运用三维离散元技术模拟落锤撞击下奥克托今颗粒的点火燃烧过程

炸药颗粒的点火燃烧过程一直是人们关注的热点问题。近年来，三维离散元技术在中尺度观测颗粒材料的动力学过程中拥有显著优势。炸药燃烧属于颗粒材料的反应动力学，运用三维离散元技术(DM3)可以有效地观测炸药燃烧传播的过程。以奥克托今(HMX)颗粒为例，本文成功模拟并观测到了HMX颗粒的燃烧反应程度，确定了颗粒开始燃烧反应的时间，以及燃烧反应传播的时间。同时，结合落锤冲击颗粒的三维图像以及其表观压强和放热功率，得到了HMX颗粒燃烧反应、燃烧传播的整个反应动力学过程，包括颗粒在冲击加载下碎化塑性变形的过程，颗粒燃烧反应放热的过程，落锤回弹颗粒喷射的过程等。同时，进一步说明了尖顶颗粒更利于颗粒点火，平顶颗粒有抑制颗粒点火的能力。     

PN结物理特性的开放式测量实验方法研究

开放式、综合性量测实验的设计与应用,在巩固基础理论知识的同时,能够有效培养学生的动手实践能力、数据处理及分析能力,一定程度代表着大学物理实验课程的教学模式改革方向。以PN结物理特性的测量实验为例,基于通用型仪器与元器件的积木式组合,设计出简单、适用的实验电路;t=17.95℃时所采集的原始实验数据经三种模式回归分析,比较验证了PN结扩散电流与电压间遵循的玻尔兹曼分布律;计算出的玻尔兹曼常数与FD-PN-4测定仪的量测值相比,其结果说明了开放式测量实验方法的有效性。     

New soft porous frameworks based on lambda-zirconium phosphate and aliphatic dicarboxylates: Synthesis and structural characterization

New dicarboxylate-functionalized pillared materials with a general formula of λ-ZrPO₄(OH)_1-x(OOC(CH₂)_nCOO)_x/2(dmso) (n=6, 8 and 10) have been prepared by post-synthesis modification of the inorganic layers of λ-zirconium phosphate (λ-ZrP), where the superficial Chloride monovalent anionic ligands of λ-layer are partially exchanged with the divalent anionic ligands of a series of long-chain aliphatic dicarboxylic acids, namely octanedioic acid, decanedioic acid and dodecanedioic acid. The synthesized materials are characterized by X-ray diffractometry, FT-IR spectrophotometry, elemental and thermogravimetric analyses. The X-ray diffraction patterns show that the obtained solid phases are pure. Furthermore, the interlayer distance of λ-ZrP systematically increases from 1.02 to 1.59 nm as a result of the incorporation of the mentioned acids inside the interlayer gallery.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Experimental and theoretical assessment of Fe-doped indium-oxide-based dilute magnetic semiconductors

Specimens of iron-doped indium oxide (In_1-xFe_x)₂O₃ with x?=?0.015, 0.03, 0.045 and 0.06, amalgamated through a traditional solid-state reaction method followed by H₂/air sintering, were characterised using an X-ray diffractometer (XRD), a vibrating sample magnetometer (VSM), and a scanning electron microscope (SEM) to investigate their structural, magnetic and morphological properties respectively. According to XRD plots, all the specimens exhibit cubic bixbyite structures along with ancillary phases. Magnetic assessment showed that In₂O₃ has a negative susceptibility, exhibiting diamagnetic behaviour at room temperature. The doping of Fe ions induces ferromagnetic (FM) ordering, which is enhanced with increasing doping content. The strength of the magnetisation increases when the specimens are exposed to H₂ but is reduced on further air sintering. A bound magnetic polaron (BMP) model is successfully fitted to the observed FM data involving localised carriers and magnetic cations. A multivariate assessment viz. a hierarchical cluster analysis (HCA) was used to corroborate and strengthen the experimental determined magnetic properties. A homogeneous particle distribution was observed in all SEM micrographs and is validated through MATLAB-based simulation by applying a watershed segmentation algorithm. Surface plots also confirm the change in magnetic properties with increase in doping concentration.     

In vitro anti‐proliferative and in silico docking studies of heteroleptic copper(II) complexes of pyridazine‐based ligands and ciprofloxacin

Three heteroleptic copper(II) complexes of the type [Cu(L^1–3)(cf)(ClO₄)] ( 1 – 3 ), where cf = ciprofloxacin, have been synthesized using pyridazine‐based ligands 3‐chloro‐6‐(salicylidenehydrazinyl)pyridazine (HL¹), 3‐chloro‐6‐(4‐diethylaminosalicylidenehydrazinyl)pyridazine (HL²) and 3‐chloro‐6‐(5‐bromosalicylidenehydrazinyl)pyridazine (HL³). Electronic spectral data and magnetic moment values suggest octahedral geometry for the synthesized copper(II) complexes. Electrochemical data of the copper(II) complexes present an irreversible one‐electron reduction wave in the cathodic potential region (E_pc) between ?0.631 and ?0.670 V. Frontier molecular orbital calculations were carried out, and the obtained low‐energy gap supports the bio‐efficacy of the complexes. All the complexes were screened for their in vitro cytotoxicity activity against three human cancerous (breast adenocarcinoma (MCF‐7), hepatoma (HepG‐2) and cervical (HeLa)) and one non‐cancerous (non‐tumorigenic human dermal fibroblast (NHDF)) cell lines using MTT assay, in which complex 2 exhibited higher activity. The apoptosis induction by the complexes was analysed using the Hoechst dye staining method with MCF‐7 cell line, which indicates higher apoptotic activity of complex 2 . A molecular docking study was carried out to ascertain the binding affinity of the synthesized heteroleptic copper(II) complexes with phosphoinositide 3‐kinase gamma (PI3Kγ) receptor.     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.