Analytic expression

An analytical approach for nonlinear buckling of functionally graded graphene platelet reinforced composite toroidal shell segments is presented in this paper. The Ritz energy procedure is executed, and radial pressure– deflection expression is constituted to obtain the postbuckling strength and critical buckling pressure of the shells.

7p viengfa 28-10-2024 3 1   Download

The research work expresses an ongoing and evolving process that has been guided and influenced by current Indigenous and non-Indigenous Australian postcolonial critical thinking and arts criticism, assisting within the development of my personal views and philosophies .This process has supported the formation of a belief system that I believe has matured throughout my research and art practices, providing a personal confidence to assert my own analytical stance on colonial history.

89p runthenight07 01-03-2023 7 2   Download

In present paper "Equation of state and thermal expansion of metals with FCC structure: Application to Cu, Al and Ni", by the statistical moment method (SMM) we obtain the equation of state for metals with cubic structure at temperature 0 K and pressure P and from that obtain the expressions of lattice parameter and thermal expansion coefficient for these metals at temperature T and pressure P.

6p runordie3 27-06-2022 13 2   Download

The analytic expressions of the free energy, the mean nearest neighbor distance between two atoms, the elastic moduli such as the Young modulus E, the bulk modulus K, the rigidity modulus G and the elastic constants C11, C12, C44 for substitution alloy AB with interstitial atom C and BCC structure under pressure are derived from the statistical moment method.

12p vijichoo2711 04-06-2021 16 1   Download

The analytical expression for the self-Kerr nonlinear coefficient in a three-level V-type atomic medium is found in the presence of the Doppler effect. Based on the analytical results, we have analyzed the enhancement and control of the Kerr nonlinear coefficient under the condition of electromagnetically induced transparency. It is shown that the Kerr nonlinear coefficient is significantly enhanced around the resonant frequency of both the probe and coupling fields.

12p nguaconbaynhay10 19-02-2021 29 4   Download

The analytic expressions of thermodynamic quantities such as the Helmholtz free energy, the internal energy, the entropy, the molar heat capacity at constant volume for molecular cryocrystals of N2 type with face-centered cubic (FCC) and hexagonal close-packed (HCP) structures in harmonic, classical and anharmonic approximations are obtained by combining the statistical moment method (SMM) and the self-consistent field method (SCFM).

10p tamynhan5 10-12-2020 12 1   Download

The analytical expressions for the wave functions of two-component Bose-Einstein Condensates are derived by means of the Gross-Pitaevskii equations in linear approximation. Based on the Bernoulli equation the shape of the interface and the dispersion relations for both phonon and ripplonare studied.

6p tamynhan5 10-12-2020 13 1   Download

We build the theory of diffusion for FCC binary interstitial alloy under pressure based on the statistical moment method, where there are the analytic expressions of the jumping frequency of interstitial atom, the effective jumping length, the correlation factor, the diffusion coefficient, and the activated energy. In limit cases, we can obtain the diffusion theory for FCC metal A under pressure.

6p tamynhan5 10-12-2020 6 1   Download

Some thermodynamic quantities of ZrxCe1-xO2/CeO2 systems are investigated by using the moment method in statistical dynamics taking into account the anharmonicity effects of lattice vibrations. The analytic expression of the Gibbs free energy, Helmholtz free energy, and specific heats at the constant volume of ZrxCe1-xO2/CeO2 systems are obtained.

11p tamynhan9 02-12-2020 13 1   Download

Thermodynamic properties of rare-earth metals have been studied using staistical moment method. The analytic expressions of the Helmholtz free energy and thermodynamic quantities were obtained. Present SMM results of nearest neighbor distance, linear thermal expansion coefficient and specific heats at constant pressure for Th and Ce metals are compared with the experimental results.

7p tamynhan8 04-11-2020 12 1   Download

The analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) caused by confined electrons in the presence of laser radiation modulated by amplitude in doped superlattices (DSL) are obtained by using the quantum kinetic equation for electrons in the case of electron–optical phonon scattering.

11p tamynhan8 04-11-2020 17 3   Download

We obtained the analytic expressions of the specific heat at constant volume of metals which are dependent on the value of q-deformed parameters. Results calculated for the specific heat at constant volume for some kinds of alkali and transition metals show good agreement with those obtained by other theories and in experiments as well.

8p tamynhan8 04-11-2020 6 2   Download

The electron – optical phonon scattering is considered in detail to studying the Ettingshausen effect in doped semiconductor superlattice under the influence of phonon confinement and laser radiation. The analytical expressions for tensors and the Ettingshausen coefficient are obtained by using the kinetic equation method.

8p tamynhan6 14-09-2020 18 2   Download

Analytical expressions for the anharmonic effective potential, local force constant, Displacement-displacement Correlation Function (DCF) CR and Debye-Waller factor described by the Mean Square Relative Displacement (MSRD) σ2 and by the Mean Square Displacement (MSD) u2of bcc crystals in the X-ray Absorption Fine Structure (XAFS) have been derived. The effective interatomic potential of the system has been considered by taking into account the influences of nearest atomic neighbors, and it contains the Morse potential characterizing the interaction of each pair of atoms.

8p 12120609 01-06-2020 14 2   Download

High-order anharmonic effective potentials and four EXAFS cumulants have been studied taking into account the influence of the nearest neighbors of absorbing and backscattering atoms by Analytical expressions of th quantum potential expanded in the fourth order which influences from the 4thcumulants. Numerical results for Ni are found to be in good a experiment and the classical theory.

6p advanger2 06-05-2018 35 0   Download

This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. ...

52p noel_noel 17-01-2013 59 5   Download

The parametric transformation of acoustic and optical phonons in doped superlattices is theoretically studied by using a set of quantum kinetic equations for the phonons. The analytic expression of parametric transformation coefficient of acoustic and optical phonons in doped superlattices is obtained, that depends non-linear on the concentration of impurities. Numerical computations of theoretical results and graph are performed for GaAs:Si/GaAs:Be doped superlattices

6p tuanlocmuido 19-12-2012 43 4   Download

Anharmonic effective potential, effective local force constant, thermal expansion coefficient, three leading cumulants, and EXAFS (Extended X-ray Absorption Fine Structure) of hcp crystals have been studied. Analytical expressions for these quantities have been derived. Numerical calculations have been carried out for Zn and Cd. They show a good agreement with experiment results measured at HASYLAB (DESY, Germany) and unnegligible anharmonic effects in the considered quantities.

7p tuanlocmuido 19-12-2012 51 2   Download

A new procedure for calculation and analysis of XAFS (X-ray Absorption Fine Structure) cumulants of hcp crystals containing dopant atom has been derived based on quantum statistical theory with generalized anharmonic correlated Einstein model. Analytical expressions for effective local force constants, correlated Einstein frequency and temperature, first cumulant or net thermal expansion, second cumulant or Debye Waller factor and third cumulant of hcp crystals containing dopant atom have been derived.

7p tuanlocmuido 19-12-2012 38 3   Download

SMOOTH AND DISCRETE SYSTEMS—ALGEBRAIC, ANALYTIC, AND GEOMETRICAL REPRESENTATIONS ˇ FRANTISEK NEUMAN Received 12 January 2004 What is a differential equation? Certain objects may have different, sometimes equivalent representations. By using algebraic and geometrical methods as well as discrete relations, different representations of objects mainly given as analytic relations, differential equations can be considered.

10p sting12 10-03-2012 30 4   Download