Parameters Γ1 Research Articles

An extended thermal pressure equation of state for sodium fluoride

The effect of pressure and temperature on the unit-cell volume of NaF has been measured by X-ray powder diffraction at ambient pressure between 12 and 300 K and neutron powder diffraction up to 5 GPa between 140 and 350 K. These data have been combined with high-pressure volume data at 300 and 950 K to 25 GPa and adiabatic bulk modulus data to 650 K to define an equation of state for NaF relating molar volume to both temperature and pressure. The model combines a fourth-order Birch–Murnaghan equation of state at 295 K with a Mie–Grüneisen–Debye model for thermal pressure. The parameters of the model set at 295 K and ambient pressure are as follows: reference unit-cell volume V 0 = 14.9724 (5) cm3 mol−1, isothermal bulk modulus K 0T = 46.79 (14) GPa, first derivative of the bulk modulus K′0T = 5.72 (12), second derivative of the bulk modulus K′′0T = −0.43 (4) GPa−1, Debye temperature T MGD = 459 (3) K, and Anderson Grüneisen parameters γ0 = 1.547 (11) and q = 0.94 (18).

On the blow-up for a Kuramoto–Velarde type equation

It is known that the Kuramoto–Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters γ1 and γ2 involved in the non-linear terms verify γ2=γ12 or γ2=0. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto–Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework γ2≠γ12 and γ2≠0, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. As a complement to it, we address an alternative result on the finite-time blow-up of smooth solutions by considering a virial-type estimate.

Dynamics and control of a plant-herbivore model incorporating Allee's effect

This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect. We specifically investigate a model that incorporates a strong predator functional response to better understand the system's qualitative behavior at positive equilibrium points. In the present study, we explore the topological classifications at fixed points, stability analysis, Neimark-Sacker, Transcritical bifurcation and State feedback control in the two-dimensional discrete-time plant-herbivore model. It is proved that for all involved parameters ς1,ϱ1,γ1 and ϒ1, discrete-time plant-herbivore model has boundary and interior fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1). Our investigation uncovers that the boundary equilibrium c2=(ς1−1ϱ1,0) experiences a transcritical bifurcation, whereas the unique positive steady-state c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) of the discrete-time plant-herbivore model undergoes a Neimark-Sacker bifurcation. To address the periodic fluctuations in grapevine population density and other unpredictable behaviors observed in the model, we propose implementing state feedback chaos control. To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent. These visual representations enhance the clarity of our research outcomes and further validate the effectiveness of the chaos control approach.

Experimental Study of Hardening Small Strain Model Parameters for Strata Typical of Zhengzhou and Their Application in Foundation Pit Engineering

The hardening small strain (HSS) model, which considers the non-linear characteristics of the shear modulus of soil in the small strain range, is commonly utilized in the numerical analysis of excavations in sensitive environments. In order to ascertain the parameters of an HSS model for strata typical of Zhengzhou, an extensive series of laboratory tests was executed. Subsequently, a statistical analysis was utilized to establish the relationships between the principal parameters. A three-dimensional finite element model was established based on the excavation of representative strata in Zhengzhou. The accuracy and applicability of the model parameters were verified using the field measurement data. In addition, an analysis of the sensitivity of the main HSS model parameters to the foundation pit deformation was also carried out. The results show that the HSS model can analyze excavation deformation with greater precision than the hardening soil (HS) model or the Mohr–Coulomb (MC) model. The small strain parameters G0ref and γ0.7 have a great influence on the horizontal displacement of the support and the vertical displacement of soil behind the wall, respectively. The research results serve as a reliable foundation for both the analysis of excavation deformation and the determination of HSS model parameters for strata typical of Zhengzhou.

