Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

Glimpsing regular lattice arrangements of primary rat hippocampal astrocytes on ultra-thin nodes of Parylene-C

In our seminal work, we reported how the biomaterial Parylene-C has the unique ability to coerce neurons and glial cells to migrate to and then grow in straight lines along serum coated rectangular parylene-C structures mounted on an oxidised silicon substrate. In this brief communication, we report how astrocyte cell bodies, from the dissociated postnatal rat hippocampus, can now to be successfully localised on an ultra-thin 13nm layer of parylene-C mounted on oxidised silicon (Figure 1). What is extremely interesting about this finding is that the astrocyte processes extended mainly in horizontal and vertical directions from the cell body thus creating a regular lattice network of individual cells. In addition, they comfortably extended a 50μm gap (equivalent to ~ 10 cell body diameters) to connect to adjacent astrocytes on neighbouring Parylene-C structures. This was found to occur repeatedly on circular geometries of 20μm diameter. In comparison to our previous work [1], we have decreased the thickness of the parylene-C structures by a factor of 10, to allow such technology to be able to be utilised for passive electrode design that requires extremely thin structures such as these. Thus, being able to culture astrocytes in regular lattice networks will pave the way for precise monitoring and stimulation of such ensembles via multi-electrode arrays, allowing a closer insight into their dynamic behaviour and their network properties.

The role of sky conditions on gross primary production in a mixed deciduous forest

The role of different sky conditions on diffuse PAR fraction (ϕ), air temperature (Ta), vapor pressure deficit (vpd) and GPP in a deciduous forest is investigated using eddy covariance observations of CO2 fluxes and radiometer and ceilometer observations of sky and PAR conditions on hourly and growing season timescales. Maximum GPP response occurred under moderate to high PAR and ϕ and low vpd. Light response models using a rectangular hyperbola showed a positive linear relation between ϕ and effective quantum efficiency (α = 0.023ϕ + 0.012, r2 = 0.994). Since PAR and ϕ are negatively correlated, there is a tradeoff between the greater use efficiency of diffuse light and lower vpd and the associated decrease in total PAR available for photosynthesis. To a lesser extent, light response was also modified by vpd and Ta. The net effect of these and their relation with sky conditions helped enhance light response under sky conditions that produced higher ϕ. Six sky conditions were classified from cloud frequency and ϕ data: optically thick clouds, optically thin clouds, mixed sky (partial clouds within hour), high, medium and low optical aerosol. The frequency and light responses of each sky condition for the growing season were used to predict the role of changing sky conditions on annual GPP. The net effect of increasing frequency of thick clouds is to decrease GPP, changing low aerosol conditions has negligible effect. Increases in the other sky conditions all lead to gains in GPP. Sky conditions that enhance intermediate levels of ϕ, such as thin or scattered clouds or higher aerosol concentrations from volcanic eruptions or anthropogenic emissions, will have a positive outcome on annual GPP, while an increase in cloud cover will have a negative impact. Due to the ϕ/PAR tradeoff and since GPP response to changes in individual sky conditions differ in sign and magnitude, the net response of ecosystem GPP to future sky conditions is non-linear and tends toward moderation of change.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

Quantitative ventilation assessments of idealized urban canopy layers with various urban layouts and the same building packing density

This paper investigates urban canopy layers (UCL) ventilation under neutral atmospheric condition with the same building area density (λp=0.25) and frontal area density (λf=0.25) but various urban sizes, building height variations, overall urban forms and wind directions. Turbulent airflows are first predicted by CFD simulations with standard k-ε model evaluated by wind tunnel data. Then air change rates per hour (ACH) and canopy purging flow rate (PFR) are numerically analyzed to quantify the rate of air exchange and the net ventilation capacity induced by mean flows and turbulence. With a parallel approaching wind (θ=0o), the velocity ratio first decreases in the adjustment region, followed by the fully-developed region where the flow reaches a balance. Although the flow quantities macroscopically keep constant, however ACH decreases and overall UCL ventilation becomes worse if urban size rises from 390m to 5km. Theoretically if urban size is infinite, ACH may reach a minimum value depending on local roof ventilation, and it rises from 1.7 to 7.5 if the standard deviation of building height variations increases (0% to 83.3%). Overall UCL ventilation capacity (PFR) with a square overall urban form (Lx=Ly=390m) is better as θ=0o than oblique winds (θ=15o, 30o, 45o), and it exceeds that of a staggered urban form under all wind directions (θ=0o to 45o), but is less than that of a rectangular urban form (Lx=570m, Ly=270m) under most wind directions (θ=30o to 90o). Further investigations are still required to quantify the net ventilation efficiency induced by mean flows and turbulence.

