Period relations for automorphic induction and applications, I

Let $K$ be a quadratic imaginary field. Let $\Pi$ (resp. $\Pi'$) be a regular algebraic cuspidal representation of $GL_{n}(K)$ (resp. $GL_{n-1}(K)$) which is moreover cohomological and conjugate self-dual. In \cite{harris97}, M. Harris has defined automorphic periods of such a representation. These periods are automorphic analogues of motivic periods. In this paper, we show that automorphic periods are functorial in the case where $\Pi$ is a cyclic automorphic induction of a Hecke character $\chi$ over a CM field. More precisely, we prove relations between automorphic periods of $\Pi$ and those of $\chi$. As a corollary, we refine the formula given by H. Grobner and M. Harris of critical values for the Rankin-Selberg $L$-function $L(s,\Pi\times \Pi')$ in terms of automorphic periods. This completes the proof of an automorphic version of Deligne's conjecture in certain cases.Comment: An abridged version is published in Comptes Rendus Math\'ematiques 353 (2015), pp. 95-10

Microscopic processes controlling the Herschel-Bulkley exponent

The flow curve of various yield stress materials is singular as the strain rate vanishes, and can be characterized by the so-called Herschel-Bulkley exponent $n=1/\beta$. A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian, and leads to $\beta=2$ in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to $\beta=1$ with logarithmic correction. This result supports that HL is not a suitable explanation for the value of $\beta$, which is instead significantly affected by finite dimensional effects. From considerations on elasto-plastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that $\beta=1+1/(d-d_f)$ where $d_f$ is the fractal dimension of avalanches and $d$ the spatial dimension. Measurements of $d_f$ then supports that $\beta\approx 2.1$ and $\beta\approx 1.7$ in two and three dimensions respectively. We discuss theoretical arguments leading to approximations of $\beta$ in finite dimensions.Comment: 9 pages, 3 figure

Sound radiation characteristics of a box-type structure

The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies

Simulating the Formation of Risk Perception

The damages of smoking on health have been taken more and more seriously, most relative studies focus on fields in sociology, psychology, public health or economy. The act of smoking itself satisfies the smoker's need for consumption, but at the same time produces negative effect such as smoking related damages. When making a decision whether to smoke or not or how much to smoke, the decision itself is hugely swayed by the smoker's own perception of risk regarding this matter. Whenever there is uncertainty involved, the decision made regarding whether to carry out the act i.e. smoking or not hugely depends upon the amount of risk perceived by each individual. Sex, age, education, health awareness and other factors affect how a perception is formed, in other words, how a "belief" is formed, and the forming process itself is a complex and intricate learning/evolving process. In this study, an agent-based computational model is employed to look at how a risk perception is formed and how the decision to smoke is made. This system can be used to observe the dynamic between anti-smoking policy and decision makers, and the resulting observation can serve as useful reference when the government is making or executing relative policies.Risk Perception, Smoking, Learning

State Transitions in Ultracompact Neutron Star LMXBs: towards the Low Luminosity Limit

Luminosity of X-ray spectral state transitions in black hole and neutron star X-ray binaries can put constraint on the critical mass accretion rate between accretion regimes. Previous studies indicate that the hard-to-soft spectral state transitions in some ultracompact neutron star LMXBs have the lowest luminosity. With X-ray monitoring observations in the past decade, we were able to identify state transitions towards the lowest luminosity limit in 4U 0614+091, 2S 0918-549 and 4U 1246-588. By analysing corresponding X-ray pointed observations with the Swift/XRT and the RXTE/PCA, we found no hysteresis of state transitions in these sources, and determined the critical mass accretion rate in the range of 0.002 - 0.04 $\dot{\rm M}_{\rm Edd}$ and 0.003 - 0.05 $\dot{\rm M}_{\rm Edd}$ for the hard-to-soft and the soft-to-hard transition, respectively, by assuming a neutron star mass of 1.4 solar masses. This range is comparable to the lowest transition luminosity measured in black hole X-ray binaries, indicating the critical mass accretion rate is not affected by the nature of the surface of the compact stars. Our result does not support the Advection-Dominated Accretion Flow (ADAF) model which predicts that the critical mass accretion rate in neutron star systems is an order of magnitude lower if same viscosity parameters are taken. The low transition luminosity and insignificant hysteresis in these ultracompact X-ray binaries provide further evidence that the transition luminosity is likely related to the mass in the disc.Comment: 12 pages, 4 figures, to appear in MNRA

An Analysis on Simulation Models of Competing Parties

Down’s spatial theory of elections (1957) has occupied a prominent theoretical status within political science. Studies use a notion of ideological distance to develop explanations for observable electoral trends. In elections, voters by observing party ideologies and using the information to make decisions for their votes because voters do not always have enough information to appraise the difference of which they are aware. The Downsian idea suggests that parties’ effort to attract votes leads them to adopt a median position. However, many studies have questioned the result and have many different conclusions. In recent years there has been an increasing interest in learning and adaptive behaviour including simulation models. In this study, we model the dynamics of competing parties who make decisions in an evolving environment and construct simulation models of party competition. We illustrate and compare their consequences by analyzing two variants of computational models.Spatial Voting Model, Party Competition, Evolutionary Modelling, Learning

Model Evolution of Heterogeneous Beliefs in an Network Economy

We model a simple communication network model for the evolution of heterogeneous beliefs in an overlapping generation economy. Each agent gathers information from his contacts and forms an inflation forecast based on this information, using the belief generating procedures. When the actual inflation is realised, an agent is in a position to learn i.e. adjust his own network strategy and belief. The learning is modelled as an evolving network process i.e. a local network of agents, with non-zero costs of communication. The network economy as a whole acts efficiently in achieving convergence to the Pareto superior equilibrium, in which agent"s perception of information is local and is subject to available resource.Network Economy, Belief Generating Procedures, Learning, Local Interactions