prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the significance of the interlayer Berry connection polarizability?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers
Publish Date: 17 Mar 2023
Author List: 

Figure

FIG  1 (a) Schematics of experimental setup (b, c) Valence band structure and intrinsic Hall conductivity with respect to in-plane input for tMoTe2 at twist angles (b) θ = 1 2 • and (c) θ = 2 • in +K valley Color coding in (b) and (c) denotes the layer composition σ z n (k) 
FIG  2  (a) The interlayer BCP G, and (b) its vorticity [∂ k × G]z on the first valence band from +K valley of 1 2 • tMoTe2 Background color and arrows in (a) denote the magnitude and vector flow, respectively Grey curves in (b) show energy contours at 1/2 and 3/4 of the band width The black dashed arrow denotes direction of increasing hole doping level Black dashed hexagons in (a, b) denote the boundary of moiré Brillouin zone (mBZ) 
FIG  3  (a-c) Three high-symmetry stacking registries for tBG with a commensurate twist angle θ = 21 8 •  Lattice geometries with rotation center on an overlapping atomic site (a, b) and hexagonal center (c) (d) Schematic of the moiré pattern when the twist angle slightly deviates from 21 8 • , here θ = 21 •  Red squares marked by A, B and C are the local regions that resemble commensurate 21 8 • patterns in (a), (b) and (c), respectively (e, f) Low-energy band structures and intrinsic Hall conductivity of the two geometries [(a) and (b) are equivalent] The shaded areas highlight energy windows ∼ ω around band degeneracies where interband transitions, not considered here, may quantitatively affect the conductivity measured 
FIG  S4 Band structure and layer composition σ z n in +K valley of tBG (left panel) and the intrinsic Hall conductivity (right panel) at three different twist angle θ The shaded areas highlight energy windows ∼ ω around band degeneracies in which the conductivity results should not be considered Here σH should be multiplied by a factor of 2 accounting for spin degeneracy 

abstract

We propose an unconventional nonlinear dynamical Hall effect characteristic of twisted bilayers  The joint action of in-plane and out-of-plane ac electric fields generates Hall currents j ∼ Ė⊥ × E in both sum and difference frequencies, and when the two orthogonal fields have common frequency their phase difference controls the on/off, direction and magnitude of the rectified dc Hall current 
This novel intrinsic Hall response has a band geometric origin in the momentum space curl of interlayer Berry connection polarizability, arising from layer hybridization of electrons by the twisted interlayer coupling  The effect allows a unique rectification functionality and a transport probe of chiral symmetry in bilayer systems 
We show sizable effects in twisted homobilayer transition metal dichalcogenides and twisted bilayer graphene over broad range of twist angles  Nonlinear Hall-type response to an in-plane electric field in a two dimensional (2D) system with time reversal symmetry has attracted marked interests   Intensive studies have been devoted to uncovering new types of nonlinear Hall transport induced by quantum geometry and their applications such as terahertz rectification and magnetic information readout  
Restricted by symmetry , the known mechanisms of nonlinear Hall response in quasi-2D nonmagnetic materials are all of extrinsic nature, sensitive to fine details of disorders , which have limited their utilization for practical applications  Moreover, having a single driving field only, the effect has not unleashed the full potential of nonlinearity for enabling controlled gate in logic operation, where separable inputs (i e , in orthogonal directions) are desirable 
The latter, in the context of Hall effect, calls for control by both out-of-plane and in-plane electric fields  A strategy to introduce quantum geometric response to out-of-plane field in quasi-2D geometry is made possible in van der Waals (vdW) layered structures with twisted stacking   Taking homobilayer as an example, electrons have an active layer degree of freedom that is associated with an out-of-plane electric dipole , whereas interlayer quantum tunneling rotates this pseudospin about in-plane axes that are of topologically nontrivial textures in the twisted landscapes  
Such layer pseudospin structures can underlie novel quantum geometric properties when coupled with out-ofplane field  Recent studies have found layer circular photogalvanic effect and layer-contrasted time-reversaleven Hall effect , arising from band geometric quantities  In this work we unveil a new type of nonlinear Hall effect in time-reversal symmetric twisted bilayers, where an intrinsic Hall current emerges under the combined action of an in-plane electric field E and an out-of-plane ac field E ⊥ (t): j ∼ Ė⊥ × E [see Fig  ] 
Having the two driving fields (inputs) and the current response (output) all orthogonal to each other, the effect is dubbed as the crossed nonlinear dynamical Hall effect  This is also the first nonlinear Hall contribution of an intrinsic nature in nonmagnetic materials without external magnetic field, determined solely by the band structures, not relying on extrinsic factors such as disorders and relaxation times 
The effect arises from the interlayer hybridization of electronic states under the chiral crystal symmetry characteristic of twisted bilayers, and has a novel band geometric origin in the momentum space curl of interlayer Berry connection polarizability (BCP)  Having two driving fields of the same frequency, a dc Hall current develops, whose on/off, direction and magnitude can all be controlled by the phase difference of the two fields, which does not affect the magnitude of the double-frequency component 
Such a characteristic tunability renders this effect a unique approach to rectification and transport probe of chiral bilayers  As examples, we show sizable effects in small angle twisted transition metal dichalcogenides (tTMDs) and twisted bilayer graphene (tBG), as well as tBG of large angles where Umklapp interlayer tunneling dominates 
Geometric origin of the effect  A bilayer system couples to in-plane and out-of-plane driving electric fields in completely different ways  The in-plane field couples to the 2D crystal momentum, leading to Berry-phase effects in the 2D momentum space   In comparison, the outof-plane field is coupled to the interlayer dipole moment p in the form of −E ⊥ p, where p = ed 0 σz with σz as the Pauli matrix in the layer index subspace and d 0 the interlayer distance 
When the system has a more than twofold rotational axis in the z direction, as in tBG and tTMDs, any in-plane current driven by the out-of-plane field alone is forbidden  It also prohibits the off-diagonal components of the symmetric part of the conductivity tensor σ ab = ∂j a /∂E ||,b with respect to the in-plane input and output 
Since the antisymmetric part of σ ab is not allowed by the Onsager reciprocity in nonmagnetic systems, all the off-diagonal components of σ ab is forbidden, irrespective of the order of out-of-plane field  On the other hand, as we will show, an in-plane Hall conductivity σ xy = −σ yx can still be driven by the product of an in-plane field and the time variation rate of an outof-plane ac field, which is a characteristic effect of chiral bilayers 
To account for the effect, we make use of the semiclassical theory   The velocity of an electron in a bilayer system is given by where k is the 2D crystal momentum  Here and hereafter we suppress the band index for simplicity, unless otherwise noted  The three contributions in this equation come from the band velocity, the anomalous velocities induced by the k -space Berry curvature Ω k and by the hybrid Berry curvature Ω kE ⊥ in the (k, E ⊥ ) space 
For the velocity at the order of interest, the k-space Berry curvature is corrected to the first order of the variation rate of out-of-plane field Ė⊥ as Here A = u k |i∂ k |u k is the unperturbed k-space Berry connection, with |u k being the cell-periodic part of the Bloch wave, whereas is its gauge invariant correction , which can be identified physically as an in-plane positional shift of an electron induced by the time evolution of the out-of-plane field 
For a band with index n, we have whose numerator involves the interband matrix elements of the interlayer dipole and velocity operators, and ε n is the unperturbed band energy  Meanwhile, up to the first order of in-plane field, the hybrid Berry curvature reads Here A E || is the k-space Berry connection induced by E || field , which represents an intralayer positional shift and whose detailed expression is not needed for our purpose 
and is its first order correction induced by the in-plane field  In addition, ε = ε + δε, where δε = eE • G Ė⊥ is the field-induced electron energy   Given that A E || is the E ⊥ -space counterpart of intralayer shift A E || , and that E ⊥ is conjugate to the interlayer dipole moment, we can pictorially interpret A E || as the interlayer shift induced by in-plane field 
It indeed has the desired property of flipping sign under the horizontal mirror-plane reflection, hence is analogous to the so-called interlayer coordinate shift introduced in the study of layer circular photogalvanic effect , which is nothing but the E ⊥ -space counterpart of the shift vector well known in the nonlinear optical phenomenon of shift current 
Therefore, the E ⊥ -space BCP eG/ can be understood as the interlayer BCP  This picture is further augmented by the connotation that the interlayer BCP is featured exclusively by interlayer-hybridized electronic states: According to Eq  ( ), if the state |u n is fully polarized in a specific layer around some momentum k, then G (k) is suppressed 
With the velocity of individual electrons, the charge current density contributed by the electron system can be obtained from where [dk] is shorthand for n d 2 k/(2π) 2 , and the distribution function is taken to be the Fermi function f 0 as we focus on the intrinsic response  The band geometric contributions to ṙ lead to a Hall current
where is intrinsic to the band structure  This band geometric quantity measures the k-space curl of the interlayer BCP over the occupied states, and hence is also a characteristic of layer-hybridized electronic states  Via an integration by parts, it becomes clear that χ int is a Fermi surface property 
Since χ int is a time-reversal even pseudoscalar, it is invariant under rotation, but flips sign under space inversion, mirror reflection and rotoreflection symmetries  As such, χ int is allowed if and only if the system possesses a chiral crystal structure, which is the very case of twisted bilayers  
Moreover, since twisted structures with opposite twist angles are mirror images of each other, whereas the mirror reflection flips the sign of χ int , the direction of Hall current can be reversed by reversing twist direction  Hall rectification and frequency doubling  This effect can be utilized for the rectification and frequency doubling of an in-plane ac input E = E 0 cos ωt, provided that the out-of-plane field has the same frequency, namely E ⊥ = E 0 ⊥ cos (ωt + ϕ) 
The phase difference ϕ between the two fields plays an important role in determining the Hall current, which takes the form of j = j 0 sin ϕ + j 2ω sin(2ωt + ϕ)  ( Here ω is required to be below the threshold for direct interband transition in order to validate the semiclassical treatment, and σ H has the dimension of conductance and quantifies the Hall response with respect to the in-plane input 
