Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems

Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results.     

Radial variation of adiabatic and diabatic spiral vortex flow in a wide annular gap

Transitions occurring after the onset of spiral vortex flow in a wide concentric annular gap of radius ratio 0.8, formed by a stationary outer cylinder and a rotatable inner cylinder, have been studied experimentally. By isothermal heating of the annular surface, it was possible to consider diabatic as well as adiabatic conditions. At an axial Reynolds number of 500 and for a range of Taylor numbers up to 10⁷, power spectra and auto-correlograms were taken at two radial positions near to the inner and outer annular surfaces; these are compared with previous results taken at mid-gap under adiabatic conditions. Measurements of turbulence intensity across the gap were made also. Probability histograms and signal traces for diabatic flow near to the outer annular surface are presented. It has been shown that the vortex transitions affect the thermal boundary layer and, consequently, the heat transfer rates at the outer surface. A positive radial thermal gradient was seen to have little effect on the flow. The imposed axial flow was shown to be stabilising under adiabatic conditions but destabilising under diabatic conditions.     

A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems

For a generalized Hamiltonian system with the action of small forces of perturbation, the Lie symmetries, symmetrical perturbation, and adiabatic invariants is presented. Based on the invariance of equations of motion for the system under general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations, and exact invariants of the system are given. Then the determining equations of Lie symmetrical perturbation and adiabatic invariants of the disturbed systems are obtained. Furthermore, in the special infinitesimal transformations, two deductions are given. At the end of the paper, one example is given to illustrate the application of the method and result.     

A model for adiabatic supersonic turbulent boundary layers

An asymptotic analysis of the equations describing supersonic turbulent flow over an adiabatic wall is carried out for high Reynolds numbers, Re, and mainstream Mach numbers, M _e=O(1). A general expression for the adiabatic-wall temperature is derived. The asymptotic theory constrains the types of turbulence models that are suitable to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement, capturing the overshoot observed in total enthalpy near the boundarylayer edge.This work was supported by NASA Langley Research Center under Grant NAG-1-832 and the Air Force Office of Scientific Research under Grants AFOSR-91-0069 and F49620-93-0130; Dr. Ruban was supported by a grant from United Technologies Corporation.     

Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems

For a generalized Birkhoffian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants are presented. On the basis of the invariance of disturbed generalized Birkhoffian system under general infinitesimal transformation of group, the determining equation of Lie symmetrical perturbation of the system is constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of non-Noether adiabatic invariants of a disturbed generalized Birkhoffian system is obtained by investigating the Lie symmetrical perturbation. Then, a new type of exact invariants of non-Noether type is given, furthermore adiabatic invariants and exact invariants of non-Noether type are obtained under the special infinitesimal transformation of group. Finally, an example is given to illustrate the application of the method and results.     

Atlas motion platform generalized kinematic model

Conventional training simulators commonly use a hexapod configuration to provide motion cues. While widely used, studies have shown that hexapods are incapable of producing the range of motion required to achieve high fidelity simulation required in many applications. A novel alternative is the Atlas motion platform. This paper presents a new generalized kinematic model of the platform which can be applied to any spherical platform actuated by three omnidirectional wheels. In addition, conditions for slip-free and singularity-free motions are identified. Two illustrative examples are given for different omnidirectional wheel configurations.     

A generalized rheological model of thixotropic materials

Summary A generalization of the rheological model of thixotropic materials, presented previously, was carried out. In the generalized rheological equation of state the yield stress depending on the structural parameter was introduced. In the generalized rate equation the difference in the destruction and recovery rates of the material structure was taken into account. A procedure leading to the determination of nine rheological parameters of the generalized model was worked out. The model was checked experimentally for a thixotropic paint.

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Zusammenfassung Eine früher dargestellte Theorie thixotroper Stoffe wird verallgemeinert, wobei eine von dem Strukturparameter abhängige Fließspannung eingeführt wird. Weiterhin wird der Unterschied zwischen der Zerstörungs-und der Wiederaufbaugeschwindigkeit der Stoffstruktur berücksichtigt. Eine Methode zur Bestimmung der neun benötigten Stoffparameter wird ausgearbeitet. Das Modell wird am Beispiel einer thixotropen Farbe experimentell geprüft.

