Comparison Between Damping Coefficients of Measured Perforated Micromechanical Test Structures and Compact Models

Measured damping coefficients of six different perforated micromechanical test structures are compared with damping coefficients given by published compact models. The motion of the perforated plates is almost translational, the surface shape is rectangular, and the perforation is uniform validating the assumptions made for compact models. In the structures, the perforation ratio varies from 24% - 59%. The study of the structure shows that the compressibility and inertia do not contribute to the damping at the frequencies used (130kHz - 220kHz). The damping coefficients given by all four compact models underestimate the measured damping coefficient by approximately 20%. The reasons for this underestimation are discussed by studying the various flow components in the models.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838

Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems

The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and in the fracture strength of quasi-brittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. We use the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the $\kappa$-Weibull distribution. We conduct statistical analysis of experimental data and simulations that show good agreement with the $\kappa$-Weibull distribution. We show the following: (1) The weakest-link theory for finite-size systems involves the $\kappa$-Weibull distribution. (2) The power-law decline of the $\kappa$-Weibull upper tail can explain deviations from the Weibull scaling observed in return interval data. (3) The hazard rate function of the $\kappa$-Weibull distribution decreases linearly after a waiting time $\tau_c \propto n^{1/m}$, where $m$ is the Weibull modulus and $n$ is the system size in terms of representative volume elements. (4) The $\kappa$-Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we show that the $\kappa$-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.Comment: 33 pages, 11 figure

Obeying a rule : Ludwig Wittgenstein and the foundations of Set Theory

In this paper we propose some reflections on Wittgenstein’s ideas about grammar and rules; then we shall consider some consequences of these for the foundations of set theory and, in particular, for the introduction of major concepts of set theory in education. For instance, a community of practice can decide to follow a particular rule that forbids the derivation of arbitrary sentences from a contradiction: since, according to Radford’s perspective, knowledge is the result of thinking, and thinking is a cognitive social praxis, the mentioned choice can be considered as a form of real and effective knowledge

Numbers and Polynomials- 50 years since the publication of Wittgenstein\u27s Bemerkungen über die Grundlagen der Mathematik (1956): Mathematical and Educational reflections

According to L. Wittgenstein, the meaning of a mathematical object is to be grounded upon its use. In this paper we consider Robinson theory Q, the subtheory of firstorder Peano Arithmetic PA; some theorems and conjectures can be interpreted over one model of Q given by a universe of polynomials; with respect to nonconstant polynomials some proofs by elementary methods are given and compared with corresponding results in the standard model of PA. We conclude that the creative power of the language can be pointed out in how the language itself is embedded into the rest of human activities, and this is an important track to follow for researchers in mathematics education

Two new intermediate polars with a soft X-ray component

Aims. We analyze the first X-ray observations with XMM-Newton of 1RXS J070407.9+262501 and 1RXS 180340.0+401214, in order to characterize their broad-band temporal and spectral properties, also in the UV/optical domain, and to confirm them as intermediate polars. Methods. For both objects, we performed a timing analysis of the X-ray and UV/optical light curves to detect the white dwarf spin pulsations and study their energy dependence. For 1RXS 180340.0+401214 we also analyzed optical spectroscopic data to determine the orbital period. X-ray spectra were analyzed in the 0.2–10.0 keV range to characterize the emission properties of both sources. Results. We find that the X-ray light curves of both systems are energy dependent and are dominated, below 3–5 keV, by strong pulsations at the white dwarf rotational periods (480 s for 1RXS J070407.9+262501 and 1520.5 s for 1RXS 180340.0+401214). In 1RXS 180340.0+401214 we also detect an X-ray beat variability at 1697 s which, together with our new optical spectroscopy, favours an orbital period of 4.4 h that is longer than previously estimated. Both systems show complex spectra with a hard (temperature up to 40 keV) optically thin and a soft (kT ∼ 85–100 eV) optically thick components heavily absorbed by material partially covering the X-ray sources. Conclusions. Our observations confirm the two systems as intermediate polars and also add them as new members of the growing group of “soft” systems which show the presence of a soft X-ray blackbody component. Differences in the temperatures of the blackbodies are qualitatively explained in terms of reprocessing over different sizes of the white dwarf spot. We suggest that systems showing cooler soft X-ray blackbody components also possess white dwarfs irradiated by cyclotron radiation

Real and complex connections for canonical gravity

Both real and complex connections have been used for canonical gravity: the complex connection has SL(2,C) as gauge group, while the real connection has SU(2) as gauge group. We show that there is an arbitrary parameter $\beta$ which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory. A value for $\beta$ could be could be singled out in the quantum theory by the Hamiltonian constraint, or by the rotation to the complex Ashtekar connection.Comment: 8 pages, RevTeX, no figure

Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A, 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.Comment: 26 page

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension