OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.

Biaxial tensile properties and elastic constants evaluation of envelope material for airship

This paper presents an experimental study to determine the tensile properties of the envelope fabric Uretek3216L under biaxial cyclic loading.First the biaxial cyclic tests were carefully carried out on the envelope material to obtain the stress-strain data and the corresponding nonlinearity and orthotropy of the material were analyzed. Then for some determination options with different stress ratios the least squares method minimizing the strain terms was used to calculate the elastic constants from the experimental data.Finally the influences of the determination options with different stress ratios and the reciprocal relationship on the elastic constants were discussed.Results show that the orthotropy of the envelope material can be attributed to the unbalanced crimp of their constitutive yarns in warp and weft directions and the elastic constants vary noticeably with the determination options as well as the normalized stress ratios.In real design practice it is more reasonable to use constants determined for specific stress states in particular stress ratios depending on the project＆#39;s needs.Also calculating the structures with two limitative sets of elastic constants instead of using only one set is recommendable in light of the great variety of the constant＆#39;s values.

Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.

Study of the Physical and Mechanical Properties of Titanium in Volume by the MEAM Method

In this work we present the results of our study on the physical and mechanical properties of titanium in volume. The work consisted in determining its physical and mechanical properties under different crystallographic structures (HCP, FCC, BCC and SC) using the Modified Embedded Atom Method (MEAM) and the MEAM potential of titanium. We used the LAMMPS calculation code, based on classical molecular dynamics, to determine the most stable structure of titanium, which is the hexagonal compact structure (HCP) with crystal parameters a = 2.952 Å and c = 4.821 Å and a cohesion energy of -4.87 eV. This structure is seconded by the cubic centred structure (BCC) with a lattice parameter a = 3.274 Å and a cohesive energy of -4.84 eV. It was shown that titanium can crystallise into a third structure which is the face-centred cubic (FCC) structure with a lattice parameter a = 4.143 Å and a cohesive energy of -4.82 eV. The results obtained in this study were compared with the theoretical results and showed considerable agreement.

Density Functional Calculations of the Mechanical, Electronic and Dynamical Properties of Antiperovskite Ca3BO (B = Pb, Ge, Sn)

An analysis of mechanical, electronic and dynamical properties of antiperovskite Ca3BO (B = Pb, Ge, Sn) in cubic phase space group Pm-3m (221) has been studied using first principle density functional theory (DFT). Ground state energy computation was done using the Projector Augmented Wave (PAW) Pseudo Potentials and the Plane Wave (PW) basis set. The Generalized Gradient Approximation (GGA) was used for the exchange correlation. The open source code QUANTUM ESPRESSO (QE) was used in this study in which plane wave basis sets are applied for the expansion of the electronic structure wave function. Thermo_pw as a post-processing code was used for the computation of mechanical properties including bulk modulus and elastic constants with their derivatives. The lattice parameters are here calculated to be 4.87 Å, 4.86 Å and 4.84 Å for Ca3BO (B = Pb, Ge, Sn) respectively which compares well with other works. This also shows that the three crystals are similar in size and in most of their properties. In addition to this, projected density of states and band structure are also computed both showing that these materials are of semi-metallic nature and are stable in cubic phase. Phonon modes at gamma are also reported.

The Time-Consistent Optimal Reinsurance Strategy of Insurance Group under the CEV Model

The article introduces proportional reinsurance contracts under the mean-variance criterion,studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies.The insurance claims process follows a jump-diffusion model,assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other.In the framework of game theory,the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically.Finally,numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations.The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.

A Comparative Study of Elastic Constants of NiTi and NiAl Alloys from First-Principle Calculations

To investigate the origin of the strong dependence of martensitic transformation temperature on composition, the elastic properties of high temperature B2 phases of both NiTi and NiAI were calculated by a first-principle method, the exact-muffin orbital method within coherent potential approximation. In the composition range of 50-56 at. pct Ni of NiTi and 60-70 at. pct Ni of NiAI in which martensitic transformation occurs, non-basalplane shear modulus c44 increases with increasing Ni content, while basal-plane shear modulus c＇ decreases. In the above composition ranges however the transformation temperature of NiAI increases with increasing Ni content while that of NiTi decreases from experimental observation. The softening of c＇ is experimentally observed only in NiAI, and the decrease of c＇ with increasing Ni content is responsible for the increase of transformation temperature. The result of the present work demonstrates that, besides c＇, c44 also influences the martensitic transformation of NiTi and plays quite important a role.

Ground state parameters,electronic properties and elastic constants of CaMg3:DFT study

The present study aims to investigate the equation of state(EOS)parameters of CaMg3 in aReCh(D09),AIFR(DO3),CU3A11(LI2)and CuTi3(L60)structures,using full potential linear muffin-tin orbitals(FP-LMTO)approach based on the density functional theory(DFT).The local density approximation(LDA)and the generalized gradient approximation(GGA)were both applied for the exchange-correlation potential term.The calculated equation of slate parameters at equilibrium,in general,agreed well with the available data of the literature.The calculations showed that under compression CaMg3 transforms from DO3 to DO9 at about 29.96GPa,and 25.1 GPa using LDA and GGA,respectively.The elastic constants C,y,aggregate moduli,Vickers hardness,sound velocity,and Debye temperature of CaMg3 in D03 structure were also reported,discussed and analyzed.Using LDA(GGA),the calculated values of Hv andθD were found at around 5.80GPa(5.93GPa)and 393.44 K(389.91 K),respectively.Electronic band structure,total density of states(TDOS)as well as the partial density of states(PDOS)have been also obtained.The electronic band structure confirms the metallic behavior of CaMg3 in DO3 phase,the valence bands are dominated by the maximum contribution of‘d’like states of Ca in the energy ranging from 2 to 3 eV for GGA,and from 4.5 to 5 eV for LDA,respectively.

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc. In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance, inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c11, c33, c55 of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c55 of the shunted piezoelectric plate with the variation of negative capacitance. The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.

First-principles study of the elastic constants and optical properties of uranium metal

We perform first-principles calculations of the lattice constants, elastic constants, and optical properties for alpha- and gamma-uranium based on the ultra-soft pseudopotential method. Lattice constants and equilibrium atomic volume are consistent pretty well with the experimental results. Some difference exists between our calculated elastic constants and the experimental data. Based on the satisfactory ground state electronic structure calculations, the optical co ductivity, dielectric function, refractive index, and extinction coefficients are also obtained. These calculated optical properties are compared with our results and other published experimental data.

Elastic constants characterization on graphite at 500℃ by the virtual fields method

In this paper the elastic constants of graphite at elevated temperature were experimentally investigated by using the virtual fields method （VFM）. A new method was presented for the characterization of mechanical properties at elevated temperature. The three-point bending tests were performed on graphite materials by an universal testing machine equipped with heating fumace. Based on the heterogeneous deformation fields measured by the digital image correlation （DIC） technique, the elastic constants were then extracted by using VFM. The measurement results of the elastic constants at 500℃ were obtained. The ef- fect on the experimental results was also analyzed. The successful results verify the feasibility of using the proposed method to measure the properties of graphite at high temperature, and the proposed method is believed to have a good potential for further applications.

Twelve Elastic Constants of Betula platyphylla Suk.

Wood elastic constants are needed to describe the elastic behaviors of wood and be taken as an important design parameter for wood-based composite materials and structural materials. This paper clarified the relationships between compliance coefficients and engineering elastic constants combined with orthotropic properties of wood, and twelve elastic constants of Betula platyphylla Suk. were measured by electrical strain gauges. Spreading the adhesive quantity cannot be excessive or too little when the strain flakes were glued. If excessive, the glue layer was too thick which would influence the strain flakes?performance, and if too little, glues plastered were not firm, which could not accurately transmit the strain. Wood as an orthotropic material, its modulus of elasticity and poissons ratios are related by two formulas:μij /Ei =μji /Ej and μij < (Ei /Ej)1/2. The results showed that the elastic constants of Betula platyphylla Suk. measured by electrical strain gauges were accurate and reliable. The results of shear elastic modulus GTL and GLR show a high linear regression correlation coefficient (> 0.95) between the reciprocal of elastic modulus MOE-1 and the square of the ratio of depth to length (h/l)2, which indicate that shear modulus values measured were reliable by three point bending experiment.

