The Lyapunov stability theorem is used to derive a control law that can be used to control the spacing between vehicles in a platoon. A third order system is adopted to model the vehicle and power-train dynamics. In addition, the concept of "Expected Spacing Error" is introduced and used to form a Lyapunov function. Then a control law that always decreases the Lyapunov function is selected. A p...

the combined effect of non-newtonian rheology and irreversible boundary reaction on dispersion in a herschel-bulkley fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. the study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion co...

Kramers-Kronig (K-K) relations exist as a consequence of causality, placing nonlocal constraints on the relationship between dispersion and absorption. The finite-bandwidth method of applying these relations is examined where the K-K integrals are restricted to the spectrum of the experimental data. These finite-bandwidth K-K relations are known to work with resonant-type data and here are appl...

Understanding tumor growth dynamics is important for planning cancer therapy, especially in radiotherapy, where standard fractionation is determined based on the assumption that tumors grow exponentially. In this chapter, we explore the ramifications of an alternative, but equally plausible, assumption of tumor growth, namely power growth law, realized in linear increase in tumor diameter. We p...

This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric...

in this paper, the homotopy analysis method (ham) is considered to obtain the solution of the schrodinger equation with a power law nonlinearity. for this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region...

The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power-law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in t...

Several types of extra-galactic high-energy transients have been discovered, which include high-luminosity and low-luminosity long-duration gamma-ray bursts (GRBs), short-duration GRBs, supernova shock breakouts (SBOs), and tidal disruption events (TDEs) without or with an associated relativistic jet. In this paper, we apply a unified method to systematically study the redshift-dependent event ...