In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular...

We report a highly sensitive means of measuring cellular dynamics with a novel interferometer that can measure motional phase changes. The system is based on a modified Michelson interferometer with a composite laser beam of 1550-nm low-coherence light and 775-nm CW light. The sample is prepared on a coverslip that is highly reflective at 775 nm. By referencing the heterodyne phase of the 1550-...

We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retroreflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of ...

Physical models of wave propagation or mechanical vibrations are becoming increasingly important for the design of algorithms for sound reproduction and sound synthesis. For sound reproduction, wave field synthesis has been established as a physically well-founded method for determining the loudspeaker driving signals of massive multichannel systems [1, 2]. On the other hand, algorithmic models...

and in which a and 6 are constants, arises in applied mathematics in two main groups of problems. The first group, of which Mathieu's problem of the transverse vibrations of a taut elliptic membrane is typical, consists of boundary problems relative to some partial differential equation, such as the wave equation, where the boundary is an ellipse—or possibly a hyperbola. Here a fundamental requ...

A novel physical mechanism is proposed to explain the temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states. It is shown that at room temperatures, stochastic broadening of molecular energy levels predominates the energy of low-frequency vibrations accompanying the tr...

We report the thermal conductivity and specific heat of amorphous silicon thin films measured from 5-300 K using silicon-nitride membrane-based microcalorimeters. Above 50 K the thermal conductivity of thin-film amorphous silicon agrees with values previously reported by other authors. However, our data show no plateau, with a low T suppression of the thermal conductivity that suggests that the...

vibration generated by vehicles during road transport has an important effect on the agricultural products damage process, particularly vegetable and fruit. modulus of elasticity is one of the most important mechanical properties of fruits and its variation can be described as one of the damage criteria during transportation. this research was conducted to evaluate the effects of vibration para...

In order to assess the effects of the sinusoidal vibrations on indices that characterise the internal quality, five samples of 30 eggs were stressed for 5 h with a constant acceleration of 0 5 g (root mean square value, r.m.s.) at frequency linearly increasing with the time in the 5–20, 20–35, 35–50, 50–65 and 65–80Hz ranges (one range for each sample). Vibration tests were carried out by means...

in this study, the mf285 tractor engine vibrations resulting from the use of different combinations of biodiesel, bioethanol and diesel as fuel were studied. engine vibrations in three directions and three engine speeds: 1000, 1600 rpm 2000 and ten fuel level was measured. to investigate the influence of measured parameters on engine vibration of factorial design in a randomized complete block ...