Performance analysis using timed Petri Nets

Petri Nets have been successfully used to model and evaluate the performance of distributed systems. Several researchers have extended the basic Petri Net model to include time, and have demonstrated that restricted classes of Petri Nets can be analyzed efficiently. Unfortunately, the restrictions prohibit the techniques from being applied to many interesting systems, e.g. communication protocols. This paper proposes a version of timed Petri Nets which accurately models communication protocols, and which can be analyzed using Timed Reachability Graphs. Procedures for constructing and analyzing these graphs are presented. The analysis is shown to be applicable to a larger class of Timed Petri Nets than previously thought. The model and the analysis technique are demonstrated using a simple communication protocol

Studies of surface two-dimensional photonic band-gap structures

Two-dimensional (2D) surface photonic band-gap (SPBG) structures can be obtained by providing a shallow corrugation of the inner surface of a waveguide wall. It can be used as a distributed mirror, a cavity, or a filter in integrated optics or microwave electronics. These structures can also be an alternative to conventional 2D PBG or 1D Bragg structures. In this article, we present the results of theoretical and experimental studies of 2D SPBG structures. Data obtained from experiments are compared with theoretical results and good agreement between theory and experiment is demonstrated. Comparison of a coaxial 2D SPBG structure with a conventional 1D Bragg structure is also presented

Cylindrical, periodic surface lattice — theory, dispersion analysis, and experiment

A two-dimensional surface lattice of cylindrical topology obtained via perturbing the inner surface of a cylinder is considered. Periodic perturbations of the surface lead to observation of high-impedance, dielectric-like media and resonant coupling of surface and non-propagating volume fields. This allows synthesis of tailored-for-purpose "coating" material with dispersion suitable, for instance, to mediate a Cherenkov type interaction. An analytical model of the lattice is discussed and coupled-wave equations are derived. Variations of the lattice dispersive properties with variation of parameters are shown, illustrating the tailoring of the structure's electromagnetic properties. Experimental results are presented showing agreement with the theoretical model

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H2_{2}

A model of the collisional kinetics of energetic hydrogen atoms, molecules, and ions in pure H$_2$ discharges is used to predict H$_\alpha$ emission profiles and spatial distributions of emission from the cathode regions of low-pressure, weakly-ionized discharges for comparison with a wide variety of experiments. Positive and negative ion energy distributions are also predicted. The model developed for spatially uniform electric fields and current densities less than $10^{-3}$ A/m$^2$ is extended to non-uniform electric fields, current densities of $10^{3}$ A/m$^2$, and electric field to gas density ratios $E/N = 1.3$ MTd at 0.002 to 5 Torr pressure. (1 Td = $10^{-21}$ V m$^2$ and 1 Torr = 133 Pa) The observed far-wing Doppler broadening and spatial distribution of the H$_\alpha$ emission is consistent with reactions among H$^+$, H$_2^+$, H$_3^+$, and H$^-H$ ions, fast H atoms, and fast H$_2$ molecules, and with reflection, excitation, and attachment to fast H atoms at surfaces. The H$_\alpha$ excitation and H$^-$ formation occur principally by collisions of fast H, fast H$_2$, and H$^+$ with H$_2$. Simplifications include using a one-dimensional geometry, a multi-beam transport model, and the average cathode-fall electric field. The H$_\alpha$ emission is linear with current density over eight orders of magnitude. The calculated ion energy distributions agree satisfactorily with experiment for H$_2^+$ and H$_3^+$, but are only in qualitative agreement for H$^+$ and H$^-$. The experiments successfully modeled range from short-gap, parallel-plane glow discharges to beam-like, electrostatic-confinement discharges.Comment: Submitted to Plasmas Sources Science and Technology 8/18/201

Periodic structure towards the terahertz region manufactured using high resolution 3D printing

Periodic structures used for high power millimetre and sub-millimetre sources that implement relativistic beam - wave interactions have historically involved the implantation of a dielectric layer around the inner wall of the interaction region or a periodic corrugated structure that serves to reduce the velocity of an internal electromagnetic wave. Moving towards the THz regime, the physical dimensions required to manufacture such a cavity become prohibitively difficult. Ongoing attempts to develop manufacturing processes that provide higher resolution have resulted in a number of viable techniques. Additive Manufacturing or 3D printing offers the possibility of producing components on this scale quickly and efficiently. Here 0.1, 0.4 and 1 THz periodic structures are realised using high resolution (16 micron) 3D printing technology

Preparing Postbaccalaureates for Entry and Success in Biomedical PhD Programs

Certain racial and ethnic groups, individuals with disabilities, and those from low socioeconomic backgrounds remain underrepresented (UR) in the biomedical sciences. This underrepresentation becomes more extreme at each higher education stage. To support UR scholars during the critical transition from baccalaureate to PhD, we established an intensive, 1-yr postbaccalaureate training program. We hypothesized that this intervention would strengthen each participant’s competitiveness for leading PhD programs and build a foundation of skills and self-efficacy important for success during and after graduate school. Scholar critical analysis skills, lab technique knowledge, and Graduate Record Examination scores all improved significantly during the program. Scholars reported significant confidence growth in 21 of 24 categories related to success in research careers. In 5 yr, 91% (41/45) of scholars transitioned directly into PhD programs. Importantly, 40% (18/45) of participating postbaccalaureate scholars had previously been declined acceptance into graduate school; however, 17/18 of these scholars directly entered competitive PhD programs following our training program. Alumni reported they were “extremely well” prepared for graduate school, and 95% (39/41) are currently making progress to graduation with a PhD. In conclusion, we report a model for postbaccalaureate training that could be replicated to increase participation and success among UR scholars in the biomedical sciences

Investigation of initiation of gigantic jets connecting thunderclouds to the ionosphere

The initiation of giant electrical discharges called as "gigantic jets" connecting thunderclouds to the ionosphere is investigated by numerical simulation method in this paper. Using similarity relations, the triggering conditions of streamer formation in laboratory situations are extended to form a criterion of initiation of gigantic jets. The energy source causing a gigantic jet is considered due to the quasi-electrostatic field generated by thunderclouds. The electron dynamics from ionization threshold to streamer initiation are simulated by the Monte Carlo technique. It is found that gigantic jets are initiated at a height of ~18-24 km. This is in agreement with the observations. The method presented in this paper could be also applied to the analysis of the initiation of other discharges such as blue jets and red sprites.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest