A Theoretical Analysis of Magnetic Particle Alignment in External Magnetic Fields Affected by Viscosity and Brownian Motion

The interaction of an external magnetic field with magnetic objects affects their response and is a fundamental property for many biomedical applications, including magnetic resonance and particle imaging, electromagnetic hyperthermia, and magnetic targeting and separation. Magnetic alignment and relaxation are widely studied in the context of these applications. In this study, we theoretically investigate the alignment dynamics of a rotational magnetic particle as an inverse process to Brownian relaxation. The selected external magnetic flux density ranges from 5μT to 5T. We found that the viscous torque for arbitrary rotating particles with a history term due to the inertia and friction of the surrounding ambient water has a significant effect in strong magnetic fields (range 1–5T). In this range, oscillatory behavior due to the inertial torque of the particle also occurs, and the stochastic Brownian torque diminishes. In contrast, for weak fields (range 5–50μT), the history term of the viscous torque and the inertial torque can be neglected, and the stochastic Brownian torque induced by random collisions of the surrounding fluid molecules becomes dominant. These results contribute to a better understanding of the molecular mechanisms of magnetic particle alignment in external magnetic fields and have important implications in a variety of biomedical applications.

Coexisting Attractors, Energy Analysis and Boundary of Lü System

In this study, first, the phenomenon of multistability in the Lü system is found, which shows the coexistence of two different point attractors and one chaotic attractor. These coexisting attractors are dependent on initial conditions of the system while the parameters of the system are fixed. Then, the Lü system is transformed to a Kolmogorov-type system, which includes the conservative torque consisting of the inertial torque and the internal torque, the dissipative torque, and the external torque. Moreover, by analyzing the combination of different types of torques and investigating the cycling of energy based on the Casimir function and Hamiltonian function, the interaction between the external torque and other torques is found to be the main reason for the Lü system to generate chaos. Finally, by investigating the Casimir function, it is found that the boundary of the Lü system is only related to system parameters.

Position Control of 1-DOF High-Precision Rotary Table using Adaptive Neuro-Fuzzy Inference System (ANFIS) Controller

Research of position control of 1-DOF high-precision rotary table using adaptive Neuro-Fuzzy inference system (ANFIS) controller has been done. In the closed-loop system without a controller, the response was oscillating and pounding caused by inertial torque. It because a rotary table receives a considerable load. Based on this, the ANFIS controller is needed to eliminate oscillations and compensate for the inertia. The result shows that there was no oscillation or overshoot with the steady-state error value of 2.27% for the reference angle of 45°, valued at 0.10% reference angle of 180°, and valued at 0% reference angle of 360°. The result proves that ANFIS controllers can eliminate oscillations with and compensate for inertia.

A Mathematical Model for Top Motions

The topic of the top motions is not new but the known publications represent wrong mathematical models for its gyroscopic effects. Recent investigations have demonstrated the physics of gyroscopic effects is more complex. On any spinning objects are acting the system of interrelated internal torques generated by their rotating mass elements and center mass. The inertial torque is produced by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum. These inertial torqueses represent the fundamental principle of gyroscope theory. The new inertial torques enables deriving mathematical models for the motions of any rotating objects that were impossible for a long time. The aim of this work is to represent mathematical models for the motions of the well-balanced top on the flat horizontal surface. This work describes the physics of the top motions and closes the problem of many years of discussion. The new analytical approach for the top’s motions definitely responds to the practical results and represents a good example of the educational process.

Inertial torques and a symmetry breaking orientational transition in the sedimentation of slender fibres

Experimental measurements of the force and torque on freely settling fibres are compared with predictions of the slender-body theory of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462). Although the flow is viscous dominated at the scale of the fibre diameter, fluid inertia is important on the scale of the fibre length, leading to inertial torques which tend to rotate symmetric fibres toward horizontal orientations. Experimentally, the torque on symmetric fibres is inferred from the measured rate of rotation of the fibres using a quasi-steady torque balance. It is shown theoretically that fibres with an asymmetric radius or mass density distribution undergo a supercritical pitch-fork bifurcation from vertical to oblique settling with increasing Archimedes number, increasing Reynolds number or decreasing asymmetry. This transition is observed in experiments with asymmetric mass density and we find good agreement with the predicted symmetry breaking transition. In these experiments, the steady orientation of the oblique settling fibres provides a means to measure the inertial torque in the absence of transient effects since it is balanced by the known gravitational torque.

