arXiv subjects

Xiao Jianhua

Publications and source records attributed to Xiao Jianhua.

8 recordsLinked to original sources

arXiv2011

Geometrical Field Theory of Hamilton Dynamic System In Rational Mechanics

When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is originated from the fact that the motion in time domain and the motion in spatial domain are coupled together completely. Generally, for a Hamilton dynamic system established by a set of general velocity functions, several abstract theories have been well established, such as Lie algebra, Symplectic manifold, Poisson brackets, and others. However, mathematically, to find out a general Hamilton function is very difficult even for very simple problems. Inspired by these abstract mathematic researches, the Hamilton dynamic system is studied by geometrical field theory of deformation. Firstly, referring to the instant configuration, the deformation tensor in spatial domain and the velocity transformation tensor in time domain are established for a dynamic system defined by a set of general velocity functions. Secondly, the general deformation tensor in velocity space domain is obtained. From continuum mechanics point, the stress tensor is defined through introducing background feature of space. Then, the general motion equations are established. Based on them, the simple motions are divided into two classes: 1) stable motion; and 2) radiating motion. Both of them have quantum solution structures. The features of space-time continuum are studied to obtain some intrinsic understanding about basic physical facts. This research shows an engineering way to treat the Hamilton dynamic system.

physics.gen-ph↗

arXiv2011

Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics

Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for smoke vortex are formulated. They are dynamic evolution equations for exact stress field and dynamic evolution equations for average stress field. For industrial application and experimental data processing, their corresponding approximation equations for viscous fluid are given. Some simple discussions are made.

physics.gen-ph↗

arXiv2010

Formulation of Deformation Stress Fields and Constitutive Equations in Rational Mechanics

In continuum mechanics, stress concept plays an essential role. For complicated materials, different stress concepts are used with ambiguity or different understanding. Geometrically, a material element is expressed by a closed region with arbitral shape. The internal region is acted by distance dependent force (internal body force), while the surface is acted by surface force. Further more, the element as a whole is in a physical background (exterior region) which is determined by the continuum where the element is embedded (external body force). Physically, the total energy can be additively decomposed as three parts: internal region energy, surface energy, and the background energy. However, as forces, they cannot be added directly. After formulating the general forms of physical fields, the deformation tensor is introduced to formulate the force variations caused by deformation. As the force variation is expressed by the deformation tensor, the deformation stress concept is well formulated. Furthermore, as a natural result, the additive decomposition gives out the definition of static continuum, which determines the material parameters in constitutive equations. Through using the exterior differentials, the constitutive equations are formulated in general form. Throughout the paper, when it is suitable, the related results are simplified to classical results for easier understanding.

physics.gen-ph↗

arXiv2010

Geometrical Field Formulation of Thermomechanics in Rational Mechanics

In modern science, the thermo mechanics motion can be traced back to quantum motion in micro viewpoint. On the other hand, the thermo mechanics is definitely related with geometrical configuration motion (phase) in macro viewpoint. On this sense, the thermomechanics should be formulated by two kinds of motion: quantum motion and configuration motion. Its principle goal ought to be bridge the gap between atomic physics and engineering practice. In this research, the configuration motion is formulated by deformation geometrical field (motion transformation tensor). The quantum motion is formulated by the wave function of quantum state. Based on these two fields, the thermo stress is formulated as the coupling of quantum motion and configuration motion. Along this line, the entropy is interpreted and formulated according to thermodynamics rules. For scalar entropy, the traditional meaning of entropy is reserved. For infinitesimal configuration variation, the formulation is degenerated to the traditional elasticity deformation. For large random configuration deformation, the formulation is degenerated to the statistical physics methods. This research supplies a possible formulation to bridge the gap between the macro deformation and the micro quantum motion.

physics.gen-ph↗

arXiv2009

Turbulence Dynamics based on Lagrange Mechanics and Geometrical Field Theory of Deformation