High-temperature order–disorder transitions in the skutterudites CoGe1.5Q1.5 (Q=S, Te)

The temperature dependence of anion ordering in the skutterudites CoGe1.5Q1.5 (Q=S, Te) has been investigated by powder neutron diffraction. Both materials adopt a rhombohedral structure at room temperature (space group R-3 ) in which the anions are ordered trans to each other within Ge2Q2 rings. In CoGe1.5S1.5, anion ordering is preserved up to the melting point of 950 °C. However, rhombohedral CoGe1.5Te1.5 undergoes a phase transition at 610 °C involving a change to cubic symmetry (space group Im-3). In the high-temperature modification, there is a statistical distribution of anions over the available sites within the Ge2Te2 rings. The structural transition involves a reduction in the degree of distortion of the Ge2Te2 rings which progressively transform from a rhombus to a rectangular shape. The effect of this transition on the thermoelectric properties has been investigated.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Antimicrobial and mechanical properties of acrylic resins with incorporated silver-zinc zeolite - part I

Objective: The purpose of this in vitro study was to evaluate the antimicrobial activity of acrylic resins containing different percentages of silver and zinc zeolite, and to assess whether the addition of zeolite alters the flexural and impact strength of the resins. Background: The characteristics of acrylic resins support microorganism development that can threaten the health of the dentures user. Material and methods: A microwave-polymerised (Onda-Cryl) and two heat-polymerised (QC20 and Lucitone 550) acrylic resins were used. The materials were handled according to the manufacturers` instructions. Fifty rectangular-shaped specimens (8 x 10 x 4mm) were fabricated from each resin and assigned to 5 groups (n = 10) according to their percentage of Irgaguard B5000 silver-zinc zeolite (0%- control, 2.5%, 5.0%, 7.5% and 10%). Flexural strength and Izod impact strength were evaluated. The antimicrobial activity against two strains of Candida albicans and two strains of Streptococcus mutans was assessed by agar diffusion method. Data were analysed statistically by one-way ANOVA and Tukey`s test at 5% significance level. Results: The addition of 2.5% of Irgaguard B5000 to the materials resulted in antimicrobial activity against all strains. Flexural strength decreased significantly with the addition of 2.5% (QC20 and Lucitone 550) and 5.0% (Onda-Cryl) of Irgaguard B5000. The impact strength decreased significantly with the addition of 2.5% (Lucitone 550) and 5.0% (QC20 and Onda-Cryl) of zeolite. Conclusion: The addition of silver-zinc zeolite to acrylic resins yields antimicrobial activity, but may affect negatively the mechanical properties, depending on the percentage of zeolite.