In experiment, the Hall output by the crossed nonlinear dynamic Hall effect can be distinguished readily from the conventional nonlinear Hall effect driven by in-plane field alone, as they are odd and even, respectively, in the inplane field  One notes that while the double-frequency component appears for any ϕ, the rectified output is allowed only if the two crossed driving fields are not in-phase or antiphase 
Its on/off, chirality (right or left), and magnitude are all controlled by the phase difference of the two fields  Such a unique tunability provides not only a prominent experimental hallmark of this effect, but also a controllable route to Hall rectification  In addition, reversing the direction of the out-of-plane field switches that of the Hall current, which also serves as a control knob 
Application to tTMDs  We now study the effect quantitatively in tTMDs, using tMoTe 2 as an example (see details of the continuum model in )  For illustrative purposes, we take ω/2π = 0 1 THz and E 0 ⊥ d 0 = 10 mV in what follows  Figures ) and (c) present the electronic band structures along with the layer composition σ z n (k) at twist angles θ = 1 2 • and θ = 2 •  
In both cases, the energy spectra exhibit isolated narrow bands with strong layer hybridization  At θ = 1 2 • , the conductivity shows two peaks ∼ 0 1e 2 /h at low energies associated with the first two valence bands  The third band does not host any sizable conductivity signal  At higher hole-doping levels, a remarkable conductivity peak ∼ e 2 /h appears near the gap separating the fourth and fifth bands 
At θ = 2 • , the conductivity shows smaller values, but the overall trends are similar: A peak ∼ O(0 01)e 2 /h appears at low energies, while larger responses ∼ O(0 1)e 2 /h can be spotted as the Fermi level decreases  One can understand the behaviors of σ H from the interlayer BCP in Eq  ( )  It favors band near-degeneracy regions in k -space made up of strongly layer hybridized electronic states 
As such, the conductivity is most pro- nounced when the Fermi level is located around such regions, which directly accounts for the peaks of response in Fig  that [∂ k × G] z is negligible at lower energies, and it is dominated by positive values as the doping increases, thus the conductivity rises initially 
When the doping level is higher, regions with [∂ k × G] z < 0 start to contribute, thus the conductivity decreases after reaching a maximum  Application to tBG  The second example is tBG  We focus on commensurate twist angles in the large angle limit in the main text , which possess moiré-lattice assisted strong interlayer tunneling via Umklapp processes  
This case is appealing because the Umklapp interlayer tunneling is a manifestation of discrete translational symmetry of moiré superlattice, which is irrelevant at small twist angles and not captured by the continuum model but plays important roles in physical contexts such as higher order topological insulator and moiré excitons  
The Umklapp tunneling is strongest for the commensurate twist angles of θ = 21 8 • and θ = 38 2 • , whose corresponding periodic moiré superlattices have the smallest lattice constant ( √ 7 of the monolayer counterpart)  Such a small moiré scale implies that the exact crystalline symmetry, which depends sensitively on fine details of rotation center, has critical influence on lowenergy response properties 
To capture the Umklapp tunneling, we employ the tight-binding model   Figures ) and (c) show two distinct commensurate structures of tBG at θ = 21 8 • belonging to chiral point groups D 3 and D 6 , respectively  The atomic configurations in Figs  ) are equivalent, which are constructed by twisting AA-stacked bilayer graphene around an overlapping atom site, and that in Fig  ) is obtained by rotating around a hexagonal center 
Band structures of these two configurations are drastically different within a low-energy window of ∼ 10 meV around the κ point   Remarkably, despite large θ, we still get σ H ∼ O(0 001) e 2 /h (D 3 ) and ∼ O(0 1) e 2 /h (D 6 ), which are comparable to those at small angles (cf  Fig  in the Supplemental Material ) 
Such sizable responses can be attributed to the strong interlayer coupling enabled by Umklapp processes   Apart from different intensities, the Hall conductivities in the two stacking configurations have distinct energy dependence: In Fig  , σ H shows a single peak centered at zero energy; In Fig  (f), it exhibits two antisymmetric peaks around zero 
The peaks are centered around band degeneracies, and their profiles can be understood from the distribution of [∂ k × G] z   Figure (d) illustrates the atomic structure of tBG with a twist angle slightly deviating from θ = 21 8 • , forming a supermoiré pattern  In short range, the local stacking geometries resemble the commensurate configurations at θ = 21 8 • , while the stacking registries at different locales differ by a translation 
Similar to the moiré landscapes in the small-angle limit, there also exist high-symmetry locales: Regions A and B enclose the D 3 structure, and region C contains the D 6 configuration  Position-dependent Hall response is therefore expected in such a supermoiré  As the intrinsic Hall signal from the D 6 configuration dominates [see Figs 
3(e) vs (f)], the net response mimics that in Fig    Discussion  We have uncovered the crossed nonlinear dynamical intrinsic Hall effect characteristic of layer hybridized electronic states in twisted bilayers, and elucidated its geometric origin in the k -space curl of interlayer BCP  It offers a new tool for rectification and frequency doubling in chiral vdW bilayers, and is sizable in tTMD and tBG 
Here our focus is on the intrinsic effect, which can be evaluated quantitatively for each material and provides a benchmark for experiments  There may also be extrinsic contributions, similar to the side jump and skew scattering ones in anomalous Hall effect  They typically have distinct scaling behavior with the relaxation time τ from the intrinsic effect, hence can be distinguished from the latter in experiments  
Moreover, they are suppressed in the clean limit ωτ 1 [(ωτ ) 2 1, more precisely]   In high-quality tBG samples, τ ∼ ps at room temperature   Much longer τ can be obtained at lower temperatures  In fact, a recent theory explaining well the resistivity of tBG predicted τ ∼ 10 −8 s at 10 K   As such, high-quality tBG under low temperatures and sub-terahertz input (ω/2π = 0 1 THz) is located in the clean limit, rendering an ideal platform for isolating the intrinsic effect 
This work paves a new route to driving in-plane response by out-of-plane dynamical control of layered vdW structures   The study can be generalized to other observables such as spin current and spin polarization, and the in-plane driving can be statistical forces, like temperature gradient  Such orthogonal controls rely critically on the nonconservation of layer pseudospin degree of freedom endowed by interlayer coupling, and constitute an emerging research field at the crossing of 2D vdW materials, layertronics, twistronics and nonlinear electronics 
This work is supported by the Research Grant Council of Hong Kong (AoE/P-701/20, HKU SRFS2122-7S05), and the Croucher Foundation  W Y  also acknowledges support by Tencent Foundation  Cong Chen, 1, 2, * Dawei Zhai, 1, 2, * Cong Xiao, 1, 2, † and Wang Yao 1, 2, ‡ 1 Department of Physics, The University of Hong Kong, Hong Kong, China 2 HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, China Extra figures for tBG at small twist angles Figure (a) shows the band structure of tBG with θ = 1 47 • obtained from the continuum model  
The central bands are well separated from higher ones, and show Dirac points at κ/κ points protected by valley U (1) symmetry and a composite operation of twofold rotation and time reversal C 2z T   Degeneracies at higher energies can also be identified, for example, around ±75 meV at the γ point  As the two Dirac cones from the two layers intersect around the same area, such degeneracies are usually accompanied by strong layer hybridization [see the color in the left panel of Fig  ] 
Additionally, it is well-known that the two layers are strongly coupled when θ is around the magic angle (∼ 1 08 • ), rendering narrow bandwidths for the central bands  As discussed in the main text, coexistence of strong interlayer hybridization and small energy separations is expected to contribute sharp conductivity peaks near band degeneracies, as shown in Fig   
In this case, the conductivity peak near the Dirac point can reach ∼ 0 1e 2 /h, while the responses around ±0 08 eV are smaller at ∼ 0 01e 2 /h  The above features are maintained when θ is enlarged, as illustrated in Figs  ) and (c) using θ = 2 65 • and θ = 6 01 •   Since interlayer coupling becomes weaker and the bands are more separated at low energies when θ increases, intensity of the conductivity drops significantly 
We stress that G is not defined at degenerate points, and interband transitions may occur when energy separation satisfies |ε n − ε m | ∼ ω, the effects of which are not included in the current formulations  Consequently, the results around band degeneracies within energy ∼ ω [shaded areas in Fig  ] should be excluded 
Context 2: Paper Info

