Performance Analysis of IRS-Aided NOMA Communications in the Presence of Imperfect SIC

The intelligent reflecting surface (IRS) is expected to be a promising technique to achieve a robust spectrum and energy efficiency. This paper investigates the advantages of IRS in enhancing performance of non-orthogonal multiple access (NOMA) communications in the presence of imperfect successive-interference-cancellation (SIC) and phase distortion (PD) caused by a non-ideal IRS. Specifically, average achievable rates (AARs) of the users are the target performance metrics. For performance evaluation, the probabilistic characterizations of signal-to-interference-plus-noise ratios (SINRs) at the users are studied. These results allow for deriving the theoretical formulas for the AAR. Monte Carlo simulations are adopted to verify the accuracy of these theoretical results. The numerical results show the effects of various key system parameters, such as source transmit power, NOMA power allocation (PA) factors, reflecting tile (RTs) allocation, the SIC imperfection factor, and the PD factor, on the AAR that provide useful information for the system’s design.

A Modified M-K Method for Accurate Prediction of FLC of Aluminum Alloy

Forming limit curve (FLC) is an important failure criterion for sheet metals in sheet metal forming, while the M-K model is widely used for the prediction of the FLC. In the M-K model, such prediction is greatly influenced by the initial thickness imperfection factor and material properties, from which the original M-K model’s theoretical derivation is proposed as a solution to the above mentioned issue in this paper. Then the relationship between the M-K model and Keeler’s empirical formula is then studied, from which a new method to predict FLC is proposed that combines the M-K model with Keeler’s empirical formula according to the previous analyses. It turns out that this new method can simplify the calculation procedure. Finally, the experimental results of two kinds of aluminum alloys, AA6016 and AA5182, have verified the effectiveness of the proposed method.

Impact of the Automatic Control of a Coal Separation Process in a Jig on its Economic Efficiency

The beneficiation process of fine coal in jigs consists of two phases: stratification of coal grains in the bed according to their density and then splitting the stratified material into the product and the discharged refuse. At first, during subsequent water pulsations induced by opening and closing of air valves, the stratification of coal grains takes place due to varied velocity of their upward and downward movement. Grains of low density migrate to upper layers and grains of high density migrate to lower layers of the bed. The material travels horizontally on a screen along the jig compartment with the flow of water. The stratification of grains due to their density is not perfect, because the velocity of their upward and downward movement depends in part on their diameter, shape and the way in which the material loosens within a given pulsation cycle. The distribution of coal density fractions in the bed, characterized by the imperfection factor I, has been investigated by many researchers. The imperfection factor I is defined as the ratio of the probable error Ep and the separation density ρ50 (I = Ep/ρ50). The distribution of coal density fractions for an ideal and a real stratification process was compared. The maximum mass of the product of the desired quality (ash content) can be achieved for the ideal process when the imperfection I = 0. The stratified bed is then, in the end part of the jig, split into the product which overflows the end wall of the compartment and the refuse (or middlings) discharged through the bottom gate. The separation density (cut point) is established by the tonnage of the discharged bottom product (opening of the discharge gate). The separation density depends also on the tonnage of raw coal feeding the jig, and its washability characteristics. The impact of variations in the separation density on product parameters has been analysed. The mass of the product is always greater when the separation density is constant over a given period of time – even if in spite of its variations the process renders the same average ash content. Hence, the conclusion is to stabilise the separation density at the desired value as accurately as possible. The analysis was performed for raw coal washed in a three-product jig at the separation densities of 1.5 and 1.8 g/cm3. Percent contents (in brackets) of density fractions in raw coal were: <1.35 g/cm3 (40%), 1.35–1.50 g/cm3 (12%), 1.50–1.65 g/cm3 (4%), 1.65–1.80 g/cm3 (4%), 1.80–1.95 g/cm3 (12%, >1.95 g/cm3 (30%) (average ash in raw coal was 35.5%). In the analysis, an increase in the imperfection by 0.02 resulted in the decrease of the product tonnage by ΔQc = 1.0%. In this case, separation densities were set to ensure the same ash content in products (for I = 0 the change in tonnage was accepted at ΔQc = 0). The simulation analysis presented in the paper focused on the impact that fluctuations in separation density have on the economic effects of a jig operation. The influence of the separation density fluctuations on the product tonnage turned out to be nonlinear; for ±0.04 g/cm3 (control system with the radiometric density meter) the decrease in the product tonnage was ca. 0.5 % and for ±0.12 g/cm3 it was ca. 5.0% (control system with a float). The above results indicate that the operation of a refuse discharge system in a jig plays an important role in the final results of coal separation process defined in terms of tonnage and quality of the product.

An Asymptotic Solution for Non-Linear Behavior of Imperfect Shallow Spherical Shells

This paper deals with non-linear behavior of an elastically restrained shallow spherical shell with imperfections and subjected to uniform normal load by the asymptotic iteration method. An asymptotic relation between the external load and central transverse displacement (deflection) of the structure incorporating the effects of the characteristic geometrical parameter, imperfection factor and edge-restraint coefficients is formulated. The corresponding solutions resulting from the use of the second and third iteration processes are compared with each other and available data. The numerical calculations show that the second iteration is adequate for the non-linear analysis of the structure. The effects of geometrical imperfections and boundary constraint coefficients on buckling of the structures are presented graphically.

A Non-Linear Model for Stability Analysis of Reticulated Shallow Shells with Imperfections

A non-linear stability problem of imperfect reticulated shallow shells with distorted rectangular meshes is investigated in this paper. The fundamental governing equations are deduced by adopting an equivalent model and the principle of the virtual work. For the reticulated shallow spherical shell under uniform vertical load, an axisymmetrical case is considered and the analytical solution of the coupled equations is given with the help of the asymptotical iteration method. Meanwhile, non-linear characteristic relations concerning load, deflection and imperfection factor are numerically analyzed. In particular, the corresponding solution degenerates to that of a reticulated circular plate when the radius of curvature of the structure R → ∞.

Buckling of Initially Imperfect Cylindrical Shells Subject to Torsion

An analytical solution based upon large-deflection shell theory is presented for the problem of the elastic instability of a thin cylindrical shell subject to torsion. The fundamental equations used are those presented by Donnell in 1934, and these equations together with the condition of stationary potential energy are employed to determine all arbitrary deflection parameters. Boundary conditions corresponding to clamped-end shells and also to shells having simply supported ends are considered. Load-deformation relations for various magnitudes of initial imperfection of the shell are determined for both boundary conditions. Lastly, values are presented for an imperfection factor based upon existing experimental evidence for clamped-end shells. The investigation described here is a continuation of work done earlier by Loo.