Series Of Poles Research Articles

SUSY partners and S-matrix poles of the one-dimensional Rosen–Morse II potential

Among the list of one-dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen–Morse II potential. The first objective is to analyse the scattering matrix corresponding to this potential. We show that it includes a series of poles corresponding to the types of redundant poles or anti-bound poles. In some cases, there are even bound states and this depends on the values of given parameters. Then, we perform different supersymmetric transformations on the original Hamiltonian using either the ground state (for those situations where there are bound states) wave functions, or other solutions that come from anti-bound states or redundant states. We study the properties of these transformations.

Large charges on the Wilson loop in mathcal{N} = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar mathcal{N} = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the ’t Hooft coupling λ are sent to infinity with the ratio J/ sqrt{lambda } fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green’s functions on the worldsheet. We derive a representation of the Green’s functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green’s functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

Asymptotic Approximations of Apostol-Genocchi Numbers and Polynomials

Asymptotic approximations of the Apostol-Genocchi numbers andpolynomials are derived using Fourier series and ordering of poles ofthe generating function. Asymptotic formulas for the Apostol-Eulernumbers and polynomials are obtained as consequence. Asymptoticformulas for special cases which include the Genocchi numbers andpolynomials are also explicitly stated.

Cercetări arheologice preventive în județul Giurgiu

The implementation works for the BRUA project imposed the making of an archaeological evaluation for the route taken by the natural gas line and, implicitly, depending on the situations, of archaeological rescue excavations. In the following, we will focus on specific results from the BRUA route area in the center of Giurgiu country – Mirău (Stoenești commune). The stratigraphy of the site is predominantly natural. All stratigraphic interventions (a very probable diagnostic survey – Cx2, two medieval pits – Cx1 and Cx3, also a series of wooden poles that we attribute to some fencing works made during the 70’s and 80’s of the twentieth century) affect a level of ancient soil and are, stratigraphicaly, covered by the level of the current one, ploughed. The pottery and archaeozoological remains are the only materials discovered and recovered. Even if the inventory of Cx3 is weaker from a quantitative point of view, the characteristics of both categories are unitary, proving both contemporaneity and identical manifestations and behaviors.

A rapid response calculation method for symmetrical floating structures based on state–space model solving in hybrid time-Laplace domain

The article focuses on proposing a new hybrid time-Laplace domain response calculation method for symmetrical floating structures by solving Cummins equation, which is depending on the state–space model identified from transfer function. Different from a time or frequency domain method, the proposed approach estimates the state–space model of a floating structure system from the transfer function in the Laplace domain and calculates the response by considering the exciting forces as an input of the state–space model. Implementing complex exponential decomposition to the retardation functions, the retardation functions in the Laplace domain are expressed using a series of poles and the corresponding residues, which avoids the numerical integral of the convolution terms in the Cummins equation and greatly improves the computational efficiency during the process of a dynamic response analysis. Three examples are applied to investigate the validity of the proposed method. The first is a simple single degree of freedom mathematical model excited by an irregular wave. Studies have shown that the response calculated by the proposed method matches well with that of a traditional Newmark-β method. Meanwhile, this approach is insensitive to the interval time of the calculation and consumes less calculation time, which means that the proposed method has higher precision and computational efficiency. The last two examples are a spar-type offshore wind turbine and a semi-submersible platform model (SEMI) in SESAM, which extend the proposed method to solve the response estimation problem of marine structures. The results of the spar-type floating structure show that the estimated responses when using the proposed method are in good agreement with the results of the traditional time domain method. By studying the response calculation of SEMI, the following conclusions can be obtained: (1) the estimated responses match well with the traditional time domain method and WASIM code of SESAM, and (2) the calculation time of the new approach is reduced significantly compared with the Newmark-β method especially under a long simulation time.

Matter Chern Simons theories in a background magnetic field

We study large N 2+1 dimensional fermions in the fundamental representation of an SU(N)k Chern Simons gauge group in the presence of a uniform background magnetic field for the U (1) global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t’ Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t’Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large N fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.

Pole representation of the dislocation segment generalized susceptibility diagonal matrix elements

Diagonal elements of the generalized susceptibility matrix in the form of expansion in a series of poles are presented. Screw dislocation segment considered. The calculation of the series coefficients for different values of the dislocation segment normalized lengths has been carried out. The real and imaginary parts of the diagonal matrix elements are calculated. The results of the calculations are presented in the figures. The figures show a good agreement of the diagonal matrix elements direct calculation results with the calculation carried out in this work.

