Approximate controllability and lack of controllability to zero of the heat equation with memory

In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class $C^1$. We examine its controllability properties both under the action of boundary controls or when the controls are distributed in a subregion of $\Omega$. We prove approximate controllability of the system and, in contrast with this, we prove the existence of initial conditions which cannot be steered to hit the target $0$ in a certain time $T$, of course when the memory kernel is not identically zero. In both the cases we derive our results from well known properties of the heat equation

Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

Scaling properties of a low-actuation pressure microfluidic valve

Using basic physical arguments, we present a design and method for the fabrication of microfluidic valves using multilayer soft lithography. These on-off valves have extremely low actuation pressures and can be used to fabricate active functions, such as pumps and mixers in integrated microfluidic chips. We characterized the performance of the valves by measuring both the actuation pressure and flow resistance over a wide range of design parameters, and compared them to both finite element simulations and alternative valve geometries

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

Customized finite element modelling of the human cornea

Aim To construct patient-specific solid models of human cornea from ocular topographer data, to increase the accuracy of the biomechanical and optical estimate of the changes in refractive power and stress caused by photorefractive keratectomy (PRK). Method Corneal elevation maps of five human eyes were taken with a rotating Scheimpflug camera combined with a Placido disk before and after refractive surgery. Patient-specific solid models were created and discretized in finite elements to estimate the corneal strain and stress fields in preoperative and postoperative configurations and derive the refractive parameters of the cornea. Results Patient-specific geometrical models of the cornea allow for the creation of personalized refractive maps at different levels of IOP. Thinned postoperative corneas show a higher stress gradient across the thickness and higher sensitivity of all geometrical and refractive parameters to the fluctuation of the IOP. Conclusion Patient-specific numerical models of the cornea can provide accurate quantitative information on the refractive properties of the cornea under different levels of IOP and describe the change of the stress state of the cornea due to refractive surgery (PRK). Patient-specific models can be used as indicators of feasibility before performing the surgery. Copyright: © 2015 Simonini, Pandolfi

Can Twitter be a source of information on allergy? Correlation of pollen counts with tweets reporting symptoms of allergic rhinoconjunctivitis and names of antihistamine drugs

Pollen forecasts are in use everywhere to inform therapeutic decisions for patients with allergic rhinoconjunctivitis (ARC). We exploited data derived from Twitter in order to identify tweets reporting a combination of symptoms consistent with a case definition of ARC and those reporting the name of an antihistamine drug. In order to increase the sensitivity of the system, we applied an algorithm aimed at automatically identifying jargon expressions related to medical terms. We compared weekly Twitter trends with National Allergy Bureau weekly pollen counts derived from US stations, and found a high correlation of the sum of the total pollen counts from each stations with tweets reporting ARC symptoms (Pearson's correlation coefficient: 0.95) and with tweets reporting antihistamine drug names (Pearson's correlation coefficient: 0.93). Longitude and latitude of the pollen stations affected the strength of the correlation. Twitter and other social networks may play a role in allergic disease surveillance and in signaling drug consumptions trends

Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Artigo publicado num número especial da revista.The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT)Italian INDAM-GNF

Harrison-Z'eldovich primordial spectrum is consistent with observations

Inflation predicts primordial scalar perturbations with a nearly scale-invariant spectrum and a spectral index approximately unity (the Harrison--Zel'dovich (HZ) spectrum). The first important step for inflationary cosmology is to check the consistency of the HZ primordial spectrum with current observations. Recent analyses have claimed that a HZ primordial spectrum is excluded at more than 99% c.l.. Here we show that the HZ spectrum is only marginally disfavored if one considers a more general reionization scenario. Data from the Planck mission will settle the issue.Comment: 4 Pages, 2 Figure

Climatology of aerosol optical properties and black carbon mass absorption cross section at a remote high-altitude site in the western Mediterranean Basin