Macroscopic Elastic Constants of Pure Metal Based on the Interactions between Microscopic Particles

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson＇s ratio is the constant that is equal to 1？3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c11 is 175.811 GPa, c12 is 58.604 GPa, c33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.

Accurate calculations of the high-pressure elastic constants based on the first-principles

The energy term corresponding to the first order of the strain in Taylor series expansion of the energy with respect to strain is always ignored when high-pressure elastic constants are calculated. Whether the modus operandi would affect the results of the high-pressure elastic constants is still unsolved. To clarify this query, we calculate the high-pressure elastic constants of tantalum and rhenium when the energy term mentioned above is considered and neglected, respectively.Results show that the neglect of the energy term corresponding to the first order of the strain indeed would influence the veracity of the high-pressure elastic constants, and this influence becomes larger with pressure increasing. Therefore, the energy term corresponding to the first-order of the strain should be considered when the high-pressure elastic constants are calculated.

Stress in Thin Films; Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transverse isotropy is expected, owing to the limited dimensionality. The usually applied models for the calculation of elastic constants of polycrystals from single crystal elastic constants (so-called grain interaction models) erroneously predict macroscopic isotropy for an (untextured) thin film. This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically elastically anisotropic behaviour (shown by non-linear sin2ψ plots). A new grain interaction model, predicting the macroscopically anisotropic behaviour of thin films, is proposed.

Elastic constants and thermodynamic properties of Mg_2Si_xSn_(1-x) from first-principles calculations

This paper stuides the elastic constants and some thermodynamic properties of Mg2SixSn1-x （x = 0, 0.25, 0.5, 0.75, 1） compounds by first-principles total energy calculations using the pseudo-potential plane-waves approach based on density functional theory, within the generalized gradient approximation for the exchange and correlation potential. The elastic constants of Mg2SixSn1-x were calculated. It shows that, at 273 K, the elastic constants of Mg2Si and Mg2Sn are well consistent with previous experimental data. The isotropy decreases with increasing Sn content. The dependences of the elastic constants, the bulk modulus, the shear modulus and the Debye temperatures of Mg2Si and Mg2Si0.5Sn0.5 on pressure were discussed. Through the quasi-harmonic Debye model, in which phononic effects were considered, the specific heat capacities of Mg2SixSn1-x at constant volume and constant pressure were calculated. The calculated specific heat capacities are well consistent with the previous experimental data.

Elastic constants of Al and TiN calculated by ab initio method

The elastic constants of Al single crystal were calculated by ab initio method for calibration. Three deformation directions were selected in order to obtain the different constants of c 11 , c 12 and c 44 . The cohesion energy curves of the three deformation directions were calculated. The results of the second order partial differential at the equilibrium point of the cohesion energy curve provide the elastic constants of the Al single crystal. The changes of crystal symmetry and lattice can lead to the deviations of the calculated cohesion energy curves and the accurate elastic constants can not be obtained, but when the correction is taken into calculation, the calculated results are very close to the literature data. It is very difficult to obtain the elastic constants of thin films by experiment and the data from the handbook are scattered in a large scale. However, the elastic constants calculated by this method can be served as a standard. Though the errors of TiN elastic constants calculated by this method are a little higher than that for Al, the results are acceptable. [

X-ray elastic constant determination and residual stress of two phase TiAl-based intermetallic alloy

To evaluate the residual stress in TiAl based alloys by X ray diffraction, X ray elastic constants (REC) of a γ TiAl alloy were determined. From these results, the stress state of a given phase in a duplex TiAl based alloy under a uniaxial tensile loading has been characterized by X ray diffraction. The results show that the X ray elastic constants and the microscopic stresses of the given phase are different from the apparent elastic constants and the macroscopic stresses of the alloy. The reason of the different distribution of the alloy was also discussed. [