Mechanics Analysis and Hardware Implementation of a New 3D Chaotic System

In this study, a new 3D chaotic system was first transformed into a Kolmogorov-type system to describe the vector field from the viewpoint of torque. In this Kolmogorov-type system, only inertial torque and non-Rayleigh dissipation exist. Thus, this is different from previously reported Kolmogorov-type systems that are generally decomposed into inertial torque, internal torque, dissipation, and external torque. Moreover, by analyzing these two torques, the physical background of the system and the key factors of chaos generation were also determined. That is, the inertial torque and non-Rayleigh dissipation are responsible for chaos generation in the new 3D chaotic system. Then, the Casimir function and Hamiltonian energy function were also analyzed to investigate the cycling of energy in the chaotic system. Finally, both an analog circuit and a Field Programmable Gate Array (FPGA) circuit were designed to implement the chaotic system. All of the experimentally obtained results are consistent with the results of numerical analysis, which did not only indicate the chaotic characteristics of the 3D chaotic system physically, but also provided physical models for engineering applications.

Modeling the inertial torque imbalance and foundation forces within an inline internal combustion engine : quantifying the equivalent mass approximation

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The main object of this dissertation is to study the dynamic analysis of an inline internal combustion engine. This dissertation presents the kinematics and kinetic analyses of an inline internal combustion engine crank mechanism, the dynamic torque imbalance and foundation forces for a single-piston and multi-piston engines are studied as well. The objectives of this dissertation are to explore the inertial-torque characteristics and foundation forces of an inline, internal combustion engine with connecting-rod joints that are evenly spaced about the centerline of the crankshaft, and to evaluate the goodness of a mass approximation that is customarily used in machine design textbooks. In this dissertation the number of pistons within the internal combustion engine is varied from 1 to 8. In order to generalize the results, the reaction force between the ground and the crank in the x-direction and y-direction equations are nondimensionalized and shown to depend upon only six nondimensional groups, all related to the mass and geometry properties of the connecting rod and crank while the reaction force between the connecting rod and the piston in the x-direction y-direction, reaction force between the crank and the connecting rod in the x-direction y-direction, reaction force between the piston and the cylinder wall, and the inertial-torque equations are nondimensionalized all related to the mass and geometry properties of the connecting rod. As shown in this dissertation, the largest torque imbalance is exhibited by a 2-piston engine. The next largest torque imbalance is exhibited by a 3-piston engine, followed by a single-piston engine (this is not monotonic). The largest foundation forces are exhibited by a single-piston engine. The next largest foundation forces are exhibited by a 2-piston engine, followed by a 3e-piston engine, and that a dramatic reduction in the foundation forces and torque imbalance may be obtained by using 4 or more pistons in the design, when using as many as 8 pistons the foundation forces and torque imbalance essentially vanishes. It should be observed that the mass approximation captures 100 percent of the variability of the actual torque imbalance for engines that are designed with an odd number of pistons equal to or greater than three. The mass approximation captures 100 percent of the variability of the actual reaction force between the piston and cylinder wall for engines that are designed with single-piston and multi-pistons. The mass approximation captures 100 percent of the variability of the actual reaction force against piston pin for engines that are designed with single-piston. It is also shown in this dissertation that the customary mass approximations for the connecting rod may be used to simplify the analysis for all engine designs without a significant loss of modeling accuracy.

Modeling the Inertial Torque Imbalance Within an Internal Combustion Engine: Quantifying the Equivalent Mass Approximation

The objectives of this research are to explore the inertial-torque characteristics of an inline, internal combustion engine with connecting-rod joints that are evenly spaced about the centerline of the crankshaft, and to evaluate the goodness of a mass approximation that is customarily used in machine design textbooks. In this research, the number of pistons within the internal combustion engine is varied from 1 to 8. In order to generalize the results, the inertial-torque equations are nondimensionalized and shown to depend upon only four nondimensional groups, all related to the mass and geometry properties of the connecting rod. As shown in this research, the inertial-torque imbalance is greatest for an engine with two pistons, and that a dramatic reduction in the torque imbalance may be obtained for engine designs that use four or more pistons. It is also shown in this paper that the customary mass approximations for the connecting rod may be used to simplify the analysis for all engine designs without a significant loss of modeling accuracy.