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In this work, we propose mathematical formulations that detail the effect of the dielectric strength of dielectric material on the spatial distribution of electric field in an infinite space with a conducting plate. Using the dielectric strength of air as the maximum limit for the magnitude of electric field intensity and the equivalence of stored charge between two different zones, we determine the size of the dielectric breakdown region (the extended region with ionized material) for the conducting strip and the conducting disk charged to an electric voltage. The size of dielectric breakdown is proportional to the square of the applied voltage, and decreases with the increase of the width/radius of the conducting strip/disk.

This works describes a promising method for rapid prototyping tape stencils for the application of solder paste. This process is appropriate for research settings requiring developmental flexibility and the ability to deal with small device dies. This work compares the volume of solder paste deposited versus aperture volume for several common tape materials and several common printed circuit board (PCB) stencil materials. The solder deposits are then reflowed to identify which aperture and solder paste parameters can generate successful solder bumps. Electrically conductive solder bonds for small bond pads (100 μm and larger) are demonstrated between silicon device dies and glass dies using this process.

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.

We present a robust method to fabricate a polydimethylsiloxane (PDMS) microfluidic device with critical channel features located near the periphery. The fabricated device has a window cutout, allowing close placement and integration of the channel with solid state circuits and devices. The flow characteristics of the fabricated device are shown to closely follow that of theoretical behavior, making it an appropriate alternative to a monolithic, cast-molded device. As an illustration of the use of this method, a novel integrated microfluidic-electronic system is demonstrated with the microfluidic channel bonded directly onto the surface of an integrated circuit while leaving access to probe pads on the chip's surface. This fabrication process has important implications in furthering the development of next generation microfluidic-based lab on chip systems.

Using the Hankel transform, the mixed boundary value problem of a conducting, circular disk on a dielectric layer in an electric field was reduced to the solution of dual integral equations. Analytical expressions of the capacitance of the electrical system to the second approximation were derived for the ratio of the layer thickness to the disk radius being larger than one and the ratio being less than one, respectively. Both expressions yield numerical results in accord with those reported in literature. The capacitance of a circular disk on a semi-infinite dielectric can be used for a ratio larger than or equal to 4. Using the results, the thickness effect on electrowetting of a disk-like conducting film on a dielectric substrate was discussed. There exists an upper bound of the electric voltage applied to the film above which the saturation of contact angle or local instability will occur.

Forget inventory control in big-box stores---what if we had RFID chips to monitor $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ $c\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}s$ in a living body? A team of researchers has started us on this road, by creating radio-frequency devices just 22 \textmu{}m across, which can be naturally taken up by live cells. Despite their size, these devices emit strong signals and can be sensed wirelessly by their corresponding transceivers. Their potential for continuous tracking of intracellular activities is quite significant for research and practice in biology and medicine.

Bioactive glasses react with the human physiological solution in control of their biofunctionality. The stress state in bioactive glasses determines the chemomechanical reaction and their biofunctionality. Using the microindentation technique, the effect of the indentation deformation on the surface damage and material dissolution of 45S5 bioglass was investigated. The indentation-induced local surface damage, including ring cracks and radial cracks, was revealed before and after the immersion tests in phosphate buffer solution (PBS). There existed a critical load for the formation of the radial cracks, which emanated from the periphery of the outmost ring crack. The growth of the radial cracks in the PBS solution displayed the stress-corrosion behavior with the crack-growth speed being a linear function of the indentation load. Fast dissolution occurred at the edges of the surface-damaged zone due to stress-assisted dissolution under the action of local tensile stress, which was different from the dissolution behavior of stress-free 45S5 bioglass.

Using Legendre polynomials, the boundary value problem of a charged, conducting hemisphere in an infinite space was reduced to the solution of an infinite system of linear, algebraic equations. Analytical solutions of electric charge and electric stress on the surface of the hemisphere were obtained. The numerical analysis revealed non-uniform distributions of the electric charge and electric stress over the surface of the hemisphere with local singularities at the edge of the hemisphere. Both the electric charge and electric stress distributions were expressed in terms of the power function with respect to the distance to the nearest hemisphere edge. The power index for the flat surface is larger than that corresponding to the spherical surface. Numerical result of the capacitance of the conducting hemisphere is the same as the result reported in the literature. There is no net force acting on the hemisphere.

Using the cavity model and the concept of the plastic-hardening modulus, a simple relationship was established between the size of an indent and the size of a semi-spherical-shell softening zone. Indentation experiments of a Cu46.25Zr45.25Al7.5Er1 bulk-metallic glass (BMG) were performed over a range of indentation loads from 500 to 4000 mN, using a Vickers indenter. The indentation hardness decreased slightly with the increase in the indentation load from 5.21 GPa at an indentation load of 500 mN to 4.66 GPa at an indentation load of 4000 mN. The evolution of shear bands underneath the indentation was studied using an interface-bonded BMG sample. Shear bands of a semi-spherical-shell shape and a line-shape were observed underneath the indentation. The dependence of the size of the shear-banding zone on the size of the indent was examined, which qualitatively supported the analytical model. The inter-banding spacing decreased with the increase in the indentation load, associated with the release of the stored strain energy.