Title: Generalized Pole-Residue Method for Dynamic Analysis of Nonlinear Systems based on Volterra Series
Publish Date: March 7, 2023
Author List: Qianying Cao (from State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology), Anteng Chang (from College of Engineering, Ocean University of China), Junfeng Du (from College of Engineering, Ocean University of China), Lin Lu (from State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology)

Figure

Fig  1: Procedure to compute the response by a combination of Volterra series and Laguerre polynomials
Fig  2: Linear frequency response function: (a) Modulus of H 1 (ω), (b) phase angle of H 1 (ω)
Fig  6: Comparison of h 1 (t) based on the analytical and reconstructed by Laguerre polynomials
Fig  11: Response for Case 1: (a) comparison between the proposed method and Runge-Kutta method, (b) contribution of the three components
Fig  18: Comparison of original excitations and reconstructed results: (a) Case 1, (b) Case 2 (c) Case 3
Fig  19: Response to irregular excitation for Case 1: (a) comparison between the proposed method and Runge-Kutta method, (b) contribution of the three components
Fig  23: Input-output dataset used to identify Volterra series: (a) input excitation, (b) output response
Fig  26: Comparison of responses between the predicted and numerical results: (a) response to regular excitation, (b) response to irregular excitation
Parameter values of the irregular excitation

abstract

Dynamic systems characterized by second-order nonlinear ordinary differential equations appear in many fields of physics and engineering  To solve these kinds of problems, time-consuming stepby-step numerical integration methods and convolution methods based on Volterra series in the time domain have been widely used 
In contrast, this work develops an efficient generalized pole-residue method based on the Volterra series performed in the Laplace domain  The proposed method involves two steps: (1) the Volterra kernels are decoupled in terms of Laguerre polynomials, and (2) the partial response related to a single Laguerre polynomial is obtained analytically in terms of the pole-residue method 
Compared to the traditional pole-residue method for a linear system, one of the novelties of the pole-residue method in this paper is how to deal with the higher-order poles and their corresponding coefficients  Because the proposed method derives an explicit, continuous response function of time, it is much more efficient than traditional numerical methods 
Unlike the traditional Laplace domain method, the proposed method is applicable to arbitrary irregular excitations  Because the natural response, forced response and cross response are naturally obtained in the solution procedure, meaningful mathematical and physical insights are gained  In numerical studies, systems with a known equation of motion and an unknown equation of motion are investigated 
For each system, regular excitations and complex irregular excitations with different parameters are studied  Numerical studies validate the good accuracy and high efficiency of the proposed method by comparing it with the fourth-order Runge-Kutta method 

Introduction

Most real dynamic systems, as encountered in mechanical and civil engineering, are inherently nonlinear and include geometric nonlinearities, nonlinear constitutive relations in material or nonlinear resistances, etc    Nonlinear problems are attracting increasing attention from engineers and scientists 
This work focuses on solving nonlinear system vibration problems, i e , computing transient responses of nonlinear oscillators under arbitrary irregular excitations based on a combination of a pole-residue operation and Volterra series  Because Volterra series are single-valued, the scope of the present study is restricted to nonlinear behaviours without bifurcations  
To analyse nonlinear vibration problems, researchers have performed extensive studies and developed various mathematical methods  Popular methods include step-by-step numerical integration methods in the time domain, such as the Runge-Kutta method  This kind of method not only requires a small time-step resolution for obtaining high-precision solutions but also is prone to numerical instability  
For a long response with small time steps, the time domain methods are very costly in computational time  Volterra series is another widely used method, which is the extension of the Duhamel integral for linear systems   Volterra series can reproduce many nonlinear phenomena, but they are very complex due to higher-dimensional convolution integrals  
Since 1980's, significant progress has been made in the general area of the Volterra series  The reader is referred to Ref  for a quite thorough literature review on the relevant topics  After 2017, most papers focus on Volterra series identification  De Paula and Marques proposed a method for the identification of Volterra kernels, which was based on time-delay neural networks 
Son and Kim presented a method for a direct estimation of the Volterra kernel coefficients  Dalla Libera et al  introduced two new kernels for Volterra series identification  Peng et al  used the measured response to identify the kernel function and performed the nonlinear structural damage detection  Only a few papers concentrated on simplifying the computation of convolution integrals 
Traditional methods for computing convolution integrals involved in the Volterra series have been performed in three distinct domains: time, frequency and Laplace  The time domain method based on Volterra series refers to discrete time convolution methods, which also suffer computational cost problems  
Both the frequency domain method and the Laplace domain method based on the Volterra series consist of three steps: (1) Volterra series are transformed into an algebraic equation in the frequency domain or Laplace domain; the algebraic equation is solved by purely algebraic manipulations; and (3) the solution in Step ( ) is transformed back to the time domain 
Many researchers have used the frequency domain method to compute the responses of nonlinear systems  Billings et al  developed a new method for identifying the generalized frequency response function (GFRF) of nonlinear systems and then predicted the nonlinear response based on these GFRFs  Carassale et al  introduced a frequency domain approach for nonlinear bridge aerodynamics and aeroelasticity 
Ho et al  computed an output frequency domain function of a nonlinear damped duffing system modelled by a Volterra series under a sinusoidal input  Kim et al  identified the higher order frequency response functions by using the nonlinear autoregressive with exogenous input technique and the harmonic probing method 
This type of frequency domain method is much more efficient than the time domain method due to the fast Fourier transform algorithm  However, the frequency domain method not only is limited by frequency resolutions but also suffers from leakage problems due to the use of discrete Fourier transforms  In addition, the frequency domain method calculates only a steady-state response 
A natural response generated by initial conditions and a cross response caused by interactions between a system and an excitation are ignored  In contrast, the Laplace domain method can calculate all response components because initial conditions are considered in the computational procedure  However, it has been restricted to analytical operations for simple excitations, such as sinusoidal excitations and exponential excitations  
The proposed method falls into the category of the Volterra series method computed in the Laplace domain  Unlike the traditional Laplace domain method, the proposed method is applicable to arbitrary irregular excitations  Because the proposed method follows a similar path as a pole-residue method for linear systems , the proposed method to solve nonlinear system vibration problems is called the generalized pole-residue method 
The main concept of the pole-residue method developed by Hu et al  was that the poles and residues of the response could be easily obtained from those of the input and system transfer function to obtain the closed-form response solution of linear systems  This method included three steps: (1) writing the system transfer function into pole-residue form; (2) writing the excitation into pole-residue form by the Prony-SS method; (3) computing the poles and residues of the response by an algebraic operation based on those from system and excitation 
Compared to Hu et al  , which was regarded as an efficient tool to compute responses of linear systems, the generalized pole-residue method in this paper is introduced to compute responses of nonlinear systems  The proposed method involves two steps: (1) the Volterra kernels are decoupled in terms of Laguerre polynomials, and (2) the partial response related to a single Laguerre polynomial is obtained analytically in terms of the pole-residue method 
Compared to the traditional pole-residue method for a linear system, one of the novelties of the generalized pole-residue method is how to deal with the higher-order poles and their corresponding coefficients  Similar to the Taylor series, the Volterra series representation is an infinite series, and convergence conditions are needed to assure that the representation is meaningful 
Because the proposed method is based on the Volterra series, only the system with convergent Volterra series representation can be treated by the proposed method  The paper is organized as follows  In Section 2, the nonlinear response is modelled by a Volterra series, and Volterra kernel functions are decoupled by Laguerre polynomials 
Then, the pole-residue method for computing explicit responses is developed in Section 3  Numerical studies and discussions are given in Section 4  Finally, the conclusions are drawn in Section 5 

Response calculation based on Volterra series

A nonlinear oscillator, whose governing equation of motion is given by where z(t, y, ẏ) represents an arbitrary nonlinear term; m, c, and k are the mass, damping and linear stiffness, respectively; y(t), ẏ(t) and ÿ(t) are the displacement, velocity and acceleration, respectively; and f (t) is the time-dependent excitation 
If the energy of excitation f (t) is limited, the nonlinear response under zero initial conditions (i e , zero displacement and zero velocity) can be represented by the Volterra series : where N is the order of Volterra series and In Eq  3, h 1 (τ ) is called the first-order Volterra kernel function, which represents the linear behaviour of the system; h n (τ 1 ,      
, τ n ) for n > 1 are the higher-order Volterra kernel functions, which describe the nonlinear behaviour of the system  The complete formulation of y(t) includes infinite series where the labour of calculating the n th term increases quickly with the growth of n  Fortunately, the response accuracy may be ensured by the first several order Volterra series 
This is proved here in numerical studies  The commonly known Laguerre polynomials are represented as : where p i is the order of the Laguerre polynomials and a i is the damping rate  The Laguerre polynomials satisfy the orthogonal relationship expressed as: By using Laguerre polynomials, the Volterra kernel function h n (t 1 ,      
, t n ) in Eq  3 can be decoupled as follows : where the coefficient is computed resorting to the orthogonal relationship in Eq  5: Substituting Eq  6 into Eq  3 yields       The above operation that uses the Laguerre polynomials to decouple Volterra higher order kernel functions has been well-developed 
The reader is referred to Refs  for details about the adopted technique  After decoupling Volterra higher order kernel functions in time, one can regroup Eq  8 into:       By denoting Eq  9 becomes The above procedure to compute the nonlinear response by a combination of Volterra series and Laguerre polynomials is schematically shown in Fig   
Volterra kernel functions h n (t 1 ,       , t n ) can be obtained by either an equation of motion or measured input-output signals  To derive a closedform solution of the response, we must obtain a closed-form solution of x i (t) first  In the following presentation, a closed-form solution of the aforementioned x i (t) and y n (t) is derived by using the pole-residue method 
3  Pole-residue method for calculating x i (t) and y n (t) Performing the Laplace transform of x i (t) in Eq  10 yields where in which Eq  13 includes a single pole and several higher-order poles  For k = 0, −a i is a single pole, and b p i (0) is a corresponding coefficient, namely, the residue  For k > 0, −a i are higher-order poles, and b p i (k) are corresponding coefficients 
For an irregular excitation signal f (t) of a finite duration of T , it can always be approximated into a pole-residue form by using the complex exponential signal decomposition method-Prony-SS : where N ℓ is the number of components; α ℓ and λ ℓ are constant coefficients, which either are real numbers or occur in complex conjugate pairs 
We define λ ℓ = −δ ℓ + iΩ ℓ , where Ω ℓ is the excitation frequency and δ ℓ is the damping factor of the ℓ th component  We denote α ℓ = A ℓ e iθ ℓ , where A ℓ is the amplitude and θ ℓ is the sinusoidal initial phase in radians  Taking the Laplace transform of Eq  15 yields Note that the concept of the Prony-SS method is similar to that of a principal component method 
A smooth excitation usually requires just several terms to achieve a good approximation  For high irregular loadings, including more terms would achieve a better approximation  Substituting Eqs  13 and 16 into Eq  12 yields Expressing xi (s) in its pole-residue form yields where λ ℓ are simple poles, and the corresponding residues are easily obtained by
and −a i are higher-order poles, and the corresponding coefficients are firstly derived as: By taking the inverse Laplace transform of Eq  18, a closed-form solution is obtained: Substituting Eqs  11 and 21 into Eq  2 yields Theoretically speaking, the proposed method for deriving the closed-form solution of the nonlinear response is applicable to any order of the Volterra series 
For practical engineering, usually only the first several order responses dominate  By setting up N = 2, Eq  22 can be simplified into three components: where the natural response, which is only related to system poles, is given by and the cross response, which is related to both system poles and excitation poles, is given by
and the forced response, which is related only to excitation poles, is given by The first term in Eq  26 is the first-order forced response governed by the excitation frequency, i e , the imaginary part of the pole λ ℓ   The second term corresponds to the second-order nonlinear forced response, which includes the sum frequency and difference frequency responses governed by λ ℓ + λ j  
Eq  26 straightforwardly offers visible information about the possible nonlinear vibrations by the cooperation of excitation frequencies  Particularly, consider a sinusoidal excitation f (t) = sin ω r t, which can be expressed as f (t) = γe λt + γ * e λ * t , where γ = −0 5i and λ = iω r   Substituting these values into Eq 
26, the second term of Eq  26 is simplified as where the first term is the difference frequency response, and the second term is the sum frequency response 

Numerical studies

In practical engineering, some systems have an accurate equation of motion  Additionally, some systems have difficulty constructing their equations of motion because of complex nonlinear dynamic behaviours and uncertain system parameters  In this article, a system with a known equation of motion is called a known system, and a system with an unknown equation of motion is called an unknown system for simplicity 
In this section, two numerical studies are presented  The first study verifies the proposed method using a known nonlinear oscillator, and the second study demonstrates the applicability of the proposed method to an unknown system  Throughout the numerical studies, the unit system is the metre-kilogramme-second (MKS) system; for conciseness, explicit units for quantities are omitted 

A known nonlinear system

This study chooses a nonlinear oscillator written as: where mass m = 1, damping c = 1, linear stiffness k 1 = 10, quadratic stiffness k 2 = 20 and cubic stiffness k 3 = 20  It is a case that has been studied in a previously published article   The linear natural frequency of the system ω 0 = k 1 /m = 3 16 and the damping ratio ζ = c/(2mω 0 ) = 15 8% 
This kind of oscillator occurs in many engineering problems, such as a model of fluid resonance in a narrow gap between large vessels 



ground_truth: The momentum space curl of the interlayer Berry connection polarizability generates the crossed nonlinear dynamical Hall effect.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What does the paper aim to solve?

Read the following text and answer briefly.

Context 2:  In the model, k 1 y represents the linear restoring force of the fluid, and k 2 y 2 and k 3 y 3 are respectively the quadratic and cubic nonlinear restoring forces of the fluid 

Volterra kernel functions

Generally, the first several order responses dominate the total response of a system  Hence, the order of the Volterra series in Eq  22 is chosen to be 3, namely, N = 3  For computing the first three order responses from Eq  22, the first three order Volterra kernel functions need to be known  Since Volterra kernel functions and corresponding frequency response functions are related by a specific Fourier transform pair, we can first write the first three orders of frequency response functions directly from Eq  28 
Then, Volterra kernel functions are obtained by the inverse Fourier transform  Based on the harmonic probing algorithm , the linear frequency response function (LFRF) H 1 (ω), the quadratic frequency response function (QFRF) H 2 (ω 1 , ω 2 ) and the cubic frequency response function (CFRF) H 3 (ω 1 , ω 2 , ω 3 ) are analytically given by:
and Figures show H 1 (ω), H 2 (ω 1 , ω 2 ) and H 3 (ω 1 , ω 2 , ω 3 ), respectively, which agree well with those reported in Ref    As expected, the modulus of H 1 (ω) in Fig  peaks near the linear natural frequency ω 0 , and the phase angle decreases monotonically from 0 to -π with increasing frequency 
Figure shows the sum frequency QFRF, where the energy converges along the line of ω 1 +ω 2 ≈ ω 0   Therefore, when the sum frequency of a two-tone excitation equals the linear resonant frequency, the second-order response may reach its maximum  Additionally, those pairs of excitations in line ω 1 + ω 2 ≈ ω 0 may produce non-negligible vibration magnitudes due to second-order nonlinear effects 
For the difference frequency QFRF in Fig  (b), the energy converges along two main lines, i e , ω 1 ≈ ω 0 and ω 2 ≈ ω 0   Figures show moduli of H 3 (ω, ω, ω) and H 3 (ω, ω, −ω), which are diagonal terms of the sum frequency CFRF and the difference frequency CFRF, respectively  While the modulus of H 3 (ω, ω, ω) peaks near ω ≈ ω 0 /3 and ω 0 , that of H 3 (ω, ω, −ω) peaks near ω ≈ ω 0 with a small hump around ω ≈ ω 0 /2 
Values at ω ≈ ω 0 /3 and ω 0 /2 may be magnified by higher-order stiffness terms in Eq  28  By performing the inverse fast Fourier transform to Eqs  29-31, the corresponding linear impulse response function h 1 (t), quadratic impulse response function h 2 (t 1 , t 2 ) and cubic impulse response function h 3 (t 1 , t 2 , t 3 ) are obtained 
Here, h 1 (t) and h 2 (t 1 , t 2 ) are plotted in Figs  , respectively, and h 3 (t, t, t) is shown in Fig    In the numerical implementation, Eqs  29-31 have been utilized with the frequency interval ∆ω = 0 1, number of frequency components N n = 1025, and cut-off frequencies 102 4 and −102 4  For decoupling Volterra kernel functions by using Laguerre polynomials, the damping rate and number of Laguerre polynomials for each order Volterra kernel function need to be determined (see Eqs  4 and 6) 
In this example, we set a 1 = a 2 = a 3 = 2 and R 1 = R 2 = R 3 = 24 because coefficients c p 1    pn become very small when R n > 24, n = 1, 2, 3  According to Eq  7, the coefficients of the first three order Volterra kernel functions are calculated, which are shown in Figs  9 and 10  For convenience, Fig  plots only c p 1 p 2 p 3 for p 3 = 0 
With the increase of the order of Laguerre polynomials, coefficients in Figs  9 and 10 gradually decrease, which illustrates how the first several orders of Laguerre polynomials dominate all orders of the Volterra kernel function  With the known Laguerre polynomials and corresponding coefficients, Volterra kernel functions are reconstructed by Eq  6 
For comparison, reconstructed Volterra kernel functions are also plotted in Figs    The reconstructed results agree well with the analytical values, which verifies the accuracy of the decomposition 

