Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Spectral fluctuation and 1/f(alpha) noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f(alpha) noise with 1 <= alpha <= 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f(alpha) noise is ubiquitous in nature.

Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

Metabolizable energy values of diets supplemented with xylanase determined with laying hens

The objective of this study was to evaluate the effect of the supplementation of xylanase in diets with reduced energy level on the apparent metabolizable energy corrected for nitrogen, determined with laying hens at 14, 36, 60 and 80 weeks of age. Four digestibility trials were conducted, using 80 Hy-line W36 laying hens aged 14, 36, 60 and 80 weeks of age. Birds were distributed in a completely randomized design in 2 x 2 factorial arrangement (energy level x inclusion of xylanase), totaling four treatments with 10 replicates of two birds each. Treatments were: positive control (balanced diet for their age); positive control + xylanase; negative control (diet with reduction of 100 kcal/kg in the level of metabolizable energy); and negative control + xylanase. Xylanase, produced by microorganism Trichoderma reesei, was added to the diets at 100 g/t (16,000 BXU/kg) for diets fed at 14 weeks and 75 g/t for diets of 36, 60 and 80 weeks (12,000 BXU/kg). The data obtained were subjected to analysis of variance at 5% probability. Supplementation of xylanase promoted higher values for AME (apparent metabolizable energy) and AME(n) (apparent metabolizable energy corrected for nitrogen) determined with 80-week-old laying hens, subjected to diet with energy level according to the nutritional requirements for their age. Supplementation of xylanase increases the matabolizability coefficient of the dietary crude protein and improves the nitrogen retention of laying hens at 14 weeks. In addition, xylanase associated with adequate levels of dietary energy promotes higher values for AME and AME(n) determined with laying hens at 80 weeks of age.

Temperature Effect on the Two-Photon Absorption Spectrum of All-trans-beta-carotene

In this report, we investigate the influence of temperature on the two-photon absorption (2PA) spectrum of all-trans-beta-carotene using the femtosecond white-light-continuum Z-scan technique. We observed that the 2PA cross-section decreases quadratically with the temperature. Such effect was modeled using a three-energy-level diagram within the sum-over-essential states approach, assuming temperature dependencies to the transition dipole moment and refractive index of the solvent. The results show that the transition dipole moments from ground to excited state and between the excited states, which governed the two-photon matrix element, have distinct behaviors with the temperature. The first one presents a quadratic dependence, while the second exhibits a linear dependence. Such effects were attributed mainly to the trans -> cis thermal interconversion process, which decreases the effective conjugation length, contributing to diminishing the transition dipole moments and, consequently, the 2PA cross-section.

Novel europium and gadolinium complexes with methaneseleninate as ligand: Synthesis, characterization and spectroscopic study

The methaneseleninate and 1,10-phenanthroline were used as ligands in the synthesis of new lanthanide complexes. The photostability, emission quantum yield (q) and quantum efficiency (eta) of the D-5(0) emitting level of the Eu3+ ion were determined. An energy level diagram was used to establish the most relevant channels involved in the ligand-to-metal intramolecular energy transfer process. The nephelauxetic effect was investigated to assess the covalency of the ligand-metal chemical bond. The values of the experimental 4f-4f intensity parameters, suggest that this ion is in a chemical environment less polarisable than in the case of complexes with beta-diketonates as ligands. (C) 2011 Elsevier B.V. All rights reserved.

Experimental and Theoretical Study on the One- and Two-Photon Absorption Properties of Novel Organic Molecules Based on Phenylacetylene and Azoaromatic Moieties

This Article reports a combined experimental and theoretical analysis on the one and two-photon absorption properties of a novel class of organic molecules with a pi-conjugated backbone based on phenylacetylene (JCM874, FD43, and FD48) and azoaromatic (YB3p2S) moieties. Linear optical properties show that the phenylacetylene-based compounds exhibit strong molar absorptivity in the UV and high fluorescence quantum yield with lifetimes of approximately 2.0 ns, while the azoaromatic-compound has a strong absorption in the visible region with very low fluorescence quantum yield. The two-photon absorption was investigated employing nonlinear optical techniques and quantum chemical calculations based on the response functions formalism within the density functional theory framework. The experimental data revealed well-defined 2PA spectra with reasonable cross-section values in the visible and IR. Along the nonlinear spectra we observed two 2PA allowed bands, as well as the resonance enhancement effect due to the presence of one intermediate one-photon allowed state. Quantum chemical calculations revealed that the 2PA allowed bands correspond to transitions to states that are also one-photon allowed, indicating the relaxation of the electric-dipole selection rules. Moreover, using the theoretical results, we were able to interpret the experimental trends of the 2PA spectra. Finally, using a few-energy-level diagram, within the sum-over-essential states approach, we observed strong qualitative and quantitative correlation between experimental and theoretical results.

