Taming Hyperchaos with Exact Spectral Derivative Discretization Finite Difference Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

Four discrete models, using the exact spectral derivative discretization finite difference (ESDDFD) method, are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is, in part, an artifact of the CEFD method, as it is absent from the ESDDFD models.

A Finite Difference Method for the Variational p-Laplacian

We propose a new monotone finite difference discretization for the variational p-Laplace operator, $$\Delta _pu=\text{ div }(|\nabla u|^{p-2}\nabla u),$$ Δ p u = div ( | ∇ u | p - 2 ∇ u ) , and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one explicit method. Finally, we exhibit some numerical simulations supporting our theoretical results. To the best of our knowledge, this is the first monotone finite difference discretization of the variational p-Laplacian and also the first time that nonhomogeneous problems for this operator can be treated numerically with a finite difference scheme.

Performance Analysis of an Adsorption Refrigeration System Working on Activated Carbon/Methanol Pair Using Finned Tube Type Adsorber Bed

Adsorption refrigeration, being a unique and eco-friendly technology, has gained popularity over conventional refrigeration systems. The present study is aimed at developing an annular finned tube adsorber model which serves as a thermal compressor in adsorption refrigeration systems. The mathematical model is addressed numerically using finite difference discretization method and explicit scheme was used for the solution. The generalized model has been simulated for activated carbon–methanol working pair. The system has an optimum cycle time of 1800s. It was found to have a highest refrigeration capacity of 260.66 kJ/kg at a regeneration temperature of 393 K and evaporator temperature of 283 K. The highest COP (Coefficient of Performance) achieved by the system is 0.3706 at a regeneration temperature of 353 K and evaporator temperature of 283 K. A highest SCP (Specific Cooling Power) of 144.8 W/kg was obtained at an evaporator temperature of 283 K and regeneration temperature of 393 K.

Nonlinear Supratransmission in Quartic Hamiltonian Lattices With Globally Interacting Particles and On-Site Potentials

We investigate a family of one-dimensional (1D) Hamiltonian semi-infinite particle lattices whose interactions involve exclusively terms of fourth order in the potential. Our aim is to examine their distinct role in the dynamics, in the absence of quadratic (harmonic) interactions, which are typically included in most studies, as they are known to play an important role in many physical phenomena. We also include in our potentials on-site terms of the sine-Gordon type, which are also considered in many studies in connection with localization effects. Our 1D lattices are subjected to sinusoidal perturbation on one end and an absorbing boundary on the other. To simulate a semi-infinite chain, we will consider a relatively long chain with string coupling. Using reliable finite difference discretization schemes, we establish the existence of nonlinear supratransmission for both short-range and long-range interactions, and demonstrate that the presence of quadratic interactions is not necessary for a system to show nonlinear supratransmission. Additionally, we provide diagrams depicting novel relations between the critical amplitude at which supratransmission is triggered versus driving frequency and a parameter measuring the length of the interactions. Our investigation also shows that the presence of on-site potentials is also not crucial for the system to present supratransmission.