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Perturbation of Symmetries and Hojman Adiabatic Invariants for Mechanical Systems with Unilateral Holonomic Constraints

The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undisturbed system with unilateral constraints is given. Based on the concept of high-order adiabatic invariant of mechanical systems, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the system with unilateral holonomic constraints is obtained, which can be called Hojman adiabatic invariant. In the end of the paper, an example is given to illustrate the application of the results.

Mei Adiabatic Invariants Induced by Perturbation of Mei Symmetry for Nonholonomic Controllable Mechanical Systems

Two types of Mei adiabatic invariants induced by perturbation of Mei symmetry for nonholonomic controllablemechanical systems are reported.Criterion and restriction equations determining Mei symmetry after beingdisturbed of the system are established.Form and existence condition of Mei adiabatic invariants are obtained.

Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems

Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.

Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems

For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.

Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.

Perturbation to Noether-Mei Symmetry and Adiabatic Invariants for Nonholonomic Mechanical Systems in Phase Space

Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.

Indexes of Indoor Thermal Environment with Asymmetrical Radiant Field

The main features of top-flcor rooms with natural ventilation are identified by investigating indoor thermal environment in summer season. One is high indoor air temperature, for this reason the indoor climate is far beyond the thermal comfort standard; the other is the inhomogeneons temperature distribution of the inner wall surfaces, and high temperature of the inner surface of the roof causes much scorching to the head of occupant. This is the characteristic of such rooms. Both features mentioned above should be considered comprehensively for the evaluation of indoor thermal environment of the top-floor rooms with asymmetric radiant field. In order to characterize the indoor thermal environment of the rooms, the heat stress index, HSI and radiant heat flux reaching human head, Q_R should be introduced simultaneously as thermal indexes for the indoor climate evaluation. The application of the indexes to a topfloor room is presented and analyzed.

Perturbation to Lie-Mei Symmetry and Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant,the perturbation to Lie-Mei symmetry and adiabatic invariantsfor Birkhoffian systems are studied.The definition of the perturbation to Lie-Mei symmetry for the system is presented,and the criterion of the perturbation to Lie-Mei symmetry is given.Meanwhile,the Hojman adiabatic invariants andthe Mei adiabatic invariants for the perturbed system are obtained.

Perturbation of Symmetries and Mei Adiabatic Invariants of Nonholonomic Systems with Servoconstraints

The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.

Analysis Theory of Asymmetric dc SQUID Driven by Thermal Noises

An analysis expression for the stationary probability distribution of asymmetric superconducting quantum interference device with two Josephson junctions (dc SQUID) driven by thermal noise is derived from two-dimensional Fokker-Planck equation, where the potential condition is satisfied. Two of the three asymmetric parameters, inductance asymmetric parameter η and critical current asymmetric parameter α, can be changed in this condition, but resistance asymmetric parameter ρ cannot be changed. The 'ripple' phenomenon of circulating current can disappear with the change of coefficient α. The effects of asymmetric parameters on current-voltage relationship and transfer function of dc SQUID system are also represented.

Perturbation to Lie Symmetry and Hojman Exact and Adiabatic Invariants of Generalized Raitzin Canonical Equation of Motion

In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.

Theoretical solution of a spherically isotropic hollow sphere for dynamic thermoelastic problems

The separation of variables method was successfully used to resolve the spherically symmetric dynamic thermoelastic problem for a spherically isotropic elastic hollow sphere. Use of the integral transform can be avoided by means of this method, which is also appropriate for an arbitrary thickness hollow sphere subjected to arbitrary thermal and mechanical loads. Numerical results are presented to show the dynamic stress responses in the uniformly heated hollow spheres.

Perturbation to Mei Symmetry and Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates

Abstract Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the perturbation to Mei symmetry for the system is presented, and the criterion of the perturbation to Mei symmetry is given. Meanwhile, the Mei adiabatic invariants for the perturbed system are obtained.

A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems

Considering full perturbation to infinitesimal generators in the Mei structure equation,a new type of Meiadiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.

Combustion characteristics of Methanol-base fuel （MBF） made by coal

Profound experimental research was made on Methanol-base fuel （MBF） mainly consisting of methanol, and the results were compared with that of diesel oil. Their respective combustion characteristics of caloric value, combustion efficiency and components of smoke were synthetically analyzed by employing the electronic weighing devices, the rotor flow-meter, intelligent flue gas analyzer, advanced bomb calorimeter, etc., referring to the feasibility of taking it as a fuel for general use. Experiment results show that Methanol-base fuel not only has superiorities on combustion characteristics but also bears energy saving and environmental protection advantages.

Thermoelastic Stress Analysis of a Finite Structure Containing an Asymmetrical-Oriented, Arbitrarily-Shaped Hole

Stresses, particularly those at geometric discontinuities, influence the structural integrity of engineering components. Motivated by the prevalence of complicated-shaped perforated components, the objective of this paper is to demonstrate the ability to stress analyze loaded finite members containing asymmetrical, irregularly-shaped cutouts. Recognizing the difficulties in obtaining purely theoretical or numerical solutions for these situations, the paper presents an expeditious means of experimentally stress analyzing such structures. Processing the load-induced temperature information with a series representation of a stress function provides the independent stress components reliably full-field, including on the edge of a hole. The stresses satisfy equilibrium and strains satisfy compatibility. In addition to being able to stress analyze complicated shapes using real, rather than complex variables, the technique is significant in which it smooths the recorded thermal information, is widely applicable, and requires neither differentiating the measured data nor knowing the elastic properties or external boundary conditions. The latter is extremely important since the external loading is often unknown in practice. That the approach provides the independent stresses is also significant since fatigue analyses and strength criteria typically necessitate knowing the individual components of stress. Present results are supported by those from a finite element analysis, strain gage measurements and load equilibrium.

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

Characteristics and mechanisms of the annual asymmetry of thermospheric mass density

In this paper, globally-averaged, thermospheric total mass density, derived from the orbits of -5000 objects at 250, 400, and 550 km that were tracked from 1967 to 2006, has been used to quantitatively study the annual asymmetry of thermospheric mass density and its mechanism（s）. The results show that thermospheric mass density had a significant annual asymmetry, which changed from year to year. The annual asymmetry at the three altitudes varied synchronously and its absolute value increased with altitudes. The results suggest that there is an annual asymmetry in solar EUV radiation that is caused by the difference in the Sun-Earth distance between the two solstices and the random variation of solar activity within a year. This change in radiation results in an annual change in the thermospheric temperature and thus the scale height of the neutral gas, and is the main cause of the annual asymmetry of thermospheric mass density. The annual asymmetry of mass density increases with altitude because of the accumulating effect of the changes in neutral temperature and scale height in the vertical direction.