Production of ball-lightning-like luminous balls by electrical discharges in silicon

We performed electric arc discharges in pure Si to generate luminous balls with lifetime in the order of seconds and several properties usually reported for natural ball lightning. This simple experiment does not rely on energy sources and excitation mechanisms that are improbable in the natural phenomenon and clearly demonstrates the role of vaporization and oxidation of Si, as proposed by the Abrahamson-Dinniss theory for ball-lightning formation.     

Isotropic compensation of diffraction-driven angular dispersion

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.     

Gouy wave modes: undistorted pulse focalization in a dispersive medium

Gouy wave modes are linear waves with finite energy that propagate without distortion at any phase and group velocity through a focal region in a dispersive medium. These features make them potentially useful for the onset and control of nonlinear interactions.     

On feedback and stable price adjustment mechanisms

Given an excess demand function of an economy, say Z(p)$Z(p)$, a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,_p0)$p(t,p_0)$ to an equilibrium _peq$p_{\mathit{eq}}$ solution of Z(p)=0$Z(p)=0$. Besides, all equilibrium points of Z(p)$Z(p)$ are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.     

Lamellar mono-amidosil hybrids doped with Rhodamine (B) methyl ester perchlorate

Ordered mono-amide cross-linked alkyl/siloxane hybrids (mono-amidosils) incorporating a Rhodamine (B) methyl ester perchlorate dye (Rh(B)CH₃ClO₄) have been synthesized through the sol–gel process and self-directed assembly. The host hybrid matrix m-A(14) is a lamellar bilayer hierarchically structured hybrid composed of short methyl-capped alkyl chains grafted to a siliceous framework through amide groups. At low dye concentration [n = 20, where n is the molar ratio of amide groups per Rh(B)CH₃ClO₄] a new lamellar structure with higher interlamellar distance than that of m-A(14) is formed, whereas at higher dye content (n = 5) this new lamellar structure coexists with that of m-A(14). The efficient encapsulation of Rh(B)CH₃ClO₄ provided by m-A(14) via hydrogen bonding interactions ensured the complete dissolution of the dye and induced a blue shift of the emission of the dye with respect to that of the isolated state, leading to an increase in the quantum yield from values below 0.01 % (measured for the isolated dye) to 4 % at n = 20. The formation of non-fluorescent H-type dimers in the sample with n = 5 accounts for the reduction of the quantum yield. The incorporation of Rh(B)CH₃ClO₄) into m-A(14) was clearly beneficial from the standpoint of the dye’s photostability, allowing to suppress photobleaching during the first 4 h. An intensification of the emission intensity by 50 and 25 % for the emission centered at 600 and 645 nm resulted, respectively, at n = 20.