71 research outputs found
Second-order corrections to mean field evolution of weakly interacting Bosons. II
No full textAbstractWe study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state
First Mediterranean Assessment Report – Chapter 5.3: Society – Human security
No full textChapter 5.3 "Society: Human Security" of the First Mediterranean Assessment Report (MAR1) published by MedECC in November 2020. The impact of climate change on human security depends not only on climate events but also on country’s contextual factors, such as geographical, social, cultural, economic, and political conditions, resulting in a substantial heterogeneous effect among Mediterranean countries.Koubi V, Behnassi M, Elia A, Grillakis M, Turhan E 2020 Human security. In: Climate and Environmental Change in the Mediterranean Basin – Current Situation and Risks for the Future. First Mediterranean Assessment Report [Cramer W, Guiot J, Marini K (eds.)] Union for the Mediterranean, Plan Bleu, UNEP/MAP, Marseille, France, pp. 515-538, doi:10.5281/zenodo.7216161
APPLICATION OF DISPERSIVE PDE TECHNIQUES TO THE STUDIES OF THE TIME-DEPENDENT HARTREE-FOCK-BOGOLIUBOV SYSTEM FOR BOSONS
No full textThe thesis provides rigorous quantitative analyses for studying quantum fluctuations of a
non-relativistic Bose gas about a Bose-Einstein condensate. In recent years, the dynamics of the condensate and the excitations of a Bose gas was shown to be well approximated by the quasifree dynamics with governing equations given by a system of coupled nonlinear dispersive PDEs called the time-dependent Hartree-Fock-Bogoliubov (HFB) system (c.f. Grillakis and Machedon, J. Fix. Point Theory A., (2013), Grillakis and Machedon, Comm. PDEs, (2017), Bach et al. in arXiv:1602.05171v2, (2018), Benedikter et al., Ann. Henri Poincare, (2018)). However, both the quantitative and qualitative analysis of the time-dependent HFB system are still in their early stages of development. Thus, the primary purposes of the thesis are to further the development of some analytic tools necessary for studying the time-dependent HFB system and use these effective equations to provide quantitative estimates for the true dynamics of the Bose gas at absolute zero temperature in Fock space norm.
The thesis comprises the entirety of the author's current and past projects on the time-dependent HFB system. Each project falls into one or more of two categories: studying the local or global well-posedness of the time-dependent HFB system, or obtaining global-in-time Fock space estimates for the error terms of the quasifree approximation to the dynamics of a system of interacting bosons. In the former category, the author employs techniques of dispersive PDE theory developed in the past three decades along with classical methods of harmonic analysis to study lower regularity solutions to the time-dependent HFB system. The lower regularity well-posedness of solutions for the time-dependent HFB system is necessary for studying norm approximation of the dynamics of a dilute Bose gas with strong interactions. In the latter category, we prove global a-priori estimates for the solutions to the HFB system and use them to obtain estimates for the error terms of the Fock space approximation
Assessment of water-induced soil erosion as a threat to cultural heritage sites: the case of Chania prefecture, Crete Island, Greece
No full textAmong the environmental threats, the intensification of natural hazards, such as soil erosion may threaten the integrity and value of cultural heritage sites. In this framework, the present study’s main objective was to identify archaeological sites susceptible by soil erosion, taking the case study of Chania prefecture in Crete Island. Remotely sensed and other available geospatial datasets were analyzed in a GIS-based empirical model, namely Unit Stream Power Erosion and Deposition (USPED), to estimate the average annual soil loss and deposition rates due to water-induced erosion in the study area. The resultant erosion map was then intersected with the locations and surrounding zones of the known archaeological sites for identifying the sites and the portions of their vicinity being at risk. The results revealed that Chania prefecture and its cultural heritage are significantly affected by both soil loss and deposition processes. Between the two processes, soil loss was found to be more intensive, influencing a larger part of the prefecture (especially to the west) as well as a higher amount of archaeological sites. The extreme and high soil loss classes were also detected to cover the most considerable portion of the sites’ surrounding area. The identification of the archaeological sites being most exposed to soil erosion hazard can constitute a basis for cultural heritage managers in order to take preventive preservation measures and develop specific risk mitigation strategies
First Mediterranean Assessment Report – Chapter 5.1: Society – Development
No full textChapter 5.1: Society – Development of the First Mediterranean Assessment Report (MAR1) published by MedECC in November 2020. Sustainable development seeks to address the needs of current and future generations with the objective of increasing well-being by balancing economic, social and environmental dimensions. Current unsustainable development patterns, such as poverty, increasing population pressure, agricultural intensification, land degradation, and air, land, rivers and ocean pollution, will be further exacerbated by climate change impacts. Environmental and climate change impacts are likely to have an effect on all economic sectors in the Mediterranean Basin, increasing production challenges and costs, affecting low-income cohorts increasingly disproportionally, and generally delaying the achievement of the Sustainable Development Goals (SDGs).Preferred citation: Dos Santos M, Moncada S, Elia A, Grillakis M, Hilmi N 2020: Development. In: Climate and Environmental Change in the Mediterranean Basin – Current Situation and Risks for the Future. First Mediterranean Assessment Report [Cramer W, Guiot J, Marini K (eds.)] Union for the Mediterranean, Plan Bleu, UNEP/MAP, Marseille, France, pp. 469-492, doi:10.5281/zenodo.710111
A note on the stability and instability of travelling wave of Korteweg-de Vries type : the periodic case.
No full textIn this paper we adapt the work of M. Grillakis, J. Shatah, and W. Strauss, or J. Bona, P.
Souganidis and W. Strauss to the periodic case in spaces having the mean zero property in order
to establish the orbital stability/instability of periodic travelling wave solutions of a generalized
Korteweg-de Vries type equatio
Pair excitations and the mean field approximation of interacting Bosons
No full textAbstract. In our previous wor
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