We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are derived through a modified version of the classical Boltzmann kinetic equation for monatomic gases. The free volumes around the gaseous molecules are introduced i...

This paper is a density functional theory (DFT) calculation of intramolecular proton transfer (IPT) in 6-hydroxypicolinic acid (6HPA, 6-hydroxypyridine-2-carboxylic acid) tautomeric forms. The transition state for the enol-to-keto transition is reported in the gas phase and in four different solvents. The planar and non-planar dimer forms of 6HPA keto and enol, respectively, were also studied i...

In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) ...

Abstract Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these available. The aim this paper formulate governing buckling beams derive critical loads based on the nonlinear peridynamic beam theory. For three types boundary condit...

Given ω ≥ 1, let Z2(ω) be the graph with vertex set Z 2 in which two vertices are joined if they agree in one coordinate and differ by at most ω in the other. (Thus Z2(1) is precisely Z .) Let pc(ω) be the critical probability for site percolation in Z2(ω). Extending recent results of Frieze, Kleinberg, Ravi and Debany, we show that limω→∞ ωpc(ω) = log(3/2). We also prove analogues of this resu...

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to infinitely many axioms, and countable model the Löwenheim–Skolem theorem. This paper presents axioms one accept get rid of these features. For matter, some twenty are formulated in non-classical first-orde...

Issues related to the construction of continuum theories of strain gradient plasticity which have emerged in recent years are reviewed and brought to bear on the formulation of the most basic theories. Elastic loading gaps which can arise at initial yield or under imposition of non-proportional incremental boundary conditions are documented and analytical methods for dealing with them are illus...

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret ...

Classical plant morphology still provides the conceptual framework for most phytomorphological investigations and highly relevant concepts and data for other botanical disciplines such as plant morphogenesis, molecular genetics, ecology, systematics, evolutionary plant biology, etc. Typical classical morphology is categorical, i.e. the diversity of plant form is reduced to mutually exclusive mo...

A generalized space-time mathematical homogenization theory, which constructs an equivalent continuum description directly from molecular dynamics (MD) equations, is developed. The noteworthy theoretical findings of this work are: (i) the coarse scale continuum equations (PDEs) obtained from the homogenization of MD equations are identical to those obtained from the classical homogenization of ...