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Analytical solution of modified point kinetics equations for linear reactivity variation in subcritical nuclear reactors adopting an incomplete gamma function approximation  [PDF]
André Luiz Pereira Rebello Junior, Aquilino Senra Martinez, Alessandro da Cruz Goncalves
Natural Science (NS) , 2012, DOI: 10.4236/ns.2012.431119
Abstract: The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.
On Low Rank Approximation of Binary Matrices  [PDF]
Chen Dan,Kristoffer Arnsfelt Hansen,He Jiang,Liwei Wang,Yuchen Zhou
Computer Science , 2015,
Abstract: We consider the problem of low rank approximation of binary matrices. Here we are given a $d \times n$ binary matrix $A$ and a small integer $k < d$. The goal is to find two binary matrices $U$ and $V$ of sizes $d \times k$ and $k \times n$ respectively, so that the Frobenius norm of $A-U V$ is minimized. There are two models of this problem, depending on the definition of the product of binary matrices: The $\mathrm{GF}(2)$ model and the Boolean semiring model. Previously, the only known results are $2$-approximation algorithms for the special case $k=1$ \cite{KDD:ShenJY09, Jiang14} (where the two models are equivalent). In this paper, we give the first results for the general case $k>1$ for both $\mathrm{GF}(2)$ and Boolean model. For the $\mathrm{GF}(2)$ model, we show that a simple column-selection algorithm achieves $O(k)$-approximation. For the Boolean model, we develop a new algorithm and show that it is $O(2^k)$-approximation. For constant $k$, both algorithms run in polynomial time in the size of the matrix. We also show that the low rank binary matrix approximation problem is NP-hard even for $k=1$, solving a conjecture in \cite{Koyuturk03}.
Exoplanets Bouncing Between Binary Stars  [PDF]
Nickolas Moeckel,Dimitri Veras
Physics , 2012, DOI: 10.1111/j.1365-2966.2012.20665.x
Abstract: Exoplanetary systems are found not only among single stars, but also binaries of widely varying parameters. Binaries with separations of 100--1000 au are prevalent in the Solar neighborhood; at these separations planet formation around a binary member may largely proceed as if around a single star. During the early dynamical evolution of a planetary system, planet--planet scattering can eject planets from a star's grasp. In a binary, the motion of a planet ejected from one star has effectively entered a restricted three-body system consisting of itself and the two stars, and the equations of motion of the three body problem will apply as long as the ejected planet remains far from the remaining planets. Depending on its energy, escape from the binary as a whole may be impossible or delayed until the three-body approximation breaks down, and further close interactions with its planetary siblings boost its energy when it passes close to its parent star. Until then this planet may be able to transition from the space around one star to the other, and chaotically `bounce' back and forth. In this paper we directly simulate scattering planetary systems that are around one member of a circular binary, and quantify the frequency of bouncing in scattered planets. We find that a great majority (70 to 85 per cent) of ejected planets will pass at least once through the space of it's host's binary companion, and depending on the binary parameters about 45 to 75 per cent will begin bouncing. The time spent bouncing is roughly log-normally distributed with a peak at about $10^4$ years, with only a small percentage bouncing for more than a Myr. This process may perturb and possibly incite instability among existing planets around the companion star. In rare cases, the presence of multiple planets orbiting both stars may cause post-bouncing capture or planetary swapping.
On the validity of the adiabatic approximation in compact binary inspirals  [PDF]
A. Maselli,L. Gualtieri,F. Pannarale,V. Ferrari
Physics , 2012, DOI: 10.1103/PhysRevD.86.044032
Abstract: Using a semi-analytical approach recently developed to model the tidal deformations of neutron stars in inspiralling compact binaries, we study the dynamical evolution of the tidal tensor, which we explicitly derive at second post-Newtonian order, and of the quadrupole tensor. Since we do not assume a priori that the quadrupole tensor is proportional to the tidal tensor, i.e. the so called "adiabatic approximation", our approach enables us to establish to which extent such approximation is reliable. We find that the ratio between the quadrupole and tidal tensors (i.e., the Love number) increases as the inspiral progresses, but this phenomenon only marginally affects the emitted gravitational waveform. We estimate the frequency range in which the tidal component of the gravitational signal is well described using the stationary phase approximation at next-to-leading post-Newtonian order, comparing different contributions to the tidal phase. We also derive a semi-analytical expression for the Love number, which reproduces within a few percentage points the results obtained so far by numerical integrations of the relativistic equations of stellar perturbations.
