On the critical condition in gravitational shock wave collision and heavy ion collisions

In this paper, we derived a critical condition for matter equilibration in heavy ion collisions using a holographic approach. A gravitational shock waves with infinite transverse extension is used to model infinite nucleus. We constructed the trapped surface in the collision of two asymmetric planar shock waves with sources at different depth in the bulk AdS and formulated a critical condition for matter equilibration in collision of "nucleus" in the dual gauge theory. We found the critical condition is insensitive to the depth of the source closer to the AdS boundary. To understand the origin of the critical condition, we computed the Next to Leading Order stress tensor in the boundary field theory due to the interaction of the nucleus and found the critical condition corresponds to the breaking down of the perturbative expansion. We indeed expect non-perturbative effects be needed to describe black hole formation.Comment: 26 pages, 3 figure

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

Entanglement and quantum phase transition in the extended Hubbard model

We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.Comment: 5 pages, 4 figure

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Compression to extension switch during the Middle Triassic orogeny of Eastern China: the case study of the Jiulingshan massif in the southern foreland of the Dabieshan

The Jiulingshan massif is an E–W trending anticlinorium in the South China Block (SCB) that forms the southern foreland of the Qinling–Dabie orogen. The Jiulingshan consists of Middle Proterozoic (ca. 1 Ga–800 Ma) metamorphic and plutonic rocks unconformably overlain by Sinian to Triassic rocks. In these cover rocks, two episodes of deformation of pre-Late Triassic age are recognized. Namely, a N–S compressional phase characterized by south verging thrusts, upright folds and vertical cleavage followed by an extensional phase characterized by layer parallel slip, collapse folds and extensional allochthons of Proterozoic slate on top of Carboniferous to Middle Triassic carbonates. The extensional tectonics appears to be a mechanical consequence of the compressional tectonics. On a regional scale, the Jiulingshan massif forms one of the domed crustal scale shear zones of the SCB that accommodated the continuing convergence that immediately followed the Qinling–Dabie collision

Disc-planet interactions in sub-keplerian discs

One class of protoplanetary disc models, the X-wind model, predicts strongly subkeplerian orbital gas velocities, a configuration that can be sustained by magnetic tension. We investigate disc-planet interactions in these subkeplerian discs, focusing on orbital migration for low-mass planets and gap formation for high-mass planets. We use linear calculations and nonlinear hydrodynamical simulations to measure the torque and look at gap formation. In both cases, the subkeplerian nature of the disc is treated as a fixed external constraint. We show that, depending on the degree to which the disc is subkeplerian, the torque on low-mass planets varies between the usual Type I torque and the one-sided outer Lindblad torque, which is also negative but an order of magnitude stronger. In strongly subkeplerian discs, corotation effects can be ignored, making migration fast and inward. Gap formation near the planet's orbit is more difficult in such discs, since there are no resonances close to the planet accommodating angular momentum transport. In stead, the location of the gap is shifted inwards with respect to the planet, leaving the planet on the outside of a surface density depression. Depending on the degree to which a protoplanetary disc is subkeplerian, disc-planet interactions can be very different from the usual Keplerian picture, making these discs in general more hazardous for young planets.Comment: 4 pages, 4 figures, accepted in Astronomy and Astrophysics Letters, minor language change

An Event Study of Chinese Tourists to Taiwan

The number of Chinese tourists visiting Taiwan has been closely related to the political relationship across the Taiwan Strait. The occurrence of political events and disasters or accidents have had, and will continue to have, a huge impact on the Taiwan tourism market. To date, there has been relatively little empirical research conducted on this issue. In this paper, tourists are characterized as being involved in one of three types of tourism: group tourism (group-type), individual tourism (individual-type), and medical cosmetology (medical-type). We use McAleer’s (2015) fundamental equation in tourism finance to examine the correlation that exists between the rate of change in the number of tourists and the rate of return on tourism. Second, we use the event study method to observe whether the numbers of tourists have changed abnormally before and after the occurrence of major events on both sides of the Strait. Three different types of conditional variance models, namely, GARCH (1,1), GJR (1,1) and EGARCH (1,1), are used to estimate the abnormal rate of change in the number of tourists. The empirical results concerning the major events affecting the changes in the numbers of tourists from China to Taiwan are economically significant, and confirm which types of tourists are most likely to be affected by such major events

Risk Spillovers in Returns for Chinese and International Tourists to Taiwan

Fluctuations in the numbers of visitors directly affect the rates of return on tourism business activities. Therefore, maintaining a firm grasp of the relationship between the changes in the numbers of Chinese tourists and international travellers visiting Taiwan is conducive to the formulation of an effective and practical tourism strategy. Although the topic of international visitors to Taiwan is important, existing research has discussed the issue of the travel demand between Chinese tourists and international travellers visiting Taiwan. This paper is the first to examine the spillover effects between the rate of change in the numbers of Chinese tourist arrivals and the rate of change in the numbers of international traveller arrivals. Using daily data for Chinese tourists and international travellers visiting Taiwan over the period from 1 January 2014 to 31 October 2016, together with the Diagonal BEKK model, the paper analyses the covolatility spillover effects between the rate of change in the numbers of international travellers and the rate of change in the numbers of Chinese tourists visiting Taiwan. The empirical results show that there is no dependency relationship between the rate of change in the numbers of Chinese tourists and the rate of change in the numbers of international travellers visiting Taiwan. However, there is a significant negative covolatility spillover effect between the rate of change in the numbers of Chinese tourists and the rate of change in the numbers of international travellers. The empirical findings suggest that Taiwan should abandon its development strategy of focusing only on a single market, namely China, and to be pro-active in encouraging visits by international travellers to Taiwan for sightseeing purposes, thereby increasing the willingness of international travellers to visit Taiwan. Moreover, with the reduction in the numbers of Chinese tour groups visiting Taiwan, and increases in the numbers of individual travellers, the Taiwan Government should change its previous travel policies of mainly attracting Chinese tour group travellers and actively promoting in-depth tourism among international tourists, by developing tourism that focuses on the special characteristics of different localities. In this way, the government can enhance the quality of Taiwan’s tourism, and also attract travellers with high spending power

Numerical analysis of integrated forming process of diagonal rolling and piercing of flange nuts

In this paper, Simufact FE software is used to establish a simulation model of three-roll diagonal roll piercing integrated forming flange nut blanks, elaborate its process principle, analyze its forming process through numerical simulation. The law of load change, equivalent plastic strain distribution and wall thickness uniformity during the piercing process and diameter reduction process were investigated, and verify the feasibility of this forming process for manufacturing flange nut blanks