Increasing thermoelectric efficiency: a dynamical systems approach

Inspired by the kinetic theory of ergodic gases and chaotic billiards, we propose a simple microscopic mechanism for the increase of thermoelectric efficiency. We consider the cross transport of particles and energy in open classical ergodic billiards. We show that, in the linear response regime, where we find exact expressions for all transport coefficients, the thermoelectric efficiency of ideal ergodic gases can approach the Carnot efficiency for sufficiently complex charge carrier molecules. Our results are clearly demonstrated with a simple numerical simulation of a Lorentz gas of particles with internal rotational degrees of freedom.     

Fluorescence quantum efficiency measurements in the presence of Auger upconversion by the thermal lens method

Mode-mismatched thermal lens (TL) measurements in Cr3+-doped fluoride crystals (LiSrAIF6 and LiSrGaF6) are reported. A nonlinear increase of the TL signal, and decrease of quantum efficiency, with increasing excitation power was observed and attributed to energy-transfer upconversion (ETU). Assuming an upconversion rate that is proportional to the excited-state population, Wup = gammaN(e), the theoretical model developed fits the experimental data well. The ETU parameters (gamma) were determined with unprecedented accuracy for low Cr concentrations. Thermo-optical parameters (K, ds/dT) were also obtained.     

Genus of cartesian products of regular bipartite graphs

Let G(n, d) denote a connected regular bipartite graph on 2n vertices and of degree d. It is proved that any Cartesian product G(n, d) × G₁(n₁, d₁) × G₂(n₂, d₂) × ? × G_m(n_m, d_m), such that max {d₁, d₂,…, d_m} ≤ d ≤ d₁ + d₂ + ? + d_m, has a quadrilateral embedding, thereby establishing its genus, and thereby generalizing a result of White. It is also proved that if G is any connected bipartite graph of maximum degree D, if Q_m is the m-cube graph, and if m ≥ D then G × Q_m has a quadrilateral embedding.     

Thioglycolic acid grafted onto silica gel and its properties in relation to extracting cations from ethanolic solution determined by calorimetric technique

Thioglycolic acid was immobilized onto silica gel surface using 3-aminopropyltrimethoxysilane as precursor silylating agent to yield silica. The amount of thioglycolic acid immobilized was 1.03 mmol per gram of silica. This new surface displayed a chelating moiety containing nitrogen, sulfur, and oxygen basic centers which are potentially capable of extracting cations from ethanolic solution, such as MCl3 ( M=Fe, Cr, and Mo). This process of extraction was carried out by the batch method when similar chemisorption isotherms were observed for all cations. The data were adjusted to a modified Langmuir equation. The sequence of the maximum retention capacity was Cr(III) > Mo(III) > Fe(III). The same adsorption was determined by calorimetric titration and the enthalpic values of -35.75 +/- 0.02, 32.90 +/- 0.15, and -84.08 +/- 0.12 kJmol(-1) for chromium, molybdenum, and iron, respectively, were obtained. From the calculated Gibbs free energy -23.4 +/- 0.2, -27.2 +/- 0.2, and -32.7 +/- 0.3 kJmol(-1), the variations in entropy obtained were 42 +/- 1, 201 +/- 1, 172 +/- 1 JK(-1)mol(-1) for the same sequence. All thermodynamic values are in agreement with the spontaneity of the proposed cation-basic center interactions for these chelating processes.     

The minimum distance of sets of points and the minimum socle degree

Let K be a field of characteristic 0. Let be a reduced finite set of points, not all contained in a hyperplane. Let be the maximum number of points of Γ contained in any hyperplane, and let . If I⊂R=K[x₀,…,x_n] is the ideal of Γ, then in Tohaˇneanu (2009) [12] it is shown that for n=2,3, d(Γ) has a lower bound expressed in terms of some shift in the graded minimal free resolution of R/I. In these notes we show that this behavior holds true in general, for any n≥2: d(Γ)≥A_n, where A_n=min{a_i−n} and ⊕_iR(−a_i) is the last module in the graded minimal free resolution of R/I. In the end we also prove that this bound is sharp for a whole class of examples due to Juan Migliore (2010) [10].     

Isomorphism Checking of I-graphs

We consider the class of I-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two I-graphs I(n, j, k) and I(n, j ₁, k ₁) are isomorphic if and only if there exists an integer a relatively prime to n such that either {j ₁, k ₁} =? {a j mod n, a k mod n } or {j ₁, k ₁} =? {a j mod n, ? a k mod n }. This result has an application in the enumeration of non-isomorphic I-graphs and unit-distance representations of generalized Petersen graphs.     

Discrimination between thermal quenching of the fluorescence and Auger upconversion processes using thermal lens technique

In this work we used the Thermal Lens (TL) technique to discriminate two important processes responsible to reduce the upper-state population and fluorescence quantum efficiency (η) in Cr³⁺ doped colquiriite crystals: the thermal quenching of the fluorescence (TQF) and the Auger upconversion (ETU). We observed a nonlinear increase of the TL signal with laser power due to the decrease of η by ETU and/or TQF. The analysis of these curves allowed the determination of the thermal load, the increase of the crystal temperature as a function of the pump excitation and the discrimination between ETU and TQF processes.