Experimental and theoretical investigation of transient edge waves excited by a piezoelectric transducer bonded to the edge of a thick elastic plate

The paper presents experimental and theoretical studies of wave phenomena accompanying transient edge waves (EW) excitation by a piezoelectric transducer attached at the edge of an elastic plate. Theoretical investigations are conducted on the basis of the three-dimensional elastodynamic theory. The boundary value problem describing non-stationary wave motion is solved with the use of integral transforms and the modal expansion technique. The asymptotic analysis with the wavenumber considered as a small or large parameter is applied to the three-dimensional problem. In the first case (long-wave vibrations) the approximate formulae for the fundamental EW's pole and corresponding residue are derived. These relations take into account the influence of the transverse shear load arising because of coupling between long-wave integral and Saint-Venant's boundary layer. In the second case (short-wave vibrations) an infinite series of poles corresponding to higher order EW is revealed. Results of numerical investigations of EW dispersion properties and waveforms are presented and used for an analysis of experimental data acquired with the use of Laser Doppler vibrometry. It is shown that the contribution of EW is predominant in the wave-field excited by the load under consideration. A good agreement between theoretical predictions and measurements is demonstrated. For the calculation of transient wave-field three different models of actuator-plate interaction are developed: in the low-frequency range the interaction is considered as a static one, while the lower and higher eigenfrequencies of the actuator are taken into account in the medium- and high-frequency ranges respectively. For the low-frequency range, an explicit analytical formula is derived for calculation of EW contribution into the transient wave-field. In the high-frequency range, the excitation of the first higher order EW is predicted by the numerical solution and observed experimentally.

Mellin amplitudes for fermionic conformal correlators

We define Mellin amplitudes for the fermion-scalar four point function and the fermion four point function. The Mellin amplitude thus defined has multiple components each associated with a tensor structure. In the case of three spacetime dimensions, we explicitly show that each component factorizes on dynamical poles onto components of the Mellin amplitudes for the corresponding three point functions. The novelty here is that for a given exchanged primary, each component of the Mellin amplitude may in general have more than one series of poles. We present a few examples of Mellin amplitudes for tree-level Witten diagrams and tree-level conformal Feynman integrals with fermionic legs, which illustrate the general properties.

Spectrum response estimation for deep-water floating platforms via retardation function representation

The key concept of spectrum response estimation with commercial software, such as the SESAM software tool, typically includes two main steps: finding a suitable loading spectrum and computing the response amplitude operators (RAOs) subjected to a frequency-specified wave component. In this paper, we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions. Based on estimated added mass and damping matrices of the structure, we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain. Then, we estimate the power density corresponding to each frequency component using the improved periodogram method. The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping. To validate the proposed method, we use a numerical semi-submerged pontoon from the SESAM. The numerical results show that the responses of the proposed method match well with those obtained from the traditional method. Furthermore, the estimated spectrum also matches well, which indicates its potential application to deep-water floating structures.

Loops in AdS from conformal field theory

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the mathcal{N} = 4 super-Yang-Mills theory.

Frequency response estimation of floating structures by representation of retardation functions with complex exponentials

This article aims at proposing a new frequency-domain response estimation method for floating structures by dealing with fluid memory effects from the view point of signal decomposition. One development is that the convolution terms are decomposed and replaced by a series of poles and corresponding residues in the Laplace domain, based on the estimated added mass and damping matrices of the structure. The advantage of the proposed method is that the frequency-dependent motion equations in the time domain can then be transformed to the Laplace domain without requiring Laplace-domain expressions of the added mass and damping. The second is that exciting wave forces are not limited to harmonic components, and each component can be purely harmonic, damped harmonic or purely damped exponential. Therefore, the problem of frequency leakage caused by using the Fourier transform can be avoided, which also means estimations of frequency-domain responses can be improved accordingly. Four examples are used to investigate the performance of the proposed method. The first is a simple retardation function, which is based on a purely analytical relationship, and it satisfies all the properties of the convolution terms in the time and frequency domains simultaneously, demonstrating the correctness of using the complex exponentials to represent the retardation functions. The second is a single degree of freedom (SDOF) mathematical model subjected to a synthesized exciting wave force. The numerical results show that the frequency response function (FRF) estimated using this approach matches well with that of the traditional method. For exciting wave forces, the proposed method can yield a better frequency-domain estimation because the proposed method is not limited to a frequency resolution. To extend the proposed method to multiple DOF systems and address applications to marine structures, a semi-submersible (SEMI) and a FPSO model in SESAM is employed respectively. One can draw the following conclusions from the numerical results: (1) the FRFs of the floating structures can be obtained by replacing the convolution terms with a series of poles and corresponding residues in the Laplace domain, and they match well with those from the traditional method; and (2) the new method can provide almost identical response estimates as those of the traditional frequency-domain method when the exciting wave forces are truly composed of purely harmonic components.

