Shape identification in inverse medium scattering problems with a single far-field pattern

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset \mathbb R^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be H\"older continuous near the corners. If $D\subset \mathbb R^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of non-scattering wavenumbers in domains with corners. As a byproduct, we show that the smoothness conditions in previous corner scattering results are only required near the corners

Molecular Dynamics Study of Charged Dendrimers in Salt-Free Solution: Effect of Counterions

Polyamidoamine (PAMAM) dendrimers, being protonated under physiological conditions, represent a promising class of nonviral, nano-sized vectors for drug and gene delivery. We performed extensive molecular dynamics simulations of a generic model dendrimer in a salt-free solution with dendrimer's terminal beads positively charged. Solvent molecules as well as counterions were explicitly included as interacting beads. We find that the size of the charged dendrimer depends non-monotonically on the strength of electrostatic interactions demonstrating a maximum when the Bjerrum length equals the diameter of a bead. Many other structural and dynamic characteristics of charged dendrimers are also found to follow this pattern. We address such a behavior to the interplay between repulsive interactions of the charged terminal beads and their attractive interactions with oppositely charged counterions. The former favors swelling at small Bjerrum lengths and the latter promotes counterion condensation. Thus, counterions can have a dramatic effect on the structure and dynamics of charged dendrimers and, under certain conditions, cannot be treated implicitly

Elastic lines on splayed columnar defects studied numerically

We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk -like roughening in 2d and ballistic behavior in 3d. Furthermore, we find that in the case of pure splayed columnar disorder in contrast to point disorder there is no entanglement transition in 3d. Entanglement can be triggered by perturbing the pure splay system with point defects.Comment: 9 pages, 11 figures. Accepted for publication in PR

Comparison of User Traffic Characteristics on Mobile-Access versus Fixed-Access Networks

We compare Web traffic characteristics of mobile- versus fixed-access end-hosts, where herein the term "mobile" refers to access via cell towers, using for example the 3G/UMTS standard, and the term "fixed" includes Wi-Fi access. It is well-known that connection speeds are in general slower over mobile-access networks, and also that often there is higher packet loss. We were curious whether this leads mobile-access users to have smaller connections. We examined the distribution of the number of bytes-per-connection, and packet loss from a sampling of logs from servers of Akamai Technologies. We obtained 149 million connections, across 57 countries. The mean bytes-per-connection was typically larger for fixed-access: for two-thirds of the countries, it was at least one-third larger. Regarding distributions, we found that the difference between the bytes-per-connection for mobile- versus fixed-access, as well as the packet loss, was statistically significant for each of the countries; however the visual difference in plots is typically small. For some countries, mobile-access had the larger connections. As expected, mobile-access often had higher loss than fixed-access, but the reverse pertained for some countries. Typically packet loss increased during the busy period of the day, when mobile-access had a larger increase. Comparing our results from 2010 to those from 2009 of the same time period, we found that connections have become a bit smaller

Role of disorder in the size-scaling of material strength

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.Comment: 4 pages 5 figure

Effect of Disorder and Notches on Crack Roughness

We analyze the effect of disorder and notches on crack roughness in two dimensions. Our simulation results based on large system sizes and extensive statistical sampling indicate that the crack surface exhibits a universal local roughness of $\zeta_{loc} = 0.71$ and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as $\zeta = 0.87$ and is also independent of material disorder. Furthermore, we note that the statistical distribution of crack profile height fluctuations is also independent of material disorder and is described by a Gaussian distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure