Some inequalities and limit theorems under sublinear expectations

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.Comment: 15 page

Shape and flow fluctuations in ultra-central Pb+Pb collisions at the LHC

In ultra-central heavy-ion collisions, anisotropic hydrodynamic flow is generated by density fluctuations in the initial state rather than by geometric overlap effects. For a given centrality class, the initial fluctuation spectrum is sensitive to the method chosen for binning the events into centrality classes. We show that sorting events by total initial entropy or by total final multiplicity yields event classes with equivalent statistical fluctuation properties, in spite of viscous entropy production during the fireball evolution. With this initial entropy-based centrality definition we generate several classes of ultra-central Pb+Pb collisions at LHC energies and evolve the events using viscous hydrodynamics with non-zero shear but vanishing bulk viscosity. Comparing the predicted anisotropic flow coefficients for charged hadrons with CMS data we find that both the Monte Carlo Glauber (MC-Glb) and Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) models produce initial fluctuation spectra that are incompatible with the measured final anisotropic flow power spectrum, for any choice of the specific shear viscosity. In spite of this failure, we show that the hydrodynamic model can qualitatively explain, in terms of event-by-event fluctuations of the anisotropic flow coefficients and flow angles, the breaking of flow factorization for elliptic, triangular and quadrangular flow measured by the CMS experiment. For elliptic flow, this factorization breaking is large in ultra-central collisions. We conclude that the bulk of the experimentally observed flow factorization breaking effects are qualitatively explained by hydrodynamic evolution of initial-state fluctuations, but that their quantitative description requires a better understanding of the initial fluctuation spectrum.Comment: 11 pages, 11 figures; In v2 and the current version, we updated all the calculations (except for Fig. 2) that do not include microscopic NN-correlations with a hard core radius of 0.9 fm. In v1, some of the results are done with a smaller hard core radius of 0.4 fm. We also reduced the statistical errors in Figs. 5-8 by increasing the simulated events to 1000 for every set of the ru

New bounds and efficient algorithm for sparse difference resultant

Let $\mathbb{P}=\{\mathbb{P}_0,\mathbb{P}_1,\dots,\mathbb{P}_n\}$ be a generic Laurent transformally essential system and $\mathbb{P}_{\mathbb{T}}=\{\mathbb{P}_0,\mathbb{P}_1,\dots,\mathbb{P}_m\} (m\leq n)$ be its super essential system. We show that the sparse difference resultant of a simplified system of $\mathbb{P}_{\mathbb{T}}$ by setting the selected $n-m$ variables to one is the same to the one of $\mathbb{P}$. Moreover, new order bounds of sparse difference resultant are obtained. Then we propose an efficient algorithm to compute sparse difference resultant which is the quotient of two determinants whose elements are the coefficients of the polynomials in the strong essential system. We analyze complexity of the algorithm. Experimental results show the efficiency of the algorithm

An experiential formula for the energy eigenvalues of a particle in a one-dimension finite-deep square well potential

We propose an experiential formula for the calculation of the energy eigenvalues of a particle moving in a one-dimension finite-deep square well potential after some physical considerations. This formula shows a simple relation between the energy eigenvalues and the potential papameters, and can be used to estimate the energy eigenvalues in a very simple way

Resonance Decay Contributions to Higher-Order Anisotropic Flow Coefficients

We show that in hydrodynamic simulations for relativistic heavy-ion collisions, strong resonance decay calculations can be performed with fewer species of particle resonances while preserving good accuracy in single particle spectra and flow anisotropies. Such partial resonance calculations boost computation efficiency by a factor of 10 which is essential for large scale event-by-event simulations.Comment: 20 pages, 4 figures, 14 table

Controlled remote state preparation via partially entangled quantum channel

We propose two controlled remote state preparation protocols via partially entangled channels. One prepares a single-qubit state and the other prepares a two-qubit state. Different from other controlled remote state preparation schemes which also utilize partially entangled channels, neither auxiliary qubits nor two-qubit unitary transformations are required in our schemes and the success probabilities are independent of the coefficients of the quantum channel. The success probabilities are 50% and 25% for arbitrary single-qubit states and two-qubit states, respectively. We also show that the success probabilities can reach 100% for restricted classes of states

