Journal of Engineering Mathematics最新文献

Using the characteristics of the governing quasi-linear system as the referencing coordinate system in the presence of a transverse magnetic field, the evolution of acceleration waves in a non-ideal relaxing gas has been examined along its characteristic path. It is demonstrated that a linear solution in the characteristic plane can behave non-linearly in the physical plane. We have determined the critical amplitude of the initial disturbance; if the initial amplitude of the compressive disturbance is greater than the critical value, the disturbance must culminate into a shock wave, while if it is less than this value, the disturbance will decay, and no shock formation will happen. We establish the criteria for shock generation and the transport equation that governs the development of weak shock waves. Acceleration waves having planar and cylindrical symmetry are analyzed as their steepening, or flattening is investigated as a function of the non-idealness parameter, relaxation parameter, adiabatic index, and magnetic field strength parameter. In both the planar and cylindrical symmetries, the shock formation process is slowed by increasing the relaxation parameter as well as the magnetic field parameter but accelerated by non-idealness and the adiabatic index. In the ideal gas case with adiabatic exponent (gamma = 2), the magnetic field has no effect on the steepening or flattening of the wavefront in both the planar and cylindrical symmetries.

Self-actuated bimorph cantilevers are implemented in a variety of micro-electro-mechanical systems. Their tip deflection relies on the unmatched coefficients of thermal expansion between layers. The thermal bimorph phenomenon is dependent on the temperature rise within the cantilever and, while previous studies have investigated variations in the thermal profile along the cantilever length, these have usually neglected variations in the thermal profile along the cantilever thickness. The current study investigates the thermal distribution across the thickness of the cantilever. The exact closed form solution to the one-dimensional problem of heat conduction in the composite (layered) domain subjected to transient volumetric heating is developed using the appropriate Green’s function. This solution is applied to a one-dimensional case study of a 3-layer cantilever with an Aluminium heater, a silicon dioxide resistive layer, and a silicon base layer. The aluminium heater experiences volumetric heating at a rate of 0.2 mW/μm³ of 5 μs duration at 100 μs intervals (10 kHz with a 1/20 duty cycle). Benchmark solutions of the temperature at select times and positions are provided. It is shown that there are negligible temperature gradients across the cantilever thickness during the heating and the first ~ 5 μs afterward. These short-lived temperature differences are positively biased with the unmatched thermal expansion coefficients between the layers, though their relative influence on bending is not clear. A simple parametric analysis indicates that the relative magnitude of the temperature differences across the cantilever (compared to the overall temperature) decreases substantially with increasing duty cycle.

An analytical model for droplet impact onto a porous substrate is presented, based on Wagner theory. An idealised substrate boundary condition is introduced, mimicking the effect of fluid entry into a genuinely porous substrate. The asymptotic analysis yields a solution for a small porous correction with free-surfaces and pressures compared with the impermeable case. On a global scale, it is found that the impact region on the substrate grows more slowly with porosity included due to loss of mass into the substrate. The spatial distribution of liquid volume flux into the substrate is also described. Locally near the turn-over regions, the expected jetting along the surface is calculated with the same volume flux but the jet is found to be slower and thicker than for an impermeable substrate.

In this paper, we consider the linear stability of ion-irradiated thin films where the typical no-penetration boundary condition has been relaxed to a phase-change or mass conservation boundary condition. This results in the modification of the bulk velocity field by the density jump across the amorphous–crystalline interface as new material enters the film and instantaneously changes volume. In other physical systems, phase change at a moving boundary is known to affect linear stability, but such an effect has not yet been considered in the context of continuum models of ion-induced nanopatterning. We also determine simple closed-form expressions for the amorphous–crystalline interface in terms of the free interface, appealing directly to the physics of the collision cascade, which was recently shown to strongly modify the critical angle at which pattern formation is predicted to begin on an irradiated target. We find that phase-change at the amorphous–crystalline boundary imparts a strong ion, target, and energy dependence and, alongside a precise description of the interfacial geometry, may contribute to a unified, predictive, and continuum-type model of ion-induced nanopatterning valid across a wide range of systems. In particular, we consider argon-irradiated silicon, where the presence of phase-change at the amorphous–crystalline interface appears to predict an experimentally observed, strong suppression of pattern formation near 1.5 keV for that system.

Nowadays, engineers and biochemical industries have benefited greatly from optimal control analysis and its computational methods. Furthermore, the optimal control theory is a powerful instrument in infectious disease modeling and control of vibration in civil engineering structures under random loadings. In this paper, a new solution representation and optimal control of second-order Hilfer fractional stochastic integro-differential systems (HFSIDSs) with non-instantaneous impulsive (NI) are studied. Existence and uniqueness of solutions are proved in the finite-dimensional space by using Schaefer’s type fixed-point theorem with low conservative conditions on nonlinear part. Further, Lagrange problem is considered to establish optimal control results for HFSIDSs with NI. Finally, a pharmacotherapy type Hilfer fractional model is discussed in the example section.