Talbot effect for the third order Lugiato-Lefever equation

We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optical cavity. It is mathematically demonstrated that the solutions of these equations follow the Talbot effect, which is a phenomenon of periodic self-imaging of an object under certain conditions of diffraction. The Talbot effect is regarded as the underlying cause of pattern formation in optical cavities.Comment: 20 page

Quantum revivals and fractality for the Schr\"odinger equation

We investigate the behavior of the Schr\"odinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov \cite{O} and Rodnianski \cite{R2} on the free Schr\"odinger evolution to the general case regarding potentials.Comment: 14page

The political culture of university students in South Korea : a comparison of before the democratic transition and today

This thesis compares the political culture of university students in South Korea before and after the democratic transition in 1987. It identifies the changes in the following: the attitudes to politics, government and media; the political socialization process; the experience of political participation; and the reasons for political participation and non-participation. Qualitative analysis was used to analyse the data collected from interviews and surveys conducted on respondents who were university students in the 1980s and current university students. It was found that compared to university students in the 1980s, current university students held less intensely negative attitudes towards the government. However, although current university students were interested in politics, they were still distrustful of politicians, did not have a political party they supported and had low levels of perceived political efficacy and political participation. Based on these findings, this thesis examined three different types of theories to explain the changes in the political culture of university students. First, demand-side theories that focus on underlying socioeconomic changes to explain changes in the political culture were used to analyse the changes in the reasons for political participation and the changes in the political socialization process. Second, intermediary-side theories that emphasise the role of media were used to examine the changes in the attitudes towards the media and the experience of latent political participation. Finally, supply-side theories that focus on the supply of politics and governance were used to explain the changes in the other elements of political culture. Close examination into the workings of democracy in South Korea since the democratic transition in 1987 revealed that there were indications of cartelisation of the political party system, which explains the low levels of political trust and perceived political efficacy reported by current university students

Assessing the ecosystem services of various types of urban green spaces based on i-Tree eco

Urban green spaces play a crucial role in maintaining urban ecosystem sustainability by providing numerous ecosystem services. How to quantify and evaluate the ecological benefits and services of urban green spaces remains a hot topic currently, while the evaluation is barely applied or implemented in urban design and planning. In this study, super-high-resolution aerial images were used to acquire the spatial distribution of urban green spaces; a modified pre-stratified random sampling method was applied to obtain the vegetation information of the four types of urban green spaces in Luohe, a common plain city in China; and i-Tree Eco model was further used to assess the vegetation structure and various ecosystem services including air quality improvement, rainfall interception, carbon storage, and sequestration provided by four types of urban green spaces. The modeling results reveal that there were about 1,006,251 trees in this area. In 2013, all the trees in these green spaces could store about 54,329 t of carbon, sequester about 4973 t of gross carbon, remove 92 t of air pollutants, and avoid 122,637 m3 of runoff. The study illustrates an innovative method to reveal different types of urban green spaces with distinct ecosystem service productivity capacity to better understand their various roles in regulating the urban environment. The results could be used to assist urban planners and policymakers to optimize urban green space structure and composition to maximize ecosystem services provision

Characterization of the dynamics in the protonic conductor CsH₂PO₄ by ¹⁷O solid-state NMR spectroscopy and first-principles calculations: correlating phosphate and protonic motion.

(17)O NMR spectroscopy combined with first-principles calculations was employed to understand the local structure and dynamics of the phosphate ions and protons in the paraelectric phase of the proton conductor CsH2PO4. For the room-temperature structure, the results confirm that one proton (H1) is localized in an asymmetric H-bond (between O1 donor and O2 acceptor oxygen atoms), whereas the H2 proton undergoes rapid exchange between two sites in a hydrogen bond with a symmetric double potential well at a rate ≥10(7) Hz. Variable-temperature (17)O NMR spectra recorded from 22 to 214 °C were interpreted by considering different models for the rotation of the phosphate anions. At least two distinct rate constants for rotations about four pseudo C3 axes of the phosphate ion were required in order to achieve good agreement with the experimental data. An activation energy of 0.21 ± 0.06 eV was observed for rotation about the P-O1 axis, with a higher activation energy of 0.50 ± 0.07 eV being obtained for rotation about the P-O2, P-O3(d), and P-O3(a) axes, with the superscripts denoting, respectively, dynamic donor and acceptor oxygen atoms of the H-bond. The higher activation energy of the second process is most likely associated with the cost of breaking an O1-H1 bond. The activation energy of this process is slightly lower than that obtained from the (1)H exchange process (0.70 ± 0.07 eV) (Kim, G.; Blanc, F.; Hu, Y.-Y.; Grey, C. P. J. Phys. Chem. C 2013, 117, 6504-6515) associated with the translational motion of the protons. The relationship between proton jumps and phosphate rotation was analyzed in detail by considering uncorrelated motion, motion of individual PO4 ions and the four connected/H-bonded protons, and concerted motions of adjacent phosphate units, mediated by proton hops. We conclude that, while phosphate rotations aid proton motion, not all phosphate rotations result in proton jumps.C.P.G. and G.K. thank the European Research Council for an Advanced Fellowship. F.B. thanks the EU Marie Curie actions FP7 for an International Incoming fellowship (grant no 275212) for financial support. J.M.G. also thanks the European Research Council for funding. G.K. thanks Dr. Song-Yul Oh (Toyota Central R&D Labs. Inc., Japan) for valuable discussion about the synthesis of 17O-enriched CDP. This work made use of the facilities of HECToR, the UK's national high-performance computing service, which is provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc and NAG Ltd, and funded by the Office of Science and Technology through EPSRC's High End Computing Programme. The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC, as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).This is the final version of the article. It first appeared from ACS via http://dx.doi.org/10.1021/jacs.5b0028

Internal generation of waves: Delta source function method and source term addition method

author's final versionIn this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases

Extended Boussinesq Equations for Rapidly Varying Topography

author's final versionWe developed a new Boussinesq-type model which extends the equations of Madsen and Sørensen (1992) by including both bottom curvature and squared bottom slope terms. Numerical experiments were conducted for wave reflection from the Booijs (1983) planar slope with different wave frequencies using several types of Boussinesq equations and extended mild-slope equation. Madsen and Sørensens model results are accurate in the whole slopes in shallow waters but inaccurate in intermediate water depths. Nwogus (1993) model results are accurate up to 1:1 (V:H) slope but significantly inaccurate for steep slopes. The present model results are accurate up to the slope of 1:1 but somewhat inaccurate for very steep slopes. Further, numerical experiments were conducted for wave reflections from a ripple patch and also a Gaussian shaped trench. For the two cases, the results of Nwogus model and the present model are accurate because these models include the bottom curvature term which is important for the cases. However, Madsen and Sørensens model results are inaccurate because this model neglects the bottom curvature term

Extended mild-slope equation for random waves

author's final versionA time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter (1995) using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography