A second row Parking Paradox

We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its nearest neighbors are not occupied yet. It can reach the first line if it is not obstructed by cars already parked in the second line (screening). b) The car parks according to the same rules, but parking in the first line can not be obstructed by parked cars in the second line (no screening). In both models, a car that can not park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first and second line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.Comment: 11 pages, 4 figure

Effect of particle polydispersity on the irreversible adsorption of fine particles on patterned substrates

We performed extensive Monte Carlo simulations of the irreversible adsorption of polydispersed disks inside the cells of a patterned substrate. The model captures relevant features of the irreversible adsorption of spherical colloidal particles on patterned substrates. The pattern consists of (equal) square cells, where adsorption can take place, centered at the vertices of a square lattice. Two independent, dimensionless parameters are required to control the geometry of the pattern, namely, the cell size and cell-cell distance, measured in terms of the average particle diameter. However, to describe the phase diagram, two additional dimensionless parameters, the minimum and maximum particle radii are also required. We find that the transition between any two adjacent regions of the phase diagram solely depends on the largest and smallest particle sizes, but not on the shape of the distribution function of the radii. We consider size dispersions up-to 20% of the average radius using a physically motivated truncated Gaussian-size distribution, and focus on the regime where adsorbing particles do not interact with those previously adsorbed on neighboring cells to characterize the jammed state structure. The study generalizes previous exact relations on monodisperse particles to account for size dispersion. Due to the presence of the pattern, the coverage shows a non-monotonic dependence on the cell size. The pattern also affects the radius of adsorbed particles, where one observes preferential adsorption of smaller radii particularly at high polydispersity.Comment: 9 pages, 5 figure

Morphology of Fine-Particle Monolayers Deposited on Nanopatterned Substrates

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius $r_0$ is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, $a$, and cell-cell separation, $b$. The model shows a surprisingly rich behavior in the space of the two dimensionless parameters $\alpha=a/2r_0$ and $\beta=b/2r_0$. Extensive Monte Carlo simulations for system sizes of $500\times500$ square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.Comment: 11 pages, 10 figures, 3 table

Gestação Gemelar Monocoriónica com Morte de Um dos Fetos: Prognóstico do Co-Gémeo Sobrevivente e Desfecho Neonatal

The incidence of single fetal death in twin pregnancy varies from 0.5% - 6.8%, leaving the surviving fetus with increased morbi-mortality. The prognosis is worse in monochorionic pregnancies. In addressing these cases it should be noted referral to tertiary center with differentiated perinatal support, induction of fetal lung maturation and termination of pregnancy if there's loss of fetal well-being or possibility of maternal complications and suspected neurological sequelae in the surviving fetus. The risk of iatrogenic prematurity should always be weighed with the possible consequences arising from the fetus staying in a hostile uterine environment. The authors describe a case of a 32-year-old pregnant woman with monochorionic/diamniotic twin pregnancy diagnosed with death of one of the fetuses due to fetal growth restriction and velamentous insertion of the umbilical cord at 30 weeks of gestation. The couple opted for termination of pregnancy at 33 weeks after documentation of brain changes in the surviving fetus.info:eu-repo/semantics/publishedVersio

Goldenhar syndrome: a rare diagnosis with possible prenatal findings

Goldenhar syndrome is a rare congenital disease associated with hemifacial hypoplasia as well as ear and ocular defects. Sometimes it is also associated with vertebral and other bone defects, cardiac malformations and central nervous system anomalies. Its aetiology is not yet clarified in the literature. We present a case of multiple malformations detected in the morphology ultrasound (at 22 weeks of gestation), namely absent nasal bones, micrognathia and absent left radius, among other defects. Genetic counselling, fetal brain MRI and cardiac sonography, which showed ventricular septal defect, were performed. 11 syndromes with poor fetal or neonatal prognosis were identified as possible diagnosis, using a genetic database and the couple asked for a medical termination of pregnancy. Postmortem examination has shown features consistent with Goldenhar syndrome

Finite-size scaling study of the ballistic deposition model in (1+1)-dimensions

We performed extensive Monte Carlo simulations of the ballistic deposition model in (1 + 1)-dimensions for several system sizes up to 1280 lattice constants, on the square lattice. Though the ballistic deposition model is generally accepted to belong to the Kardar Parisi-Zhang (KPZ) universality class, strong corrections to scaling prevent numerical estimates of the exponents close to the asymptotic values. We obtained a ³ 0.40, b ³ 0.30, and z ³ 1.16, which are consistent with the expected KPZ values of a = 1/2, b = 1/3, and z = 3/2. We found a slow, and even non monotonic, convergence of the exponents towards the asymptotic values, which corroborates previous claims in the literature of strong corrections to scaling