Reliability of a method for evaluating porosity in denture base resins

Background: The method of porosity analysis by water absorption has been carried out by the storage of the specimens in pure water, but it does not exclude the potential plasticising effect of the water generating unreal values of porosity. Objective: The present study evaluated the reliability of this method of porosity analysis in polymethylmethacrylate denture base resins by the determination of the most satisfactory solution for storage (S), where the plasticising effect was excluded. Materials and methods: Two specimen shapes (rectangular and maxillary denture base) and two denture base resins, water bath-polymerised (Classico) and microwave-polymerised (Acron MC) were used. Saturated anhydrous calcium chloride solutions (25%, 50%, 75%) and distilled water were used for specimen storage. Sorption isotherms were used to determine S. Porosity factor (PF) and diffusion coefficient (D) were calculated within S and for the groups stored in distilled water. anova and Tukey tests were performed to identify significant differences in PF results and Kruskal-Wallis test and Dunn multiple comparison post hoc test, for D results (alpha = 0.05). Results: For Acron MC denture base shape, FP results were 0.24% (S 50%) and 1.37% (distilled water); for rectangular shape FP was 0.35% (S 75%) and 0.19% (distilled water). For Classico denture base shape, FP results were 0.54% (S 75%) and 1.21% (distilled water); for rectangular shape FP was 0.7% (S 50%) and 1.32% (distilled water). FP results were similar in S and distilled water only for Acron MC rectangular shape (p > 0.05). D results in distilled water were statistically higher than S for all groups. Conclusions: The results of the study suggest that an adequate solution for storing specimens must be used to measure porosity by water absorption, based on excluding the plasticising effect.

Dynamic picture of the inner asteroid belt: implications for the density, size and taxonomic distributions of real objects

In this paper, we construct a dynamic portrait of the inner asteroidal belt. We use information about the distribution of test particles, which were initially placed on a perfectly rectangular grid of initial conditions, after 4.2 Myr of gravitational interactions with the Sun and five planets, from Mars to Neptune. Using the spectral analysis method introduced by Michtchenko et al., the asteroidal behaviour is illustrated in detail on the dynamical, averaged and frequency maps. On the averaged and frequency maps, we superpose information on the proper elements and proper frequencies of real objects, extracted from the data base, AstDyS, constructed by Milani and Knezevic. A comparison of the maps with the distribution of real objects allows us to detect possible dynamical mechanisms acting in the domain under study; these mechanisms are related to mean-motion and secular resonances. We note that the two- and three-body mean-motion resonances and the secular resonances (strong linear and weaker non-linear) have an important role in the diffusive transportation of the objects. Their long-lasting action, overlaid with the Yarkovsky effect, may explain many observed features of the density, size and taxonomic distributions of the asteroids.

Confinement-induced phase transition in a DNA-lipid hydrated complex

We study the effect of the soft confinement by fluid lipid bilayers on the spatial organisation of DNA molecules in a DNA-zwitterionic lipid hydrated lamellar complex. The confinement is increased by dehydrating the complex in a controlled way, which leads to a decrease of the water channel thickness separating the periodically stacked bilayers. Using grazing-incidence small-angle X-ray scattering on an oriented thin film, we probe in situ as dehydration proceeds the structure of the DNA-lipid complex. A structural phase transition is evidenced, where an apparently disordered phase of DNA rods embedded within the one-dimensionally ordered lipid lamellar phase observed at high hydration is replaced by a 2D hexagonal structure of DNA molecules intercalated between the lipid bilayers. Copyright (C) EPLA, 2010

Crystallization of nordstrandite in ethylene glycol water solutions: electron microscopic studies

The present work shows the growth of nordstrandile microcrystals observed by transmission and scanning electron microscopy. Nordstrandite was synthesised from non-crystalline aluminium hydroxide reacted in 20% ethylene glycol/water solution, at room temperature. This material was characterized by TEM, SEM, SAED, XRD and EDS/TEM, during six month and revealed the formation and growth of nordstrandite. Fibrillar pseudoboehmite is the only aluminium hydroxide which could be identified during the first two weeks. The nuclei grow, from complete dissolution/recrystallization of pseudoboehmite fibrils, into platy rectangular microscrystals of nordstrandite. Some tabular microcrystals recrystallise, forming after six months only the mufti-point nordstrandite stars. This electron-optical study suggest that the star shape results from the overlapping of rectangular plates, and pseudoboehmite fibrils act as the precursor of nordstrandite crystallisation in ethylene glycol/water solution.

Influence of different light sources and photo-activation methods on degree of conversion and polymerization shrinkage of a nanocomposite resin

The purpose of this study was to evaluate the influence of different light sources and photo-activation methods on degree of conversion (DC%) and polymerization shrinkage (PS) of a nanocomposite resin (Filtek (TM) Supreme XT, 3M/ESPE). Two light-curing units (LCUs), one halogen-lamp (QTH) and one light-emitting-diode (LED), and two different photo-activation methods (continuous and gradual) were investigated in this study. The specimens were divided in four groups: group 1-power density (PD) of 570 mW/cm(2) for 20 s (QTH); group 2-PD 0 at 570 mW/cm(2) for 10 s + 10 s at 570 mW/cm(2) (QTH); group 3-PD 860 mW/cm(2) for 20 s (LED), and group 4-PD 125 mW/cm(2) for 10 s + 10 s at 860 mW/cm(2) (LED). A testing machine EMIC with rectangular steel bases (6 x 1 x 2 mm) was used to record the polymerization shrinkage forces (MPa) for a period that started with the photo-activation and ended after two minutes of measurement. For each group, ten repetitions (n = 40) were performed. For DC% measurements, five specimens (n = 20) for each group were made in a metallic mold (2 mm thickness and 4 mm diameter, ISO 4049) and them pulverized, pressed with bromide potassium (KBr) and analyzed with FT-IR spectroscopy. The data of PS were analyzed by Analysis of Variance (ANOVA) with Welch`s correction and Tamhane`s test. The PS means (MPa) were: 0.60 (G1); 0.47 (G2); 0.52 (G3) and 0.45 (G4), showing significant differences between two photo-activation methods, regardless of the light source used. The continuous method provided the highest values for PS. The data of DC% were analyzed by Analysis of Variance (ANOVA) and shows significant differences for QTH LCUs, regardless of the photo-activation method used. The QTH provided the lowest values for DC%. The gradual method provides lower polymerization contraction, either with halogen lamp or LED. Degree of conversion (%) for continuous or gradual photo-activation method was influenced by the LCUs. Thus, the presented results suggest that gradual method photo-activation with LED LCU would suffice to ensure adequate degree of conversion and minimum polymerization shrinkage.

Effect of different dental composite resins on the polymerization process

Dental composite resins possess good esthetic properties, and are currently among the most popular dental restorative materials. Both organic and inorganic phases might influence the material behavior, the filler particle features and rate are the most important factors related to improvement of the mechanical properties of resin composites. Thus, the objective of this study was to evaluate the effect of three different composite resins on the polymerization process by Vickers hardness test. The samples were prepared using three different composite resins, as follow: group I-P-60 (3M/ESPE); group II-Herculite XRV (Kerr), and group III-Durafill (Heraeus-Kulzer). The samples were made in a polytetrafluoroethylene mould, with a rectangular cavity measuring 7 mm in length, 4 mm in width, and 3 mm in thickness. The samples were photo-activated by one light-curing unit based on blue LEDs (Ultrablue III-DMC/Brazil) for 20 and 40 s of irradiation times. The Vickers hardness test was performed 24 h after the photo-activation until the standardized depth of 3 mm. The Vickers hardness mean values varied from 158.9 (+/- 0.81) to 81.4 (+/- 1.94) for P-60, from 138.7 (+/- 0.37) to 61.7 (+/- 0.24) for Herculite XRV, and from 107. 5 (+/- 0.81) to 44.5 (+/- 1.36) for Durafill composite resins photo-activated during 20 s for the 1st and 2nd mm, respectively. During 40 s of photo-activation, the Vickers hardness mean values were: from 181.0 (+/- 0.70) to 15.6 (+/- 0.29) for P-60, and from 161.8 (+/- 0.41) to 11.2 (+/- 0.17) for Herculite XRV composite resins, for the 1st and 3th mm, respectively. For Durafill composite resin the mean values varied from 120.1 (+/- 0.66) to 61.7 (+/- 0.20), for the 1st and 2nd mm, respectively. The variation coefficient (CV) was in the most of the groups lower than 1%, then the descriptive statistic analysis was used. The Vickers hardness mean values for Durafill were lower than P-60 and Herculite XRV composite resins for 20 and 40 s of irradiation time. The polymerization process was greatly affected by the composition of the composite resins.