Ray shooting and intersection searching amidst fat convex polyhedra in 3-space

We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in . The data structure uses O(n^2+ε) storage and preprocessing time, and queries can be answered in O(log²n) time. A trade-off between storage and query time is also possible: for any m with n<m<n², we can construct a structure that uses O(m^1+ε) storage and preprocessing time such that queries take time.We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in . For any m with n<m<n³, we can construct a structure that uses O(m^1+ε) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m^1/3)logn+k) time, where k is the number of answers.     

Magnetic properties of (Ce1−xLax)PdIn2

We report on results of X-ray powder diffraction, magnetization and specific heat measurements of the pseudo-ternary (Ce_1−xLa_x)PdIn₂ system with x=0; 0.2; 0.4 and 0.6. The results show a linear increase of the unit cell volume and a reduction of the ferromagnetic transition as La content increases. The Debye temperature, Sommerfeld coefficient and crystal field parameters were estimated from specific heat data, and are found to be weakly dependent of the Ce concentration. Also, the variation of magnetic entropy at T_C is only weakly dependent on x (ΔS≅0.92Rln2) indicating that T_K/T_C is approximately constant along the series. The T_C and T_K behaviors are explained by the variation of the exchange parameter due to the volume change when Ce is replaced by La. Our results indicate that the chemical pressure is the dominant effect rather than the chemical disorder for determining the physical proprieties of the (Ce_1−xLa_x)PdIn₂ system.     

Investigation on the magnetocaloric effect in DyNi2, DyAl2 and Tb1−nGdnAl2 (n=0, 0.4, 0.6) compounds

The magnetocaloric effect (MCE) in the DyNi₂, DyAl₂ and Tb_1−nGd_nAl₂ (n=0, 0.4, 0.6) was theoretically investigated in this work. The DyNi₂ and DyAl₂ compounds are described considering a model Hamiltonian which includes the crystalline electrical field anisotropy. The anisotropic MCE was calculated changing the magnetic field direction from 〈1 1 1〉 to 〈0 0 1〉 in DyNi₂ and from 〈1 0 0〉 to 〈0 1 1〉 in DyAl₂. The influence of the second- and first-order spin-reorientation phase transitions on the MCE that occurs in these systems is discussed. For the calculations of the MCE thermodynamic quantities in the Tb_1−nGd_nAl₂ systems we take into account a two sites magnetic model, and good agreement with the available experimental data was obtained.     

Increased viability of odontoblast-like cells subjected to low-level laser irradiation

Studies have shown that the increase of cell metabolism depends on the low level laser therapy (LLLT) parameters used to irradiate the cells. However, the optimal laser dose to up-regulate pulp cell activity remains unknown. Consequently, the aim of this study was to evaluate the metabolic response of odontoblast-like cells (MDPC-23) exposed to different LLLT doses. Cells at 20000 cells/cm² were seeded in 24-well plates using plain culture medium (DMEM) and were incubated in a humidified incubator with 5% CO₂ at 37°C. After 24 h, the culture medium was replaced by fresh DMEM supplemented with 5% (stress by nutritional deficit) or 10% fetal bovine serum (FBS). The cells were exposed to different laser doses from a near infrared diode laser prototype designed to provide a uniform irradiation of the wells. The experimental groups were: G1: 1.5 J/cm² + 5% FBS; G2: 1.5 J/cm² + 10% FBS; G3: 5 J/cm² + 5% FBS; G4: 5 J/cm² + 10% FBS; G5: 19 J/cm² + 5% FBS; G6: 19 J/cm² + 10% FBS. LLLT was performed in 3 consecutive irradiation cycles with a 24-hour interval. Non-irradiated cells cultured in DMEM supplemented with either 5 or 10% FBS served as control groups. The analysis of the metabolic response was performed by the MTT assay 3 h after the last irradiation. G1 presented an increase in SDH enzyme activity and differed significantly (Mann-Whitney test, p < 0.05) from the other groups. Analysis by scanning electron microscopy showed normal cell morphology in all groups. Under the tested conditions, LLLT stimulated the metabolic activity of MDPC-23 cultured in DMEM supplemented with 5% FBS and exposed to a laser dose of 1.5 J/cm². These findings are relevant for further studies on the action of near infrared lasers on cells with odontoblast phenotype.     

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.     

Persistence stability for geometric complexes

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, ?ech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and ?ech complexes built on top of compact spaces.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

On the merits of Raman spectroscopy and thermogravimetric analysis to asses carbon nanotube structural modifications

Raman spectroscopy, thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy, and transmission electron microscopy are used to assess structural changes generated on the surface of multi-walled (MWCNTs) and single-walled (SWCNTs) carbon nanotubes. Different levels of structural modifications are generated by the use of acidic oxidative treatments. It is found that Raman spectroscopy is a very powerful technique to assess structural modification of SWCNTs with initial low defect concentration. For MWCNTs grown by chemical vapor deposition, which already contain a high density of structural defects in their as-produced state, Raman spectroscopy is not a very sensitive tool to detect the generation of further defects or other structural modifications introduced through acidic treatments. For this later case, TGA is a sensitive technique to assess structural modifications on the nanotubes.