Stochastic numerical computing for entropy optimized of Darcy-Forchheimer nanofluid flow: Levenberg Marquardt Algorithm

The work in hand examines the entropy generation of magnetohydrodynamic Darcy-Forchheimer nanofluid flow model (MHD-DFNM) over a stretched surface via Artificial back propagated neural networks with Levenberg Marquardt Algorithm (ABNN-LMA). Two types of nanoparticles i.e Silicon dioxide (SiO2) and Molybdenum disulfide (MoS2) and continuous phase liquid i.e propylene glycol is considered. The PDEs of MHD-DFNM are transformed into coupled ODEs via appropriate (similarity) transformations. The reference dataset is obtained by the variation of 1st and 2nd order slip parameters (γ1 and γ2), porosity parameter (β), viscosity parameter (λ), radiation parameter(R), volume friction coefficient(ϕ), heat generation/absorption parameter(Q), Biot number (B1) and Eckert number (Ec) from Homotopy Analysis Method (HAM). The reference data is executed in training/testing/validation sets to find and analyze the approximated solution of designed ABNN-LMA as well as it’s comparison with reference data solution. The better performance is consistently certified with Mean Squared Error (MSE) curves, regression index and error histogram study. Results reveal that, increase in values of porosity parameter declines the velocity profile for both SiO2 and MoS2 nanoparticles suspended in propylene glycol nanofluids. The thermal profile improves for both SiO2 − propylene glycol and MoS2 − propylene glycol nanofluids when heat generation parameter increases.

A method of calculating volume dependence second and third order Grüneisen parameter for MgO

In the paper, we have analyzed the volume dependence Grüneisen parameter of MgO in the different models. The Grüneisen parameter and its logarithmic volume derivatives so called the second (q) and third order Grüneisen parameter (λ) are formulated in the different models. We also introduced the generalized formula from the fitting of experimental data for MgO solids in these models. The experimental initial Grüneisen parameters (γ0) is comparable with the different model of calculations. We perform the calculation of the volume dependence of second and third order Grüneisen parameters according to the different models. The calculated results show the volume dependence of the second order and third order Grüneisen parameters in this case. We found that the parameter q decrease with decreasing volume dependence. We also found that the parameter λ increase with decreasing volume dependence.

Onset of instability in Hadley–Prats flow in a weakly heterogeneous porous layer with viscous dissipation

The stability of a flow subjected to an inclined temperature gradient (Hadley-type flow) in a horizontal porous media is studied in the presence of a basic horizontal mass flow (Prats flow). Therefore, the basic flow is called the Hadley–Prats flow. A weak vertical heterogeneity in permeability and conductivity is considered. The effect of viscous dissipation is taken to be non-negligible. The Rayleigh number corresponding to the vertical thermal gradient RaC is considered as an eigenvalue. Other parameters are the Péclet number (Pe) associated with the horizontal through flow, horizontal Rayleigh number (RaH) associated with the horizontal temperature gradient, Gebhart number (Ge) associated with viscous dissipation; parameters γ1 and γ2 represent the changes in permeability and conductivity, respectively. A linear stability analysis is done and the governing equations are solved numerically to obtain the critical Rayleigh number and wave number. Longitudinal and transverse rolls are discussed. Longitudinal rolls are the preferred modes for instability in most scenarios. It is found that when throughflow is present, the heterogeneity in permeability can show a stabilizing effect for longitudinal rolls but destabilizing effect for transverse rolls and vice versa depending on the direction of the throughflow. Increase in conductivity also may stabilize or destabilize the flow depending on the mass flow and viscous heating. The horizontal thermal gradient shows interesting effects in the presence of weak heterogeneity and horizontal throughflow. Significant change in the critical Rayleigh number is observed even for small values of the horizontal Rayleigh number.

Crashworthiness analysis and optimization of bionic corrugated sandwich structures

