Dynamical properties of discrete breathers in curved chains with first and second neighbor interaction

We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi¿Pasta¿Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

The influence of energy changes in breathers

This work studies the dynamical behavior of breathers in a single nonlinear lattice under the influence of energy changes. To create the breather we used the anti-continuous limit and studied its stability through the Floquet theory. Using the information entropy we calculated the effective number of oscillators with significant energy and determined if there is or not the formation of a spatially localized structure.

Stability of breathers in simple mechanical models for DNA

This work studies through the Floquet theory the stability of breathers generated by the anti-continuous limit. We used the Peyrard-Bishop model for DNA and two kinds of nonlinear potential: the Morse potential and a potential with a hump. The comparison of their stability was done in function of the coupling parameter. We also investigate the dynamic behaviour of the system in stable and unstable regions. Qualitatively, the dynamic of mobile breathers resembles DNA.

Formação e estabilidade de Breathers no modelo de Peyrard-Bishop para o DNA

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Coupled scalar fields oscillons and breathers in some lorentz violating scenarios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

Bumps, breathers, and waves in a neural network with spike frequency adaptation

In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon the non-local network connectivity, synaptic response, and firing rate of a single neuron. A phenomenological model of SFA is examined whereby the firing rate is taken to be a simple state-dependent threshold function. As in the case without SFA classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps). Importantly an analysis of bump stability using recent Evans function techniques shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Direct numerical simulations both confirm our theoretical predictions and illustrate the rich dynamic behavior of this model, including the appearance of self-replicating bumps.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

Changes in facial morphology after adenotonsillectomy in mouth-breathing children

Background. Morphological and dentofacial alterations have been attributed to impaired respiratory function. Objective. To examine the influence of mouth breathing (MB) on children facial morphology before and after adenoidectomy or adenotonsillectomy. Methods. Thirty-three MB children who restored nasal breathing (NB) after surgery and 22 NB children were evaluated. Both groups were submitted to lateral cephalometry, at time 1 (T1) before and at time 2 (T2) 28 months on average postoperatively. Results. Comparison between the MB and NB groups at T1 showed that mouth breathers had higher inclination of the mandibular plane; more obtuse gonial angle; dolichofacial morphology; and a decrease in the total and inferior posterior facial heights. Twenty-eight months after the MB surgical intervention, they still presented a dolichofacial morphologic pattern. During this period, MB altered the face growth direction and decreased their mandible plane inclination, with reduction in the SN.GoGn, PP.MP, SNGn, and ArGo.GoMe parameters as well as an increase in BaN.PtGn. Conclusion. After the MB rehabilitation, children between 3 and 6 years old presented significant normalization in the mandibular growth direction, a decrease in the mandible inclination, and an increase in the posterior facial height. Instead, they still persisted with a dolichofacial pattern when compared with nasal breathers.

Cephalometric evaluation of facial pattern and hyoid bone position in children with obstructive sleep apnea syndrome

Objectives: To assess the development of face and hyoid bone in children with obstructive sleep apnea syndrome (OSAS) through lateral cephalometries. Materials and methods: Children aged 7-10 years with mixed dentition and with no previous otorhinolaryngologic, orthodontic or speech therapy treatments were studied. Twenty nasal breathers were compared to 20 mouth breathing children diagnosed as OSAS patients. All children underwent otorhinolaryngologic evaluation and cephalometries; children with OSAS also underwent nocturnal polysomnography in a sleep laboratory. Results: Children with OSAS presented increase in total and lower anterior heights of the face when compared to nasal breathers. In addition, children with OSAS presented a significantly more anterior and inferior position of the hyoid bone than nasal breathers. No significant differences in upper, anterior or posterior heights of the face were observed between groups. Conclusion: The results suggest that there are evident and early changes in facial growth and development among children with OSAS, characterized by increased total and inferior anterior heights of the face, as well as more anterior and inferior position of the hyoid bone. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Craniocervical posture and hyoid bone position in children with mild and moderate asthma and mouth breathing

Introduction The objective of the present study was to assess the craniocervical posture and the positioning of the hyoid bone in children with asthma who are mouth breathers compared to non-asthma controls. Methods The study was conducted on 56 children, 28 of them with mild (n = 15) and moderate (n = 13) asthma (14 girls aged 10 79 +/- 1 31 years and 14 boys aged 9 79 +/- 1.12 years), matched for sex, height, weight and age with 28 non-asthma children who are not mouth breathers The sample size was calculated considering a confidence interval of 95% and a prevalence of 4% of asthma in Latin America. Eighteen variables were analyzed in two radiographs (latero-lateral teleradiography and lateral cervical spine radiography), both obtained with the head in a natural position The independent t-test was used to compare means values and the chi-square test to compare percentage values (p < 0 05) Intraclass correlation coefficient (ICC) was used to verify reliability. Results. The Craniovertebral Angle (CVA) was found to be significantly smaller in asthma than in control children (106.38 +/- 766 vs. 111 21 +/- 7.40. p = 0 02) and the frequency of asthma children with an absent or inverted hyoid triangle was found to be significantly higher compared to non-asthma children (36% vs 7%, p = 0.0001). The values of the inclination angles of the superior cervical spine in relation to the horizontal plane were significantly higher in moderate than in mild asthma children (CVT/Hor 85 10 +/- 725 vs. 90 92 +/- 6.69, p = 0 04 and C1/Hor. 80 93 +/- 5.56 vs 85 00 +/- 4 20, p = 0 04) Conclusions These findings revealed that asthma children presented higher head extension and a higher frequency of changes in hyoid bone position compared to non-asthma children and that greater the asthma severity greater the extension of the upper cervical spine. (C) 2010 Elsevier Ireland Ltd. All rights reserved.