The turbulence field is stacked on the laminar flow. In this research, the laminar flow is described as a macro deformation which forms an instant curvature space. On such a curvature space, the turbulence is viewed as a micro deformation. So, the fluid flow is described by the geometrical field theory of finite deformation. Based on the Lagrange mechanics and the deformation energy concept, using the Least Action Principle, the Euler-Lagrange motion equations are obtained. According to A E Green formulation, the stress concept is introduced by deformation tensor. The fluid motion is described by the multiplication of a macro deformation tensor and a micro deformation tensor. By this way, the geometrical field of fluid motion is well constructed. Then, the spatial derivative of deformation energy is expressed by the gradient of deformation tensors. By this way, the deformation energy related items in the Euler-Lagrange motion equations are expressed by the stress tensor and deformation tensor. The obtained Euler-Lagrange motion equations, then, are decomposed into average deformation equations and turbulence equations. For several special cases, the new results are compared with the conventional Navier-Stokes equation with Reynolds stress modification.The comparisons also show that the Bernoulli Equation is a natural precondition for the conventional Navier-Stokes equation.Generally, the turbulence wave is an inward-traveling wave. Unlike the normal outward-traveling wave related with the average deformation, the inward-traveling wave is the intrinsic feature of turbulence. So, the turbulence is well defined by the equations obtained in this research. For several typical cases, the simplified turbulence wave equations are given out with simple discussion.

physics.gen-ph↗

arXiv2005

Gravity Field and Electromagnetic Field-Finite Geometrical Field Theory of Matter Motion Part Two

Gravity field theory and electromagnetic field theory are well established and confirmed by experiments. The Schwarzschild metric and Kerr Metric of Einstein field equation shows that the spatial differential of time gauge is the gravity field. For pure time displacement field, when its spatial differentials are commutative, conservative fields can be established. When its spatial differentials are non-commutative, Maxwell electromagnetic field equations can be established. When the contra-covariant is required for the non-commutative field, both Lorentz gauge and Coulomb gauge are derived in this research. The paper shows that the light is a special matter in that the addition of its Newtonian mass and its Coulomb electric charge is zero. In fact, this conclusion is true for the electromagnetic wave in vacuum. For the conservative field, the research shows that once the mass density and the Coulom charge dendity are given, the macro spacetime feature is completely determined. Both of them are intrisinc features of macro matter in cosimic background. However, for the cosmic ages old events, the spatial curvature may be cannot be ignored. On this sense, the oldest gravity field has the largest curvature of space. This point is very intrinsic for astronomy matters.

physics.gen-ph↗

arXiv2005

Inertial System and Special Relativity Finite Geometrical Field Theory of Matter Motion Part One

Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying concepts of relativity theory. In four-dimensional spacetime continuum, the displacement field of matter motion is measurable quantities. Based on these measurements, a finite geometrical field can be established. On this sense, the matter motion in physics is viewed as the deformation of spacetime continuum. Suppose the spacetime continuum is isotropic, based on the least action principle, the general motion equations can be established. In this part, Newton motion and special relativity are discussed. Based on the finite geometrical field theory of matter motion, the Newton motion equation and the special relativity can be derived simply based on the isotropy of spacetime continuum and the definition of inertial system. This research shows that the Lorentz transformation is required by both of the inertial system definition and the time gauge invariance for inertial systems. Hence, the special relativity is the logic conclusion of time invariance in inertial system. The source independent of light velocity supports the isotropy of inertial system rather than the concept of proper time, which not only causes many paradox, such as the twin-paradox, but also causes many misunderstanding and controversial arguments. The singularity of Lorentz transformation is removed in other parts of finite geometrical field theory, where the gravity field, electromagnetic field, and quantum field will be discussed with the time displacement field.

physics.gen-ph↗

arXiv2005

Motion Equation of Vorticity for Newton Fluid

The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this propose, the velocity gradient field is decomposed as the stack of non-rotation field and pure-rotation field. By introducing the Chen S+R decomposition, the rotational flow is redefined. For elastic fluid, the research shows that for Newton fluid, the local average rotation always produces an additional pressure on the rotation plane. This item is deterministic rather than stochastic (as Reynolds stress) or adjustable. For non-elastic fluid, such as air, the research shows that the rotation will produce an additional stress along the rotation axis direction, that is on the normal direction of rotation plane. This result can be used to explain the lift force connected with vortex. The main purpose of this research is to supply a solvable mathematical model for the calculation of vorticity and pressure when suitable boundary condition is adapted. Based on this understanding, some way to control the movement of vortices may be produced.

physics.flu-dyn↗