Gamma Ray Burst Prompt Emission Variability in Synchrotron and Synchrotron Self-Compton Lightcurves

Gamma Ray Burst prompt emission is believed to originate from electrons accelerated in a highly relativistic outflow. "Internal shocks" due to collisions between shells ejected by the central engine is a leading candidate for electron acceleration. While synchrotron radiation is generally invoked to interpret prompt gamma-ray emission within the internal shock model, synchrotron self-Compton (SSC) is also considered as a possible candidate of radiation mechanism. In this case, one would expect a synchrotron emission component at low energies, and the naked-eye GRB 080319B has been considered as such an example. In the view that the gamma-ray lightcurve of GRB 080319B is much more variable than its optical counterpart, in this paper we study the relative variability between the synchrotron and SSC components. We develop a "top-down" formalism by using observed quantities to infer physical parameters, and subsequently to study the temporal structure of synchrotron and SSC components of a GRB. We complement the formalism with a "bottom-up" approach where the synchrotron and SSC lightcurves are calculated through a Monte-Carlo simulations of the internal shock model. Both approaches lead to the same conclusion. Small variations in the synchrotron lightcurve can be only moderately amplified in the SSC lightcurve. The SSC model therefore cannot adequately interpret the gamma-ray emission properties of GRB 080319B.Comment: 13 pages, 4 figures, accepted for publication in MNRA

A Rate-Splitting Based Bound-Approaching Transmission Scheme for the Two-User Symmetric Gaussian Interference Channel with Common Messages

This paper is concerned with a rate-splitting based transmission strategy for the two-user symmetric Gaussian interference channel that contains common messages only. Each transmitter encodes its common message into multiple layers by multiple codebooks that drawn from one separate code book, and transmits the superposition of the messages corresponding to these layers; each receiver decodes the messages from all layers of the two users successively. Two schemes are proposed for decoding order and optimal power allocation among layers respectively. With the proposed decoding order scheme, the sum-rate can be increased by rate-splitting, especially at the optimal number of rate-splitting, using average power allocation in moderate and weak interference regime. With the two proposed schemes at the receiver and the transmitter respectively, the sum-rate achieves the inner bound of HK without time-sharing. Numerical results show that the proposed optimal power allocation scheme with the proposed decoding order can achieve significant improvement of the performance over equal power allocation, and achieve the sum-rate within two bits per channel use (bits/channel use) of the sum capacity

Modulation of galactic cosmic rays during the unusual solar minimum between cycles 23 and 24

During the recent solar minimum between cycles 23 and 24 (solar minimum $P_{23/24}$) the intensity of Galactic Cosmic Rays (GCRs) measured at the Earth was the highest ever recorded since space age. It is the purpose of this paper to resolve the most plausible mechanism for this unusually high intensity. A GCR transport model in three-dimensional heliosphere based on a simulation of Markov stochastic process is used to find the relation of cosmic ray modulation to various transport parameters, including solar wind (SW) speed, distance of heliospheric boundary, magnitude of interplanetary magnetic field (IMF) at the Earth, tilt angle of heliospheric current sheet (HCS), values of parallel and perpendicular diffusion coefficients. We calculate GCR proton energy spectra at the Earth for the last three solar minima $P_{21/22}$, $P_{22/23}$, and $P_{23/24}$, with the transport parameters obtained from observations. Besides weak IMF magnitude and slow SW speed, we find that a possible low magnetic turbulence, which increases the parallel diffusion and reduces the perpendicular diffusion in the polar direction, might be an additional possible mechanism for the high GCR intensity in the solar minimum $P_{23/24}$.Comment: Accepted for publication in JGR space physic

Avoiding vincular patterns on alternating words

A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1w_3\cdots$ (when the word is up-down) or $w_1>w_2w_4<\cdots$ (when the word is down-up). The study of alternating words avoiding classical permutation patterns was initiated by the authors in~\cite{GKZ}, where, in particular, it was shown that 123-avoiding up-down words of even length are counted by the Narayana numbers. However, not much was understood on the structure of 123-avoiding up-down words. In this paper, we fill in this gap by introducing the notion of a cut-pair that allows us to subdivide the set of words in question into equivalence classes. We provide a combinatorial argument to show that the number of equivalence classes is given by the Catalan numbers, which induces an alternative (combinatorial) proof of the corresponding result in~\cite{GKZ}. Further, we extend the enumerative results in~\cite{GKZ} to the case of alternating words avoiding a vincular pattern of length 3. We show that it is sufficient to enumerate up-down words of even length avoiding the consecutive pattern $\underline{132}$ and up-down words of odd length avoiding the consecutive pattern $\underline{312}$ to answer all of our enumerative questions. The former of the two key cases is enumerated by the Stirling numbers of the second kind.Comment: 25 pages; To appear in Discrete Mathematic

A finite-strain hyperviscoplastic model and undrained triaxial tests of peat

This paper presents a finite-strain hyperviscoplastic constitutive model within a thermodynamically consistent framework for peat which was categorised as a material with both rate-dependent and thermodynamic equilibrium hysteresis based on the data reported in the literature. The model was implemented numerically using implicit time integration and verified against analytical solutions under simplified conditions. Experimental studies on the undrained relaxation and loading-unloading-reloading behaviour of an undisturbed fibrous peat were carried out to define the thermodynamic equilibrium state during deviatoric loading as a prerequisite for further modelling, to fit particularly those model parameters related to solid matrix properties, and to validate the proposed model under undrained conditions. This validation performed by comparison to experimental results showed that the hyperviscoplastic model could simulate undrained triaxial compression tests carried out at five different strain rates with loading/unloading relaxation steps.Comment: 30 pages, 16 figures, 4 tables. This is a pre-peer reviewed version of manuscript submitted to the International Journal of Numerical and Analytical Methods in Geomechanic

Pattern-avoiding alternating words

A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1w_3\cdots$ (when the word is up-down) or $w_1>w_2w_4<\cdots$ (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 123-avoiding up-down words of even length is given by the Narayana numbers, which is also the case, shown by us bijectively, with 132-avoiding up-down words of even length. We also give formulas for enumerating all other cases of avoidance of a permutation pattern of length 3 on alternating words