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Notation a rheological parameter in eq. [26], s^–1 - A rheological parameter in eq. [16] - b rheological parameter in eq. [26] - c function in eq. [21] - averaged value of functionc in eq. [28] - c function in the rate equation [23], defined by eq. [21] - G function [1] defining material of the rate type - h function [2] determining the state of thixotropic fluid - k rheological parameter in the Herschel-Bulkley equation [17] or, in special case, in eq. [8], Ns ⁿ /m² - K function in eq. [18], Ns ^m /m² - m rheological parameter in eq. [18] or, in special case, in eq. [10] - n rheological parameter in the Herschel-Bulkley model [17] or, in special case, in eq. [8] - s rheological parameter in eq. [16] - t time, s - x arbitrary real variable - rheological parameter in eq. [9], s - shear rate, s^–1 - structural parameter, defined by eq. [2] - substantial derivative of structural parameter, s^–1 - _e function [6] describing the equilibrium curve in the coordinate system ( ) - ₀ initial value of structural parameter (att = 0) - natural time function of the thixotropic material, defined by eq. [22] - shear stress, N/m² - substantial derivative of shear stress, N/m² s - _e function describing equilibrium flow curve in the coordinate system ( ) - ₀ equilibrium yield stress, defined by eq. [12], N/m² - _y function of structural parameter describing the yield stress - function in eq. [11] Notation used in the algorithm:(Appendix) i,j,k integer - k _e (i) ordinal number of the experimental point at which the line of _i = const intersects the equilibrium flow curve - l _i number of the experiments of the type stepchange of the shear rate - l _j number of experimental points in one experiment of the type step-change of the shear rate - n _e number of experimental points on the equilibrium flow curve - n _k number of experimental points on the line of constant - n _y number of lines of constant - t(j) measured time interval (from the moment of the step-change of shear rate) - abscissa of the experimental point of ordinal numberk on the line of _i = const, in the coordinate system ( ) - abscissa of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system ( ) - shear rate at which the experiment of the type step-change of shear rate was carried out - _e (i) ordinate of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system ( ) - _y (i) value of yield stress at = _i - _s (i,j) experimental value of shear stress at constant value of shear rate (2i) for time intervalt(j) - (i,k) ordinate of the experimental point of ordinal numberk on the line of _i = const, in the coordinate system ( ) - ₀ the admissible value of the difference between the experimental and theoretical value of shear stress With 4 figures and 1 table     

A generalized model of structural reversed plasticity

This paper describes and experimentally verifies a simplified generalized force-local deformation model capable of simulating the stable fluctuating elastoplastic response displayed by structural systems subjected to proportional cyclic loads. The principal generalized force-deformation characteristics of these systems under cyclic proportional loads are outlined. Essential stable force-deformation features related to the model are memory of prior deformation and the Masing kinematic hardening rule which states that the force-deformation hysteresis-loop shape is obtained by magnifying the cyclic force-deformation curve by a factor of two. Five types of structural specimens made from three metals were cyclically stabilized using an incremental step-loading sequence after which their stable cyclic deformation responses were generated. The proposed modeling process was then used to simulate each of these fifteen stable responses with generally good accuracy. The maximum hysteresis loop tip prediction error did not exceed 7.7 percent of the corres-ponding range of force. The model is readily adaptable to digital computation and it should be useful for fatigue-analysis procedures or earth-quake-response studies.     

On a statistical-kinetic model for generalized continua

Dedicated to Bernard Coleman on the occasion of his 60^th birthday     

A generalized network model for polymeric liquids

A kinetic model was developed for relating the molecular structure and the rheological behaviour of polymer-like materials in which bonds are being created and broken. In particular, the stress contribution of molecules that are not a part of the network was taken account of. In two limiting cases the model introduced here is identical to the transient-network model and the bead-spring model, respectively. Model predictions were interpreted and compared with measurements on an L.D.-polyethylene melt, available from literature, and an S.I.S.-blockcopolymer solution. In both cases information was obtained about the network and the kinetic processes occurring in a state of rest and during steady-shear flow, assuming the model to be valid.     