Sinusoidal excitation

From Eq  28, we consider a sinusoidal excitation where A and Ω are the amplitude and the frequency, respectively  Five cases of A and Ω are shown in Table   Excitation frequencies in Cases 1 and 2 are larger than the linear natural frequency (ω 0 ≈ 3 16), those in Case 3 are very close to ω 0 , and those in Cases 4 and 5 are smaller than ω 0  
All cases have same amplitudes  The poles of a sinusoidal excitation are λ 1,2 = ±iΩ, and the residues are α 1,2 = ∓iA/2  Numerical values of excitation poles and residues for different cases are listed in Table   Table : Parameter values, poles and residues of the sinusoidal excitation Substituting poles and residues of the excitation, as well as those of the system into Eqs 
20 and 19, response coefficients β p i ,k corresponding to system poles −a i and response coefficients γ p i ,ℓ corresponding to excitation poles λ ℓ are calculated, respectively  According to Eq  22, the first three orders of responses for each case in Table are calculated  Figures )-15(a) show the comparison of responses obtained by the proposed method and the fourth-order Runge-Kutta method with ∆t = 10 −4  
For Cases 1 and 2, the first-order responses agree well with the total responses obtained by the Runge-Kutta method, and the higher-order responses only slightly improve the transient parts  For Cases 3-5, the sum of the first three orders of responses is in good agreement with the Runge-Kutta solution 
When the response nonlinearity increases, higher-order responses need to be considered  In other words, the proposed method can accurately compute the nonlinear responses by choosing a small number N of Volterra series terms  Figures )-15(b) show the contributions of the three response components for the five cases 
In each case, the first-order response is the most dominant component, and the contributions of secondand third-order responses are much less than those of the first-order response  Especially for Cases 1 and 2, whose excitation frequencies are far from the linear natural frequency, second-and thirdorder responses are close to zero 
This may be because the QFRF and CFRF approach zero when the frequency is larger than 4 rad/s (see Figs  )  Furthermore, the mean values of the first-order responses are approximately zero, and those of the second-order responses are always smaller than zero, which are the difference frequency components in Eq  27 
Moreover, it is clearly observed that second-order responses for Cases 3-5 exhibit a periodic oscillation with a period near half of that for the first-order response, which is excited by the sum frequency component of the excitation (see second part of Eq  27)  Compared with steady-state solutions of first-and second-order responses, those of third-order responses in Cases 3-5 are no longer single regular motions 
By performing the FFT, frequency spectra of these three third-order responses are shown in Fig    We find that these three third-order responses are all dominated by their own fundamental harmonic component and the third harmonic (triple frequency) component  Figure shows the computational time to calculate the response of the oscillator for Case 1 by the proposed method, the fourth-order Runge-Kutta method and the convolution method 
The proposed method, which has an explicit solution, is much more efficient in computational time than the latter two methods, which need small time steps to obtain high-precision solutions  In particular, the efficiency of the proposed method increases with the length of the response time  Computation time (sec )
t=0 02s Convolution, t=0 02s Convolution, t=0 001s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the proposed method, the fourth-fifth order Runge-Kutta method and the convolution method regular loading in Case 1

Irregular excitation

In Eq  28, considering an irregular excitation consisting of several cosine functions where N f is the number of cosine components; A n , Ω n and θ n are the amplitude, frequency and phase angle of the n th component, respectively  Table lists three cases of these parameters  In each case, the amplitudes of all components are the same, and phase angles θ n uniformly distributed between 0 and 2π are randomly generated 
To decompose the excitation into a pole-residue form, the Prony-SS method is used, whose concept is similar to that of a principal component method  The readers are referred to Ref  for details  The chosen rank of each case is also shown in Table   Figure shows the comparison of original excitations and reconstructed results of these three cases, which all have excellent agreement 
show the results computed by the fourth-order Runge-Kutta method  In all cases, the sums of the first three orders of responses agree well with those obtained by the Runge-Kutta method  The contributions of the first three orders of responses for each case are plotted in Figs  )-21(b)  Similarly, the system vibration is dominated by the first-order response 
However, the contributions of second-and third-order significantly grow with increasing excitation magnitude and frequency number  Furthermore, when the magnitude of the nonlinear response becomes large, sharp troughs are present  This phenomenon may be induced by the nonlinear stiffness  While the first-order response fails to capture these troughs, the higher-order responses successfully capture these troughs 
Figure plots the computational time to calculate the response of the oscillator for the irregular loading in Case 1 by the proposed method and the fourth-fifth order Runge-Kutta method, respectively  While the fourth-fifth order Runge-Kutta method is more efficient under a small response length, the proposed method becomes much more efficient when the response length is larger than about 130 s 
In addition, the proposed method obtains the explicit response solution, so one can directly obtain the response value at a specific time t p instead of integrating from 0 to t p for traditional numerical methods  Computation time (sec ) Proposed, t=0 02s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the method and the fourth-fifth order Runge-Kutta method for irregular loading in Case 1

An unknown nonlinear

To check the applicability of the proposed method to an unknown nonlinear system, a known input excitation and its corresponding response are used to identify its Volterra kernel functions  When the Volterra kernel functions are known, we can follow the procedure in Section 4 1 to predict system responses 
In this study, the input excitation is white noise with a constant power spectrum S 0 = 0 001, and the corresponding response is obtained by solving Eq  28 by the fourth-order Runge-Kutta method, which is shown in Fig    From Section 4 1, we determine that the sum of the first two orders of responses agrees well with the total response 
In this study, the order of Volterra series N is chosen to be 2, damping rates of Laguerre polynomials are a 1 = a 2 = 2, and numbers of Laguerre polynomials are R 1 = R 2 = 24  To estimate the first two orders of Volterra kernel functions, a matrix equation is constructed using excitation data and response data 
By using the least square method to solve this matrix equation, coefficients c p 1 and c p 1 p 2 in Eq  8 are identified  Figure plots c p 1 and c p 1 p 2 , respectively, which have good agreement with the exact results in Fig    Then, the first two order Volterra kernel functions are constructed by Eq  6 
Compared with the exact results in Figs  , the identified Volterra kernel functions in Fig  completely agree well with the exact solutions  Note that the white noise excitation, which can excite more frequency components of the response, is chosen to obtain good Volterra kernel functions  A regular excitation f (t) = sin(πt) and an irregular excitation f (t) = N f n=1 A n cos(Ω n t + θ n ) with A n = 0 3 and Ω n varying from 0 to 40 with equal interval 1 are chosen as input excitations 
The predicted responses, along with results obtained by the fourth-order Runge-Kutta method, are shown in Fig    In both cases, the proposed method accurately predicts system responses  As presented in Eq  23, a nonlinear response is the sum of three terms: natural response y s (t), forced response y f (t) and cross response y c (t) 
These individual terms, as well as their sum to two excitations, are shown in Figs  27 and 28, respectively  As shown in Figs  and 28, both first-and second-order responses include the natural response y s (t) and the forced response y f (t), but the cross response y c (t) only exists in second-order responses 
When t becomes larger, both y s (t) and y c (t) diminish due to the presence of system damping, and the total response is entirely governed by y f (t)  Moreover, we notice some features at t = 0 for these components, including y s (0) = −y f (0) for the first-order response and y s (0) + y f (0) = −y c (0) for the second-order response, which are due to imposed zero initial conditions 

