A new formulation for fictitious mass of viscous dynamic relaxation method

Abstract

In this article, a new relationship is proposed for the fictitious mass of viscous dynamic relaxation (DR) method. First, incremental equations are derived for DR steps. Using transformed Gershgörin theory, a new relationship is achieved for fictitious mass of viscous DR by formulating modified time step ratio. This procedure presents a new algorithm for the viscous DR method. To evaluate the numerical efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed with elastic linear and geometrically nonlinear behaviors. Results show that by using the proposed algorithm for fictitious mass, the convergence rate of the viscous DR method is improved so that the proposed algorithm presents the structural response with lower iterations in comparison with other common DR techniques.

Communicated by Joerg Fehr.     

The extremal function for K9= minors

We prove the extremal function for $K_9^{=}$ minors, where $K_9^{=}$ denotes the complete graph $K_9$ with two edges removed. In particular, we show that any graph with $n\ge 8$ vertices and at least $6n-20$ edges either contains a $K_9^{=}$ minor or is isomorphic to a graph obtained from disjoint copies of $K_8$ and $K_{2,2,2,2,2}$ by identifying cliques of size 5. We utilize computer assistance to prove one of our lemmas.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase,Phase Transition by Wang–Landau Method

We study the nature of the smectic–isotropic phase transition using a mobile 6-state Potts model. Each Potts state represents a molecular orientation. We show that with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang–Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Experimental review of the ϒ(1S, 2S, 3S) physics at e+e− colliders and the LHC

The three lowest-lying \mathrm{\Upsilon } states, i.e., \mathrm{\Upsilon }(1S), \mathrm{\Upsilon }(2S), and \mathrm{\Upsilon }(3S), composed of bb¯ pairs and below the BB ¯ threshold, provide a good platform for the researches of hadronic physics and physics beyond the Standard Model. They can be produced directly in e⁺e⁻ colliding experiments, such as CLEO, Babar, and Belle, with low continuum backgrounds. In these experiments, many measurements of the exclusive \mathrm{\Upsilon }(1S) and \mathrm{\Upsilon }(2S) decays into light hadrons, which shed light on the “80% rule” for the Okubo–Zweig–Iizuka suppressed decays in the bottomonium sector, were carried out. Meanwhile, many studies of the charmonium and bottomonium productions in \mathrm{\Upsilon }(1S, 2S, 3S) decays were performed, to distinguish different Quantum Chromodynamics (QCD) models. Besides, exotic states and new physics were also extensively explored in \mathrm{\Upsilon }(1S, 2S, 3S) decays at CLEO, BaBar, and Belle. The \mathrm{\Upsilon }(1S, 2S, 3S) states can also be produced in pp collisions and in collisions involving heavy ions. The precision measurements of their cross sections and polarizations at the large hadron collider (LHC), especially in the CMS, ATLAS, and LHCb experiments, help to understandΥproduction mechanisms in pp collisions. The observation of the sequentialΥsuppression in heavy ion collisions at CMS, LHCb, and ALICE is of great importance for verifying the quark–gluon plasma predicted by QCD. In this article, we review the experimental results on \mathrm{\Upsilon }(1S, 2S, 3S) at e⁺e⁻ colliders and the LHC, and summarize their prospects at Belle II and the LHC.     

p-adic超几何函数与Dwork超曲面上的有理点

p-adic超几何函数是经典的Gauss超几何函数在有限域上的模拟,与许多数论问题都有联系.设Fq是q元有限域,λ∈Fq,n为正整数.本文研究了Dwork超曲面Dλ^n:x1^n+x2^n+…+xn^n=nλx1x2…xn及其推广形式上的Fq-有理点,并在n与q(q-1)互素时给出了由p-adic超几何函数表示的各种Fq-有理点个数的公式,从而修正和改进了Barman与Goodson等人的结论.     

Absorption enhancement of ultrathin crystalline silicon solar cells with frequency upconversion nanosphere arrays

A design of ultrathin crystalline silicon solar cells patterned with α-NaEr_(0.2)Y_(0.8)F_4 upconversion nanosphere(NSs) arrays on the surface was proposed. The light trapping performance ofα-NaEr_(0.2)Y_(0.8)F_4 NSs with different ratios of sphere diameter to sphere pitch was systematically studied by COMSOL Multiphysics. The influence of different NS diameters and ratio to the average optical absorption of ultrathin crystalline silicon solar cell was calculated, as well as the short circuit current densities. The results show that the average optical absorption of solar cells with 2.33 μm silicon covered by α-NaEr_(0.2)Y_(0.8)F_4 NSs of 100 nm in diameter and 5.2 in ratio has improved by 8.5% compared to planar silicon solar cells with the same thickness of silicon. The light trapping performance of different thicknesses of silicon solar cells with the optimized configuration of NSs was also discussed. The results indicate that our structure enhances the light absorption. The presented model will be the basis for further simulations concerning frequency upconversion of α-NaEr_(0.2)Y_(0.8)F_4 materials.