Energy, Momentum, and Force in Classical Electrodynamics: Application to Negative-index Media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M - these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t)= E(r,t)\timesH(r,t)/c^2 emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.Comment: 9 pages, 4 figures, 21 equations, 19 reference

A nonlinear theory for fibre-reinforced magneto-elastic rods

We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the elastomeric matrix. We deduce closed form expressions of the quasi-static motion of the rod in terms of the external magnetic field and of the body forces. The dependences of the motion on the shape of the inclusions, their orientation, their anisotropic magnetic properties and the Young modulus of the matrix are analysed and discussed. Two case studies are presented in which the rod is used as an actuator suspended in a cantilever configuration. This work can foster new applications in the field of soft-actuators

TORQUE RESPONSE OF THIN-FILM FERROMAGNETIC PRISMS IN UNIFORM MAGNETIC FIELDS AT MACRO AND MICRO SCALES

The non-contact nature of magnetic actuation makes it useful in a variety of microscale applications, from microfluidics and lab-on-a-chip devices to classical MEMS or even microrobotics. Ferromagnetic materials like nickel are particularly attractive, because they can be easily deposited and patterned using traditional lithography-based microscale fabrication methods. However, the response of ferromagnetic materials in a magnetic field can be difficult to predict. When placed in a magnetic field, high magnetization is induced in these ferromagnetic materials, which in turn generates force and/or torque on the ferromagnetic bodies. The magnitude and direction of these forces are highly dependent on the type of material used, the volume and aspect ratio of the ferromagnetic material, as well as the spatial distribution and magnitude of the magnetic field. It is important to understand these complex interactions in order to optimize force and torque generated, particularly given common limitations found in microfabrication, where it is often challenging to deposit large volumes of ferromagnetic material using conventional microdeposition methods, and power availability is also often limited, which in turn limits the ability to generate strong electromagnetic fields for actuation. This work represents a theoretical analysis and experimental validation in macro scale to determine best practices when designing ferromagnetic actuators for microscale applications. Specifically, the use of nickel thin film prisms actuated in spatially uniform electromagnetic fields. These constraints were chosen because uniform magnetic fields can be readily generated with a simple and inexpensive Helmholtz coil design, and the uniformity makes actuation force independent of location, minimizing the need for spatial precision in devices. Nickel can also be easily deposited using evaporation or sputtering, generally in forms of thin-films

Design, characterization and control of thermally-responsive and magnetically-actuated micro-grippers at the air-water interface

The design and control of untethered microrobotic agents has drawn a lot of attention in recent years. This technology truly possesses the potential to revolutionize the field of minimally invasive surgery and microassembly. However, miniaturization and reliable actuation of micro-fabricated grippers are still challenging at sub-millimeter scale. In this study, we design, manufacture, characterize, and control four similarly-structured semi-rigid thermoresponsive micro-grippers. Furthermore, we develop a closed loop-control algorithm to demonstrate and compare the performance of the said grippers when moving in hard-to-reach and unpredictable environments. Finally, we analyze the grasping characteristics of three of the presented designs. Overall, not only does the study demonstrate motion control in unstructured dynamic environments-at velocities up to 3.4, 2.9, 3.3, and 1 body-lengths/s with 980, 750, 250, and 100 μm-sized grippers, respectively-but it also aims to provide quantitative data and considerations to help a targeted design of magnetically-controlled thin micro-grippers

Beyond the second order magnetic anisotropy tensor: Higher-order components due to oriented magnetite exsolutions in pyroxenes, and implications for paleomagnetic and structural interpretations

Exsolved iron oxides in silicate minerals can be nearly ideal paleomagnetic recorders, due to their single-domain-like behaviour and the protection from chemical alteration by their surrounding silicate host. Because their geometry is crystallographically controlled by the host silicate, these exsolutions possess a shape preferred orientation that is ultimately controlled by the mineral fabric of the silicates. This leads to potentially significant anisotropic acquisition of remanence, which necessitates correction to make accurate interpretations in paleodirectional and paleointensity studies. Here, we investigate the magnetic shape anisotropy carried by magnetite exsolutions in pyroxene single crystals, and in pyroxene-bearing rocks based on torque measurements and rotational hysteresis data. Image analysis is used to characterize the orientation distribution of oxides, from which the observed anisotropy can be modelled. Both the high-field torque signal and corresponding models contain components of higher order, which cannot be accurately described by second order tensors usually employed to describe magnetic fabrics. Conversely, low-field anisotropy data do not show this complexity and can be adequately described with second-order tensors. Hence, magnetic anisotropy of silicate-hosted exsolutions is field-dependent and this should be taken into account when interpreting isolated ferromagnetic fabrics, and in anisotropy corrections

The effect of distance and dimensions of magnets on nonlinear behavior of piezomagnetoelastic bimorph energy harvester

This paper presents the effect of distance and dimensions of magnetson chaotic behavior and voltage level of a vibratory piezo-magneto-elastic bimorph energy harvesting system. The bimorph model comprises two iezoelectriclayers on a cantilever base structure with one tip magnet as well as two external magnets. The mathematical model is extracted by using distributed model. The validity of the extracted model verified by previously published experimental results.In order to study the nonlinear dynamic of the bimorph, bifurcation diagram, phase plane portrait, time history response, Poincare map, power spectra diagram, and maximum Lyapunov exponents are used. In the bifurcation diagrams, the control parameters are the distances and dimensions of the magnets. It is shown that in the specific region of the control parameters, the sub-harmonic or super-harmonic behavior has minimum harvested voltage and irregular regions has maximum voltage. Also specific dimensions of tip magnet can influence greatly the dynamic behavior as well as output voltage. So these obtained results can give good insights about parameters identification and realization of the nonlinear behavior to reach the broadband higher harvested voltage of the system</span

Applications of Magnetic Materials in Soft Robotics

Magnetic materials can be used in modern soft robotics as a method for external stimulus actuation and motion control. By combining aspects of biology and mechanics, devices are fabricated to create a structure capable of complex movement. Applications that these devices are subject to can be broken down into four groups to summarize magnetics influence. These groups are flexible soft robotics, rigid design approaches, liquid metal groups, and novel stimulus methods. Flexible soft robotics involve magnetic materials placed into different elastomers primarily for use in locomotion. The resulting torque from the ferromagnetic particles in an external magnetic field will deform the elastomer causing locomotion. Rigid design approaches will use a hybrid of hard and soft magnetic materials to create a switch for gripping payloads. The process of actuating the switch is done by manipulating the magnetization of the soft material so that it is attracted or repelled from its hard material counterpart. Attaching paramagnetic particles to this device will allow locomotion for payload delivery applications. Liquid metal groups utilize both gallium-based compounds due to their low melting points and ferrofluid in both magnetic and fluid mechanic applications. Lastly, the novel stimulus methods include a variety of stimulus events such as varying light, temperature, and pH levels to modify magnetics influence on the device