885 research outputs found
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.Comment: 25 pages, 2 figure
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.Comment: 39 pages, no figure
Quantum Field and Cosmic Field-Finite Geometrical Field Theory of Matter Motion Part Three
This research establishes an operational measurement way to express the
quantum field theory in a geometrical form. In four-dimensional spacetime
continuum, the orthogonal rotation is defined. It forms two sets of equations:
one set is geometrical equations, another set is the motion equations. The
Lorentz transformation can be directly derived from the geometrical equations,
and the proper time of general relativity is well expressed by time
displacement field. By the motion equations, the typical time displacement
field of matter motion is discussed. The research shows that the quantum field
theory can be established based on the concept of orthogonal rotation. On this
sense, the quantum matter motion in physics is viewed as the orthogonal
rotation of spacetime continuum. In this paper, it shows that there are three
typical quantum solutions. One is particle-like solution, one is
generation-type solution, and one is pure wave type solution. For each typical
solution, the force fields are different. Many features of quantum field can be
well explained by this theoretic form. Finally, the general matter motion is
discussed, the main conclusions are: (1). Geometrically, cosmic vacuum field
can be described by the curvature spacetime; (2). The spatial deformation of
planet is related with a planet electromagnetic field; (3). For electric charge
less matter, the volume of matter will be expanding infinitely; (4).For strong
electric charge matter, it shows that the volume of matter will be contracting
infinitely.Comment: 22 pages, no figure
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.Comment: 16 pages, no figure
Evolution of Continuum from Elastic Deformation to Flow
Traditionally, the deformation of continuum is divided into elastic, plastic,
and flow. For a large deformation with cracking, they are combined together.
So, for complicated deformation, a formulation to express the evolution of
deformation from elastic to flow will help to understand the intrinsic relation
among the related parameters which relate the deformation with a stress field.
To this purpose, Eringen polar decomposition and Trusedell polar decomposition
are formulated by explicit formulation of displacement field, based on Chen
additive decomposition of deformation gradient. Then the strain introduced by
the multiplicative decomposition and the strain introduced by the additive
decomposition are formulated explicitly with displacement gradient. This
formulation clears the intrinsic contents of strains defined by taking the
Eringen polar decomposition and Trusedell polar decomposition. After that, it
shows that the plastic deformation can be expressed as the irreversible local
average rotation. For initial isotropic simple elastic material, the
path-dependent feature of classical plasticity theory is naturally expressed in
Chen strain definition. It is founded that for initially isotropic material the
motion equations require a non-symmetric stress for dynamic deformation and a
symmetric stress for static deformation. This controversy between dynamic
deformation and static deformation can be used to explain the cracking or
buckling of solid continuum. Finally, the research shows that the flow motion
of continuum can be expressed by the same formulation system. So, it forms an
evolution theory from elastic deformation to flow of continuum.Comment: 25 pages, no figure
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.Comment: 32 pages, 7 figure
Investigating Epithelial-To-Mesenchymal Transition with Integrated Computational and Experimental Approaches
The transition between epithelial and mesenchymal (EMT) is a fundamental
cellular process that plays critical roles in development, cancer metastasis,
and tissue wound healing. EMT is not a binary process but involves multiple
partial EMT states that give rise to a high degree of cell state plasticity.
Here, we first reviewed several studies on theoretical predictions and
experimental verification of these intermediate states, the role of partial EMT
on kidney fibrosis development, and how quantitative signaling information
controls cell commitment to partial or full EMT upon transient signals. Next,
we summarized existing knowledge and open questions on the coupling between EMT
and other biological processes, such as the cell cycle, epigenetic regulation,
stemness, and apoptosis. Taken together, EMT is a model system that has
attracted increasing interests for quantitative experimental and theoretical
studies.Comment: 37 pages, 6 figures, accepted in Physical Biolog
Lyapunov exponents and related concepts for entire functions
Let be an entire function and denote by be the spherical
derivative of and by the -th iterate of . For an open set
intersecting the Julia set , we consider how fast and tend to . We also study
the growth rate of the sequence for .Comment: 20 page
On the rational relationship between Heisenberg principle and general relativity
The research shows that the Heisenberg principle is the logic results of
general relativity principle. If inertia coordinator system is used, the
general relativity will logically be derived from the Heisenberg principle. The
intrinsic relation between the quantum mechanics and general relativity is
broken by introducing pure-imaginary time to explain the Lorentz
transformation. Therefore, this research shows a way to establish an unified
field theory of physicsComment: 5 pages, no figure
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.Comment: 37 pages, no figure
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