Evidence of the participation of electronic excited states in the mechanism of positronium formation in substitutional Tb1-xEux(dpm)(3) solid solutions studied by optical and positron annihilation spectroscopies

Positronium formation in the bimary molecular solid solutions Tb1-xEux (dpm)(3) (dpm = dipivaloylmethanate) has been investigated. A strong linear correlation between the D-5(4) Tb(III) energy level excited state lifetime and the positronium formation probability has been observed. This correlation indicates that the ligand-to-metal charge transfer LMCT states act in both luminescence quenching and positronium formation inhibition, as previously proposed. A kinetic mechanism is proposed to explain this correlation and shows that excited electronic states have a very important role in the positronium formation mechanism.

Study of singlet excited state absorption spectrum of lutetium bisphthalocyanine using the femtosecond Z-scan technique

In this study we investigate the singlet excited state absorption of lutetium bisphthalocyanine (LuPc2) over a wide spectral range. It was observed distinct nonlinear absorption behaviors; saturable (SA) and reverse saturable absorption (RSA). The RSA effect was observed below 640 and above 680 nm, while SA occurs around the Q-band region, located around 660 nm. To describe the main singlet-singlet transitions, we employed the rate equation model considering the simplified three-energy level diagram. Our results reveal a ratio between excited and ground state absorption smaller than 0.05 at the Q-band region, and of approximately 4 for the other regions. (C) 2012 Elsevier B.V. All rights reserved.

A theoretical study of SnF2+, SnCl2+, and SnO2+ and their experimental search

We present a detailed theoretical study of the stability of the gas-phase diatomic dications SnF2+, SnCl2+, and SnO2+ using ab initio computer calculations. The ground states of SnF2+, SnCl2+, and SnO2+ are thermodynamically stable, respectively, with dissociation energies of 0.45, 0.30, and 0.42 eV. Whereas SnF2+ dissociates into Sn2+ + F, the long range behaviour of the potential energy curves of SnCl2+ and SnO2+ is repulsive and wide barrier heights due to avoided crossing act as a kind of effective dissociation energy. Their equilibrium internuclear distances are 4.855, 5.201, and 4.852 a(0), respectively. The double ionisation energies (T-e) to form SnF2+, SnCl2+, and SnO2+ from their respective neutral parents are 25.87, 23.71, and 25.97 eV. We combine our theoretical work with the experimental results of a search for these doubly positively charged diatomic molecules in the gas phase. SnO2+ and SnF2+ have been observed for prolonged oxygen (O-16(-)) ion beam sputtering of a tin metal foil and of tin (II) fluoride (SnF2) powder, respectively, for ion flight times of about 10(-5) s through a magnetic-sector mass spectrometer. In addition, SnCl2+ has been detected for O-16(-) ion surface bombardment of stannous (tin (II)) chloride (SnCl2) powder. To our knowledge, SnF2+ is a novel gas-phase molecule, whereas SnCl2+ had been detected previously by electron-impact ionization mass spectrometry, and SnO2+ had been observed before by spark source mass spectrometry as well as by atom probe mass spectrometry. We are not aware of any previous theoretical studies of these molecular systems. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758475]

Effect of interaction with micelles on the excited-state optical properties of zinc porphyrins and J-aggregates formation

This work reports on the photophysical properties of zinc porphyrins meso-tetrakis methylpyridiniumyl (Zn2+TMPyP) and meso-tetrakis sulfonatophenyl (Zn2+TPPS) in homogeneous aqueous solutions and in the presence of sodium dodecyl sulfate (SDS) and cetyltrimethyl ammonium bromide (CTAB) micelles. The excited-state dynamic was investigated with the Z-scan technique, UV-Vis absorption, and fluorescence spectroscopy. Photophysical parameters were obtained by analyzing the experimental data with a conventional five-energy-level diagram. The interaction of the charged side porphyrin groups with oppositely charged surfactants can reduce the electrostatic repulsion between porphyrin molecules leading to aggregation, which affected the porphyrin characteristics such as absorption cross-sections, lifetimes and quantum yields. The interaction between anionic ZnTPPS with cationic CTAB micelles induced the formation of porphyrin J-aggregates, while this effect was not observed in the interaction of ZnTMPyP with SDS micelles. This difference is, probably, due to the difference in electrostatic repulsion between the porphyrin molecules. The insights obtained by these results are important for the understanding of the photophysical behavior of porphyrins, regarding potential applications in pharmacokinetics as encapsulation of photosensitizer for drug delivery systems and in its interaction with cellular membrane.

