Extreme compression behaviour of equations of state

The extreme compression (P→∞) behaviour of various equations of state with K′_∞>0 yields (P/K)_∞=1/K′_∞, an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K^′=dK/dP, and K′_∞, the value of K^′ at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch–Murnaghan equation, Poirier–Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ_∞, the third-order Grüneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.     

Mechanical stability and thermodynamic properties of OsC from first-principles calculations

The elastic and thermodynamic characteristics of OsC crystal have been predicted through a method of density functional theory within the generalized gradient approximation (GGA). Compared with WC-type OsC, NaCl-type OsC is not only energy unfavorable but also mechanics unstable. The five independent elastic constants (C_ij), bulk modulus (B₀), the dependence of bulk modulus on temperature and pressure as well as the thermal expansion coefficient (α_V) at various temperatures for WC-type OsC are discussed. According to our calculations, WC-type OsC should be an ultra-incompressible material with high bulk modulus about 381 GPa. In addition, the bulk modulus will increase with increasing pressure while decrease with increasing temperature. The researches on the thermal expansion coefficient indicate that there will be a knee point during the process of thermal expansion coefficient variation versus increasing temperature. Our results may provide useful information for theoretical and experimental investigation of OsC.     

Study on CYCIAE-100 radiation field and residual radioactivity

The accelerators should be properly designed to make the radiation field produced by beam loss satisfy the dose limits. The radiation field for high intensity H- cyclotron includes prompt radiation and residual radiation field. The induced radioactivity in accelerator components is the dominant source of occupational radiation exposure if the accelerator is well shielded. The source of radiation is the beam loss when cyclotron is operating. In this paper, the radiation field for CYCIAE-100 is calculated using Monte Carlo method and the radioactive contamination near stripping foil is studied. A method to reduce the dose equivalent rate of maintenance staff is also given.     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.     

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300 Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1 kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1 kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45 dB cm⁻¹ to 3.77 dB cm⁻¹ for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

线性互补问题基于模同步块多重分裂方法的收敛性

通过利用不动点迭代来研究线性互补问题,根据基模同步多重分裂迭代方法将其线性互补问题的系数矩阵是点的形式推广到块H+的形式,并且分析了当系数矩阵是块矩阵时线性互补问题解的收敛情况。     

Colour symmetry double point groups

Thirty four distinct composition series arising out of the 32 crystallographic double point groups are employed to re-derive in a simple and elegant fashion all the 169 distinct colour symmetry groups generated by the 32 double point groups, exploiting the idea of colour generators. The advantage of the method employed and some possible applications of these colour groups are discussed. The resulting colour groups are tabulated.     

脊形波导中导模传输与损耗的分析与计算

本文运用有效折射率法把脊形波导化成等效二维平板波导后,再运用微分法求出弱吸收情况下波导模的吸收损耗,其方法简便,精确度高.