Probing shock acceleration in BL Lac jets through X-ray polarimetry: the time-dependent view

ABSTRACT Polarimetric measurements, especially if extended at high energy, are expected to provide important insights into the mechanisms underlying the acceleration of relativistic particles in jets. In a previous work, we have shown that the polarization of the synchrotron X-ray emission produced by highly energetic electrons accelerated by a mildly relativistic shock carries essential imprints of the geometry and the structure of the magnetic fields in the downstream region. Here, we present the extension of our analysis to the non-stationary case, especially suitable to model the highly variable emission of high-energy emitting BL Lacs. We anticipate a large ($\Pi \approx 40{{\ \rm per\ cent}}$), almost time-independent degree of polarization in the hard/medium X-ray band, a prediction soon testable with the upcoming mission IXPE. The situation in other bands, in particular in the optical, is more complex. A monotonic decrease of the optical degree of polarization is observed during the development of a flare. At later stages, Π reaches zero and then it starts to increase, recovering large values at late times. The instant at which Π = 0 is marked by a rotation of the polarization angle by 90°. However, at optical frequencies, it is likely that more than one region contribute to the observed emission, potentially making it difficult to detect the predicted behaviour.

Degree Equal Dominating Set of a Graph

A subset D of V is called dominating set if for any vertex u in V-D, there exist at least one vertex v in D such that u and v are adjacent. A subset D of a graph G is called a degree equal dominating set of G if for any u in V-D, there exists v in D such that u and v are adjacent and deg(u) = deg(v). In a social network, members who are neighbors and who have equal status can dominate each other. In the sense, the domination is symmetric. A graph model for this network leads to the concept of degree equal domination. In this paper we define and study the degree equal dominating set of a graph, degree equal irredundant sets in a graph, independent degree equal dominating set of a graph, degree equal complete graphs, 2-equal packing number of a graph.

Bank Customers' Action Analysis Based on Conductive Transformation

With the development of economic globalization, the bank market has become increasingly competitive. The bank must take measure to attract more customers, change market status and maximize the profit. Take some bank as an example, the active transformations are increasing deposit rate and decreasing loan rate. In this paper, conductive transformation is used to analyze bank customers' action changes induced by active transformations. With conductive degree, the influence of bank behavior on customer behavior can be seen. With independent degree, we can see which behavior changes can affect bank profit, and how active transformations influent bank market status.

The Micromorphic Approach to Generalized Heat Equations

In this paper, the micromorphic approach, previously developed in the mechanical context is applied to heat transfer and shown to deliver new generalized heat equations as well as the nonlocal effects. The latter are compared to existing formulations: the classical Fourier heat conduction, the hyperbolic type with relaxation time, the gradient of temperature or entropy theories, the double temperature model, the micro-temperature model or micro-entropy models. A new pair of thermodynamically-consistent micromorphic heat equations are derived from appropriate Helmholtz-free energy potentials depending on an additional micromorphic temperature and its first gradient. The additional micromorphic temperature associated with the classical local temperature is introduced as an independent degree of freedom, based on the generalized principle of virtual power. This leads to a new thermal balance equation taking into account the nonlocal thermal effects and involving an internal length scale which represents the characteristic size of the system. Several existing extended generalized heat equations could be retrieved from constrained micromorphic heat equations with suitable selections of the Helmholtz-free energy and heat flux expressions. As an example the propagation of plane thermal waves is investigated according to the various generalized heat equations. Possible applications to fast surface processes, nanostructured media and nanosystems are also discussed.

Local properties of random mappings with exchangeable in-degrees

In this paper we investigate the ‘local’ properties of a random mapping model, T n D̂, which maps the set {1, 2, …, n} into itself. The random mapping T n D̂ , which was introduced in a companion paper (Hansen and Jaworski (2008)), is constructed using a collection of exchangeable random variables D̂ 1, …, D̂ n which satisfy In the random digraph, G n D̂ , which represents the mapping T n D̂ , the in-degree sequence for the vertices is given by the variables D̂ 1, D̂ 2, …, D̂ n , and, in some sense, G n D̂ can be viewed as an analogue of the general independent degree models from random graph theory. By local properties we mean the distributions of random mapping characteristics related to a given vertex v of G n D̂ - for example, the numbers of predecessors and successors of v in G n D̂ . We show that the distribution of several variables associated with the local structure of G n D̂ can be expressed in terms of expectations of simple functions of D̂ 1, D̂ 2, …, D̂ n . We also consider two special examples of T n D̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine, for these examples, exact and asymptotic distributions for the local structure variables considered in this paper. These distributions are also of independent interest.

Local properties of random mappings with exchangeable in-degrees

In this paper we investigate the ‘local’ properties of a random mapping model, TnD̂, which maps the set {1, 2, …, n} into itself. The random mapping TnD̂, which was introduced in a companion paper (Hansen and Jaworski (2008)), is constructed using a collection of exchangeable random variables D̂1, …, D̂n which satisfy In the random digraph, GnD̂, which represents the mapping TnD̂, the in-degree sequence for the vertices is given by the variables D̂1, D̂2, …, D̂n, and, in some sense, GnD̂ can be viewed as an analogue of the general independent degree models from random graph theory. By local properties we mean the distributions of random mapping characteristics related to a given vertex v of GnD̂ - for example, the numbers of predecessors and successors of v in GnD̂. We show that the distribution of several variables associated with the local structure of GnD̂ can be expressed in terms of expectations of simple functions of D̂1, D̂2, …, D̂n. We also consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine, for these examples, exact and asymptotic distributions for the local structure variables considered in this paper. These distributions are also of independent interest.

Dynamic Characteristics Analysis of an Escalator Using the Computational Dynamics Program

Predicting dynamic characteristics of an escalator by means of the computational dynamic analysis is a meaningful subject, and has not been thoroughly investigated before. The general purposed kinematic and dynamic analysis program, DADS which has been shown to be effective in the dynamic analysis of multi-body, is utilized to analyze the interaction of the escalator to be more than 900 independent degree-of-freedom. Thousands of friction contact elements are applied to correctly simulate impact, permanent contact and temporary contact of rollers and the handrail. The presented model is experimentally verified to substantiate the accuracy and efficacy.

Axisymmetric Thin Shell Analyses With Reduced Degrees-of-Freedom

The formulation of a simple but effective unidimensional isoparametric displacement-based thin axisymmetric element is presented. The geometry is approximated by using cubic interpolation functions along the shell midsurface generatrix line and the element displacement field is represented by two spatial translation degrees-of-freedom only. The element kinematics incorporates membrane and bending strain components with the assumption of zero transverse shear deformations in the longitudinal and circumferential directions of the shell. This condition allows formulation of the element without using rotation as an independent degree-of-freedom, but continuity conditions between elements should be properly accounted for. The interaction effects between two adjoining elements or between an element and a rigid flange are modeled by using a penalty procedure to enforce continuity on the derivatives in the element midsurface radial displacements. The element formulation has been implemented and the results of various sample analyses are given to illustrate its effectiveness.