Vacuum polarization for neutral particles in 2+1 dimensions

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.Comment: REVTeX, 7 pages, no figur

Essays on rising income inequality and quality of life in contemporary China

The primary contribution of the thesis is to propose the idea of collaboration from self efforts and social efforts to promote well-being in the research area of income inequality. The literature merely concerns the effect of income inequality on well-being based on social efforts which reflect on the measurement of income inequality according to social comparison. The thesis argues that this unilateral examination is unable to achieve coherence and unity between theory and empirical structure with respect to individual well-being and its corresponding statistical evidence is likely biased. Hence, the thesis introduces the new two-effort framework which enables a comprehensive and fair evaluation of social efforts such as government assistance and action on the issue of inequality. Through the application of such an idea into the analysis of China’s income inequality, the thesis has the following unprejudiced conclusions. China’s economy has retained strong growth over the past decades. Yet, the road to relieve the parallel outcome of rising income inequality from the robust growth is not optimistic. There is appreciable government policy on living standards in the short run but unfortunately, sustainable government intervention is scarce. This claim is drawn from three investigations of inequality by: i) examining the returns on social efforts and self efforts with respect to income inequality on living standards; ii) the influence of economic opportunity and security on individual income inequality; and iii), a case study of social efforts, government policy, particularly focusing on residential electricity pricing on household life burden

Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.Comment: 16 page

Block-block entanglement and quantum phase transitions in one-dimensional extended Hubbard model

In this paper, we study block-block entanglement in the ground state of one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests richer structure than that of the local (single site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density-wave, the spin-density-wave, and phase-separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement. Scaling analysis shows that ${\rm log}_2(l)$ behavior of the block-block entanglement may exist in both non-critical and the critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.Comment: 8 pages, 9 figure

Pore-scale dynamics and the multiphase Darcy law

Synchrotron x-ray microtomography combined with sensitive pressure differential measurements were used to study flow during steady-state injection of equal volume fractions of two immiscible fluids of similar viscosity through a 57-mm-long porous sandstone sample for a wide range of flow rates. We found three flow regimes. (1) At low capillary numbers, Ca, representing the balance of viscous to capillary forces, the pressure gradient, ∇ P , across the sample was stable and proportional to the flow rate (total Darcy flux) q t (and hence capillary number), confirming the traditional conceptual picture of fixed multiphase flow pathways in porous media. (2) Beyond Ca ∗ ≈ 10 − 6 , pressure fluctuations were observed, while retaining a linear dependence between flow rate and pressure gradient for the same fractional flow. (3) Above a critical value Ca > Ca i ≈ 10 − 5 we observed a power-law dependence with ∇ P ∼ q a t with a ≈ 0.6 associated with rapid fluctuations of the pressure differential of a magnitude equal to the capillary pressure. At the pore scale a transient or intermittent occupancy of portions of the pore space was captured, where locally flow paths were opened to increase the conductivity of the phases. We quantify the amount of this intermittent flow and identify the onset of rapid pore-space rearrangements as the point when the Darcy law becomes nonlinear. We suggest an empirical form of the multiphase Darcy law applicable for all flow rates, consistent with the experimental results

Effective video multicast over wireless internet

With the rapid growth of wireless networks and great success of Internet video, wireless video services are expected to be widely deployed in the near future. As different types of wireless networks are converging into all IP networks, i.e., the Internet, it is important to study video delivery over the wireless Internet. This paper proposes a novel end-system based adaptation protocol calledWireless Hybrid Adaptation Layered Multicast (WHALM) protocol for layered video multicast over wireless Internet. In WHALM the sender dynamically collects bandwidth distribution from the receivers and uses an optimal layer rate allocation mechanism to reduce the mismatches between the coarse-grained layer subscription levels and the heterogeneous and dynamic rate requirements from the receivers, thus maximizing the degree of satisfaction of all the receivers in a multicast session. Based on sampling theory and theory of probability, we reduce the required number of bandwidth feedbacks to a reasonable degree and use a scalable feedback mechanism to control the feedback process practically. WHALM is also tuned to perform well in wireless networks by integrating an end-to-end loss differentiation algorithm (LDA) to differentiate error losses from congestion losses at the receiver side. With a series of simulation experiments over NS platform, WHALM has been proved to be able to greatly improve the degree of satisfaction of all the receivers while avoiding congestion collapse on the wireless Internet