The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations

This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

Relativistic length agony continued

An attempt is made to remedy confusing treatments of some basic relativistic concepts and results in recent papers by Franklin (2010 {\it Eur. J. Phys.} {\bf 31} 291-8) and by McGlynn and van Kampen (2008 {\it Eur. J. Phys.} {\bf 29} N63-N67). The authors' misconceptions are recurrent points in the literature

How many dark energy parameters?

For exploring the physics behind the accelerating universe a crucial question is how much we can learn about the dynamics through next generation cosmological experiments. For example, in defining the dark energy behavior through an effective equation of state, how many parameters can we realistically expect to tightly constrain? Through both general and specific examples (including new parametrizations and principal component analysis) we argue that the answer is 42 - no, wait, two. Cosmological parameter analyses involving a measure of the equation of state value at some epoch (e.g. w_0) and a measure of the change in equation of state (e.g. w') are therefore realistic in projecting dark energy parameter constraints. More elaborate parametrizations could have some uses (e.g. testing for bias or comparison with model features), but do not lead to accurately measured dark energy parameters.Comment: 10 pages, 1 figur

Importance of Supernovae at z>1.5 to Probe Dark Energy

The accelerating expansion of the universe suggests that an unknown component with strongly negative pressure, called dark energy, currently dominates the dynamics of the universe. Such a component makes up ~70% of the energy density of the universe yet has not been predicted by the standard model of particle physics. The best method for exploring the nature of this dark energy is to map the recent expansion history, at which Type Ia supernovae have proved adept. We examine here the depth of survey necessary to provide a precise and qualitatively complete description of dark energy. Realistic analysis of parameter degeneracies, allowance for natural time variation of the dark energy equation of state, and systematic errors in astrophysical observations all demonstrate the importance of a survey covering the full range 0<z<2 for revealing the nature of dark energy.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

The flow of two zinc oxide-eugenol-based endodontic sealers

Background/Aim. Endodontic sealers (ES) for obturation are usually prepared with a slight variation of their components both on purpose or unintentionally. Considering that fact, as well as a frequent use of compaction techniques with the applied force to gutta-percha and ES of 1-3 kg, the aim of this study was to investigate the flow of two zinc-oxide eugenol ES in regard to the applied force and a variation of sealer’s components. Methods. The experimental group samples of both ES were prepared according to the manufacturer’s instructions, applied between pair of glass slabs and loaded by weights of 1 and 2 kg, respectively (American National Standard, Specification No. 57). Some samples of one ES were prepared as thick consistency with 10% more powder and some as thin mixture with 10% less powder than the standard prescription. These semples had been exposed to the load of 2 kg. The control group included samples of both ES prepared as standard prescription but exposed to the weight of one glass slab only. The spread ES appeared as a regular circle 10 min upon mixing and weighting. Measuring of the circle diameter was done by an orthodontic ruler. The flow of the used ES was considered the function of its spread diameter. Results. Application of 1 vs 2 kg load for both regularly mixed sealers in the scope of disk diameter (flow) was statistically insignificant (p &gt; 0.05). This means that the stated null hypothesis that there would be no significant difference in flow rate among the regularly mixed sealers at the level of α = 0.05 is accepted. The findings about difference in the disk diameter in regard to mixing variation of Endomethasone indicate that the null hypothesis that there would be no significant difference in flow rate between the regular and thick mixed mass at the level of α = 0.05 is accepted. In the comparison of regular and thin mix a significant difference was noted and the null hypotesis is rejected (p &lt; 0.01). The control group results displayed Roth 801 as less viscous than Endomethasone sealer (p &lt; 0.01). Conclusion. Application of 1 or 2 kg pressure on the samples of both exposed sealers does not significantly affect the flow values as well as comparison of the regular to thick consistency of Endomethasone while comparison of its regular to thin mass shows a significant difference

Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables

We perform a comprehensive study of a class of dark energy models - scalar field models where the effective potential can be described by a polynomial series - exploring their dynamical behavior using the method of flow equations that has previously been applied to inflationary models. Using supernova, baryon oscillation, CMB and Hubble constant data, and an implicit theoretical prior imposed by the scalar field dynamics, we find that the LCDM model provides an excellent fit to the data. Constraints on the generic scalar field potential parameters are presented, along with the reconstructed w(z) histories consistent with the data and the theoretical prior. We propose and pursue computationally feasible algorithms to obtain estimates of the principal components of the equation of state, as well as parameters w_0 and w_a. Further, we use the Monte Carlo Markov Chain machinery to simulate future data based on the Joint Dark Energy Mission, Planck and baryon acoustic oscillation surveys and find that the inverse area figure of merit improves nearly by an order of magnitude. Therefore, most scalar field models that are currently consistent with data can be potentially ruled out by future experiments. We also comment on the classification of dark energy models into "thawing'" and "freezing" in light of the more diverse evolution histories allowed by this general class of potentials.Comment: 22 pages and 12 figures, minor clarifications and a new Figure (#9) added in v3, matches the published PRD version. Chains and high-res figures are available at http://kicp.uchicago.edu/~dhuterer/DE_FLOWROLL/de_flowroll.htm