A LIE GROUP FRAMEWORK FOR COMPOSITE PARTICLES AND HARMONIC OSCILLATOR MASS SPECTRUM

1989 ◽  
Vol 04 (16) ◽  
pp. 4069-4081
Author(s):  
PRATUL BANDYOPADHYAY
Keyword(s):  
Mass Spectrum ◽  
Harmonic Oscillator ◽  
Composite System ◽  
Internal Variable ◽  
Mass Splitting ◽  
Internal Symmetry ◽  
Internal Variables ◽  
Direction Vector ◽  
Covariant Method ◽  
Time Point

A harmonic oscillator mass spectrum is developed through a relativistic covariant method in unifying the external and internal variables of a hadron leading to a dynamical Lie algebra. It is shown that through the introduction of an internal variable ξμ, which behaves as a 'direction vector', attached to each space-time point, χμ, and the spatial extension, Xi, of the composite system, we can uniquely determine a harmonic oscillator mass spectrum. This is valid even when the constituents are taken to be massless. Moreover, when these internal variables are associated with the internal symmetry, the mass splitting due to the internal symmetry breaking is incorporated in this formalism and no adhoc consideration is necessary. The mass spectrum of the neutral isovector and isoscalar mesons is computed in this framework.

TWISTOR GEOMETRY, SPINOR STRUCTURE AND NATURE OF SUPERSPACE

1989 ◽  
Vol 04 (05) ◽  
pp. 1111-1123 ◽  
Author(s):  
PRATUL BANDYOPADHYAY ◽  
PRADIP GHOSH
Keyword(s):  
Minkowski Space ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Base Space ◽  
Internal Space ◽  
Direction Vector ◽  
Spinor Structure ◽  
Minkowski Space Time ◽  
Time Point

The nature of superspace is studied here from the viewpoint of eight-component conformal spinors which can be split into two Cartan semispinors having two internal helicities corresponding to particle and anti-particle states. This leads to the generation of internal symmetry through reflection group. It is shown that each member of the doublet can be taken to behave as twistors in complexified Minkowski space-time. This helps us to introduce a spinor structure at each space-time point and the spinor coordinate gives rise to the internal helicity. This may be achieved through the introduction of a direction vector attached to each space-time point. Superspace here appears as a bundle space where the base space is the ordinary Minkowski space-time and the spinorial coordinates generated through the introduction of the direction vector from the fibre. This suggests that the internal space of hadrons is anisotropic in nature.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

HOLOMORPHIC QUANTUM MECHANICS, CONFORMAL REFLECTION AND THE INTERNAL SYMMETRY OF HADRONS

1989 ◽  
Vol 04 (17) ◽  
pp. 4449-4467 ◽  
Author(s):  
PRATUL BANDYOPADHYAY
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Composite System ◽  
Conformal Geometry ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Internal Space ◽  
Minkowski Space Time ◽  
Antiparticle State

It is shown here that the holomorphic quantum mechanics in a complexified Minkowski space-time helps us to study the geometrical feature of the internal space of a particle and its relevance with conformal geometry. It is noted that the conformal reflection can be depicted in the formalism of an internal helicity which takes the value [Formula: see text] and [Formula: see text] for the particle and antiparticle state. This again can be described in the framework of holomorphic quantum mechanics in terms of the half-orbital angular momentum of a constituent in an anisotropic space in the sense of Minkowski space-time with a fixed lz value for the particle and antiparticle configuration when a composite system is considered. A massive or massless spinor moving with such characteristic in the configuration of a composite system can be depicted as a Cartan semispinor and behaves as a twistor. The doublet of such spinors with opposite helicities represent an eight-component conformal spinor. The internal symmetry group SU(3) for a composite system of hadrons can then be realized from the reflection group. This formalism reveals the microlocal region of a complexified Minkowski space-time as a twistor space.

