Proceedings of the National Academy of Sciences, India Section A: Physical Sciences最新文献

In this paper we discuss the Busemann-Hausdorff volume form and Holmes-Thompson volume form for the warped product Finsler metrics. With the help of these volume forms we obtain the E-curvature and the S-curvature for this class of metrics. Further, we show that the notion of isotropic E-curvature and isotropic S-curvature are equivalent for this class of metrics.

In this paper, the self-similar solutions for a strong cylindrical or spherical blast (shock) wave in real gas and inert solid particles mixture are analyzed on the basis of the perturbation method. The similarity solution in analytical forms is derived for first-order approximation, and a set of ODE for second-order approximations is also derived using the perturbation method proposed by Sakurai in perfect gas. The physical variable’s distribution in the entire flow field after the blast wave is shown in the figures. The effects of the ratio of the density of the solid inert particles to the initial gas density, mass concentration of particles, and the parameter of real gas effect on the physical variables, the peak pressure on blast wave and the damage radius of blast wave are investigated. It is found that the peak pressure on the blast wave and the damage radius of the blast wave both decrease with an increase in the value mass concentration of solid particles or non-idealness of the gas in the mixture. A comparison has also been made between the cylindrical and spherical geometries. It is found that the blast (shock) wave is more influential in the case of spherical geometry in contrast to that in the cylindrical geometry case. Also, the blast wave decay is due to an increase in the solid particle’s mass concentration or gas non-idealness parameter, and its strength increases with an increase in the ratio of the solid particles to the initial gas density.

In this paper, we have proposed an inventory model for non-instantaneous deteriorating items. To reduce the rate of deterioration, retailers or vendors spend some money to prevent product degradation/decay, known as preservation technology, which is also inserted. In the sequel, the seller provides the buyers with a partial trade credit policy because the partial trade-credit policy is more efficient than a full trade-credit policy. After all, it reduces the possibility of loss for the lender. The main objective of this study is to reduce the total unit cost by determining the replenishment cycle time, order quantity, and preservation technology cost. The mathematical formulation and solution of all possible conditions of the partial trade-credit policy for deteriorating items have been inserted. Numerous theorems and lemmas have been inserted to obtain the optimal solution analytically. Several previous inventory models have been given as exceptional cases. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.

The structure of the plane viscous shock-front in a two-phase gas–solid particle medium is investigated with the help of Navier–Stokes relation using the method of wave-front analysis. The analytical expressions for physical flow variables, i.e. the particle velocity, temperature, pressure, and change-in-entropy within the shock transition region have been derived taking into consideration the two-phase flow gas model. The influence on the structure of the shock-front due to the variation of different flow parameters such as coefficient of viscosity, Mach number, dust loading parameter, and the mass concentration of solid particles in the mixture is analysed. The thickness of the shock-front is calculated with varying different dust flow parameters within the shock transition region. In addition, variations in the thickness due to the viscosity and the shock strength have been observed. The results are compared with the case of dust-free medium. Interestingly, our findings confirm that flow parameters have a reasonable impact on the structure of a steady shock-front.

The lower bound finite element limit analysis technique in conjunction with the second-order conic optimization is used to determine the uplift resistance of pipeline buried in spatially random cohesionless soil. The Cholesky decomposition method is employed to produce the spatially random discretized soil domain. The Monte Carlo simulation technique is implemented to obtain the probabilistic responses. The mean uplift factor and the failure probability of the pipeline for a wide range of practical cases of soil spatial variability are provided as the design charts. It is found that for the smaller value of correlation distance, the deterministic uplift factor is always higher than the mean uplift factor; however, with the increase in the correlation distance, the difference between the deterministic uplift factor and the mean uplift factor reduces. The probability of failure of pipeline is found to be increasing with the reduction in the magnitude of correlation distance and factor of safety. The influence of the soil spatial variability on the failure mechanism is also studied in detail.

Starting with the traditional Wien-bridge sinusoidal oscillator, the grounded-capacitor Wien-bridge sinusoidal oscillator, and adjoint network theorem, four types of the current-mode Wien-bridge sinusoidal oscillator, namely Type A, Type B, Type C and Type D, are discussed by using the second generation current-controlled conveyor (CCCII). Their oscillating condition and oscillating frequency can be separately and electronically varied by setting bias currents of the CCCIIs linearly. Type B oscillator employs four CCCIIs and two grounded capacitors only, it is helpful in integrated circuits, so it is the simplest and most economical circuit with least distortion. The circuit analysis and computer analysis results have been run to sustain the involved method.

Due to the inherent variation across fog, cloud and end devices, task offloading and resource allocation have become complicated issues in a heterogeneous fog–cloud computing environment (HFCE). This study makes an effort to resolve the issue using two popular multi-criteria decision-making (MCDM) techniques, i.e. the analytic hierarchy process (AHP) and technique for order of preference by similarity to ideal solution (TOPSIS). In this study, we present a rank-based computation offloading algorithm for mapping of workflow tasks on three tiers of resources in HFCE. The five performance criteria taken into account are execution time, energy consumption, total cost, resource availability at a specific tier and the processing speed of resources. These performance criteria of the fog, cloud and end devices are evaluated by cascading two separate MCDM techniques. The AHP is used to calculate the priority weights between all the five criteria of evaluation. The TOPSIS method is used to rank the final fog, cloud and end devices, based on the weights of criteria yielded by AHP, and to calculate fuzzy values before offloading each corresponding task. Afterwards, a task can be offloaded to a corresponding resource tier based on the rank. Simulation results demonstrate that the proposed algorithm outperforms conventional offloading algorithms in the HFCE by including performance and cost criteria while offloading decision making, especially in cases where the amount of tasks is large.

In the present paper, we consider the higher-order (j-th order, (jin textbf{N}_{0})) Bernstein–Kantorovich operators, which are connected with the Bernstein polynomials. We estimate some direct results including the Voronovskaja-kind asymptotic formula, simultaneous approximation and error estimations. In the end, we present comparative study through graphical representation and numerically interpret the upper bound of the error value.

This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.

This study was carried out to evaluate the functionality of an existing reinforced concrete structure under various ground motions along with its seismic resilience. An existing high-rise G + 10 storey reinforced concrete building which was designed for a specific ground motion with peak ground acceleration (PGA) of 0.36 g was subjected to various seismicity with respect to different ground motions of PGA ranges from 0.10 to 1.70 g. For each case, the performance level and structural damage ratio were estimated by performing nonlinear static pushover analysis. The influences of different ground motions on the structural functionality and seismic resilience were examined using three recovery functions namely, linear, trigonometric and exponential. The result shows that the maximum number of hinges formed with the performance level close to or just exceeding the level of collapse prevention at the maximum considered PGA of 1.50 g and 1.70 g with loss of resilience up to 36.25%. The maximum level of PGA that the existing building would withstand along with likelihood of recovery has been obtained.