Poisson Conservation Research Articles

A perturbative thermal analysis for an electro-osmotic flow in a slit microchannel based on a Lubrication theory

In this work, we develop a new thermal analysis for an electro-osmotic flow in a rectangular microchannel. The central idea is very simple: the Debye length that defines the length of the electrical double-layer depends on temperature T. Therefore, if exists any reason to include variable temperature effects, the above length should be utilized with caution because it appears in any electro-osmotic mathematical model. For instance, the presence of the Joule effect is a source that can generate important longitudinal temperature gradients along the microchannel and the isothermal hypothesis is no longer valid. In this manner, the Debye length is altered and as a consequence, new longitudinal temperature gradient terms appear into the resulting governing equations. These terms are enough to change the electric potential and the flow field. Taking into account the above comments, in the present study the momentum equations together with the energy and Poisson conservation equations are solved by using a regular perturbation technique. For this purpose, we introduce a dimensionless parameter α that measures the temperature deviations of a reference temperature. For practical cases, this parameter is small compared with unity and the theoretical predictions show; however, that for the used values of this parameter, the volumetric flow rate decreases in comparison with the isothermal case.

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Fractional Lorentz-Dirac Model and Its Dynamical Behaviors

In the paper, we construct a new kind of fractional dynamical model, i.e. the fractional Lorentz-Dirac model, and explore dynamical behaviors of the model. We find that the fractional Lorentz-Dirac model possesses Lie algebraic structure and satisfies generalized Poisson conservation law, and then a series of Poisson conserved quantities of the model are given. Further, the relation between conserved quantity and integral invariant of the model is studied, and it is proved that, using the Poisson conserved quantities, we can construct a series of integral invariants of the model. Finally, the stability for the manifolds of equilibrium state of the fractional Lorentz-Dirac model is studied.

Lie Algebraic Structure and Poisson Conservation Law for One Class of Multi-Dimensional Coupled Oscillators

This paper researches Lie algebraic structure and Poisson conservation law for one class of multi-dimensional coupled oscillators. The equations of motion are established, and the coupled terms in the equations of motion are eliminated by introducing normal transformations. The Lie algebraic structure and Poisson conservation law are given. Finally, an example is given to illustrate the results.

Lie algebraic structure and generalized Poisson conservation law for fractional generalized Hamiltonian systems

Based on definition of Riemann–Liouville fractional derivatives, we find that the fractional generalized Hamiltonian system possesses consistent algebraic structure and Lie algebraic structure, and the generalized Poisson conservation law of the fractional generalized Hamiltonian system is investigated. As special cases of this paper, the conditions under which a fractional generalized Hamiltonian system can be reduced to a generalized Hamiltonian system and a classical Hamiltonian system are given, and the Lie algebraic structure and Poisson conservation law of these special dynamical systems are obtained, respectively. Then, by using the method and results of this paper, we construct three kinds of new fractional dynamical model, i.e. a fractional Henon–Heiles model, a fractional Euler–Poinsot model of a rigid body and a fractional Volterra model of the three species groups, and their Poisson conserved quantities are obtained.

Fractional generalized Hamiltonian mechanics and Poisson conservation law in terms of combined Riesz derivatives

In this paper, we present a new kind of fractional dynamical equations, i.e., the fractional generalized Hamiltonian equations in terms of combined Riesz derivatives, and it is proved that the fractional generalized Hamiltonian system possesses consistent algebraic structure and Lie algebraic structure, and the Poisson conservation law of the fractional generalized Hamiltonian system is investigated. Then the conditions, which a fractional generalized Hamiltonian system can be reduced to a generalized Hamiltonian system, a fractional Hamiltonian system and a Hamiltonian system are given. Further, the conserved quantities of a fractional dynamical system are given to illustrate the method and results of the application. At last, a new fractional Volterra model of the three species groups is presented and its conserved quantities are obtained, by using the method of this paper.