To improve the crashworthiness of thin-walled sandwich structures, a series of bionic corrugated sandwich structures with triangular elements (the height-to-width ratios of the elements are defined as γ) were designed inspired by the structures of shrimp chelas, including single-layer, double-layer and three-layer corrugated sandwich structures (γ1, γ2 and γ3 denotes the height-to-width ratios of single-layer, double-layer and three-layer elements, respectively). To analyze the deformation and mechanical response of the bionic thin-walled structures, the finite element method was adopted based on LS-DYNA and HyperMesh. By taking the initial peak load Fp and specific energy absorption Es as crashworthiness indexes, the influences of γ on the crashworthiness of the corrugated sandwich structures were discussed. The crashworthiness of the single-layer sandwich structures becomes worse gradually when the parameters γ exceed a certain value. For the double-layer sandwich structures, the influences of the parameters γ2 in the lower layers on the crashworthiness is greater than that of the parameters γ1 in the upper layers.. The Fp decreases by 37.8% with the increase of γ2, which means the greater γ2 of the lower layer is beneficial to improve the crashworthiness of the structure. For the three-layer sandwich structures, the influence of γ on crashworthiness indexes was investigated by range and variance analysis methods. The results show that the γ3 has the most significant influence on Es, and the significance level reaches 0.1. Finally, the optimal parameters of the bionic corrugated sandwich structures were obtained by using the multi-objective particle swarm optimization method based on a polynomial regression (PR) meta model. The optimal results show that the crashworthiness of the single-layer corrugated sandwich structures improves with the increase of γ. For the double-layer corrugated sandwich structures, The γ of the lower layer affects the crashworthiness more significantly than the γ of the upper layer. The three-layer corrugated sandwich structure with lower γ has higher Es. The optimal dimensions of the single-layer, double-layer and three-layer structures are γ = 0.8; γ1 = 0.5 and γ2 = 1.2; γ1 = 0.6, γ2 = 0.6 and γ3 = 0.9, respectively. The above results are helpful for the design of the thin-walled sandwich structures.

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution.

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

Thermoelastic properties of zircon: Implications for geothermobarometry

Abstract A thermal-pressure equation of state has been determined for zircon (ZrSiO4) that characterizes its thermoelastic behavior at metamorphic conditions. New pressure-volume (P-V) data from a “Mud Tank” zircon have been collected from 1 bar to 8.47(1) GPa using X-ray diffraction, and elastic moduli were measured from room temperature up to 1172 K by resonance ultrasound spectroscopy. These data were fitted simultaneously with temperature-volume (T-V) data from the literature in EosFit7c using a new scaling technique. The parameters of a third-order Birch-Murnaghan EoS with a Mie-Grüneisen-Debye model for thermal pressure have compressional EoS parameters K0T = 224.5(1.2) GPa, K0T′ = 4.90(31) with a fixed initial molar volume V0 = 39.26 cm3/mol and thermal parameters γ0 = 0.868(15), q = 2.37(80), and ΘD = 848(38) K. EoS parameters that describe the variation of unit-cell parameters with pressure and temperature were determined using an isothermal-type EoS. This new EoS confirms that zircons are stiffer than garnets and exhibit a much lower thermal expansion. This results in steep isomekes between zircon and garnets, which makes zircon trapped as inclusions in garnets at metamorphic conditions a good piezothermometer.

Speed-dependent broadening of the [formula omitted] fine-structure lines

Pressure broadening of the molecular oxygen fine-structure lines near 60 GHz was experimentally reexamined in the range of rotational quantum numbers up to N=39, in the pure gas at room temperature. The analysis of a representative set of individual line profiles with N varying from 1 to 21 included the speed dependence of collisional relaxation, which affects absorption by 0.25–0.5% of maximum at low pressures. The ratio of the two speed-dependence parameters γ0 and γ2 exhibits no notable variation with N. Obtained data are compared with similar parameters of other oxygen bands in the near-infrared and visible spectral ranges. Assuming similar speed dependence in air as for pure oxygen, we find that at 1-atm pressure, the impact of introducing speed-dependent line mixing and broadening coefficients into a model for the atmospheric oxygen 60-GHz band is 0.05–0.1% of maximum absorption, much smaller than the influence of either first- or second-order speed-independent line mixing.

Global and exponential attractors for extensible thermoelastic plate with time-varying delay

A class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time-dependent delay in the internal feedback are considered. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of global solution. The proof with or without rotational inertia, does not depend on the parameters γ1 and γ2 of time-dependent delay. Moreover, the existence of compact global and exponential attractors is proved through a stabilizability estimate. This estimate which is established under restrictions on γ1 and γ2 and independently of the rotational inertia parameter ϖ, provides bounds on the attractors' fractal dimension. Other property such as additional smoothness of global attractors with respect to parameter ϖ is also presented. Furthermore, the existence of a generalized fractal exponential attractor is also derived. Finally, we show that the family of global attractors is continuous with respect to the parameter ϖ in some sense.

