Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

A coherent picture of water at extreme negative pressure.

International audienceLiquid water at atmospheric pressure can be supercooled to 41 C (ref. 1) and superheated to C302 C (ref. 2). Experiments involving fluid inclusions of water in quartz suggest that water is capable of sustaining pressures as low as 140 MPa before it breaks by cavitation3. Other techniques, for which cavitation occurs consistently at around 30MPa (ref. 4), produce results that cast doubt on this claim. Here we reproduce the fluid-inclusion experiment, performing repeated measurements on a single sample--a method used in meteorology5, bioprotection6 and protein crystallization7, but not yet in liquid water under large mechanical tension. The resulting cavitation statistics are characteristic of a thermally activated process, and both the free energy and the volume of the critical bubble are well described by classical nucleation theory when the surface tension is reduced by less than 10%, consistent with homogeneous cavitation. The line of density maxima of water at negative pressure is found to reach 922:8 kgm3 at around 300 K, which further constrains its contested phase diagram

Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv admin note: substantial text overlap with arXiv:1202.525

Efficient Erbium-doped waveguide amplifier insensitive to power fluctuations

We describe an efficient erbium-doped waveguide amplifier insensitive to output power variation by means of optical gain clamping. Output power suitable for metro applications and gain flatness over full C-band are demonstrated. We also show that this technology is suitable for transparent WDM ring network. In fact the possible recirculation of amplified spontaneous emission noise or laser power leaking from mirrors will not impact the device performance making robust to transients for next generation reconfigurable WDM ring networks

Erbium-doped waveguide amplifier for reconfigurable WDM metro networks

Transient dynamic due to signal power fluctuations is the main impairment in reconfigurable transparent wavelength-division-multiplexing metro networks design. In this letter, we demonstrate an optical-gain-clamped erbium-doped waveguide amplifier using fiber Bragg grating filters. We show both theoretically and experimentally that it is virtually insensitive to signal transient and that it reduces overshoot by 10 dB compared to standard erbium-doped fiber amplifiers. The device modeling shows that short highly doped optical amplifiers are insensitive to input signal level transient and will outperform longer fiber-based identical operating condition amplifiers. In fact, erbium-doped waveguide optical amplifiers do not exhibit any transient dynamic effect that can be detrimental after accumulation along the amplifier chain. In addition, waveguide amplifiers will require less extra pump to stabilize optical clamping, thus reducing clamping implementation cost