Continuum Surface Energy from a Lattice Model

We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with general binary interactions in two dimensions. A new bond counting approach is used, which reduces the problem to the lattice point problem of number theory. The main contribution is an explicit formula for the surface energy density as a function of the deformation gradient and boundary normal. The result is valid for a large class of domains, including faceted (polygonal) shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26 pages. Abstract changed. Section 2 split into 2. Section (4) added material. V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs added.V 5,intro changed V.6 address reviewer's comment

Forecasting the price of gold

This article seeks to evaluate the appropriateness of a variety of existing forecasting techniques (17 methods) at providing accurate and statistically significant forecasts for gold price. We report the results from the nine most competitive techniques. Special consideration is given to the ability of these techniques to provide forecasts which outperforms the random walk (RW) as we noticed that certain multivariate models (which included prices of silver, platinum, palladium and rhodium, besides gold) were also unable to outperform the RW in this case. Interestingly, the results show that none of the forecasting techniques are able to outperform the RW at horizons of 1 and 9 steps ahead, and on average, the exponential smoothing model is seen providing the best forecasts in terms of the lowest root mean squared error over the 24-month forecasting horizons. Moreover, we find that the univariate models used in this article are able to outperform the Bayesian autoregression and Bayesian vector autoregressive models, with exponential smoothing reporting statistically significant results in comparison with the former models, and classical autoregressive and the vector autoregressive models in most cases

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

A Mission to Explore the Pioneer Anomaly

The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8.74 \pm 1.33)\times 10^{-10} {\rm m/s^2}$. This signal has become known as the Pioneer anomaly. The inability to explain the anomalous behavior of the Pioneers with conventional physics has contributed to growing discussion about its origin. There is now an increasing number of proposals that attempt to explain the anomaly outside conventional physics. This progress emphasizes the need for a new experiment to explore the detected signal. Furthermore, the recent extensive efforts led to the conclusion that only a dedicated experiment could ultimately determine the nature of the found signal. We discuss the Pioneer anomaly and present the next steps towards an understanding of its origin. We specifically focus on the development of a mission to explore the Pioneer Anomaly in a dedicated experiment conducted in deep space.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020", 19-21 April 2005, ESTEC, Noordwijk, The Netherland

Magnetoresistance of a 2-dimensional electron gas in a random magnetic field

We report magnetoresistance measurements on a two-dimensional electron gas (2DEG) made from a high mobility GaAs/AlGaAs heterostructure, where the externally applied magnetic field was expelled from regions of the semiconductor by means of superconducting lead grains randomly distributed on the surface of the sample. A theoretical explanation in excellent agreement with the experiment is given within the framework of the semiclassical Boltzmann equation.Comment: REVTEX 3.0, 11 pages, 3 Postscript figures appended. The manuscript can also be obtained from our World Wide Web server: http://roemer.fys.ku.dk/randmag.ht

Fundamental Physics with the Laser Astrometric Test Of Relativity

The Laser Astrometric Test Of Relativity (LATOR) is a joint European-U.S. Michelson-Morley-type experiment designed to test the pure tensor metric nature of gravitation - a fundamental postulate of Einstein's theory of general relativity. By using a combination of independent time-series of highly accurate gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on interplanetary scales (to a precision respectively better than 0.1 picoradians and 1 cm), LATOR will significantly improve our knowledge of relativistic gravity. The primary mission objective is to i) measure the key post-Newtonian Eddington parameter \gamma with accuracy of a part in 10^9. (1-\gamma) is a direct measure for presence of a new interaction in gravitational theory, and, in its search, LATOR goes a factor 30,000 beyond the present best result, Cassini's 2003 test. The mission will also provide: ii) first measurement of gravity's non-linear effects on light to ~0.01% accuracy; including both the Eddington \beta parameter and also the spatial metric's 2nd order potential contribution (never measured before); iii) direct measurement of the solar quadrupole moment J2 (currently unavailable) to accuracy of a part in 200 of its expected size; iv) direct measurement of the "frame-dragging" effect on light by the Sun's gravitomagnetic field, to 1% accuracy. LATOR's primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today's solar system. We discuss the mission design of this proposed experiment.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020," 19-21 April 2005, ESTEC, Noodrwijk, The Netherland

On the effect of interactions beyond nearest neighbours on non-convex lattice systems

We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Public opinion and environmental policy output: a cross-national analysis of energy policies in Europe

This article studies how public opinion is associated with the introduction of renewable energy policies in Europe. While research increasingly seeks to model the link between public opinion and environmental policies, the empirical evidence is largely based on a single case: the US. This limits the generalizability of findings and we argue accordingly for a systematic, quantitative study of how public opinion drives environmental policies in another context. Theoretically, we combine arguments behind the political survival of democratic leaders with electoral success and environmental politics. Ultimately, we suggest that office-seeking leaders introduce policies that seem favorable to the domestic audience; if the public prefers environmental protection, the government introduces such policies in turn. The main contribution of this research is the cross-country empirical analysis, where we combine data on the public's environmental attitudes and renewable energy policy outputs in a European context between 1974 and 2015. We show that as public opinion shifts towards prioritizing the environment, there is a significant and positive effect on the rate of renewable energy policy outputs by governments in Europe. To our knowledge, this is the first systematic, quantitative study of public opinion and environmental policies across a large set of countries, and we demonstrate that the mechanisms behind the introduction of renewable energy policies follow major trends across European states

The Moral of the Tale: Stories, Trust, and Public Engagement with Clinical Ethics via Radio and Theatre.

Trust is frequently discussed with reference to the professional-patient relationship. However, trust is less explored in relation to the ways in which understanding of, and responses to, questions of ethics are discussed by both the "public" and "experts." Public engagement activity in healthcare ethics may invoke "trust" in analysing a moral question or problem but less frequently conceives of trust as integral to "public engagement" itself. This paper explores the relationship between trust and the ways in which questions of healthcare ethics are identified and negotiated by both "experts" and the public. Drawing on two examples from the author's "public engagement" work-a radio programme for the British Broadcasting Corporation and work with a playwright and theatre-the paper interrogates the ways in which "public engagement" is often characterized. The author argues that the common approach to public engagement in questions of ethics is unhelpfully constrained by a systemic disposition which continues to privilege the professional or expert voice at the expense of meaningful exchange and dialogue. By creating space for novel interactions between the "expert" and the "public," authentic engagement is achieved that enables not only the participants to flourish but also contributes to trust itself