Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here we study the statistics of ingredients and recipes taken from Brazilian, British, French, and Medieval cookbooks. We find universal distributions with scale invariant behavior. We propose a copy-mutate process to model culinary evolution that fits very well our empirical data. We find a cultural "founder effect" produced by the nonequilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted by our model, which may have applications in other kinds of evolutionary processes.
Calculations are presented for the femtosecond time‐evolution of intensities of beams diffracted by perfect Bragg crystals illuminated with radiation expected from X‐ray free‐electron lasers (XFELs) operating through the self‐amplified spontaneous emission (SASE) process. After examining the case of transient diffraction of an electromagnetic delta‐function impulse through flat, single‐ and double‐crystal monochromators, the propagation of a 280 fs‐duration SASE XFEL pulse of 8 keV photons through the same optics is discussed. The alteration of the sub‐femtosecond spiky microbunched temporal structure of the XFEL pulse after it passes through the system is shown for both low‐order (broad bandwidth) and high‐order (narrow bandwidth) crystal reflections. Finally, the shot‐to‐shot statistical fluctuations of the integrated diffracted intensity is simulated. Implications of these results for XFEL applications are addressed.
USA X-ray free-electron lasers (XFELS) designed to operate at w 1~wavelengths are currently being proposed by several laboratories as the basis for the next (4th) generation of synchrotrons radiation sources. The unique radiation properties of these proposed sources, which include 200 fs pulse d uration and peak beam brilliance in excess of 1033 photon/(s .1%-bw mrad2 mm2), offer the possibility of ultrafast time-resolved experiments, perhaps down to 10 fs resolution levels using pulse compression or slicing techniques. Motivated by such potential applications, this paper addresses the relevant instrumentation issue of perfect crystal dynamical diffraction of ultrashort x-ray pulses when the pulse lengths become comparable to the extinction length scales. The basic calculations reported here show the transient time-dependent diffraction from perfect crystals excited by plane-wave delta-function electromagnet ic impulses. Time responses have been calculated for 8 keV photon ener~, for reflected and transmitted beams in both Bragg and Laue cases. Interesting difhction effects arise, and their implications for XFEL
A simplified Walecka-type model is investigated in a cosmological scenario. The model includes fermionic, scalar and vector fields as sources. It is shown that their interactions, taking place in a Robertson-Walker metric, could be responsible for the transition of accelerated-decelerated periods in the early universe and a current accelerated regime. It is also discussed the role of the fermionic field as the promoter of the accelerated regimes in the early and the late stages of the universe.
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