approach documented so far (A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Metal Ions, 1970; J. R. Pilbrow, J. Magn. Reson., 1978, 31, 479; F. Trandafir et al., Appl. Magn. Reson., 2007, 31, 553; M. Fittipaldi et al., J. Phys. Chem. B, 2008, 112, 3859), in which the E(Sx2 - Sy2) term is putatively treated to the second order. To show the usefulness of the present approach, we exploit FeIII(Cl)OEP (S = 5/2) (OEP: 2,3,7,8,12,13,17,18-octaethylporphyrin) and CoIIOEP (S = 3/2) well magnetically diluted in the diamagnetic host crystal lattice of NiIIOEP. The advantage of single-crystal ESR spectroscopy lies in the fact that the molecular information on the principal axes of the magnetic tensors is crucial in comparing with reliable theoretical results. In high spin states of metallocomplexes with sizable ZFS in pseudo-octahedral symmetry, their fine-structure ESR transitions for the principal z-axis orientation appear in the lower field far from g = 2 at the X-band, disagreeing with the putative intuitive picture obtained using relevant ESR spectroscopy. A ReIII,IV dinuclear complex in a mixed valence state exemplifies the cases, whose fine-structure/hyperfine ESR spectra of the neat crystals have been analyzed in their principal-axis system. The DFT-based/ab initio MO calculations of the magnetic tensors for all the high spin entities in this work were carried out.

Long-term dynamical evolution of Tundra-type orbits

Tundra-type orbits are elliptical geosynchronous orbits located at the critical inclination. The long-term dynamical evolution of this type of special orbit is investigated in this paper. First, the effect of Earth’s gravitational potential is examined. A simplified Hamiltonian of Tundra-type orbits subjected to Earth’s gravitational potential is presented through a strict magnitude comparison of the involved terms. Based on this simplified Hamiltonian with two degrees of freedom, the equilibrium points of the orbits subjected to Earth’s gravitational potential and their stabilities are discussed. This simplified Hamiltonian is then reduced to a one-degree-of-freedom system dominating the intermediate-period motion of the orbits approximately. In particular, the main characteristic parameters of the intermediate-period motion for nominal Tundra-type orbits and the corresponding specific results for three Sirius satellites in such orbits are presented. Second, the effect of lunisolar perturbations is examined. A magnitude comparison elementarily illustrates that the effect of tesseral harmonics of the Earth’s gravitational potential on the long timespan evolution of Tundra-type orbits is negligible compared to that of lunisolar perturbations. A simplified dynamical model including lunisolar perturbations is then presented. Based on this simplified dynamical model, the influences of lunar precession, the initial longitude of the ascending node, the initial argument of perigee, and the initial epoch on the long-term dynamical evolution of the orbits are comparatively analyzed. Finally, numerical calculations with exact perturbation models are conducted to verify the theoretical analysis and to provide more information about the dynamical evolution of Tundra-type orbits.

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the ({\pi},{\pi}) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.

Towards a self-consistent halo model for the nonlinear large-scale structure

The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: $(i)$ they do not enforce the stress-energy conservation of matter; $(ii)$ they are not guaranteed to recover exact perturbation theory results on large scales. Here, we provide a formulation of the halo model ("EHM") that remedies both drawbacks in a consistent way, while attempting to maintain the predictivity of the approach. In the formulation presented here, mass and momentum conservation are guaranteed on large scales, and results of perturbation theory and the effective field theory can in principle be matched to any desired order on large scales. We find that a key ingredient in the halo model power spectrum is the halo stochasticity covariance, which has been studied to a much lesser extent than other ingredients such as mass function, bias, and profiles of halos. As written here, this approach still does not describe the transition regime between perturbation theory and halo scales realistically, which is left as an open problem. We also show explicitly that, when implemented consistently, halo model predictions do not depend on any properties of low-mass halos that are smaller than the scales of interest.

Robust and efficient monolithic fluid‐structure‐interaction solvers

SummaryWe construct new robust and efficient preconditioned generalized minimal residual solvers for the monolithic linear systems of algebraic equations arising from the finite element discretization and Newton's linearization of the fully coupled fluid–structure interaction system of partial differential equations in the arbitrary Lagrangian–Eulerian formulation. We admit both linear elastic and nonlinear hyperelastic materials in the solid model and cover a large range of flows, for example, water, blood, and air, with highly varying density. The preconditioner is constructed in form of, where,, andare proper approximations to the matricesL,D, andUin theLDUblock factorization of the fully coupled system matrix, respectively. The inverse of the corresponding Schur complement is approximated by applying a few cycles of a special class of algebraic multigrid methods to the perturbed fluid sub‐problem, which is obtained by modifying corresponding entries in the original fluid matrix with an explicitly constructed approximation to the exact perturbation coming from the sparse matrix–matrix multiplications. The numerical studies presented impressively demonstrate the robustness and the efficiency of the preconditioner proposed in the paper. Copyright © 2016 John Wiley & Sons, Ltd.

Strongly interacting Bose–Fermi mixtures in one dimension

We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.

Many-body Green's function theory for electron-phonon interactions: Ground state properties of the Holstein dimer.

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

Cosmological perturbations and quasistatic assumption inf(R)theories

$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\Psi$, and the curvature potential, $\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasi-static behaviours in $f(R)$ gravity. In addition, regardless the validity of quasi-static approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable $f(R)$ gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to $k=10 c^{-1} \mathcal{H}_0$.

A Hybrid UTD-ACGF Technique for DOA Finding of Receiving Antenna Array on Complex Environment

When a receiving antenna array operates on a complex environment, the ideal phase differences of the receiving voltages of the antenna array are significantly distorted by both mutual coupling and platform scattering. This distortion causes performance degradation of the direction of arrival (DOA) algorithms. For estimating and compensating for the phase distortion, an analysis of the receiving voltages of the receiving antenna array on the platform is required. In this paper, we propose a hybrid UTD-ACGF technique for modeling port voltages of the receiving antenna array on a complex environment. The complex environment is modeled by UTD technique, and the antenna array is modeled by ACGF. In order to explain the coupling effect between the complex environment and the antenna array, we use the first perturbation series approximation based on the exact mutual coupling perturbation series. The hybrid UTD-ACGF results are verified through comparison to MoM results. Finally, we statistically define a distortion matrix that has a relation between the distorted port voltages and the ideal port voltages. The distorted port voltages are evaluated using the hybrid UTD-ACGF technique as a backbone. In order to enhance the performance of the DOA algorithm, we efficiently estimate and compensate for the distortion matrix. A DOA simulation using the MUSIC algorithm is performed to confirm the compensatory effect of the distortion matrix.

Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states.

We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis.

ULOF transient behaviour of metal-fuelled fast breeder reactor cores as a function of core size and perturbation methods

The safety behaviour of metal-fuelled fast breeder reactor cores may be assessed by their transient behaviour during anticipated unprotected transients. Out of such transients, unprotected loss of flow accident (ULOFA) has been recognized as an event important for determining reactor safety due to the positive sodium void coefficient of reactivity and the remote possibility of complete power failure as initiator. Reactor safety under ULOFA condition is particularly based on the inherent feedbacks, which is calculated using the removal worths and Doppler constants. As the removal worth is a strong function of reactor size, ULOF analyses are carried out in three different reactor size viz. 120MWe, 500MWe and 1000MWe. The study reveals that smaller metal cores are safer than larger cores with respect to the ULOF accidents in the pre-disassembly phase. The present study also shows that the use of exact perturbation based reactivity worths introduce no significant changes in the safety behaviour of metal fuel reactor compared to that with the use of first order perturbation worths in pre-disassembly phase. The first order approximation is found to be valid as the expansion of materials in the core during ULOFA is small before the core enters the disassembly phase.

Exact third-order density perturbation and one-loop power spectrum in general dark energy models

Under the standard perturbation theory (SPT), we obtain the fully consistent third-order density fluctuation and kernels for the general dark energy models without using the Einstein–de Sitter (EdS) universe assumption for the first time. We also show that even though the temporal and spatial components of the SPT solutions cannot be separable, one can find the exact solutions to any order in general dark energy models. With these exact solutions, we obtain the less than % error correction of one-loop matter power spectrum compared to that obtained from the EdS assumption for k=0.1 hMpc−1 mode at z=0(1,1.5). Thus, the EdS assumption works very well at this scale. However, if one considers the correction for P13, the error is about 6 (9, 11)% for the same mode at z=0(1,1.5). One absorbs P13 into the linear power spectrum in the renormalized perturbation theory (RPT) and thus one should use the exact solution instead of the approximation one. The error on the resummed propagator N of RPT is about 14 (8, 6)% at z=0(1,1.5) for k=0.4 hMpc−1. For k=1 hMpc−1, the error correction of the total matter power spectrum is about 3.6 (4.6, 4.5)% at z=0(1,1.5). Upcoming observation is required to archive the sub-percent accuracy to provide the strong constraint on the dark energy and this consistent solution is prerequisite for the model comparison.

Fully nonlinear and exact perturbations of the Friedmann world model: non-flat background

We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.

Recursive structure in the definitions of gauge-invariant variables for any order perturbations

The construction of gauge-invariant variables for any order perturbations is discussed. Explicit constructions of the gauge-invariant variables for perturbations to the forth order are shown. From these explicit constructions, the recursive structure in the definitions of gauge-invariant variables for any order perturbations is found. Through this recursive structure, the correspondence with the fully non-linear exact perturbations is briefly discussed.

The impact of westerly wind bursts and ocean initial state on the development, and diversity of El Niño events

Westerly wind bursts (WWBs) that occur in the western tropical Pacific are believed to play an important role in the development of El Nino events. Here, following the study of Lengaigne et al. (Clim Dyn 23(6):601–620, 2004), we conduct numerical simulations in which we reexamine the response of the climate system to an observed wind burst added to a coupled general circulation model. Two sets of twin ensemble experiments are conducted (each set has control and perturbed experiments). In the first set, the initial ocean heat content of the system is higher than the model climatology (recharged), while in the second set it is nearly normal (neutral). For the recharged state, in the absence of WWBs, a moderate El Nino with a maximum warming in the central Pacific (CP) develops in about a year. In contrast, for the neutral state, there develops a weak La Nina. However, when the WWB is imposed, the situation dramatically changes: the recharged state slides into an El Nino with a maximum warming in the eastern Pacific, while the neutral set produces a weak CP El Nino instead of previous La Nina conditions. The different response of the system to the exact same perturbations is controlled by the initial state of the ocean and the subsequent ocean–atmosphere interactions involving the interplay between the eastward shift of the warm pool and the warming of the eastern equatorial Pacific. Consequently, the observed diversity of El Nino, including the occurrence of extreme events, may depend on stochastic atmospheric processes, modulating El Nino properties within a broad continuum.

Phases of correlated spinless fermions on the honeycomb lattice

We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion $V_2$ induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large $V_2$ by mean-field theory. Consequently, the system undergoes a direct transition from the semimetal to the charge-modulated phase. For the latter, charge fluctuations also play a key role. While the phase, which is related to pinball liquids, is stabilized by the repulsion $V_2$, the energy of its low-lying charge excitations scales with the electronic hopping $t$, as in a band insulator.