Accurate ab initio potential energy surfaces for the (3)A '' and (3)A ' electronic states of the O(P-3) plus HBr system

In this work, we report the construction of potential energy surfaces for the (3)A '' and (3)A' states of the system O(P-3) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O(P-3) + HBr -> OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A '' electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A' surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A '' and 4.16 kcal/mol for the (3)A' state. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705428]

Analysis of plant LTR-retrotransposons at the fine-scale family level reveals individual molecular patterns

Background: Sugarcane is an important crop worldwide for sugar production and increasingly, as a renewable energy source. Modern cultivars have polyploid, large complex genomes, with highly unequal contributions from ancestral genomes. Long Terminal Repeat retrotransposons (LTR-RTs) are the single largest components of most plant genomes and can substantially impact the genome in many ways. It is therefore crucial to understand their contribution to the genome and transcriptome, however a detailed study of LTR-RTs in sugarcane has not been previously carried out. Results: Sixty complete LTR-RT elements were classified into 35 families within four Copia and three Gypsy lineages. Structurally, within lineages elements were similar, between lineages there were large size differences. FISH analysis resulted in the expected pattern of Gypsy/heterochromatin, Copia/euchromatin, but in two lineages there was localized clustering on some chromosomes. Analysis of related ESTs and RT-PCR showed transcriptional variation between tissues and families. Four distinct patterns were observed in sRNA mapping, the most unusual of which was that of Ale1, with very large numbers of 24nt sRNAs in the coding region. The results presented support the conclusion that distinct small RNA-regulated pathways in sugarcane target the lineages of LTR-RT elements. Conclusions: Individual LTR-RT sugarcane families have distinct structures, and transcriptional and regulatory signatures. Our results indicate that in sugarcane individual LTR-RT families have distinct behaviors and can potentially impact the genome in diverse ways. For instance, these transposable elements may affect nearby genes by generating a diverse set of small RNA's that trigger gene silencing mechanisms. There is also some evidence that ancestral genomes contribute significantly different element numbers from particular LTR-RT lineages to the modern sugarcane cultivar genome.

Low Level Laser Therapy as an Adjunctive Technique In the Management of Temporomandibular Disorders

The purpose of this study was to assess the effect of low level laser therapy on subjects with intra-articular temporomandibular disorders (IA-TMD), and to quantify and compare severity of signs and symptoms before, during, and after the laser applications. The sample consisted of 45 subjects randomly divided into three groups (G) of 15 subjects each: G-I: 15 individuals with IA-TMD submitted to an energy dose of 52.5 J/cm(2); G-II: dose of 105.0 J/cm(2); and G-III: placebo group (0 J/cm(2)). In all groups, the applications were performed on condylar points on the masseter and anterior temporalis muscles. Two weekly sessions were held for five weeks, totaling 10 applications. The assessed variables were: mandibular movements and painful symptoms evoked by muscle palpation. These variables were measured before starting the study, then immediately after the first, fifth, and tenth laser application, and finally, 32 days after completing the applications. The results showed that there were statistically significant differences for G-I and G-II at the level of 1% between the doses, as well as between assessments. Therefore, it was concluded that the use of low level laser increased the mean mandibular range of motion and reduced painful symptoms in the groups that received effective treatment, which did not occur in the placebo group.

Effect of low-level laser therapy after rapid maxillary expansion on proliferation and differentiation of osteoblastic cells

The aim of this study was to investigate the osteoblastic activity of cells derived from the midpalatal suture upon treatment with low-level laser therapy (LLLT) after rapid maxillary expansion (RME). A total of 30 rats were divided into two groups: experimental I (15 rats with RME without LLLT) and experimental II (15 rats with RME + LLLT). The rats were euthanized at 24 h, 48 h, and 7 days after RME, when the osteoblastic cells derived from the rats' midpalatal suture were explanted. These cells were cultured for periods up to 17 days, and then in vitro osteogenesis parameters and gene expression markers were evaluated. The cellular doubling time in the proliferative stage (3-7 days) was decreased in cultured cells harvested from the midpalatal suture at 24 and 48 h after RME + LLLT, as indicated by the increased growth of the cells in a culture. Alkaline phosphatase activity at days 7 and 14 of the culture was increased by LLLT in cells explanted from the midpalatal suture at 24 and 48 h and 7 days after RME. The mineralization at day 17 was increased by LLLT after RME in all periods. Results from the real-time PCR demonstrated that cells harvested from the LLLT after RME group showed higher levels of ALP, Runx2, osteocalcin, type I collagen, and bone sialoprotein mRNA than control cells. More pronounced effects on ALP activity, mineralization, and gene expression of bone markers were observed at 48 h after RME and LLLT. These results indicate that the LLLT applied after RME is able to increase the proliferation and the expression of an osteoblastic phenotype in cells derived from the midpalatal suture.