Conclusions

Considering arbitrary irregular excitations, an efficient generalized pole-residue method to compute the nonlinear dynamic response modelled by the Volterra series was developed  A core of the proposed method was obtaining poles and corresponding coefficients of Volterra kernel functions, then those of each order response modelled by each order Volterra series 
Once the poles and corresponding coefficients of Volterra kernel functions and excitations were both available, the remaining derivation could follow a similar pole-residue method that had been developed for ordinary linear oscillators  To obtain the poles and corresponding coefficients of Volterra kernel functions, two steps were included: (1) using Laguerre polynomials to decouple higher-order Volterra kernel functions with respect to time and (2) obtaining poles and corresponding coefficients of Laguerre polynomials in the Laplace domain 
Because the proposed method gave an explicit, continuous response function of time, it was much more efficient than traditional numerical methods  Moreover, many meaningful physical and mathematical insights were gained because not only each order response but also the natural response, the forced response and the cross response of each order were obtained in the solution procedure 
To demonstrate that the proposed method was not only suitable for a system with a known equation of motion but also applicable to a system with an unknown equation of motion, two numerical studies were conducted  For each study, regular excitations and complex irregular excitations with different parameters were investigated 
The efficiency of the proposed method was verified by the fourth-order Runge-Kutta method  This paper only computes the response under zero initial conditions  The response under non-zero initial conditions will be investigated in our future work 
Context 3: Transport Aircraft for IAF - Page 67 - Bharat Rakshak
Transport Aircraft for IAF
Re: Transport Aircraft for IAF
Postby abhik » 17 Nov 2014 05:55
+1, Air India recently sold their entire fleet of Boeing 777s 
afaik the A330 MRTT does not make any structural mods or add anything internally in cargo or passenger cabin  it just relies on the intrinsic 110 tons of fuel  external refueling pods are added and internally the control station and cameras for the operator i guess 
so its a easy conversion from a passenger layout to the AAR mode - mostly ripping out the passenger cabin of all extra stuff and retuning the FCS for any changes in COG 
this should have been pursued years ago
the IL78 adds a palletized drum tank system inside its cargo bay due to paucity of intrinsic fuel but it can be removed and a/c converted back to cargo hauling or send off to russia for Phalcon structural mods if we want it that way  they will however need to change engines to PS90 as they have the old engines
http://www airplane-pictures net/images     7/5616 jpg
the RAF is already gone that route in 2011
http://www defensenews com/article/2011     -Refuelers
LONDON - Airbus Military has delivered the first of 12 A330-200 airliners due to be converted into in-flight refueling planes for the British Royal Air Force by Cobham Aviation Services 
The aircraft, part of an order of 14 jets, will be modified with aerial refueling pods and other equipment at Cobham's newly refurbished facility in Bournemouth, England  The first two aircraft have already been converted by Airbus in Spain 
The multirole tanker aircraft are being provided to the RAF under a private finance initiative service deal led by Airbus parent EADS 
Seven of the planes will be operated full time by the RAF  The remainder will be available for lease in the third-party market, with the proviso that they can be returned to British military service to meet any surge in demand 
All of the aircraft, to be known as the Voyager in RAF service, will be fitted with two wing-mounted refueling pods, while half the fleet will also be fitted for, but not necessarily with, a center-line mounted unit  The refueling units are being supplied by Cobham 
The first aircraft will become operational in a passenger and freight transport role by the end of this year to start relieving pressure on the RAF's hard-pressed assets 
Despite the increasing fragility of current RAF in-flight refueling operations, the new capability is not contracted to start being used in this role until 2015 
All 14 Voyagers are scheduled to be available for RAF operations by the middle of the decade  The A330 will replace the increasingly ancient Tristar and VC-10 refuelers now in service 
Push the 6 Il-476 from refueler to AEW duty  Phalcon them up
Not sure if that is a good path to follow  For one they all should be sent to pasture in about 8 years  Then if the are to be phalconed up - the requires major structural changes  Not worth that cost 
Whatever happened ot the two new ones that were supposed ot be ordered?
the IL78 can be easily converted back to IL76 cargo hauling  only the fuel tank inside cargo bay needs removal   infact that was even mentioned in initial days as swing role fuel/cargo 
Postby Cybaru » 17 Nov 2014 07:55
I am talking about the new il78 that we ordered recently in refueling role  Sorry for the mix up  They are the same platform, that I why i used 476 or 76 to identify it 
777 carries more internal fuel than the A330  We suck!
From the KC-777 program 
http://www globalsecurity org/military/     kc-777 htm
"the KC-777 would be 209 feet long with a wingspan of 212 feet, 7 inches  That's the same size as the 777-200LR commercial jet  The KC-777 would be able to carry far more fuel, cargo and passengers than either the KC-767 or the Airbus A330 tanker  The KC-767 offers more operational flexibility, while the KC-777 would be better suited for long-range strategic missions in which more cargo needs to be delivered  The KC-777 would be able to carry more than 350,000 pounds (160,000 kilograms) of fuel and offload more than 220,000 pounds (100,000 kg) of it on a mission of 500 nautical miles (900 kilometers)  On the other hand, the KC-767 can lift off with more than 200,000 pounds (90,000 kg) of fuel and offload more than 130,000 pounds (60,000 kg) in a similar mission  The KC-777 would be able to deliver 200 percent more fuel after flying 1,000 nautical miles than older Air Force KC-135s  The KC-777 could carry up to 37 pallets of cargo, compared to the 19 pallets for the KC-767 "
Postby Cosmo_R » 18 Nov 2014 04:31
Viv S wrote: From Ajai Shukla's article -
HAL points out that, since each Avro flies barely 350 hours every year, most of them have a residual life of about 80,000 hours  In a request for information (RFI) released on August 15, HAL has proposed replacing the aircraft’s engines (Rolls Royce Dart) with “modern fuel efficient engines” 
So, the IAF's Avros have a residual life of 228 years at the current rate of usage  Ain't life grand?
At zero up time, it could reach infinity 
Relax Cy  Kc777 has no client  Usaf is going with kc767 and almost everyone else with a330 
We don't have the number of heavies and long missions of usaf else I would say convert an124 
KC777 will be extremely expensive given the demand/backlog for the 777 and the 777x  Any buyer would have to virtually pay for the increase in capacity 
I think the 767 production line is closed  so the proposed KC767 Boeing is supposed to deliver 18 by 2017  that can be managed from mothballed and cargo hauler airframes on the market 
but to meet the final order of around 180 will they not have to open the production line unless such a huge number were available on the market?
I do get the spider feel this program again will be cancelled in favour of a in-production plane like the 777X ?
I wasn't suggesting we get the KC777  All I was doing was comparing what possibly the 777 could offload compared to A330  It carries 171000 liters of fuel versus 130000 liters that the A330 carries  If we had older 777s in stock, we could have quite easily converted them to this config  The cost to us would be miniscule just the refurbishing cost vs acquiring a new type 
Singha wrote: I think the 767 production line is closed  so the proposed KC767 Boeing is supposed to deliver 18 by 2017  that can be managed from mothballed and cargo hauler airframes on the market 
The Line is open, they have a backlog of around 50 (All Fed ex), with Fed Ex placing a small order this year  The Pegasus order is for all new builds, and so will the follow on order  The only reason for any nation to buy the 767 tanker is going to be because of the ability to hard bargain with Boeing given that the commercial future of the 767 is dead  This also allows a potential buyer to purchase cheap spares from the open market, or club its logistical and inventory purchase with that of the USAF  Other than that and perhaps availability (which would be doubtful once USAF pushes through a larger order) there is really no technical reason to purchase the this tanker over the A330 which by all accounts is a superior tanker in addition to being a much much better airliner in general 
IAI is doing conversations for the 767 and its called the 767 MMTT
http://www iai co il/sip_storage/FILES/1/38471 pdf
Cybaru wrote: I wasn't suggesting we get the KC777  All I was doing was comparing what possibly the 777 could offload compared to A330  It carries 171000 liters of fuel versus 130000 liters that the A330 carries  If we had older 777s in stock, we could have quite easily converted them to this config  The cost to us would be miniscule just the refurbishing cost vs acquiring a new type 
The cost of converting a commercial airliner to a tanker, certifying it and running a full fledged test program is by no means small  There is absolutely no justification for that sort of cost over and above the capability that that A330 provides  If it were a certified and tested conversion, that would be a different matter 
Postby Kartik » 21 Nov 2014 12:27
Cybaru wrote:
Why? If the airframe can handle more flight hours, why not?
because it is a very very old airframe as is  Maintenance spares won't be available easily even as of now, then imagine how it'll be 20-30 years from now   and as things stood anyway, the HS-748 offered very little in terms of payload and range versus a C-295 class aircraft  The C-295 offers a very credible light transport, whereas the HS-748's role in the IAF was more akin to a transport trainer and for communication duties with little operational use  Having seen a dozen or so HS-748s parked at Vadodara airport all through my childhood, I never once saw one in the air  They just seemed to be stored out in the open  Upon asking an IAF transport pilot who was my friend's father, he remarked "zyaada kaam ke nahi hain yeh" 
Why would you expend more capital on what is essentially an obsolete airframe, even if theoretically it had not yet reached its service life? You'd have to re-engine it, put new avionics on board and even that wouldn't suffice for para dropping requirements  it was operationally never suitable for para dropping, which is an important mission for transport aircraft and had deficiencies in hot and high climes as well 
Unfortunately, the 748 was never meant to be a military transport  At the request of IAF, its door was enlarged to enable larger cargo items to be loaded and to allow para dropping without hitting the tail plane  However, to load a jeep in it, a 30-ft long ramp was required  The jeep would drive in and insert its front wheels into the aircraft  Then it had to be manually lifted and turned to get it in  Unloading it was just as difficult  Para dropping of troops or cargo even from the aircraft with the enlarged door was considered too dangerous with the risk of hitting the tail plane  The aircraft's performance at hot and high airfields was hopelessly inadequate  Eventually IAF acquired the tail-loading An-32s which were powered specifically for IAF's need for operating in the Himalayas 
BRF article -Avro in IAF service
Now unless you want to overcome all these through a costly, time consuming engineering re-design program, that too without access to original documents since this airplane was designed in the 1960s, there is no question of keeping them going for another 40 years  By which time the original design would be over 80 years old and with no one on earth but the IAF as an operator and HAL as the agency supporting it  Hardly a situation anyone would want 
abhik wrote: +1, Air India recently sold their entire fleet of Boeing 777s 
Only 5 of the Boeing 777-200LR, to Etihad Airways, which IMO was a bad decision  they could have reconfigured the airplanes with just 2 classes and continued to fly them to the US, non-stop 
The remaining 3 777-200LR were offered for lease but are still a part of AI's fleet since they didn't find any takers  This particular model hardly sold much and was developed for ultra-long range flights  it was the least successful 777 model and clearly AI goofed up on the configuration by going for these in place of the 300ER  The economics however didn't make too much sense for AI eventually 
there are 13 777-300ER as a part of their fleet ahd their economics is much better 
Govt  to decide tomorrow on whether to go ahead and allow the IAF to verify the technical details of the C-295 bid by Tata-Airbus instead of scrapping the tender due to single vendor situation 
The government will decide on Saturday whether to press ahead with the Rs 13,000 crore mega project for the private sector to supply 56 medium transport aircraft to the IAF despite only a single bidder, the Tata-Airbus consortium, being in the fray 
Though the defence acquisitions council (DAC) chaired by Manohar Parrikar will take the final decision, MoD sources on Tuesday said the "emerging dominant view" is that green signal should be given to the crucial project designed to promote Indian private sector's entry into the domestic aerospace arena with foreign collaboration 
"The Tata-Airbus technical and commercial bid is a credible offer submitted in a competitive environment  The other seven contenders backed out for one reason or the other," said a source 
IAF has now sought the clearance of the DAC -- the first such meeting to be chaired by Parrikar after becoming defence minister on November 10 -- to begin technical evaluation of the C-295 aircraft offered by Airbus Defence & Space and Tata Advanced Systems 
Though it has become a single-vendor situation, the DAC can approve it if it wants as per existing procurement procedures  Of the eight foreign aviation majors that got the global tender, American Boeing and Lockheed-Martin as well as Brazilian Embraer said they did not manufacture the class of aircraft being sought by IAF 
Refusing to take part in the tender, Russian Rosoboronexport said it wanted a fresh design and development project  Antonov of Ukraine wanted yet another extension of the bid submission deadline due to the ongoing conflict in Crimea  Swedish Saab said it had shut down its assembly line for such aircraft 
Then, Alenia Aermacchi was linked to Italian conglomerate Finmeccanica, which has been slapped with "a partial ban" after the infamous VVIP helicopter scandal  "All this left only the European consortium Airbus  The DAC will have to take a call since re-tendering may lead to the same situation," said the source 
Incidentally, it was the Modi government's first DAC in July -- then headed by Arun Jaitley - which revived the Avro replacement project after it was put on hold by the UPA-2 regime last year due to strong opposition from the powerful PSU lobby and ministers like Praful Patel, as reported by TOI earlier 
Apart from the critical need to encourage the private sector to enter defence production in a big way, especially in the aerospace arena where Hindustan Aeronautics enjoys a monopoly, its felt the defence PSU's order books are already overflowing with projects 
Fingers crossed  Hopefully sense will prevail 
Why was lr got? Er is capable of Dubai to sfo nonstop 
Lr is overkill unless we want Delhi to Peru  
Singha wrote: Why was lr got? Er is capable of Dubai to sfo nonstop 
they wanted it for non-stop routes from India to the west coast of the US  But with fuel prices going higher and with the lower seat count on the 777-200LR, the seat mile costs grew too high  A 3 class configuration only made matters worse  A higher density configuration with more economy class seats and just 12-15 Business class seats would have been better perhaps, especially if they didn't have very high First Class load factors 
LR and ER is better if you want to have a better payload down below for long haul  Ultimately, the best bet is going to come form the 787's that take a fewer people (so you can do the longer routes) with still a competitive CASM, and the B and F class folks will pay good money for newer aircraft 
Postby Kartik » 04 Dec 2014 12:55
Lets see if there is any forward movement on the stalled MTA project once Putin arrives in New Delhi
Major defence deals to be signed during Putin-Modi summit
In this connection, it is expected that during the summit, Russia and India may ultimately resolve several long-delayed agreements on military-technical cooperation projects between the two countries and sign them finally for their implementation  These agreements, above all, include joint Fifth Generation Fighter Aircraft (FGFA) project and joint development of Multi-role Transport Aircraft (MTA) 
A final deal on FGFA for production has been delayed because the Indian Air Force (IAF) did not approve the design and work-share  Now Russia has reportedly agreed that the jet would be a two-seat design, not a one-seater  India’s work-share would also be increased from18 percent to 25 percent, and even up to 40-50 percent in the near future, in view of the steady development of the Indian aviation industry 
Defence and SecurityAccording to the agreement, India’s stealth air-to-air missile “Astra” along with Indo-Russian BrahMos supersonic cruise missile will be mounted on the FGFA 
The preliminary design agreement on FGFA had been signed in 2010 between Indian HAL and Russian Sukhoi Design Bureau to build the jet for the use by both countries



