Conformal invariance for nonholonomic system of Chetaev's type with variable mass

Conformal invariance and conserved quantities for a nonholonomic system of Chetaev's type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system's conformal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.

On the Quantum Mechanical Treatment of the Bateman-Morse-Feshbach Damped Oscillator with Variable Mass

The harmonic oscillator with time-dependent (indefinite and variable) mass subject to the force proportional to velocity is studied by extending Bateman’s dual Lagrangian and Hamiltonian formalism. To study the quantum analog of such a dissipative system, the Batemann-Morse-Feshback classical Hamiltonian of the damped harmonic oscillator with varying (time-dependent) mass is canonically quantized. In order to discuss the stability of the quantum dissipative system due to the influence of varying mass and the dissipative force, we derived a formula for the vacuum state of the dissipative system with the help of quantum field theoretical framework. It is shown that the formula based on this simple model could be used to study the influence of dissipation such as the instability due to the dissipative force and/or the variable mass. It is understood that the change in the oscillator mass corresponds to a control parameter in quantum dissipative systems.

A New Heat Transfer Model for Multi-Gradient Drilling with Hollow Sphere Injection

Multi-gradient drilling is a new offshore drilling method.The accurate calculation of the related wellbore temperature is of great significance for the prediction of the gas hydrate formation area and the precise control of the wellbore pressure.In this study,a new heat transfer model is proposed by which the variable mass flow is properly taken into account.Using this model,the effects of the main factors influencing the wellbore temperature are analyzed.The results indicate that at the position where the separation injection device is installed,the temperature increase of the fluid in the drill pipe is mitigated due to the inflow/outflow of hollow spheres,and the temperature drop of the fluid in the annulus also decreases.In addition,a lower separation efficiency of the device,a shallower installation depth and a smaller circulating displacement tend to increase the temperature near the bottom of the annulus,thereby helping to reduce the hydrate generation area and playing a positive role in the prevention and control of hydrates in deepwater drilling.

A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization

Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.

Flow Simulation of a Horizontal Well with Two Types of Completions in the Frame of a Wellbore–Annulus–Reservoir Model

Well completions are generally used to connect a reservoir to the surface so that fluids can be produced from orinjected into it. With these systems, pipe flows are typically established in the horizontal sections of slotted screencompletions and inflow control device (ICD) completions;moreover, an annular flow exists in the region betweenthe pipe and the borehole wall. On the basis of the principles of mass and momentum conservation, in the presentstudy, a coupling model considering the variable mass flow of the central tubing, the variable mass flow of theannular tubing and the reservoir seepage is implemented to simulate the wellbore–annulus–reservoir behaviorin the horizontal section of slotted-screen and ICD completions. In earlier models, only the central tubing variablemass flow and reservoir seepage flow were considered. The present results show that the closer the heel end, thegreater is the flow per unit length in the central tubing from the annulus. When external casing packers are notconsidered, the predicted production rate of the slotted screen completion, which is obtained using the variablemass flow model not taking into account the annulus flow, is 9.51% higher than the rate obtained using the (complete) model with annulus flow. In addition, the incomplete model forecasts the production of ICD completion ata 70.98% higher rate. Both models show that the pressure profile and flow profile of the borehole wall are relatively uniform in the wellbore–annulus–reservoir in horizontal wells.