Dissipative spectral transfers of turbulent plasma pulsations

We discuss the excitation of low-frequency (^s _em_e/m_i) acoustic vibrations by a beam of transverse (rf) waves. It is found that under certain conditions the dispersion (and not simply the excitation increment) of the low-frequency acoustic vibrations is uniquely connected with the rf wave energy density.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 23–29, November–December, 1969.The estimates from (4.5) can be obtained similarly.     

Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows

The generalized Newtonian fluid, as an important kind of non-Newtonian fluids, has been widely used in both science and engineering. In this paper, we present a multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid, and validate the model through a detailed comparison with analytical solutions and some published results. The accuracy and stability of the present model are also studied, and compared with those of the popular single-relaxation-time lattice Boltzmann model. Finally, the limit and potential of the multiple-relaxation-time lattice Boltzmann model are briefly discussed.     

A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity

The aim of this article is to study the quasistatic evolution of a three-dimensional elastic-perfectly plastic solid which satisfies the Prandtl-Reuss law. The evolution of the field of stresses -which solves a time dependent variational inequality — and that of the field of displacements u, have been described in previous works [15], [26], [35], [36], [37] but it was not shown there that and u satisfy indeed the Prandtl-Reuss constitutive law. In this article we find and u in a class of functions which are sufficiently regular for the Prandtl-Reuss law to make sense and we prove that and u satisfy the constitutive law. This result is attained by considering the elastic-perfectly plastic model as the limit of a family of elastic-visco-plastic models like those of Norton and Hoff. The Norton-Hoff type models which we introduce depend on a viscosity parameter > 0; we study the perturbed models (i.e. > 0 fixed) and then we pass to the limit 0.Dedicated to James Serrin on the occasion of his 60^th Birthday     

A one-parameter generalized self-consistent model for isotropic multiphase composites

The classical generalized self-consistent model (GSCM) is recognized to be suitable and efficient for estimating the effective moduli of an isotropic composite consisting of an isotropic host matrix and an isotropic inclusion phase. The present work aims to enlarge the scope of the GSCM so that it becomes applicable to a good number of important situations where the phases cannot be differentiated as the host matrix and inclusions. This objective is achieved first by inserting into the unknown effective medium a coated composite sphere whose core is made of the unknown effective medium and whose coatings are formed of the constituent phases and then by imposing an energy equivalency condition. The equations thus obtained to characterize the effective bulk and shear moduli involve a microstructural parameter which turns out to be capable of describing in some sense how far a microstructure is from the host matrix/inclusion morphology. The important case of two-phase composites is studied in detail to illustrate the salient features of the proposed model.     

Hopf-zero bifurcation in a generalized Gopalsamy neural network model

In this paper, we study Hopf-zero bifurcation in a generalized Gopalsamy neural network model. By using multiple time scales and center manifold reduction methods, we obtain the normal forms near a Hopf-zero critical point. A comparison between these two methods shows that the two normal forms are equivalent. Moreover, bifurcations are classified in two-dimensional parameter space near the critical point, and numerical simulations are presented to demonstrate the applicability of the theoretical results.     

Internal pulsations in flows of finely dispersed suspensions

The results are given of calculations for the flow of a finely dispersed suspension when momentum and energy are exchanged between individual particles exclusively through the ambient fluid, i.e., the role of direct collisions between particles is negligible. Using the results, one can not only calculate the rms characteristics of the pseudoturbulence and, in particular, find the stresses in the dispersed phase but also to give a natural explanation of the phenomena observed in experiments on sedimentation and hydrodynamic self-diffusion of particles in monodisperse suspensions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 91–100, May–June, 1993.     

Effect of high-amplitude flow pulsations on heat transfer

We present results of an experimental study of the effect of flow pulsations on turbulent heat transfer in the transverse direction in propagation of sound waves. A significant increase in heat-transfer intensity was recorded at mean-square pressure pulsation amplitude p=168–180 dB at frequency f=100–150 Hz. The dependence of heat-transfer intensity on acoustic field characteristics is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–172, March–April, 1975.