Video Primal Sketch: A Unified Middle-Level Representation for Video

This paper presents a middle-level video representation named Video Primal Sketch (VPS), which integrates two regimes of models: i) sparse coding model using static or moving primitives to explicitly represent moving corners, lines, feature points, etc., ii) FRAME /MRF model reproducing feature statistics extracted from input video to implicitly represent textured motion, such as water and fire. The feature statistics include histograms of spatio-temporal filters and velocity distributions. This paper makes three contributions to the literature: i) Learning a dictionary of video primitives using parametric generative models; ii) Proposing the Spatio-Temporal FRAME (ST-FRAME) and Motion-Appearance FRAME (MA-FRAME) models for modeling and synthesizing textured motion; and iii) Developing a parsimonious hybrid model for generic video representation. Given an input video, VPS selects the proper models automatically for different motion patterns and is compatible with high-level action representations. In the experiments, we synthesize a number of textured motion; reconstruct real videos using the VPS; report a series of human perception experiments to verify the quality of reconstructed videos; demonstrate how the VPS changes over the scale transition in videos; and present the close connection between VPS and high-level action models

Fluctuating flow angles and anisotropic flow measurements

Event-by-event fluctuations in the initial density distributions of the fireballs created in relativistic heavy-ion collisions lead to event-by-event fluctuations of the final anisotropic flow angles, and density inhomogeneities in the initial state cause these flow angles to vary with the transverse momentum of the emitted particles. It is shown that these effects lead to characteristically different transverse momentum dependencies for anisotropic flow coefficients extracted from different experimental methods. These differences can be used to experimentally constrain flow angle fluctuations in the final state of heavy-ion collisions which, in turn, are sensitive to the initial state density fluctuations and the shear viscosity of the expanding fireball medium.Comment: 11 pages, incl. 8 figures. v2: several figures and corresponding discussions added, Sec. III significantly rewritten. No qualitative change in conclusions but more precise and detailed discussion of the results. To appear in Physical Review

Realization of high-capacity hydrogen storage using carbon atomic chains: the role of terminations

The capacity of carbon atomic chains with different terminations for hydrogen storage is studied using first-principles density functional theory calculations. Unlike the physisorption of H2 on the H-terminated chain, we show that two Li (Na) atoms each capping one end of the carbon chain can hold ten H2 molecules with optimal binding energies for room temperature storage. The hybridization of the Li 2p states with the H2 sigma orbitals contributes to the H2 adsorption. However, the binding mechanism of the H2 molecules on Na arises only from the polarization interaction between the charged Na atom and the H2. Moreover, additional H2 molecules can be bound to the carbon atoms at the chain ends due to the charge transfer between Li 2s2p (Na 3s) and C 2p states. Importantly, dimerization of these isolated metal-capped chains does not affect the hydrogen binding energy significantly. In addition, a single chain can be stabilized effectively by termination on the C60 clusters. With a hydrogen uptake of > 10 wt % on Li-coated C60-Cn-C60 (n = 5, 8), the Li12C60-Cn-Li12C60 complex, without reducing the number of adsorbed H2 molecules per Li, can serve as better building blocks of polymers than the (Li12C60)2 dimer. These findings suggest a new route to design cluster-assembled storage materials based on terminated sp carbon chains.Comment: 19 pages, 8 figure

Synchrotron X-ray tomography investigation of 3D morphology of intermetallic phases and pores and their effect on the mechanical properties of cast Al-Cu alloys

The influence of Fe content on the three-dimensional (3D) morphology of Fe-rich intermetallic phases (Fe phases), Al2Cu, and pores and mechanical properties of cast Al-5.0Cu-0.6Mn alloys with 0.5 and 1.0 wt. % Fe are characterized using synchrotron X-ray tomography and a tensile test. The results show that both Fe phases and Al2Cu exhibit a complex 3D network structure, and the pores are irregular with complex interconnected and near-globular shape. As the Fe content increases from 0.5 % to 1.0 %, the volume fraction and equivalent diameter of Fe phases decrease, whereas both their interconnectivities decrease. Skeletonization analysis shows that the Chinese-script-shaped Fe phase is compacted than the plate-like Fe phases. The equivalent diameter and sphericity of pores vary with Fe content, and their relationships follow exponential functions, Y = 7.14*X-1.29 and Y = 7.06*X-1.20, respectively. The addition of Fe results in a decrease in the ultimate tensile strength and elongation from 223.7 MPa to 199.8 MPa and from 5.51 % to 3.64 %, respectively, owing to increasing volume fraction of sharp-edged Fe phases and pores, resulting in stress concentration during tensile test.Comment: 27 pages, 13 figure