Incomplete Hankel and Modified Bessel Functions: A Class of Special Functions for Electromagnetics

Cicchetti, R.; Faraone, A.

doi:10.1109/tap.2004.835269

Cited by 33 publications

(50 citation statements)

References 14 publications

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“…These expressions can be written in terms of the incomplete modified Bessel functions [114] but this proves to be an unilluminating exercise. However, it is possible that slightly simpler expressions can be found under appropriate approximations such as the assumption that the neutrinos are produced either ultra-relativistically or non-relativistically over the duration of production.…”

Section: Appendix A: Quantum Kinetic Equationmentioning

confidence: 99%

The case for mixed dark matter from sterile neutrinos

Lello

Boyanovsky

2016

J. Cosmol. Astropart. Phys.

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Sterile neutrinos are SU (2) singlets that mix with active neutrinos via a mass matrix, its diagonalization leads to mass eigenstates that couple via standard model vertices. We study the cosmological production of heavy neutrinos via standard model charged and neutral current vertices under a minimal set of assumptions: i) the mass basis contains a hierarchy of heavy neutrinos, ii) these have very small mixing angles with the active (flavor) neutrinos, iii) standard model particles, including light (active-like) neutrinos are in thermal equilibrium. If kinematically allowed, the same weak interaction processes that produce active-like neutrinos also produce the heavier species. We introduce the quantum kinetic equations that describe their production, freeze out and decay and discuss the various processes that lead to their production in a wide range of temperatures assessing their feasibility as dark matter candidates. The final distribution function at freeze-out is a mixture of the result of the various production processes. We identify processes in which finite temperature collective excitations may lead to the production of the heavy species. As a specific example, we consider the production of heavy neutrinos in the mass range M h 140 MeV from pion decay shortly after the QCD crossover including finite temperature corrections to the pion form factors and mass. We consider the different decay channels that allow for the production of heavy neutrinos showing that their frozen distribution functions exhibit effects from "kinematic entanglement" and argue for their viability as mixed dark matter candidates. We discuss abundance, phase space density and stability constraints and argue that heavy neutrinos with lifetime τ > 1/H 0 freeze out of local thermal equilibrium, and conjecture that those with lifetimes τ ≪ 1/H 0 may undergo cascade decay into lighter DM candidates and/or inject non-LTE neutrinos into the cosmic neutrino background. A comparison is made between production through pion decays with the production of non-resonant production via active-sterile mixing.

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Section: Appendix A: Quantum Kinetic Equationmentioning

confidence: 99%

The case for mixed dark matter from sterile neutrinos

Lello

Boyanovsky

2016

J. Cosmol. Astropart. Phys.

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“…In this way, the transient electromagnetic field radiated outside S h can be evaluated, without any limitation involving the time, by using Equations (1) and (2) in combination with the analytical closed-form expression (14) of the general IMSBF. On the other hand, the electromagnetic field behavior in the frequency domain can be readily derived by application of the unilateral Laplace transform operator L t {·} to both sides of (1) and (2). So, making judicious use of the time scaling and frequency shifting properties of L t {·} yields, after some algebra, the following vector representation:…”

Section: Numerical Applicationmentioning

confidence: 99%

“…They are widely adopted in various scientific fields, such as mathematical physics and electromagnetics. Recently, incomplete Hankel functions have been introduced in [2] to determine the electromagnetic field distribution associated with progressive and evanescent wave contributions excited in truncated cylindrical structures. On the other hand, as shown in [3], the transient electromagnetic field radiated in Fraunhofer region by a general antenna can be expressed as a non-uniform spherical wave expansion in terms of incomplete modified spherical Bessel functions (IMSBFs) [4].…”

Section: Introductionmentioning

confidence: 99%

Incomplete Bessel Polynomials: A New Class of Special Polynomials for Electromagnetics

Caratelli¹,

Babur²,

Shibelgut³

et al. 2015

PIER M

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Abstract-A new class of incomplete Bessel polynomials is introduced, and its application to the solution of electromagnetic problems regarding transient wave radiation phenomena in truncated spherical structures is discussed. The general definition and main analytical properties of said special functions are provided. The definition is such that the interrelationships between the incomplete polynomials parallel, as far as it is feasible, those for canonical Bessel polynomials.

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“…Details about the properties of k + ν (a, b) can be found in [16]. 2) MGF of the end-to-end SNR: Substituting the CCDF of γ c , which is presented in (7), into (2), the MGF of γ c can be obtained as shown in (10), in which…”

Section: Statistics Of Snr and Performance Analysismentioning

confidence: 99%

Low-Complexity Combining Schemes in Dual-Hop AF Relaying Systems

Gaaloul

Radaydeh

Alouini

2011

2011 IEEE 73rd Vehicular Technology Conference (VTC Spring)

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Abstract-This paper investigates the performance of different low-complexity combining schemes in the context of dual-hop amplify-and-forward relaying networks. It is assumed that the relay uses single transmit (receive) antenna due to space limitation and to reduce the processing complexity. On the other hand, the transmitter and the receiver use antenna arrays to improve the overall diversity gain. However, this gain is achieved at the expense of increased processing complexity and power consumption. To this end, some combining schemes aiming at reducing the processing complexity and decreasing the number of active receive channels are investigated. Through the analysis, new formulas for the end-to-end signal-to-noise ratio statistics in slowly varying and frequency flat Rayleigh fading channels are derived, which are then used to present some performance measures. Numerical and simulation results are presented to clarify the trade-off between the achieved diversity gain and the receive processing complexity. I. INTRODUCTIONIt is well-known that relaying techniques can improve the spectral efficiency of wireless systems and mitigate the severe effect of large-scale fading. Moreover, the use of multiple antennas schemes in relaying networks have also shown further improvements in system capacity and communication reliability [1], [2]. Various diversity combining schemes have been studied in the context of multiple-antenna relaying systems [3]- [9]. However, an important aspect of employing diversity methods in such scenarios is to maintain as low processing complexity and power consumption as possible while satisfying a target performance level. This paper investigates different combining schemes with reduced processing complexity for dual-hop relaying networks employing the simple amplify-and-forward (AF) relaying protocol. The performance of this protocol can be improved when the channel state information (CSI) of the preceding hop is available to control the relaying gain, and it may be useful when simple relaying is required and/or when the transmitted data is time-sensitive [10], [11].For the dual-hop AF relaying system under consideration, the relaying station is assumed to use single antenna in each direction due to space limitation and processing power constraints. On the other hand, different low-complexity configurations are investigated assuming uncorrelated antenna arrays at the transmitter and the receiver. Specifically, the scheme proposed in [12] is adopted to considerably reduce the power drain from the battery while satisfying a target performance.

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Incomplete Hankel and Modified Bessel Functions: A Class of Special Functions for Electromagnetics

Cited by 33 publications

References 14 publications

The case for mixed dark matter from sterile neutrinos

The case for mixed dark matter from sterile neutrinos

Incomplete Bessel Polynomials: A New Class of Special Polynomials for Electromagnetics

Low-Complexity Combining Schemes in Dual-Hop AF Relaying Systems

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