A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.     

On Permutable Congruences on Antigroups of Finite Rank

We find necessary and sufficient conditions for any two congruences on an antigroup of finite rank to be permutable.     

Thickness decrease of a grafted polyelectrolyte membrane exposed to shear flow

The effect of the shear flow on the thickness change of a polyelectrolyte membrane grafted onto a glass substrate was directly investigated with a flow cell combined with a confocal laser scanning microscope. The membrane thickness decreased proportionally to an increase in the shear stress of the flow when the shear rate exceeded a critical value of 1 s^?1. The higher the ionic strength was of the fluid, the greater the thinning effect was. The correlation between the critical shear rate and the relaxation of the polymer in the gel membrane was examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2808–2815, 2003     

The fifth dimension: Theodor Kaluza's ground‐breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.     

An Experimental Investigation into the Acoustic Characteristics of Fluid-filled Porous Structures—A Simplified Model of the Human Skull Cancellous Structure

In nature, shape and structure evolve from the struggle for better performance. Often, biological structures combine multiple beneficial properties, making research into mimicking them very complex. Presented here is a summary of observations from a series of experiments performed on a material that closely resembles the human skull bone’s cancellous structure under acoustic loads. Transmission loss through flat and curved open-cell polyurethane foam samples is observed using air and water as the two interstitial fluids. Reduction in strength and stiffness caused by porosity can be recovered partially by filling the interstitial pores with a fluid. The test findings demonstrate the influence of the interstitial fluid on the mechanical characteristics of a porous structure in a quantitative manner. It is also demonstrated that the transmission loss does not depend only on the mass per unit area of the structure as predicted by acoustic mass law. Current tests also demonstrate that the transmission loss is more sensitive to the interstitial fluid than the shape and support conditions of the structures. Test observations thus support the concepts of “moisture-sensitivity of biological design” and the “law of hierarchy in natural design”.     

Growth of Sb-Bi gradient single crystals

The growth conditions and structural quality of Sb-Bi gradient single crystals with Bi content from 2 to 18 at %, grown by the Czochralski method with solid phase feed, are investigated. Bi distribution in the crystals along their pulling direction are studied by electron probe microanalysis and the change in the interplanar spacing is analyzed by double-crystal X-ray diffraction. It is established that the pulling rate and feed mass affect the Bi distribution in Sb-Bi single crystals.     

Thermal-performance evaluation of coolant passages with staggered arrays of pin fins

Three-dimensional laminar forced convection including steady-periodic transition is investigated up to periodic-chaotic transition in the fully developed region of coolant passages with staggered arrays of pin fins. Comparative examples concern overall pressure losses and heat transfer characteristics of circular, square and elliptical pins made of nickel and copper. In the numerical model, transient conjugate heat transfer is assumed and space periodicities in pressure, velocity components and temperatures are taken into account. In the range of operative conditions investigated, overall friction factors increase almost linearly with the Reynolds number, while the increase of overall Nusselt numbers with the Reynolds number is characterized by two slope changes connected with the onset of streamwise vortices, and the shedding of transverse vortices, respectively. The use of copper, instead of nickel, increases the overall Nusselt number with all shapes, but is particularly beneficial to the elliptical section. Square pins are characterized by the highest values of friction factors, but are also the best performers as far as convection enhancing is concerned. The reverse is true for the elliptical pins which are characterized by the lowest values of friction factors, but are the worst performers as far as convection enhancing is concerned. On the basis of overall performances, the elliptical pins made of copper are the best choice, at least in the upper range of Reynolds numbers investigated.