A differential method for bounding the ground state energy

For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a normalisation factor or a matrix element). It just requires the determination of the absolute minimum and maximum in the whole configuration space of the local energy associated with a normalisable trial function (the calculation of the norm is not needed). After a general introduction, the method is applied to three non-integrable systems: the asymmetric annular billiard, the many-body spinless Coulombian problem, the hydrogen atom in a constant and uniform magnetic field. Being more sensitive than the variational methods to any local perturbation of the trial function, this method can used to systematically improve the energy bounds with a local skilled analysis; an algorithm relying on this method can therefore be constructed and an explicit example for a one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes

Recent theoretical work suggests that violation of the Equivalence Principle might be revealed in a measurement of the fractional differential acceleration $\eta$ between two test bodies -of different composition, falling in the gravitational field of a source mass- if the measurement is made to the level of $\eta\simeq 10^{-13}$ or better. This being within the reach of ground based experiments, gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the "Galileo Galilei on the Ground" (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following paper (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation -in particular its normal modes (Part I) and rejection of common mode effects (Part II)- can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining quantitative agreement with the available experimental data on the frequencies of the normal modes, and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan 16, 2006. 16 2-column pages, 9 figure

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

In-Situ Sample Preparation for Radiochemical Analyses of Surface Water

A new method for improved radionuclide sample analysis of surface water has been demonstrated at the Savannah River Site, a U.S. Department of Energy production facility, currently in standby. The method makes uses of selective solid phase extraction (SPE) disks being placed in a modified portable aqueous sampler

What is health promotion ethics?

editorialWhat does it mean to think about the ethics of health promotion? When most of us think ‘ethics’ we think of the Human Research Ethics Committee applications required for research projects. But I’m thinking of something quite different here: the ethics of health promotion practice. Health promotion ethics is an attempt to answer questions such as: Can we provide a moral justification for what we are doing in health promotion? or What is the right thing to do in health promotion, and how can we tell? As other authors have argued, sometimes these questions are ignored in health promotion in favour of scientific and technical questions about effectiveness. But there is increasing recognition that health promotion is a moral project, that health promotion can be practised in ways that are more or less ethical, and thus that considering ethics in health promotion is just as important as – and related to – considering the evidence about whether or not health promotion works. 1-5 The number of publications about health promotion ethics has been slowly increasing since the 1980s, including in this journal, where authors have particularly argued the importance of being explicit about values in health promotion. If something has value, it has worth or importance. 6 Authors in the HPJA have suggested that health promotion practitioners value: health and wellbeing as opposed to the mere absence of disease, justice, environmental sustainability, empowerment, respect for culture, and truth telling. 3, 7, 8 But concern has been expressed that although these things are valued in health promotion, this may not always influence the way that health promotion is implemented and evaluated.NHMR

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Some flows in shape optimization

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem

Limits to mode-localized sensing using micro- and nanomechanical resonator arrays

In recent years, the concept of utilizing the phenomenon of vibration mode-localization as a paradigm of mechanical sensing has made profound impact in the design and development of highly sensitive micro- and nanomechanical sensors. Unprecedented enhancements in sensor response exceeding three orders of magnitude relative to the more conventional resonant frequency shift based technique have been both theoretically and experimentally demonstrated using this new sensing approach. However, the ultimate limits of detection and in consequence, the minimum attainable resolution in such mode-localized sensors still remain uncertain. This paper aims to fill this gap by investigating the limits to sensitivity enhancement imposed on such sensors, by some of the fundamental physical noise processes, the bandwidth of operation and the noise from the electronic interfacial circuits. Our analyses indicate that such mode-localized sensors offer tremendous potential for highly sensitive mass and stiffness detection with ultimate resolutions that may be orders of magnitude better than most conventional micro- and nanomechanical resonant sensors

Predictive Model for Human-Unmanned Vehicle Systems

Advances in automation are making it possible for a single operator to control multiple unmanned vehicles. However, the complex nature of these teams presents a difficult and exciting challenge for designers of human–unmanned vehicle systems. To build such systems effectively, models must be developed that describe the behavior of the human–unmanned vehicle team and that predict how alterations in team composition and system design will affect the system’s overall performance. In this paper, we present a method for modeling human–unmanned vehicle systems consisting of a single operator and multiple independent unmanned vehicles. Via a case study, we demonstrate that the resulting models provide an accurate description of observed human-unmanned vehicle systems. Additionally, we demonstrate that the models can be used to predict how changes in the human-unmanned vehicle interface and the unmanned vehicles’ autonomy alter the system’s performance.Lincoln Laborator