On the Role of Symmetry in Vibrational Strong Coupling: The Case of Charge‐Transfer Complexation

It is well known that symmetry plays a key role in chemical reactivity. Here we explore its role in vibrational strong coupling (VSC) for a charge‐transfer (CT) complexation reaction. By studying the trimethylated‐benzene–I₂ CT complex, we find that VSC induces large changes in the equilibrium constant K_DA of the CT complex, reflecting modifications in the ΔG° value of the reaction. Furthermore, by tuning the microfluidic cavity modes to the different IR vibrations of the trimethylated benzene, ΔG° either increases or decreases depending only on the symmetry of the normal mode that is coupled. This result reveals the critical role of symmetry in VSC and, in turn, provides an explanation for why the magnitude of chemical changes induced by VSC are much greater than the Rabi splitting, that is, the energy perturbation caused by VSC. These findings further confirm that VSC is powerful and versatile tool for the molecular sciences.     

Impact of High-Pressure Homogenization on the Cell Integrity of Tetradesmus obliquus and Seed Germination

Microalgae have almost unlimited applications due to their versatility and robustness to grow in different environmental conditions, their biodiversity and variety of valuable bioactive compounds. Wastewater can be used as a low-cost and readily available medium for microalgae, while the latter removes the pollutants to produce clean water. Nevertheless, since the most valuable metabolites are mainly located inside the microalga cell, their release implies rupturing the cell wall. In this study, Tetradesmus obliquus grown in 5% piggery effluent was disrupted using high-pressure homogenization (HPH). Effects of HPH pressure (100, 300, and 600 bar) and cycles (1, 2 and 3) were tested on the membrane integrity and evaluated using flow cytometry and microscopy. In addition, wheat seed germination trials were carried out using the biomass at different conditions. Increased HPH pressure or number of cycles led to more cell disruption (75% at 600 bar and 3 cycles). However, the highest increase in wheat germination and growth (40–45%) was observed at the lowest pressure (100 bar), where only 46% of the microalga cells were permeabilised, but not disrupted. Non-treated T. obliquus cultures also revealed an enhancing effect on root and shoot length (up to 40%). The filtrate of the initial culture also promoted shoot development compared to water (21%), reinforcing the full use of all the process fractions. Thus, piggery wastewater can be used to produce microalgae biomass, and mild HPH conditions can promote cell permeabilization to release sufficient amounts of bioactive compounds with the ability to enhance plant germination and growth, converting an economic and environmental concern into environmentally sustainable applications.     

Failure of the Hasse principle for Enriques surfaces

We construct an Enriques surface X over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer–Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on X, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.     

An improved mixed numerical-experimental method for stress field calculation

In this work a numerical-experimental method is used to study the dynamic behavior of an aluminum plate subjected to a small mass impact. The out-of-plane displacements, due to transient bending wave propagation, were assessed for successive time instants, using double pulse TV-holography, also known as pulsed ESPI. The experimental setup and the image processing methods were improved to allow the calculation of the plate transient stress field. Integral transforms are used to obtain the strain fields from spatial derivatives of displacements noisy data. A numerical simulation of the plate transient response was carried out with FEM Ansys^®. For this purpose a PZT transducer was used to record the impact force history, which was inputted in the numerical model. Finally, the comparisons between numerical and experimental results are presented in order to validate the present methodology.     

Chaos in spacecraft attitude motion in Earth's magnetic field

The rotational motion of a satellite with a magnetic stabilization system is discussed. The motion is described by a nonautonomous differential equation, with the magnetic moment of the satellite as a parameter. The global phase portrait of the problem is investigated in a wide range of magnetic-parameter values, using a numerical realization of the method of Poincare point maps. New periodic solutions of the problem are found, and an analysis is carried out of the evolution of the phase portrait and the bifurcation of periodic solutions with varying magnetic-parameter values. The values of the magnetic parameter that must be avoided in the design of the satellite magnetic stabilization system are discussed. (c) 1999 American Institute of Physics.     

Stability and forced oscillations

In this paper we derive a differential-difference equation for a circuit involving a lossless transmission line and we give conditions for global asymptotic stability of an equilibrium point, existence and stability of forced oscillations. Some of such problems have been investigated for an equation obtained by R. K. Brayton [Quart. J. Appl. Math.24 (1967), 289–301; O. Lopes, SIAM J. Appl. Math., to appear; M. Slemrod, J. Math. Anal. Appl.36 (1971), 22–40] but, for ours (which governs the same physical problem), better results can be proved. By using suitable Liapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality.     

Elemental distribution by synchrotron X-ray microfluorescence of prostate 3D cell culture

Prostate cancer is a highly prevalent disease and ranks second among malignant neoplasms that affect men around the world, behind lung cancer alone. Trace elements are very important and are involved in many cellular processes. The X-ray microfluorescence technique is an advanced tool of high spatial resolution, sensitivity, multielemental analysis, and nondestructiveness for trace element study. This study aimed to investigate the elemental distribution in spheroids obtained through the following human prostate cell lines using synchrotron X-ray microfluorescence: tumor cell line androgen independent (DU145), tumor cell line androgen dependent (LNCaP), and normal cell line (RWPE-1). The measurements were performed with a standard geometry of 45° of incidence, excited by a white beam using a pixel of 25 μm and an acquisition time of 300 ms/pixel at the X-ray fluorescence beamline at the Synchrotron Light National Laboratory (Campinas, Brazil). The synchrotron X-ray microfluorescence results showed differences between groups in all elements analyzed and suggested that further studies should be performed to understand the relationship of these trace elements with the progression and development of the disease.     

A Review of Fractional Order Entropies

Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful.     

Convergence rates for Markov chain order estimates using EDC criterion

The Efficient Determination Criterion (EDC) generalizes the AIC and BIC criteria and provides a class of consistent estimators for the order of a Markov chain with finite state space. In this note, we derive rates of convergence for the EDC estimates. *Partially supported by CNPq, CAPES/PROCAD, FAPDF/PRONEX, FINATEC and FUNPE/UnB. **Partially supported by CAPES.     

Two-dimensional incompressible viscous flow around a small obstacle

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω₀ and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier–Stokes system, with initial vorticity ω₀ + γδ, where δ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in Iftimie et al. (Comm. Part. Differ. Eqn. 28, 349–379 (2003)), where the effect of the small obstacle appears in the coefficients of the PDE and not only in the initial data. The main ingredients of the proof are L ^p − L ^q estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato’s fixed point method, energy estimates, renormalization and interpolation.