Cyclic subsemigroups of symmetric inverse semigroups

A generalization of the cycle notation for permutations is introduced for partial one-one transformations (charts). Notational representation theorems for charts that generalize those of permutations are given. Notational multiplication of charts is developed and then applied to yield a transparent proof of Frobenius' result which bounds the idempotent in the cyclic subsemigroup. Lastly, the well known result that the structure of the cyclic subgroups of the finite symmetric groups is determined from combinations of disjoint cycles is generalized to the cyclic subsemigroups of the finite symmetric inverse semigroups.     

Some Penrose transforms in complex differential geometry

In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The other concerns obstructions to the embedding of CR structures on the three-sphere. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Development of a micromachined piezoelectric microphone for aeroacoustics applications

This paper describes the design, fabrication, and characterization of a bulk-micromachined piezoelectric microphone for aeroacoustic applications. Microphone design was accomplished through a combination of piezoelectric composite plate theory and lumped element modeling. The device consists of a 1.80-mm-diam, 3-microm-thick, silicon diaphragm with a 267-nm-thick ring of piezoelectric material placed near the boundary of the diaphragm to maximize sensitivity. The microphone was fabricated by combining a sol-gel lead zirconate-titanate deposition process on a silicon-on-insulator wafer with deep-reactive ion etching for the diaphragm release. Experimental characterization indicates a sensitivity of 1.66 microVPa, dynamic range greater than six orders of magnitude (35.7-169 dB, re 20 microPa), a capacitance of 10.8 nF, and a resonant frequency of 59.0 kHz.     

Solitary electromagnetic pulses detected with super-Alfvénic flows in Earth's geomagnetic tail

Solitary nonlinear (deltaB/B>1) electromagnetic pulses have been detected in Earth's geomagnetic tail accompanying plasmas flowing at super-Alfvénic speeds. The pulses in the current sheet had durations of approximately 5 s, were left-hand circularly polarized, and had phase speeds of approximately the Alfvén speed in the plasma frame. These pulses were associated with a field-aligned current J(parallel) and observed in low density (approximately 0.3 cm(-3)), high temperature (T(e) approximately T(i) approximately 3x10(7) K), and beta approximately 10 plasma that included electron and ion beams streaming along B. The wave activity was enhanced from below the ion cyclotron frequency to electron cyclotron and upper hybrid frequencies. The detailed properties suggest the pulses are nonlinearly steepened ion cyclotron or Alfvén waves.     

Coupled whispering gallery modes in a multilayer-coated microsphere

Whispering gallery modes in a microsphere coated with three layers of high, low, and high refractive indices (RIs) are considered. Coastal modes and inland modes, centered on the outer and inner high-RI layers, exist as different radial modes. At right values of RI and thickness of the three layers, an inland mode and a coastal mode couple to produce a radial distribution of the photonic field that resembles bonding and antibonding orbitals. The coupling occurs across a layer of the middle low-RI layer, much thicker than the wavelength of light. The coupling is analyzed in a quantum-mechanical analog of a one-dimensional particle in a double-well potential.     

Reply to the Comment by S. J. Kowalski,TIPM 40, 113, 2000

Transport in Porous Media -     

Melt shear rheology of carbon nanofiber/polystyrene composites

The rheological behavior and morphology of carbon nanofiber/polystyrene (CNF/PS) composites in their melt phase have been characterized both through experimental measurements and modeling. Composites prepared in the two different processes of solvent casting and melt blending are contrasted; melt-blended and solvent-cast composites were each prepared with CNF loadings of 2, 5, and 10 wt%. A morphological study revealed that the melt blending process results in composites with shorter CNFs than in the solvent-cast composites, due to damage caused by the higher stresses the CNFs encounter in melt blending, and that both processes retain the diameter of the as-received CNFs. The addition of carbon nanofiber to the polystyrene through either melt blending or solvent casting increases the linear viscoelastic moduli, G′ and G″, and steady-state viscosity, η, in the melt phase monotonically with CNF concentration, more so in solvent cast composites with their longer CNFs. The melt phase of solvent-cast composites with higher CNF concentrations exhibit a plateau of the elastic modulus, G′, at low frequencies, an apparent yield stress, and large first normal stress difference, N ₁, at low strain rates, which can be attributed to contact-based network nanostructure formed by the long CNFs. A nanostructurally-based model for CNF/PS composites in their melt phase is presented which considers the composite system as rigid rods in a viscoelastic fluid matrix. Except for two coupling parameters, all material constants in the model for the composite systems are deduced from morphological and shear flow measurements of its separate nanofiber and polymer melt constituents of the composite. These two coupling parameters are polymer–fiber interaction parameter, σ, and interfiber interaction parameter, C _I. Through comparison with our experimental measurements of the composite systems, we deduce that σ is effectively 1 (corresponding to no polymer–fiber interaction) for all CNF/PS nanocomposites studied. The dependence of CNF orientation on strain rate which we observe in our experiments is captured in the model by considering the interfiber interaction parameter, C _I, as a function of strain rate. Applied to shear flows, the model predicts the melt-phase, steady-state viscosities, and normal stress differences of the CNF/PS composites as functions of shear rate, polymer matrix properties, fiber length, and mass concentration consistent with our experimental measurements.     

The Forchheimer equation: A theoretical development

In this paper we illustrate how the method of volume averaging can be used to derive Darcy's law with the Forchheimer correction for homogeneous porous media. Beginning with the Navier-Stokes equations, we find the volume averaged momentum equation to be given by $$\langle v_\beta \rangle = - \frac{K}{{\mu _\beta }} \cdot (\nabla \langle p_\beta \rangle ^\beta - \rho _\beta g) - F\cdot \langle v_\beta \rangle .$$ The Darcy's law permeability tensor, K, and the Forchheimer correction tensor, F, are determined by closure problems that must be solved using a spatially periodic model of a porous medium. When the Reynolds number is small compared to one, the closure problem can be used to prove that F is a linear function of the velocity, and order of magnitude analysis suggests that this linear dependence may persist for a wide range of Reynolds numbers.     

Soviet and Japanese oversnow vehicles

The Soviet Union has an overwhelming need for oversnow and adverse terrain transport since by their own definition over 60% of their country is considered as Arctic. They have developed a wide range of configurations and types of vehicles to fit their production capabilities and needs. Their vehicles in general are not sophisticated but rather emphasize ease of maintenance and simplicity. Their research however is based on investigating even exotic vehicle configurations.

Japan on the other hand has limited its work to a small number of vehicles to fit their limited needs in the Northern Islands. Their research has been based mainly on the development and improvement of a snow/road track which can be used to meet their specialized military requirements.     

On using non-Gaussian distributions to perform statistical linearization

In statistical linearization non-linear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure. The recipes require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response. Because the exact non-linear response distribution is unknown it has become traditional to use a Gaussian distribution as an approximation to the exact distribution. With the modern computing tools now available it is easy to use non-Gaussian distributions which can provide better approximations in cases where Gaussian distributions are not appropriate. Examples are displayed for power-law oscillators with stiffening and softening springs, and for the Duffing oscillator, and for a double-well oscillator. Two families of probability distributions with varying shape are studied.