Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique

Entropy and Correlation Functions of a Driven Quantum Spin Chain

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy, as well as the finite spin correlation length, are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin 1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinants calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg

A phenomenological model of the superconducting state of the Bechgaard salts

We present a group theoretical analysis of the superconducting state of the Bechgaard salts, e.g., (TMTSF)_2PF_6 or (TMTSF)_2ClO_6. We show that there are eight symmetry distinct superconducting states. Of these only the (fully gapped, even frequency, p-wave, triplet) 'polar state' is consistent with the full range of the experiments on the Bechgaard salts. The gap of the polar state is d(k) (psi_uk,0,0), where psi_uk may be any odd parity function that is translationally invariant.Comment: 4 pages, no figure

A Predictive Study of Students’ Self-regulated Learning Skills and Their Roles in the Social Network Interaction of Online Discussion Board

Online learners’ learning skills and behaviors are challenging for educators to foresee, particularly what skills may be related to certain social interaction behaviors. Self-regulated learning (SRL) skills are critical to online learning. It is unclear how SRL skills may predict social network interaction. This study empirically investigated: How will SRL skills predict students’ network roles (i.e., in-degree, out-degree, betweenness centrality, closeness centrality, eigenvector centrality, reciprocated vertex pair ratio, & PageRank) in the social network discussions of discussion board within online courses? The predictive utility of SRL skills for betweenness and closeness centralities was supported. Learners with greater SRL skills play more influential roles in online discussion network. Learners with higher SRL skills tend to connect to others based on flow and distance of the connections, rather than how prominent (eigenvector) and prestigious (PageRank) of their connections

Reexamination of a multisetting Bell inequality for qudits

The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome

Consensus definitions of 14 severe acute toxic effects for childhood lymphoblastic leukaemia treatment: a Delphi consensus

Although there are high survival rates for children with acute lymphoblastic leukaemia, their outcome is often counterbalanced by the burden of toxic effects. This is because reported frequencies vary widely across studies, partly because of diverse definitions of toxic effects. Using the Delphi method, 15 international childhood acute lymphoblastic leukaemia study groups assessed acute lymphoblastic leukaemia protocols to address toxic effects that were to be considered by the Ponte di Legno working group. 14 acute toxic effects (hypersensitivity to asparaginase, hyperlipidaemia, osteonecrosis, asparaginase-associated pancreatitis, arterial hypertension, posterior reversible encephalopathy syndrome, seizures, depressed level of consciousness, methotrexate-related stroke-like syndrome, peripheral neuropathy, high-dose methotrexate-related nephrotoxicity, sinusoidal obstructive syndrome, thromboembolism, and Pneumocystis jirovecii pneumonia) that are serious but too rare to be addressed comprehensively within any single group, or are deemed to need consensus definitions for reliable incidence comparisons, were selected for assessment. Our results showed that none of the protocols addressed all 14 toxic effects, that no two protocols shared identical definitions of all toxic effects, and that no toxic effect definition was shared by all protocols. Using the Delphi method over three face-to-face plenary meetings, consensus definitions were obtained for all 14 toxic effects. In the overall assessment of outcome of acute lymphoblastic leukaemia treatment, these expert opinion-based definitions will allow reliable comparisons of frequencies and severities of acute toxic effects across treatment protocols, and facilitate international research on cause, guidelines for treatment adaptation, preventive strategies, and development of consensus algorithms for reporting on acute lymphoblastic leukaemia treatment

Convertibility between two-qubit states using stochastic local quantum operations assisted by classical communication

In this paper we classify the four-qubit states that commute with UUVV, where U and V are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC