The double well potential in quantum mechanics: a simple, numerically exact formulation

The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum mechanic

A Novel Approach for the Particle-in-Cell Modelling of Gridded Ion Engine Plume Neutralisation

The Particle-in-Cell modelling of gridded ion engine plume neutralisation has been simplified when compared to traditional methods. This results in significantly less computational resources being required. The NSTAR engine was modelled as a reference, where simulated specific impulse values were found to be 5% higher than the real engine. This method will be most suited to rapid prototyping and optimisation studies, where speed of simulations is an important factor

Review of experience of family medicine in Europe and Central Asia (Vol. 3): Bosnia and Herzegovina case study

This report summarizes the findings of four case studies that review the experience of family medicine in Europe and Central Asia (ECA) Region. It is part of a study comprising five volumes that review the experience of family medicine in four countries in ECA--Armenia, Bosnia and Herzegovina, Kyrgyz Republic and Moldova. The report reviews the experience, draws lessons, and establishes an evidence base for detailed analysis. The study presents best practices for policy dialogue and future investments by the World Bank and other financial institutions. The detailed case studies compare these countries and draw common themes and issues. Comparisons are made with best-developed or existing models in the OECD and other countries in the Europe and Central Asia Region that have already undertaken family medicine reform

Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere

Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork' structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the modes beyond the instrumental horizon (EoR/CD window). We show that this structure largely arises due to strong instrumental polarization leakage ($\sim30\%$) towards {Cas\,A} ($\sim21$ kJy at 81 MHz, brightest source in northern sky), which is far away from primary field of view. We measure an extremely small ionospheric diffractive scale ($r_{\text{diff}} \approx 430$ m at 60 MHz) towards {Cas\,A} resembling pure Kolmogorov turbulence compared to $r_{\text{diff}} \sim3 - 20$ km towards zenith at 150 MHz for typical ionospheric conditions. This is one of the smallest diffractive scales ever measured at these frequencies. Our work provides insights in understanding the nature of aforementioned effects and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA) in the same frequency window.Comment: 20 pages, 11 figures, accepted for publication in MNRA

Realistic following behaviors for crowd simulation

International audienceWhile walking through a crowd, a pedestrian experiences a large number of interactions with his neighbors. The nature of these interactions is varied, and it has been observed that macroscopic phenomena emerge from the combination of these local interactions. Crowd models have hitherto considered collision avoidance as the unique type of interactions between individuals, few have considered walking in groups. By contrast, our paper focuses on interactions due to the following behaviors of pedestrians. Following is frequently observed when people walk in corridors or when they queue. Typical macroscopic stop-and-go waves emerge under such traffic conditions. Our contributions are, first, an experimental study on following behaviors, second, a numerical model for simulating such interactions, and third, its calibration, evaluation and applications. Through an experimental approach, we elaborate and calibrate a model from microscopic analysis of real kinematics data collected during experiments. We carefully evaluate our model both at the microscopic and the macroscopic levels. We also demonstrate our approach on applications where following interactions are prominent

Prospects for detecting the 21cm forest from the diffuse intergalactic medium with LOFAR

We discuss the feasibility of the detection of the 21cm forest in the diffuse IGM with the radio telescope LOFAR. The optical depth to the 21cm line has been derived using simulations of reionization which include detailed radiative transfer of ionizing photons. We find that the spectra from reionization models with similar total comoving hydrogen ionizing emissivity but different frequency distribution look remarkably similar. Thus, unless the reionization histories are very different from each other (e.g. a predominance of UV vs. x-ray heating) we do not expect to distinguish them by means of observations of the 21cm forest. Because the presence of a strong x-ray background would make the detection of 21cm line absorption impossible, the lack of absorption could be used as a probe of the presence/intensity of the x-ray background and the thermal history of the universe. Along a random line of sight LOFAR could detect a global suppression of the spectrum from z>12, when the IGM is still mostly neutral and cold, in contrast with the more well-defined, albeit broad, absorption features visible at lower redshift. Sharp, strong absorption features associated with rare, high density pockets of gas could be detected also at z~7 along preferential lines of sight.Comment: 12 pages, 13 figures. MNRAS, in pres

Photoswitching in nanoporous, crystalline solids: an experimental and theoretical study for azobenzene linkers incorporated in MOFs

In this article, we use the popular photoswitchable molecule, azobenzene, to demonstrate that the embedding in a nanoporous, crystalline solid enables a precise understanding of light-induced, reversible molecular motion. We investigate two similar azobenzene-containing, pillared-layer metal–organic frameworks (MOFs): Cu2(AzoBPDC)2(BiPy) and Cu2(NDC)2(AzoBiPy). Experimental results from UV-vis spectroscopy and molecular uptake experiments as well as theoretical results based on density-functional theory (DFT) show that in the Cu2(AzoBPDC)2(BiPy) MOF structure, the azobenzene side groups undergo photoisomerization when irradiated with UV or visible light. In a very similar MOF structure, Cu2(NDC)2(AzoBiPy), the experimental studies show an unexpected absence of photoisomerization. The DFT calculations reveal that in both MOFs the initial and final states of the photoswitching process (the trans and the cis conformation) have similar energies, which strongly suggests that the reason for the effective blocking of photoswitching in the AzoBiPy-based MOFs must be related to the switching process itself. More detailed calculations show that in Cu2(NDC)2(AzoBiPy) a naphthalene linker from the molecular framework blocks the photoisomerization trajectory which leads from the trans to the cis conformation. For Cu2(AzoBPDC)2(BiPy), as a result of the different geometry, such a steric hindrance is absent