Fluctuating-bias controlled electron transport in molecular junctions

We consider the problem of transport through a multiterminal molecular junction in the presence of a stochastic bias, which can also be used to describe transport through fluctuating molecular energy levels. To describe these effects, we first make a simple extension of our previous work [Phys. Rev. B 91, 125433 (2015)] to show that the problem of tunneling through noisy energy levels can be mapped onto the problem of a noisy driving bias, which appears in the Kadanoff-Baym equations for this system in an analogous manner to the driving term in the Langevin equation for a classical circuit. This formalism uses the nonequilibrium Green's function method to obtain analytically closed formulas for transport quantities within the wide-band limit approximation for an arbitrary time-dependent bias and it is automatically partition free. We obtain exact closed formulas for both the colored and white noise-averaged current at all times. In the long-time limit, these formulas possess a Landauer-B\uttiker--type structure which enables the extraction of an effective transmission coefficient for the transport. Expanding the Fermi function into a series of simple poles, we find an exact formal relation between the parameters which characterize the bias fluctuations and the poles of the Fermi function. This enables us to describe the effect of the temperature and the strength of the fluctuations on the averaged current which we interpret as a quantum analog to the classical fluctuation-dissipation theorem. We use these results to convincingly refute some recent results on the multistability of the current through a fluctuating level, simultaneously verifying that our formalism satisfies some well-known theorems on the asymptotic current. Finally, we present numerical results for the current through a molecular chain which demonstrate a transition from nonlinear to linear $I\text{\ensuremath{-}}V$ characteristics as the strength of fluctuations is increased, as well as a stochastic resonance effect in the conductance of this system.

Dynamic analysis of offshore structures with non-zero initial conditions in the frequency domain

The state of non-zero conditions is typically treated as fact when considering the dynamic analysis of offshore structures. This article extends a newly proposed method [1] to manage the non-zero initial conditions of offshore structures in the frequency domain, including new studies on original environmental loads reconstruction, response comparisons with the commercial software ANSYS, and a demonstration using an experimental cantilever beam. The original environmental loads, such as waves, currents, and winds, that act on a structure are decomposed into multiple complex exponential components are represented by a series of poles and corresponding residues. Counter to the traditional frequency-domain method, the non-zero initial conditions of offshore structures could be solved in the frequency domain. Compared with reference [1], an improvement reported in this article is that practical issues, including the choice of model order and central-processing-unit (CPU) time consumption, are further studied when applying this new method to offshore structures. To investigate the feasibility of the representation of initial environmental loads by their poles and corresponding residues, a measured random wave force collected from a column experiment at the Lab of Ocean University of China is used, decomposed, reconstructed and then compared with the original wave force; then, a numerical offshore platform is used to study the performance of the proposed method in detail. The numerical results of this study indicate that (1) a short duration of environmental loads are required to obtain their constitutive poles and residues, which implies good computational efficiency; and (2) the proposed method has a similar computational efficiency to traditional methods due to the use of the inverse Fourier transform technique. To better understand the performance, of time consumption and accuracy of the proposed method, the commercial software ANSYS is used to determine responses from the time history analysis. Comparisons of the results between the proposed method and the ANSYS results demonstrate that the proposed method produces high accuracies that are similar to the time-domain method and good computational efficiencies, which are similar to the traditional frequency-domain method. Finally, a steel cantilever beam is used to demonstrate the proposed method.

Sideband mixing in intense laser backgrounds

The electron propagator in a laser background has been shown to be made up of a series of sideband poles. In this paper we study this decomposition by analysing the impact on the sidebands of the residual gauge freedom in the Volkov solution. We show that these gauge transformations do not alter the location of the poles although the wave function renormalisation is gauge dependent. Our identification of the propagator from the diagonal part of the two-point function in the laser background is maintained but we show that the sideband structures mix under residual gauge transformations.

Partition functions in even dimensional AdS via quasinormal mode methods

In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension $\Delta$) in even-dimensional AdS$_{d+1}$ space, using the quasinormal mode method developed in arXiv:0908.2657 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane $H_2$, we find a series of zero modes for negative real values of $\Delta$ whose presence indicates a series of poles in the one-loop partition function $Z(\Delta)$ in the $\Delta$ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in arXiv:0908.2657. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. in arXiv:1103.3627 and Banerjee et al. in arXiv:1005.3044. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS$_2$ black hole. They are also interpretable as matrix elements of the discrete series representations of $SO(2,1)$ in the space of smooth functions on $S^1$. We generalize our results to general even dimensional AdS$_{2n}$, again finding a series of zero modes which are related to discrete series representations of $SO(2n,1)$, the motion group of $H_{2n}$.

Local cubic vertex functions for three massless higher even spin fields on spaces [formula omitted]: An analytic approach

Local cubic vertex functions of three higher even spin fields on AdSD are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter ϵ. In fact N-point Green functions of such conserved currents produce a series of poles up to the order N−1. The method works for even D and maintains covariance at any step. The resulting formula is quite concise.

Scattering in plane-wave backgrounds: Infrared effects and pole structure

We consider two aspects of scattering in strong plane wave backgrounds. First, we show that the infra-red divergences in elastic scattering depend on the structure of the background, but can be removed using the usual Bloch-Nordsieck approach. Second, we analyse the infinite series of shifted-mass-shell poles in the particle (Volkov) propagator using lightfront quantisation. The complete series of poles is shown to describe a single, on-shell, propagating particle.

Strategy for designing broadband epsilon-near-zero metamaterials

A strategy is proposed to design a certain kind of metamaterial with near-zero electric permittivity over a broad frequency band, i.e., the broadband epsilon-near-zero (ENZ) metamaterials. Based on the Bergman–Milton spectral representation of the effective permittivity, the design is first carried out in the dimensionless spectral space, where the effective permittivity of the ENZ metamaterials is mathematically determined by a series of zeros and poles (singularities), which can be easily arranged as required by the operating band. Then, through a fast inverse algorithm, the mathematical structures of the ENZ metamaterials can be transformed back to their physical structures, which can be put into practical applications. The effective permittivity of the designed ENZ metamaterials is examined, and the distribution of the electric field inside the designed ENZ metamaterials is also explored, in order to reveal the physical reason behind the broadband ENZ phenomenon.

Improved Multipole Broadband Time-Domain Impedance Boundary Condition

ACOUSTIC liners are widely used in industry for noise reduction. They are indispensable noise-suppression devices for jet engines. Acoustic liners are effective over a wide band of frequencies. To account for such characteristics, broadband impedance models are used for time-domain computation. The acoustic impedance of a surface, Z ! , is originally defined in the frequency domain. Problems involving noise propagation over impedance surfaces may be solved in the time domain. Time-domain methods have obvious advantages over frequency-domain methods for broadband and nonlinear problems. However, because an impedance boundary condition is set up for use in the frequency domain, an equivalent time-domain impedance boundary condition is needed. Mathematically, the time-domain equivalent may be derived by taking its inverse Fourier transform. For the equivalent time-domain impedance condition to be physical, the impedance function must be causal, real, and passive [1]. In general, the inverse Fourier transform of a frequency-domain impedance boundary condition would lead to a convolution integral. Computation of the convolution integral is time consuming. However, if the impedance can be represented by a sum of certain special functions, the evaluation of the convolution may be carried out in a simple systematic manner. Tam and Auriault [2] introduced a three-parameter time-domain impedancemodel. Thismodel can provide accurate representation of liner impedance for single discrete frequency problems. But the three-parameter model cannot offer a general representation of liner impedance over awide band of frequencies. Rienstra [1] proposed an extended Helmholtz resonator model. The free parameters of the model are the geometrical dimensions of the resonator. The impedance of the model is derived by the response of the Helmholtz resonator to periodic acoustic input. A comparison study by Richter et al. [3] indicated that a numerical instability could occur in some cases. A filtering technique has to be applied for avoiding this problem. Recently, Reymen et al. [4] developed a new and efficient time-domain impedance boundary condition based on the use of recursive convolution. The key to their method is the representation of the impedance by a series of simple poles in the complex plane. For the method to work efficiently, the value of the function in the convolution integral within a time step must be approximated by a linear or quadratic function. This impedance model has been proven to be physical, causal, and real. The primary objective of this paper is to develop an improved multipole broadband time-domain impedance boundary condition. A secondary objective is to derive an analytical solution for problems involving damping of broadband acoustic input by liners with broadband impedance characteristics. These solutions may serve for benchmarking numerical computations involving broadband sound. This paper is organized as follows. Section II discusses the improved multipole broadband impedance model. The implementation of the time-domain impedance boundary condition is presented in Sec. III. Section IV presents analytical solutions of twodimensional problems with broadband incident acoustic waves. These solutions are then used to validate numerical results with a liner having broadband impedance properties. Section IV concludes this work.