Internal Variable Modeling of the Creep of Monolithic Ceramics

1995 ◽  
Author(s):  
Charles S. White ◽  
Radwan M. Hazime
Keyword(s):  
Grain Boundaries ◽  
Elevated Temperatures ◽  
Internal Variable ◽  
Complete Characterization ◽  
Tensile Creep ◽  
Internal Variables ◽  
Variable Model ◽  
The Road ◽  
Monolithic Ceramics

Abstract Ceramics are assuming an important role for use in power generation. One of the road blocks is a complete characterization of the deformation and life of advanced ceramics at elevated temperatures. Substantial high temperature creep testing has been conducted in recent years. Most commonly, Norton’s law for deformation and the Monkman-Grant relationship for failure have been used to correlate test data. In this paper, internal variable modeling is discussed as an alternative to Norton’s Law/Monkman-Grant. Through the use of internal variables, micromodeling of the important mechanisms can be extended to the macroscopic behavior. Also, the effects of simultaneous or competing phenomena can be considered. An example is the growth of lenticular cavities on the two grain boundaries of certain silicon nitrides while the grain boundaries are crystallizing. The results of a preliminary internal variable model for HIPed silicon nitride is presented and compared with tensile creep experiments.

An Internal Variable Update Procedure for the Treatment of Inelastic Material Behavior within an ALE-Description of Rolling Contact

2007 ◽  
Vol 9 ◽  
pp. 157-171 ◽  
Author(s):  
M. Ziefle ◽  
U. Nackenhorst
Keyword(s):  
Contact Problems ◽  
Internal Variable ◽  
Rolling Contact ◽  
Material Behavior ◽  
Internal Variables ◽  
Arbitrary Lagrangian Eulerian ◽  
Element Analysis ◽  
Integration Schemes ◽  
Inelastic Material ◽  
Ale Methods

Arbitrary Lagrangian Eulerian (ALE) methods provide a well established basis for the numerical analysis of rolling contact problems, the theoretical framework is well developed for elastic constitutive behavior. Special measures are necessary for the treatment of history dependent and explicitly time dependent material behavior within the relative–kinematic ALE– picture. In this presentation a fractional step approach is suggested for the integration of the evolution equation for internal variables. A Time–Discontinuous Galerkin (TDG) method is introduced for the numerical solution of the related advection equations. The advantage of TDG–methods in comparison with more traditional integration schemes is studied in detail. The practicability of the approach is demonstrated by the finite element analysis of rolling tires.

Constitutive Equations for the Rate-Dependent Deformation of Metals at Elevated Temperatures

1982 ◽  
Vol 104 (1) ◽  
pp. 12-17 ◽  
Author(s):  
L. Anand
Keyword(s):  
Dynamic Recrystallization ◽  
Strain Rate ◽  
Strain Hardening ◽  
Constitutive Equations ◽  
Elevated Temperatures ◽  
Internal Variable ◽  
Internal Variables ◽  
Homologous Temperature ◽  
Static Recovery ◽  
Rate Dependent

Approximate constitutive equations are proposed for use in the analysis of the rate-dependent deformation of metals at temperatures in excess of a homologous temperature of 0.5. The constitutive equations are formulated within the scope of some recent theories of elastoviscoplasticity with internal variables, but employ only a single scalar internal variable representing an isotropic resistance to plastic flow offered by the internal microstructural state of the material. The special constitutive euqations incorporate strain hardening of the Voce type, and account for the effects of the prior histories of strain rate and temperature undergone by the material. These equations, however, do not represent the important effects of static recovery or of static and dynamic recrystallization.

Two-Temperature Thermodynamics for Metal Viscoplasticity: Continuum Modeling and Numerical Experiments

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Shubhankar Roy Chowdhury ◽  
Gurudas Kar ◽  
Debasish Roy ◽  
J. N. Reddy
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Internal Variable ◽  
Thermodynamic System ◽  
Internal Variables ◽  
Face Centered Cubic ◽  
Dynamic Simulations ◽  
Face Centered ◽  
Atomic Lattices ◽  
Two Temperature