Modeling and complexity of stochastic interacting Lévy type financial price dynamics

In attempt to reproduce and investigate nonlinear dynamics of security markets, a novel nonlinear random interacting price dynamics, which is considered as a Lévy type process, is developed and investigated by the combination of lattice oriented percolation and Potts dynamics, which concerns with the instinctive random fluctuation and the fluctuation caused by the spread of the investors’ trading attitudes, respectively. To better understand the fluctuation complexity properties of the proposed model, the complexity analyses of random logarithmic price return and corresponding volatility series are preformed, including power-law distribution, Lempel–Ziv complexity and fractional sample entropy. In order to verify the rationality of the proposed model, the corresponding studies of actual security market datasets are also implemented for comparison. The empirical results reveal that this financial price model can reproduce some important complexity features of actual security markets to some extent. The complexity of returns decreases with the increase of parameters γ1 and β respectively, furthermore, the volatility series exhibit lower complexity than the return series

Limit distributions of generalized order statistics in a stationary Gaussian sequence

In this paper we study the limit distributions of extreme, intermediate and central m-generalized order statistics, as well as m-dual generalized order statistics, of a stationary Gaussian sequence under equi-correlated set up. Moreover, the result of extremes is extended to a wide subclass of generalized order statistics, as well as dual generalized order statistics, when the parameters γ1,n, γ2,n, … , γn,n are assumed to be pairwise different.

On the Transmission of Colour Image over Double Generalized Gamma FSO Channel

In this paper performance analysis of colour image Free Space Optics (FSO) transmission over Double Generalized Gamma (DGG) turbulence communication channel is carried out. At the reception side, we have used an average bit error rate (ABER) for reconstructed image performance measure, as the function of FSO link transmission parameters, such as propagation distance, Rytov variance and turbulence shaping and severity parameters (γ1, γ2, m1, m2). Obtained results cover a large number of colour image FSO transmission scenarios, for Gamma-Gamma, Double-Weibull and K turbulence models channels considered as special cases.DOI: http://dx.doi.org/10.5755/j01.eie.23.2.18004

Electrical and optical conductivities of hole gas in p-doped bulk III–V semiconductors

We study electrical and optical conductivities of hole gas in p-doped bulk III-V semiconductors described by the Luttinger Hamiltonian. We provide exact analytical expressions of the Drude conductivity, inverse relaxation time for various impurity potentials, Drude weight, and optical conductivity in terms of the Luttinger parameters γ1 and γ2. The back scattering is completely suppressed as a result of the helicity conservation of the heavy and light hole states. The energy dependence of the relaxation time for the hole states is different from the Brooks-Herring formula for electron gas in n-doped semiconductors. We find that the inverse relaxation time of heavy holes is much less than that of the light holes for Coulomb-type and Gaussian-type impurity potentials and vice-versa for a short-range impurity potential. The Drude conductivity increases non-linearly with the increase in the hole density. The exponent of the density dependence of the conductivity is obtained in the Thomas-Fermi limit. The Drude weight varies linearly with the density even in the presence of the spin-orbit coupling. The finite-frequency optical conductivity goes as ω, and its amplitude strongly depends on the Luttinger parameters. The Luttinger parameters can be extracted from the optical conductivity measurement.

