Mountain winds (revisited)

The prediction of extremely high wind speeds, at ground level on the downstream side of a mountain range, is possible by solving the initial value problem for a two-layered nonlinear shallow water model of the atmosphere. Three different numerical methods are described to find the solutions which may involve shocks: (1) the vonNeumann-Richtmyer artificial viscosity method, (2) a filtering scheme, and (3) a hybrid method

Numerical methods for meteorology and climatology

Efficient numerical methods for long term weather forecasting are developed. One implicit and one explicit scheme are compared as to accuracy

Chaotic root-finding for a small class of polynomials

In this paper we present a new closed-form solution to a chaotic difference equation, $y_{n+1} = a_2 y_{n}^2 + a_1 y_{n} + a_0$ with coefficient $a_0 = (a_1 - 4)(a_1 + 2) / (4 a_2)$, and using this solution, show how corresponding exact roots to a special set of related polynomials of order $2^p, p \in \mathbb{N}$ with two independent parameters can be generated, for any $p$

Comfort with Communication in Palliative and End of Life Care (C-COPE)

The C-COPE instrument is based on literature review, content from the COMFORT model, and iterative input from four content experts. The COMFORT communication model is grounded in patient-centered care and narrative medicine, where patients, families, and the healthcare team value each other’s story and collaboratively identify wishes and goals of care. COMFORT communication skills include bearing witness, understanding health literacy, actively listening, understanding family communication patterns, talking through the tension, embracing patient and family goals of care, and learning to collaborate with members of the team. The C-COPE operationalizes the key components of the COMFORT model: Communication, Orientation and opportunity, Mindful presence, Family, Openings, Relating, and Team. The 28-item instrument includes two ranked items and 26 items rated on a 5-point Likert-type scale (1 = not difficult, 2 = slightly difficult, 3 = uncertain, 4 = difficult, 5 = very difficult) to assess healthcare professional comfort with palliative and end-of-life communication. The range of possible C-COPE total scores is 26-130 points, with higher scores indicating less comfort with palliative and end-of-life communication. Rated items were categorized according to patient communication, family communication, and team communication. Preliminary psychometric analysis based on this pilot test of the C-COPE instrument supports test-retest reliability with ICC \u3e 0.77, internal reliability for total score with Cronbach’s alpha = 0.91, and four factors with Cronbach’s alpha ranging from 0.81- 0.90

Information-disturbance tradeoff in estimating a maximally entangled state

We derive the amount of information retrieved by a quantum measurement in estimating an unknown maximally entangled state, along with the pertaining disturbance on the state itself. The optimal tradeoff between information and disturbance is obtained, and a corresponding optimal measurement is provided.Comment: 4 pages. Accepted for publication on Physical Review Letter

Causality re-established

Causality never gained the status of a "law" or "principle" in physics. Some recent literature even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of reversibility of laws of physics, based either on determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such causality notion appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establish a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The causality notion is logically completely independent of the misidentified concept of "determinism", and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude arguing that causality naturally establishes an arrow of time. This implies that the scenario of the "Block Universe" and the connected "Past Hypothesis" are incompatible with causality, and thus with quantum theory: they both are doomed to remain mere interpretations and, as such, not falsifiable, similar to the hypothesis of "super-determinism". This article is part of a discussion meeting issue "Foundations of quantum mechanics and their impact on contemporary society".Comment: Presented at the Royal Society of London, on 11/12/ 2017, at the conference "Foundations of quantum mechanics and their impact on contemporary society". To appear on Philosophical Transactions of the Royal Society

An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES velocities. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We find that a four-planet model is preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses and orbits using an n-body model in three-dimensional space. Based on the radial velocities alone, we find that a 99% credible interval provides upper limits on the mutual inclinations for the three resonant planets ($\Phi_{cb}<6.20^\circ$ for the "c" and "b" pair and $\Phi_{be}<28.5^\circ$ for the "b" and "e" pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar ($\Phi_{cb}<2.60^\circ$ and $\Phi_{be}<7.87^\circ$), suggesting the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples available at https://github.com/benelson/GJ87