Investigation of GSM Signal Variation Depending Weather Conditions
Sel uk Helhel; ükrü zen;Hüseyin G ksu
PIER B , 2008, DOI: 10.2528/PIERB07101503
Abstract: This work proposes a site attenuation method to calculate the intensity of the field received by a mobile phone on a two-lane highway. To validate the model, radio propagation measurement was carried out through the intercity connection highway of the City of Isparta. The measurement system consisted of live radio base stations transmitting at 900 MHz and 1800 MHz. Downlink signal strength level data were collected by using TEMS test mobile phones, and were analyzed by TEMS Investigation, MapInfo and Google earth. Transmitted power-into-antenna was 14 W for both 900 MHz and 1800 MHz. Both base station sectors are facing towards the same direction having a 14 dBi gain. A proposed approximation was compared with real data. The results indicate that wet white pine trees cause 3 dB to 6 dB extra loss at 1800 MHz and about 1 dB to 3 dB extra loss at 900 MHz. Although 1800 MHz transmitter is 10 m higher, it loses its advantage in signal strength at longer distances.
Impact of the nuclear equation of state on the last orbits of binary neutron stars  [PDF]
M. Bejger,D. Gondek-Rosinska,E. Gourgoulhon,P. Haensel,K. Taniguchi,J. L. Zdunik
Physics , 2004, DOI: 10.1051/0004-6361:20041441
Abstract: We present calculations of quasiequilibrium sequences of irrotational binary neutron stars based on realistic equations of state (EOS) for the whole neutron star interior. Three realistic nuclear EOSs of various softness and based on different microscopic models have been joined with a recent realistic EOS of the crust, giving in this way three different EOSs of neutron-star interior. Computations of quasiequilibrium sequences are performed within the Isenberg-Wilson-Mathews approximation to general relativity. For all evolutionary sequences, the innermost stable circular orbit (ISCO) is found to be given by mass-shedding limit (Roche lobe overflow). The EOS dependence on the last orbits is found to be quite important: for two 1.35 M_sol neutron stars, the gravitational wave frequency at the ISCO (which marks the end of the inspiral phase) ranges from 800 Hz to 1200 Hz, depending upon the EOS. Detailed comparisons with 3rd order post-Newtonian results for point-mass binaries reveals a very good agreement until hydrodynamical effects (dominated by high-order functions of frequency) become important, which occurs at a frequency ranging from 500 Hz to 1050 Hz, depending upon the EOS.
Analytical Bounds between Entropy and Error Probability in Binary Classifications  [PDF]
Bao-Gang Hu,Hong-Jie Xing
Mathematics , 2012,
Abstract: The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the closed-form solutions of conditional entropy without involving any approximation. Two basic types of classification errors are investigated in the context of binary classification problems, namely, Bayesian and non-Bayesian errors. We theoretically confirm that Fano's lower bound is an exact lower bound for any types of classifier in a relation diagram of "error probability vs. conditional entropy". The analytical upper bounds are achieved with respect to the minimum prior probability, which are tighter than Kovalevskij's upper bound.
Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests  [PDF]
E. Gourgoulhon,P. Grandclement,K. Taniguchi,J. -A. Marck,S. Bonazzola
Physics , 2000, DOI: 10.1103/PhysRevD.63.064029
Abstract: We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with gamma=2.
Analytical analysis of small-amplitude perturbations in the shallow ice stream approximation
G. H. Gudmundsson
The Cryosphere Discussions , 2008,
Abstract: New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow ice stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow ice sheet approximation, and with solutions of the full Stokes equations. The shallow ice stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow ice sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow ice stream approximation overestimates the effects of bedrock perturbations on surface topography for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow ice stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow ice stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow ice sheet approximation. In contrast to the shallow ice sheet approximation, the shallow ice stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed. In accordance with the full system solutions, the shallow ice sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.
Multivariate approximation in total variation  [PDF]
A. D. Barbour,Malwina J. Luczak,Aihua Xia
Mathematics , 2015,
Abstract: The paper lays the framework for the discrete normal approximation in total variation of random vectors in $Z^d$, using Stein's method. We derive an appropriate Stein equation, together with bounds on its solutions and their differences, and use them to formulate a general discrete normal approximation theorem. We illustrate the use of the method in three settings: sums of independent integer valued random vectors, equilibrium distributions of Markov population processes, and random vectors exhibiting an exchangeable pair. We conclude with an application to random colourings of regular graphs.
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