Initial uptake of NO2 on methane flame soot

A thermostated flow reactor with a movable soot-coated insert coupled to a high-resolution mass spectrometer with low-energy electron ionization is used to study the uptake of NO2 reagent gas at [NO2] = 1 × 1012−2 × 1013 cm−3 and a humidity of [H2O] = 5 × 1012−1.8 × 1015 cm−3. The BET (Brunnauer-Emmett-Teller) method is used to determine the specific surface area of the soot coating: (40 ± 10 (2σ)) m2/g. A set of time-dependent uptake coefficients of NO2 on fresh soot coatings in this range of reactant gas concentrations is determined. An analysis of the experimental data shows that the uptake coefficient depends on the time as 1/γ(t) = 1/γ0 + c1t and yields the dependences of the parameters γ0 and c1 on the NO2 concentration: 1/γ0 = c2 + c3[NO2] and c1 = k[NO2] with constants c2 = (6.5 ± 1.3) × 103, c3 = (5.6 ± 1.3) × 10−10 cm3 molecule−1, and k = (2.4 ± 0.2) × 10−10 cm3 molecule−1 s−1. The gas-phase products of NO2 uptake on soot are NO and HONO, with the NO yield constituting ∼50% of the reacted NO2. It is experimentally demonstrated that an increase in the humidity causes no changes in the uptake coefficient and in the composition and ratio of the products. The initial stage of NO2 uptake on a methane soot coating is described using the Langmuir adsorption model, according to which the process of uptake consists of a sequence of elementary steps, such as reversible adsorption, surface complex formation, and its subsequent unimolecular decomposition to form products. Interpretation of the experimental dependence γ0 = f([NO2]) enables to estimate the Langmuir constant for the NO2-methane soot pair, KL = (8.6 ± 2.6) × 10−14 cm3 molecule−1, the rate constant for NO2 desorption from the soot coating, kd = (530 ± 160) s−1, and the rate constant for the monomolecular decomposition of the surface complex, kr = (8.2 ± 2.5) × 10−2 s−1.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Small strain stiffness and stiffness degradation curve of Bangkok Clays

The small strain stiffness and the stiffness degradation curve of soils are required in advanced numerical analyses of geotechnical engineering problems. The shear modulus at small strain (Gmax) and the reference shear strain parameter (γ0.7) are, for instance, two of the input parameters in a finite element analysis with the hardening soil model with small strain stiffness. The stiffness and strength parameters for the hardening soil model of soft and stiff Bangkok Clays has recently been published (Surarak et al., 2012). This paper is a continuation on the previous study on the stiffness of Bangkok Clay, and focuses on the small strain characteristics. The data are from the Bangkok MRT Blue line project as well as comprehensive studies at Chulalongkorn University and the Asian Institute of Technology. Based on these laboratory and field testing data, the parameters Gmax and γ0.7 can be determined using well-known empirical correlations and the concept of threshold shear strain. Finally, a comparison between the measured data and predictions is made.

Kinetic Mechanism of ClONO2 Uptake on Polycrystalline Film of NaCl

Kinetic studies and the mechanism determination of ClONO2 uptake on polycrystalline NaCl were carried out using a coated-insert flow tube reactor combined with high-resolution, low-energy electron-impact mass spectrometer under the following conditions: p = 1-2 Torr, linear flow velocity v = 3.5-75 m s(-1), T = 293 and 387 K, [ClONO2] = (0.5-25) x 10(12) molecules cm(-3). The salt was deposited as a film from nonsaturated aqueous solution on the sliding rod. The temporal dependences of the uptake coefficient and the partial uptake coefficients leading to a formation of the prime Cl2 and HOCl products were measured for different ClONO2 concentrations. These dependences are established to be described by gamma = gamma0 exp(-t/tau) + gamma(s), gamma(0,s)(-1) = a(0,s) + b(0,s)[ClONO2]. In the framework of the proposed kinetic model, the data are explained and the main elementary kinetic parameters of the uptake are evaluated. The model is based on a combination of Langmuir adsorption, formation of surface complexes on initial active sites, Z(ch), followed by their unimolecular decomposition. Decomposition is proposed to proceed concurrently in two channels, one of which is a released surface site that conserves the properties of the initial site. In the other channel, the initial Z(ch) transforms into Z(ph) followed by steady-state uptake and reproduction of final Z(ph). The model gives an analytical expression for experimental parameters gamma0, gamma(s), and tau in terms of elementary rate constants and the reactant volume concentration. The final objective of the proposed model is the extrapolation of gamma0, gamma(s), and tau parameters to real tropospheric conditions.