ground_truth: The paper aims to solve nonlinear system vibration problems efficiently.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Besides the Boeing C-17, what other transport aircraft is the IAF considering for acquisition?

Read the following text and answer briefly.

Context 3:  The final design contract was to be signed in July-August 2012  But the deadline has already passed  According to the Indian media reports, under the programme, India is expected to build 200 fighter jets at the cost of $30 billion 
FGFA is not the only Indo-Russia joint project  The two countries also signed an agreement on the joint development of MTA in 2007, based on Il-214 Russian plane  The cost of the $600 million project is being equally shared by the two countries  The MTA, when developed, will have ready market for 205 aircraft - 45 for the Indian Air Force, 100 for the Russian Air Force, and 60 more for exporting to friendly countries  The international market for MTA is estimated at 390 planes  Under the agreement, thirty percent of the annual production of planes could be exported to third countries 
The MTA was expected to go in service with the Russian and Indian Air Forces in 2015  But the project faced a number of problems, delaying the development of the MTA  The project got into rough weather after India felt there was nothing much for Indian engineers and scientists to do in the design and development of the MTA 
However, all the issues related to the project were resolved with the Russians when the HAL undertook to carry out design and development of its work-share of MTA at Aircraft R&D Centre at Bangalore  Russian Ilyushin Design Bureau and the Irkut Corporation and HAL are participating in the project  The first flight is expected to take place in 2017-18 
The MTA would replace the AN- 32 aircraft being used by the IAF  It will be used for both cargo and troop transportation, para-drop and air drop of supplies, including low-altitude parachute extraction system 
BrahMos missile exports a challenging proposition
Another key deal expected to be signed during the summit, is for the development of “BrahMos mini missile” by the Indo-Russian joint venture BrahMos Aerospace which manufactures supersonic cruise missile  BrahMos’ new CEO Sudhir Mishra recently said he was hopeful that a deal to develop the mini version of the missile will be signed during Putin’s summit with Modi 
“We are hoping to sign a tripartite agreement between DRDO, NPOM lab and BrahMos Aerospace during the planned visit of Russian President in December,” Mishra said 
He said that the new missile will have a speed of 3 5 mach and carry a payload of 300 km up to a range of 290 km  In size, it will be about half of the present missile, which is around 10 metres long  The missile can be integrated with different platforms, including submarines and FGFA  It is planned to be inducted into service by 2017 
Modi-Abbott to upgrade defence ties
A new dimension:
In a first, India and Australia will also set up a mechanism to discuss “synergies in integrating defence system”, including research and development cooperation on integrating defence equipment that both countries currently purchase, for example, U S’s C-17 Globemaster III, according to officials 
^^That report about MTA is fishy  First it says that India has nothing to learn from an existing design (duh) and then says the issue has been resolved  How? Next it says India's need is 45 planes to replace over 100 An-32s  It also speculates about the export potential which may be nonexistent unless we sell it for peanuts 
This is a scam which only aims to create screwdriver jobs at HAL, stall any attempt to introduce private players into the aviation market and continue the Russian gravy train  My fear is the Russkies have our testiments in a firm grip with key components of Brahmos, nuke subs, Su30mki etc and we may be jerked around 
(They need to be more definitive about "MTA" - Multirole vs  Medium)
The Indians had not selected an engine (among other things) for the MTA with the Russians  Perhaps that has been resolved now 
On export numbers, IIRC, it was the responsibility of Rosoboronexport  ?????
Kartik wrote: The MTA would replace the AN- 32 aircraft being used by the IAF  It will be used for both cargo and troop transportation, para-drop and air drop of supplies, including low-altitude parachute extraction system 
Pardon my ignorance  The Avro and An-32 have different upgrade paths  How are the replacements for these venerable aircraft different in terms of use cases in IAF  Cannot one platform replace both these types? (Either MTA or C-295)
In this case, I feel they should have just gone with screwdrivergiri (production tech) and got to market first  There is no jet-powered transporter in this range! Just license produce the IL-214 with the PD-14M, glass cockpit and a state-of-the-art COTS avionics computer 
In my view, it was a low hanging fruit, which they completely messed up! They could have learnt on how to adopt the plane for the 160-200 seater 
indranilroy wrote: They could have learnt on how to adopt the plane for the 160-200 seater 
Yes, the MTA project should fold the Avro, An-32 and the regional transport role and become a conversion project rather a development one  The driving numbers will come from the regional transport (thousands in India itself) rather than the Avro or medium transport roles (max 300 between them)  This changes the ball game and introduces all kinds of possibilities  But I'm pretty sure that the Il-214/MTA is not the way to go because it will take a decade or more to arrive  A good possibility was another Antonov, the An-148 but it has some mechanical glitches apparently besides being bogged down in the Ukraine mess  Maybe the Russians can "relocate" the aircraft to Russia? The other possibility is the BAe-146 which is ironically another Avro  We should remember that both the HS-748 "Avro" and An-32 were regional airliners that were converted to military use, not the other way around  HAL or a private firm will pick up a lot of experience in the conversion process itself 
The Sukhoi Superjet is already in production/orders,with over 100+ for Russian and intl  customers  It is ideal for regional transport,perfect for flights to smaller Tier-2/3 cities from metros  If we really want a regional jet this is the fastest way toi go,we can set up a manufacturing unti here for the same at an HAL unit 
Postby shaun » 05 Dec 2014 15:24
Its an international projects, with components outsourced from different international vendors   Over 30 foreign partnership companies are involved in the project and partly financed by Italy 
Sukhoi is good for passenger use but wont be suitable for military, rough field use  The shoulder wing jets like the An-148 have slower speeds and better ground clearance  The Bae-146 was usedby Druk Air in Bhutan so it should do OK in the ALGs  If we don't fold our requirements then we should go with something like the Superjet which we will at least be able to make in India and also modify to stretched versions  Unless we have a clear path to operational clearance within 10 yrs for the RTA project vetted by our top industrial houses, it is pie-in-the-sky and should be dropped  The RTA will be big enough to keep 2-3 factories humming and leapfrog our capabilities  If we don't get our act together almost immediately, we will miss the boat, just like our trainer fiascos 
I don't think Superjet fits into our scheme of things  We should think as a country and see to it that our programs don't trample on each other 
First, the more certain ones:
1  Mahindras NM5 and Airvans can care of the low-cost but sturdy 5,8,10 and 18-seater section 
2  Saras had such great potential for being the high performance 14-18 seater  But I have almost given up on it  This section will most probably be taken up by the Tata-built Do-228 NG 
3  We should standardize the C-295 as the Avro/An-32 replacement and create a 70-80 seater variant out of it 
And then the more wishful ones:
1  If the RTA is going to be a jet, then make it a 100-130 seater  I don't expect the first prototype to take the sky before 2025  I feel it is too big of a jump where we don't even have a base  With LCA, at least we were at least license producing other fighters 
4  Building on the IL-214, the MTA was on a more sure footing  But, I can't see how the first prototype can to take to the sky before 2019(more than 10 years since MTAL was formed)! If the transport plane materializes, then one can imagine making a civilian 150-200 seater version of the same  But this program needs a push  Will Putin's visit be able to galvanize this into the next symbol of Indo-Russian cooperation  Probably not!
Postby GeorgeWelch » 12 Dec 2014 23:39
http://www ctvnews ca/canada/defence-de     -1 2144472
The Defence Department intends to purchase a Boeing C-17 Globemaster III, a large military transport plane that comes with a price tag of just under $200 million, CTV News has learned
It's difficult to get a good count, but by some sources, if this and the 4 Australia planes go through, there will only be 5 left 
X-Posting from FGFA thread 
Despite Putin’s visit, two pacts on military aircraft still in doldrums
President Vladimir Putin may have come and gone but stalemate largely persists over two key long-pending India-Russian defence projects, the fifth-generation fighter aircraft (FGFA) and military multirole transport aircraft (MTA) 
The deadlock over the MTA, which were initially envisaged to gradually replace IAF's ageing fleet of the medium-lift AN-32 aircraft, seems to be much more serious  India now wants to ascertain the cost viability of the twin-engine transport aircraft in comparison to similar planes available in the market 
There are also questions about the MTA's "predicted timelines for delivery" as well as its failure to meet the high-altitude requirements, which need to be answered before India even thinks of inking the full-scale contract for the project, said sources 
Postby Gyan » 13 Dec 2014 12:29
indranilroy wrote: I don't think Superjet fits into our scheme of things  We should think as a country and see to it that our programs don't trample on each other 
1  Mahindras NM5 and Airvans can care of the low-cost but sturdy 5,8,10 and 18-seater section  Righto
2  Saras had such great potential for being the high performance 14-18 seater  But I have almost given up on it  This section will most probably be taken up by the Tata-built Do-228 NG  We need future extended variants of presurrized aircraft like 30 seater Saras and say 30 seater unpressurized Do-328 NG 
3  We should standardize the C-295 as the Avro/An-32 replacement and create a Civilian turboprop pressurized cabin 70-80 seater variant out of it 
1  If the RTA is going to be a jet, then make it a 100-130 seater  Agreeeeeed I don't expect the first prototype to take the sky before 2025  I feel it is too big of a jump where we don't even have a base  With LCA, at least we were at least license producing other fighters  Though I think that we should participate in Russian MS-21 and also the wide body follow on 
4  Building on the IL-214, the MTA was on a more sure footing  But, I can't see how the first prototype can to take to the sky before 2019(more than 10 years since MTAL was formed)! If the transport plane materializes, then one can imagine making a civilian 150-200 seater version of the same  Though I think that we should participate in Russian MS-21 and also the wide body follow on  But this program needs a push  Will Putin's visit be able to galvanize this into the next symbol of Indo-Russian cooperation  Probably not!
Absence of any specifics on Sukhoi Superjet, MS-21, Wide body aircraft, Mi-38, MRTA, FGFA, even after Putin visit is very disappointing 
FlightGlobal- Boeing sitting on 8 unsold C-17s
By: Dan ParsonsWashington DCSource: Flightglobal com
This story is sourced from Flightglobal com 12 hours agoBoeing has sold two more C-17 transports to an undisclosed customer, but it will likely end the year with eight unsold white tails 
There are 10 Boeing C-17 airlifters in various stages of assembly at the company’s Long Beach, California, production facility 
Two of the aircraft are spoken for by an unnamed customer, Boeing says  Boeing is trying to sell off the other eight white tails, which will be the last produced before the factory is shuttered sometime in the summer of 2015 
The 279th – and final – C-17 fuselage will be mated to its wings in January or February, programme spokeswoman Tiffany Pitts tells Flightglobal  The operation is California’s last remaining aircraft production line and the lone widebody military aircraft production line in the USA, according to Boeing 
At least two countries – Australia and Canada – have publicly announced an intention to purchase a C-17, though neither factor into Boeing’s future planning, Pitts says  Until contracts are finalised, the number available remains eight, she says  The Royal Canadian Air Force already has four C-17As, according to Flightglobal’s World Air Forces 2014 directory 
Canadian news outlets reported earlier in December that the air force would buy one C-17 with money left over at the end of 2015 
Australia is further along with its bid to purchase C-17s  The US Defense Security Cooperation Agency in November announced Australia was approved to buy up to four C-17s and support equipment for $1 6 billion 
Boeing has plans to store any unsold C-17s following closure of its production line, Pitts says 
“I’m hoping they all will be sold before then, but we’ve had plans in place for a very long time to store and maintain the aircraft if that doesn’t happen,” she says 
the IAF will need to factor in the demand vs availability of C-17s and stock up with a follow-on order quickly  The initial plan to have 16 C-17s may not fructify, considering that there are just 8 left now, with Australia having announced plans to buy 4 more 
why are they closing the line if it has demands ???
Real estate sales tactics probably  Buy now last 8 3bhk flats Saar 
krishnan wrote: why are they closing the line if it has demands ???
It requires 3 years lead time to order raw materials/parts from all of its sub-vendors  All current firm orders have been fulfilled, and no new orders have come  Anticipating a need for a few more aircrafts, they produced 10 extra (self-funded) units before production winded down  Bottom line is they don't make money keeping an idle plant around with all its employees and infrastructure  At most what they will likely do is keep a limited infrastructure around for a few more years in case a bunch of new orders come  They can then see if it makes business sense to re-open the plant 
Postby Aditya_V » 17 Dec 2014 12:19
Wish this can be brought to the notice of Journos/ Poster when slamming LCA/ Arjun and other indigenous projects  If there are no orders there will be no efficiency 
Dec 10, 2014 :: Russia launches Il-76MDM upgrade programme
Russia's Ilyushin has started to upgrade a first Russian Air Force (VVS) Ilyushin Il-76MD 'Candid' military transport aircraft to Il-76MDM standard, company officials have told IHS Jane's   The main features of the upgrade include refurbished engines and upgraded avionics 
The modernisation is being conducted at the VVS's Military Transport Aviation (MTA) maintenance facility based at the Ilyushin division in Zhukovsky city near Moscow 
A senior Ilyushin official told IHS Jane's that the upgrade of the first aircraft will be finished in 18 months  Subsequent aircraft will take less time to complete the process, however  When the modernisation is finished the initial Il-76MDM will undergo state trials  The upgrade process for subsequent aircraft will begin when the trials programme is completed 
IHS Jane's was previously told by a VVS senior official that the modernisation of 41 MTA Il-76MDs is planned by 2020  While the Il-76MDM upgrade retains the old D-30KP engine (compared with the PS-90A engine equipping the new Il-76MD-90A/Il-476), the modernisation effort should match the aircraft's onboard electronics with those of the newbuild Il-76MD-90A  This and other efforts mean the cost of modernising the Il-76MD to Il-76MDM is only a third of that of a newbuild Il-76MD-90A 
The existing D-30KP engines are to be enhanced to increase their service life  The overall aircraft's service life will be extended by 15 years 
The upgrade works are planned to be conducted in an aviation repair factory or in the MTA's aircraft maintenance facility  As a result, the Ulyanovsk-based Aviastar-SP plant, which is building the Il-76MD-90A, is not involved in the Il-76MD to Il-76MDM modernisation programme 
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ground_truth: The IAF is considering the acquisition of the Airbus A330 MRTT (Multi-Role Tanker Transport) besides the Boeing C-17.