Global Well-Posedness of 2D Second Grade Fluid Equations in Exterior Domain

In this article, we consider 2D second grade fluid equations in exterior domain with Dirichlet boundary conditions. For initial data $\boldsymbol{u}_0 \in \boldsymbol{H}^3(\Omega)$, the system is shown to be global well-posed. Furthermore, for arbitrary $T > 0$ and $s \geq 3$, we prove that the solution belongs to $L^\infty([0, T]; \boldsymbol{H}^s(\Omega))$ provided that $\boldsymbol{u}_0$ is in $\boldsymbol{H}^s(\Omega)$

Singular limit of 2D second grade fluid past an obstacle

In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid model is a well-known non-Newtonian model, with two parameters: $\alpha$ representing length-scale, while $\nu > 0$ corresponding to viscosity. We prove that, under the constraint condition $\nu = {o}(\alpha^\frac{4}{3})$, the second grade fluid with a suitable initial velocity converges to the Euler fluid as $\alpha$ tends to zero. Moreover, we estimate the convergence rate of the solution of second grade fluid equations to the one of Euler fluid equations as $\nu$ and $\alpha$ approach zero

Entanglement in the Quantum Heisenberg XY model

We study the entanglement in the quantum Heisenberg XY model in which the so-called W entangled states can be generated for 3 or 4 qubits. By the concept of concurrence, we study the entanglement in the time evolution of the XY model. We investigate the thermal entanglement in the two-qubit isotropic XY model with a magnetic field and in the anisotropic XY model, and find that the thermal entanglement exists for both ferromagnetic and antiferromagnetic cases. Some evidences of the quantum phase transition also appear in these simple models.Comment: 7 pages, 6 figs, revised version submitted to Phys. Rev.

Entanglement in spin-one Heisenberg chains

By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.Comment: 7 pages and 4 figure

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Natural Coevolution of Tumor and Immunoenvironment in Glioblastoma.

Isocitrate dehydrogenase (IDH) wild-type glioblastoma (GBM) has a dismal prognosis. A better understanding of tumor evolution holds the key to developing more effective treatment. Here we study GBM\u27s natural evolutionary trajectory by using rare multifocal samples. We sequenced 61,062 single cells from eight multifocal IDH wild-type primary GBMs and defined a natural evolution signature (NES) of the tumor. We show that the NES significantly associates with the activation of transcription factors that regulate brain development, including MYBL2 and FOSL2. Hypoxia is involved in inducing NES transition potentially via activation of the HIF1A-FOSL2 axis. High-NES tumor cells could recruit and polarize bone marrow-derived macrophages through activation of the FOSL2-ANXA1-FPR1/3 axis. These polarized macrophages can efficiently suppress T-cell activity and accelerate NES transition in tumor cells. Moreover, the polarized macrophages could upregulate CCL2 to induce tumor cell migration. SIGNIFICANCE: GBM progression could be induced by hypoxia via the HIF1A-FOSL2 axis. Tumor-derived ANXA1 is associated with recruitment and polarization of bone marrow-derived macrophages to suppress the immunoenvironment. The polarized macrophages promote tumor cell NES transition and migration. This article is highlighted in the In This Issue feature, p. 2711

Prevalence of and risk factors for non-suicidal self-injury in rural China: Results from a nationwide survey in China

Background Non-suicidal self-injury (NSSI) is a highly prevalent and serious public health problem among adolescents worldwide. However, to date there were no studies assessing the prevalence of NSSI defined by suggested DSM-5 criteria among Chinese adolescents. We aimed to conduct a nationwide survey to explore the prevalence of and risk factors for NSSI among school-based adolescents in rural China. Methods A total sample of 15,623 adolescents in rural China were enrolled by using a multistage sampling method. Data was collected by self-report questionnaires including demographic characteristics, neglect, maltreatment, loneliness, resilience, social support and emotional management ability. NSSI was defined by suggested DSM-5 criteria, according to which the engagement in self-injury took place more than 5 times a year. Multinomial logistic regression models were used to estimate the association between risk factors and NSSI. Results There were 12.2% of adolescents (n = 1908) met the suggested DSM-5 criteria. Approximately 29% reported a history of NSSI at least once during the last year. Significant differences were found in several demographic factors including gender, ethnicity, grade, and family structure between adolescents with and without experiencing NSSI. The top three NSSI behaviors among adolescents with NSSI experience were hitting self, pinching, and pulling hair, with a prevalence rate of 16.7%, 14.1% and 11.2%, respectively. Female, Han ethnicity, fathers’ education level, neglect, maltreatment, loneliness, social support, suicidal behaviors and emotional management ability were significantly associated with NSSI by multivariate analysis. No significant relationship was found between resilience and risk of NSSI. Limitation The DSM-5 has proposed 6 groups of criteria for NSSI, we only used criteria on frequency given its more accepted feasibility and pragmatic application. Consequently, it may different from other prevalence that estimated by other criteria. Conclusion To the best of our knowledge, this is the first study reporting prevalence of NSSI defined by suggested DSM-5 criteria among adolescent in rural China. In comparison to finding from the similar samples of adolescents, Chinese rural adolescents seem to have a relative higher prevalence. The potential risk factors for NSSI include female, father's education, Han ethnicity, psychosocial factors and suicide behaviors. More evidence for further understanding of context of the occurrence, improving access to health care utilization, and identifying the role of psychosocial factors and family relationship, is needed for the prevention and management of NSSI.Published versio