A physics-based model for dislocation mediated thermoviscoplastic deformation in metals is proposed. The modeling is posited in the framework of internal-variables theory of thermodynamics, wherein an effective dislocation density, which assumes the role of the internal variable, tracks permanent changes in the internal structure of metals undergoing plastic deformation. The thermodynamic formulation involves a two-temperature description of viscoplasticity that appears naturally if one considers the thermodynamic system to be composed of two weakly interacting subsystems, namely, a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees-of-freedom (DOFs) of defect motion. Starting with an idealized homogeneous setup, a full-fledged three-dimensional (3D) continuum formulation is set forth. Numerical exercises, specifically in the context of impact dynamic simulations, are carried out and validated against experimental data. The scope of the present work is, however, limited to face-centered cubic (FCC) metals only.

scholarly journals On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept

1983 ◽  
Vol 105 (2) ◽  
pp. 153-158 ◽  
Author(s):  
J. L. Chaboche ◽  
G. Rousselier
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Internal Variable ◽  
Cyclic Behavior ◽  
Internal Variables ◽  
Plastic Behavior ◽  
Hardening Rules ◽  
Plastic Strain Tensor ◽  
Natural Description

The description of monotonic and cyclic behavior of material is possible by generalizing the internal stress concept by means of a set of internal variables. In this paper the classical isotropic and kinematic hardening rules are briefly discussed, using present plastic strain tensor and cumulated plastic strain as hardening variables. Some additional internal variables are then proposed, giving rise to many possibilities. What is called the “nonlinear kinematic hardening” leads to a natural description of the nonlinear plastic behavior under cyclic loading, but is connected to other concepts such as the Mroz’s model, limited to only two surfaces, and similarities with other approaches are pointed out in the context of a generalization of this rule to viscoplasticity.

scholarly journals Macroscopic Internal Variables and Mesoscopic Theory: A Comparison considering Liquid Crystals

2017 ◽  
Author(s):  
Christina Papenfuss ◽  
Wolfgang Muschik
Keyword(s):  
Distribution Function ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
State Space ◽  
Internal Variable ◽  
Internal Variables ◽  
Alignment Tensor ◽  
Balance Equations ◽  
Flexible Fibers ◽  
Mesoscopic Theory

Internal and mesoscopic variables differ from each other fundamentally: both are state space variables, but mesoscopic variables are additional equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.

scholarly journals Mass spectrum and strong decays of tetraquark $${\bar{c}}{\bar{s}} qq$$ states

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Guang-Juan Wang ◽  
Lu Meng ◽  
Li-Ye Xiao ◽  
Makoto Oka ◽  
Shi-Lin Zhu
Keyword(s):  
Mass Spectrum ◽  
Hyperfine Interactions ◽  
Large Mass ◽  
Mass Splitting ◽  
Wave Functions ◽  
Tetraquark State ◽  
Strong Decay ◽  
S Wave ◽  
Different Color ◽  
Partner State

AbstractWe systematically study the mass spectrum and strong decays of the S-wave $${\bar{c}}{\bar{s}} q q$$ c ¯ s ¯ q q states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine interactions. The hyperfine potential leads to the mixing between different color configurations, and to the large mass splitting between the two ground states with $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) and $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) . We calculate their strong decay amplitudes into the $${\bar{D}}^{(*)}K^{(*)}$$ D ¯ ( ∗ ) K ( ∗ ) channels with the wave functions from the mass spectrum calculation and the quark-interchange method. We examine the interpretation of the recently observed $$X_0(2900)$$ X 0 ( 2900 ) as a tetraquark state. The mass and decay width of the $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) state are $$M=2941$$ M = 2941 MeV and $$\Gamma _X=26.6$$ Γ X = 26.6 MeV, respectively, which indicates that it might be a good candidate for $$X_0(2900)$$ X 0 ( 2900 ) . Meanwhile, we also obtain an isospin partner state $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) with $$M=2649$$ M = 2649 MeV and $$\Gamma _{X\rightarrow {\bar{D}} K}=48.1$$ Γ X → D ¯ K = 48.1 MeV, respectively. Future experimental search for X(2649) will be very helpful.

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