Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems

The limits of flexural wave absorption by open lossy resonators are analytically and numerically reported in this work for both the reflection and transmission problems. An experimental validation for the reflection problem is presented. The reflection and transmission of flexural waves in 1D resonant thin beams are analyzed by means of the transfer matrix method. The hypotheses, on which the analytical model relies, are validated by experimental results. The open lossy resonator, consisting of a finite length beam thinner than the main beam, presents both energy leakage due to the aperture of the resonators to the main beam and inherent losses due to the viscoelastic damping. Wave absorption is found to be limited by the balance between the energy leakage and the inherent losses of the open lossy resonator. The perfect compensation of these two elements is known as the critical coupling condition and can be easily tuned by the geometry of the resonator. On the one hand, the scattering in the reflection problem is represented by the reflection coefficient. A single symmetry of the resonance is used to obtain the critical coupling condition. Therefore the perfect absorption can be obtained in this case. On the other hand, the transmission problem is represented by two eigenvalues of the scattering matrix, representing the symmetric and anti-symmetric parts of the full scattering problem. In the geometry analyzed in this work, only one kind of symmetry can be critically coupled, and therefore, the maximal absorption in the transmission problem is limited to 0.5. The results shown in this work pave the way to the design of resonators for efficient flexural wave absorption

Fractional vs. ordinary control systems: What does the fractional derivative provide?

[EN] The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.Conejero, JA.; Franceschi, J.; Picó-Marco, E. (2022). Fractional vs. ordinary control systems: What does the fractional derivative provide?. Mathematics. 10(15):1-18. https://doi.org/10.3390/math10152719118101

Nonlinear waves in a chain of magnetically coupled pendula

A motivation for the study of reduced models like one-dimensional systems in Solid State Physics is the complexity of the full problem. In recent years our group has studied theoretically, numerically and experimentally wave propagation in lattices of nonlinearly coupled oscillators. Here, we present the dynamics of magnetically coupled pendula lattices. These macroscopic systems can model the dynamical processes of matter or layered systems. We report the results obtained for harmonic wave propagation in these media, and the different regimes of mode conversion into higher harmonics strongly influenced by dispersion and discreteness, including the phenomenon of acoustic dilatation of the chain, as well as some results on the propagation of localized waves i.e., solitons and kinks.Generalitat Valenciana APOSTD/2017/042Umiversitat Politècnica de València PAID-01-14Ministerio de Economía y Competitividad (MINECO), Spain FIS2015-65998-C2-2-PJunta de Andalucía 2017/FQM-28

Genetic basis of adaptation in Arabidopsis thaliana: Local adaptation at the seed dormancy QTL DOG1

Local adaptation provides an opportunity to study the genetic basis of adaptation and investigate the allelic architecture of adaptive genes. We study DELAY OF GERMINATION 1 (DOG1), a gene controlling natural variation in seed dormancy in Arabidopsis thaliana and investigate evolution of dormancy in 41 populations distributed in four regions separated by natural barriers. Using F ST and Q ST comparisons, we compare variation at DOG1 with neutral markers and quantitative variation in seed dormancy. Patterns of genetic differentiation among populations suggest that the gene DOG1 contributes to local adaptation. Although Q ST for seed dormancy is not different from F ST for neutral markers, a correlation with variation in summer precipitation supports that seed dormancy is adaptive. We characterize dormancy variation in several F 2-populations and show that a series of functionally distinct alleles segregate at the DOG1 locus. Theoretical models have shown that the number and effect of alleles segregatin at quantitative trait loci (QTL) have important consequences for adaptation. Our results provide support to models postulating a large number of alleles at quantitative trait loci involved in adaptation. © 2012 The Author(s). Evolution © 2012 The Society for the Study of Evolution.Peer Reviewe

Quantum algorithm for the Laughlin wave function

We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth scales as $2n-3$. We further prove the optimality of the circuit using permutation theory arguments and we compute exactly how entanglement develops along the action of each gate. Finally, we discuss its experimental feasibility decomposing the qudits and the gates in terms of qubits and two qubit-gates as well as the generalization to arbitrary filling fraction.Comment: 4 pages, 5 figure

Liquid-liquid equilibrium and partitioning features of bovine trypsin in Ucon 50 HB5100 /sodium citrate aqueous two phase systems

The phase diagrams of Ucon 50-HB-5100, a non-ionic random copolymer of ethylene oxide and propylene oxide (EOPO) and sodium citrate aqueous two-phase systems were determined at different pHs (5.20 and 8.20) and temperatures (5, 20 and 40º C). The binodal curves were determined by refractive index and enzymatic assay of the solution and described using a four-parameter sigmoidal equation, the reliability of the measured tie line compositions was ascertained by correlation equations given by Othmer Tobias and Bancroft. The two-phase area was expanded by increasing both pH and temperature. The partitioning of bovine trypsin and a-chymotrypsin, proteases of similar physico-chemical properties was investigated in order to evaluate the applicability of partitioning as a putative method to isolate from pancreas and to obtain any information about their partitioning mechanism. The effect of different factors such as pH, tie line length and the presence of an inorganic salt on the protein partition coefficient were analyzed.Se caracterizaron las curvas binomiales correspondientes a los sistemas bifásicos acuosos formados por Ucon 50-HB-5100, un copolímero al azar de óxido de etileno y óxido de propileno (EOPO) y citrato de sodio a diferentes pHs (5,20 y 8,20) y temperaturas (5, 20 y 40º C). Las curvas binomiales se obtuvieron por determinación del índice de refracción y ensayos enzimáticos de las soluciones correspondientes; las composiciones de las líneas de unión se corroboraron por las ecuaciones propuestas por Othmer Tobias y Bancroft. El aumento del pH y la temperatura condujeron a un aumento del área bifásica. También se ensayó el comportamiento de reparto de dos proteasas tripsina y α-quimotripsina con el objetivo de emplear los principios de partición como método de aislamiento y purificación de Tripsina a partir de páncreas bovino y de obtener información acerca del mecanismo de partición de la misma. Se analizó el efecto del pH, longitud de la línea de unión y presencia de sales inorgánicas sobre el coeficiente de partición de las enzimas

Liquid–liquid equilibrium of the Ucon 50-HB5100/sodium citrate aqueous two-phase systems

The phase diagrams of Ucon 50-HB5100/sodium citrate aqueous two-phase systems were determined at 5, 20 and 40 ◦C. Two medium pHs 5.20 and 8.20 were assayed. The binodal curves were satisfactorily described using a four-parameter sigmoidal equation. The two-phase area was expanded by increasing both pH and temperature. The reliability of the measured tie line compositions was ascertained by correlation equations given by Othmer–Tobias and Bancroft.VALNATURACONICETALFA II-0440-FA-Exchange programme between Universities of the European Union and Latin Americ