The multiple-scale transport equation in one space dimension

This study examines the behavior of the one-dimensional non-homogeneous transport equation of the form u_t= u_x+f, «1. The solution consists of behavior which changes on two different time scales, one rapid and one slow. This time scale behavior is known. Additionally, however, we find here that because of the presence of the non-homogeneous forcing termf, and large wave speed 1/, there is a component of the solution which will vary only on a very large spatial scale. This large space-scale solution persists throughout all time, even after the source term of the solution has been shut off. The analysis of this large spacescale behavior is the focus of this paper. Numerical experiments highlight some of our results. These results have applications in fields such as meteorology, and other areas where multiple time scales are of interest.This work was supported in part by NSF grant NSF-DMS93-21728.     

Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion $$\omega_t+\alpha (\omega_t)-\Delta \omega-\Delta_p{\omega} \ni f$$ where α is a maximal monotone operator in ${\mathbb{R}^2}$ and Δ _p denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W ^1,p , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms.     

On Multi-threaded Metrical Task Systems

Traditionally, on-line problems have been studied under the assumption that there is a unique sequence of requests that must be served. This approach is common to most general models of on-line computation, such as Metrical Task Systems. However, there exist on-line problems in which the requests are organized in more than one independent thread. In this more general framework, at every moment the first unserved request of each thread is available. Therefore, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities.In this paper we introduce Multi-threaded Metrical Task Systems, that is, the generalization of Metrical Task Systems to the case in which there are many threads of tasks. We study the problem from a competitive analysis point of view, proving lower and upper bounds on the competitiveness of on-line algorithms. We consider finite and infinite sequences of tasks, as well as deterministic and randomized algorithms. In this work we present the first steps towards a more general framework for on-line problems which is not restricted to a sequential flow of information.     

The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics.     

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.