Monodromy and irreducibility criteria with algorithmic applications in characteristic zero

Consider a projective algebraic variety V, which is the set of all common zeros of homogeneous polynomials of degrees less than d in n + 1 variables over a field of characteristic zero. We suggest an algorithm that decides whether two (or more) given points of V belong to the same irreducible component of V. We also show how to construct, for each s < n, an (s + 1)-dimensional plane in the projective space such that the intersection of every irreducible component of dimension n — s of V with the constructed plane is transversal and is an irreducible curve. These algorithms are deterministic and polynomial in dⁿ and the input size. Bibliography: 9 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 292, 2002, pp. 130–152.This revised version was published online in April 2005 with a corrected cover date and article title.     

On the Definition of Temperature in FPU Systems

It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for Fermi–Pasta–Ulam systems, in conditions in which energy equipartition between the modes is not attained. We find that the temperature should be rather identified with the mean value of the energy of the low frequency modes.     

The Spectrum of a Linearized 2D Euler Operator

We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.     

Simultaneous determination of trace cadmium and mercury in Chinese herbal medicine by non-dispersive atomic fluorescence spectrometry using intermittent flow vapor generator.

A method was proposed for the simultaneous determination of trace cadmium and mercury by vapor generation non-dispersive atomic fluorescence spectrometry using an intermittent flow system. The effects of the parameters on the performance were studied systematically. The parameters such as acid concentration of the reaction medium, flow rate of the carrier gas and shield gas, the observation height and the atomizer temperature, etc. which affected the sensitivity, were optimized. Ascorbic acid, cobalt ion and thiourea were used as enhancement reagents or masking agents to enhance the generation efficiency of the volatile species of Cd and Hg. The mechanisms of their effects on vapor generation were investigated. In the presence of thiourea and ascorbic acid, the influences of some coexisting elements on the determination of cadmium and mercury were investigated. The detection limits (3sigma) were 0.010 microg l(-1) for Cd and 0.019 microg l(-1) for Hg, respectively. The relative standard deviations for Cd and Hg at 1.00 microg l(-1) were 2.6% and 0.97% (n = 11), respectively. The proposed method has been satisfactorily applied to the determination of trace cadmium and mercury in Chinese herbal medicine.     

On the dynamic electromechanical loading of dielectric elastomer membranes

Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure.     

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”.