Journal of Engineering Mathematics最新文献

Shallow-water fluid sloshing in the Lagrangian Particle Path formulation, with the addition of an energy-extracting porous baffle, is simulated numerically using a symplectic numerical scheme which captures, in an essential way, the energy exchange. The fluid motion in a rectangular vessel is dynamically coupled to a surface-piercing porous baffle. The fluid transmission through the baffle is characterized by a nonlinear Darcy–Forchheimer model equation. The numerical scheme is symplectic, based on the implicit-midpoint rule, and thus is strategically designed to maintain the energy partition between the fluid and vessel throughout numerous time steps. Our results demonstrate the non-conservative nature of the system, with the porous baffle effectively dissipating energy from the overall system. Furthermore, we present findings that demonstrate the role of time-periodic variations in baffle porosity on energy dissipation. By manipulating the frequency and magnitude of this time-dependent variability, it is established that a greater amount of energy can be extracted from the system compared with the optimal fixed porosity baffle. These results shed new light on potential strategies for enhancing energy dissipation in such configurations.

This study focuses on modeling ideal nonuniform standing beams and towers supporting a constant top mass. We also analyze their dynamical stability, as determining the design parameters influencing their shape and stability holds significant value for structural engineering. Initially, we employ a statical mechanics approach to balance the mechanical and gravitational forces. By solving an initial-value problem, we derive the cross-sectional areas of the columns. Our findings reveal that these areas, rather than the shapes, are the primary contributors to the engineering performance of the columns. Additionally, the top mass acts as a multiplying factor for the cross-sectional areas, and the density distribution along the column determines whether the top should be heavier or lighter. Furthermore, we demonstrate that exponential, parabolic, or linear cross-sections with significantly wider base profiles are crucial for accommodating heavier top loads. Moving on to the dynamical analysis, we consider two ideal tower configurations: FC and SC. Numerical and analytical results reveal that higher modes exhibit shorter amplitudes. FC modes necessitate higher design parameters to resist buckling phenomena, whereas SC modes show lower resistance to vibrational deflections. In terms of stability, a heavier top mass enhances the vertical beam’s stability, while towers with parabolic bases are more susceptible to instabilities.

Surface-attached air bubbles are known to provide lubricating (i.e., drag reducing) benefits but their contribution to inhibiting heat transfer is not as well understood. The present theoretical study considers Stokes flow around a solid sphere and uses matched asymptotic expansions to estimate the degree of thermal insulation offered by an encapsulating air layer of uniform thickness. Key to our analysis is to derive an expression for the Nusselt number in terms of the air layer thickness and the Péclet number, (text{ Pe}_w), of the surrounding liquid, here assumed to be water. This latter parameter, which characterizes advective to diffusive heat transport, is assumed to be small such that our zeroth- and first-order solutions are, respectively, proportional to (text{ Pe}_w^0) and (text{ Pe}_w^1). Although small (text{ Pe}_w) favors small free stream velocities, forced convection will dominate over natural convection only if the free stream velocity (and/or the solid sphere radius) exceeds a certain threshold. This requirement constrains the solution space; on the other hand, it is straightforward to generalize our analysis so that it considers fluid pairs other than water and air.

Given two phases in equilibrium in a porous solid, the heavy phase lying above the light phase in a gravitational field, we stabilize this adverse density arrangement by heating from below and derive a formula for how steep the temperature gradient must be to do this. The input temperature gradient has two effects on the stability of our system. Its effect on the heat convection is destabilizing, its effect on the heat conduction at the surface is stabilizing. By directing our attention to the case of zero growth rate, we obtain the critical value of the input temperature gradient as it depends on the permeability of the porous solid, the density difference across the surface, the distance between the planes bounding our system, and the physical properties. Our problem makes connections to the Bénard problem where it has two, one, or no critical points, and to the Rayleigh–Taylor problem where it has no critical points.

The Expectation Maximization (EM) algorithm, a popular method for maximum likelihood estimation of parameters, requires a complete data space and construction of a conditional expectation. For many statistical models, these may not be straightforward. This paper proposes a simpler Alternating Minimization (AM) algorithm using a probability generating function (pgf)-based divergence measure for estimation in univariate and bivariate distributions. The performance of the estimation method is studied for the negative binomial and Neyman Type-A distributions in the univariate setting, while for bivariate cases, the bivariate Poisson and the bivariate negative binomial distributions are considered. Comparison is made with direct optimization of pgf-based divergence measure and maximum likelihood (ML) estimates. Results produced via AM in both simulated and real-life datasets show an improvement in comparison to direct pgf optimization, especially in the bivariate setting, with the execution time showing an improvement for large sample sizes when compared to ML. Goodness-of-fit tests show that the pgf divergence measure with AM estimates mostly perform similarly to the ML estimates in terms of power of the test.