Aerosol light scattering (&sigma;_sp), backscattering (&sigma;_bsp) and absorption (&sigma;_ap) were measured at Montsec (MSC; 42°3' N, 0°44' E, 1570 m a.s.l.), a remote high-altitude site in the western Mediterranean Basin. Mean (±SD) &sigma;_sp, &sigma;_bsp and &sigma;_ap were 18.9 ± 20.8, 2.6 ± 2.8 and 1.5 ± 1.4 Mm⁻¹, respectively at 635 nm during the period under study (June 2011–June 2013). Mean values of single-scattering albedo (SSA, 635 nm), the scattering Ångström exponent (SAE, 450–635 nm), backscatter-to-scatter ratio (<i>B</i> / <i>S</i>, 635 nm), asymmetry parameter (<i>g</i>, 635 nm), black carbon mass absorption cross section (MAC, 637 nm) and PM_2.5 mass scattering cross section (MSCS, 635 nm) were 0.92 ± 0.03, 1.56 ± 0.88, 0.16 ± 0.09, 0.53 ± 0.16, 10.9 ± 3.5 m² g⁻¹ and 2.5 ± 1.3 m² g⁻¹, respectively. The scattering measurements performed at MSC were in the medium/upper range of values reported by Andrews et al. (2011) for other mountaintop sites in Europe due to the frequent regional recirculation scenarios (SREG) and Saharan dust episodes (NAF) occurring mostly in spring/summer and causing the presence of polluted layers at the MSC altitude. However, the development of upslope winds and the possible presence of planetary boundary layer air at MSC altitude in summer may also have contributed to the high scattering observed. Under these summer conditions no clear diurnal cycles were observed for the measured extensive aerosol optical properties (&sigma;_sp, &sigma;_bsp and &sigma;_ap). Conversely, low &sigma;_sp and &sigma;_ap at MSC were measured during Atlantic advections (AA) and winter regional anticyclonic episodes (WREG) typically observed during the cold season in the western Mediterranean. Therefore, a season-dependent decrease in the magnitude of aerosol extensive properties was observed when MSC was in the free troposphere, with the highest free-troposphere vs. all-data difference observed in winter and the lowest in spring/summer. The location of MSC station allowed for a reliable characterization of aerosols as a function of the main synoptic meteorological patterns. The SAE was the lowest during NAF and showed an inverse correlation with the outbreak intensity, indicating a progressive shift toward larger particles. Moreover, the strength of NAF episodes in the region led to a slope of the scattering vs. absorption relationship among the lowest reported for other mountaintop sites worldwide, indicating that MSC was dominated by dust aerosols at high aerosol loading. As a consequence, SSA showed a nearly monotonic increase with increasing particle concentration and scattering. The SAE was the highest during SREG, indicating the presence of polluted layers dominated by smaller particles. Correspondingly, the asymmetry parameter was lower under SREG compared with NAF. The MAC and MSCS were significantly higher during NAF and SREG compared to AA and WREG, indicating an increase of absorption and scattering efficiencies associated with the summer polluted scenarios. The optical measurements performed at the MSC remote site were compared with those simultaneously performed at a regional background station in the western Mediterranean Basin located at around 700 m a.s.l. upstream of the MSC station

Variability of aerosol optical properties in the Western Mediterranean Basin

Aerosol light scattering, absorption and particulate matter (PM) concentrations were measured at Montseny, a regional background site in the Western Mediterranean Basin (WMB) which is part of the European Supersite for Atmospheric Aerosol Research (EUSAAR). Off line analyses of 24 h PM filters collected with Hi-Vol instruments were performed for the determination of the main chemical components of PM. Mean scattering and hemispheric backscattering coefficients (@ 635 nm) were 26.6±23.2 Mm&lt;sup&gt;−1&lt;/sup&gt; and 4.3±2.7 Mm&lt;sup&gt;−1&lt;/sup&gt;, respectively and the mean aerosol absorption coefficient (@ 637 nm) was 2.8±2.2 Mm&lt;sup&gt;−1&lt;/sup&gt;. Mean values of Single Scattering Albedo (SSA) and Ångström exponent (&lt;i&gt;å&lt;/i&gt;) (calculated from 450 nm to 635 nm) at MSY were 0.90±0.05 and 1.3±0.5 respectively. A clear relationship was observed between the PM&lt;sub&gt;1&lt;/sub&gt;/PM&lt;sub&gt;10&lt;/sub&gt; and PM&lt;sub&gt;2.5&lt;/sub&gt;/PM&lt;sub&gt;10&lt;/sub&gt; ratios as a function of the calculated Ångström exponents. Mass scattering cross sections (MSC) for fine mass and sulfate at 635 nm were 2.8±0.5 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt; and 11.8±2.2 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt;, respectively, while the mean aerosol absorption cross section (MAC) was 10.4±2.0 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt;. The variability in aerosol optical properties in the WMB were largely explained by the origin and ageing of air masses over the measurement site. The MAC values appear dependent of particles aging: similar to the expected absorption cross-section for fresh emissions under Atlantic Advection episodes and higher under aerosol pollution episodes. The analysis of the Ångström exponent as a function of the origin the air masses revealed that polluted winter anticyclonic conditions and summer recirculation scenarios typical of the WMB led to an increase of fine particles in the atmosphere (&lt;i&gt;å&lt;/i&gt; = 1.5±0.1) while the aerosol optical properties under Atlantic Advection episodes and Saharan dust outbreaks were clearly dominated by coarser particles (&lt;i&gt;å&lt;/i&gt; = 1.0±0.4). The sea breeze played an important role in transporting pollutants from the developed WMB coastlines towards inland rural areas, changing the optical properties of aerosols. Aerosol scattering and backscattering coefficients increased by around 40 % in the afternoon when the sea breeze was fully developed while the absorption coefficient increased by more than 100 % as a consequence of the increase in the equivalent black carbon concentration (EBC) observed at MSY under sea breeze circulation