L2L^2 Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations

The multiconfiguration methods are widely used by quantum physicists and chemists for numerical approximation of the many electron Schr\"odinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time well-posedness in the Sobolev space $H^2$ for bounded interactions (C. Lubichand O. Koch} with initial data in $H^2$, in the energy space for Coulomb interactions with initial data in the same space (Trabelsi, Bardos et al.}, as well as global well-posedness under a sufficient condition on the energy of the initial data (Bardos et al.). The present contribution extends the analysis by setting an $L^2$ theory for the MCTDHF for general interactions including the Coulomb case. This kind of results is also the theoretical foundation of ad-hoc methods used in numerical calculation when modification ("regularization") of the density matrix destroys the conservation of energy property, but keeps invariant the mass.Comment: This work was supported by the Viennese Science Foundation (WWTF) via the project "TDDFT" (MA-45), the Austrian Science Foundation (FWF) via the Wissenschaftkolleg "Differential equations" (W17) and the START Project (Y-137-TEC) and the EU funded Marie Curie Early Stage Training Site DEASE (MEST-CT-2005-021122

Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations

We study a modified three-dimensional incompressible anisotropic Navier-Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy-Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier-Stokes equations.Comment: To appear in ESAIM: Mathematical Modelling and Numerical Analysi

Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model

In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtaining improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the setting and convergence analysis of the data assimilation algorithm

Global Well-Posedness of a 3D MHD Model in Porous Media

In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimer-extended-Darcy" law of flow in porous media

Analysis of the MultiConfiguration time-dependent Hartree-Fock equations

Die Multiconfigurationsmethoden sind eine natürliche Verbesserung der wohlbekannten einfachen Näherungen der linearen N-Teilchen Schrödinger Gleichung für Atom- und Molekül-systeme mit binärer Wechselwirkung, die realistischerweise mit dem Coulomb Potential modelliert wird. Modelle wie MCTDHF werden intensiv verwendet für numerische Simulationen in der Quantenphysik/ chemie. Die vorliegende Arbeit legt die ersten mathematisch rigorosen Fundamente der MCTDH(F) Gleichungen mit singulärer Coulomb-Wechselwirkung. Wir formulieren in einer für die mathematische Analysis besonders geeigneten Weise das assoziierte Anfangswertproblem, für das wirWohlgestelltheitsresultate zeigen abhängig von der Regularität der Anfangsdaten, mit und ohne Annahmen über den Rang der assoziierten Dichtematrix. Weiters präsentieren wir numerische Simulationen eines vereinfachten Models, mit besonderem Interesse an der so genannten Korrelation, welche eine der wesentlichen Motivationen und Vorteile der Multikonfigurationsmethoden ist im Vergleich zu Hartree-Fock Modellen.The multiconfiguration methods are a natural improvement of well-known simple models for approximating the linear N body Schrödinger equation for atomic and molecular systems with binary - Coulomb in realistic situations- interactions, like the Hartree and the Hartree-Fock equation. Models like MCTDHF are intensively used for numerical simulations in quantum physics/chemistry. However, from the mathematical point of view, these equations are yet poorly understood. The present contribution gives the first rigorous mathematical foundation of the MCTHDH(F) equations with the singular Coulomb interaction. In particular, we formulate in a convenient way for the mathematical analysis the associated initial value problem for which we obtain well-posedness results depending on the regularity of the initial data, with and without an assumption on the rank of the associated density matrix. Also, numerical simulations of a toy model are presented with particular interest to the so called correlation which is one of the main motivations and advantage of the multiconfiguration methods compared to Hartree-Fock models

Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree–Fock equations: A sufficient condition

AbstractThe multiconfiguration time-dependent Hartree–Fock (MCTDHF for short) system is an approximation of the linear many-particle Schrödinger equation with a binary interaction potential by nonlinear “one-particle” equations. MCTDHF methods are widely used for numerical calculations of the dynamics of few-electron systems in quantum physics and quantum chemistry, but the time-dependent case still poses serious open problems for the analysis, e.g. in the sense that global-in-time existence of solutions is not proved yet. In this letter we present the first result ever where global existence is proved under a condition on the initial datum that it has to be somewhat close to the “ground state”

A New Stability Criterion for IoT Systems in Smart Buildings: Temperature Case Study

The concept of smart cities emerged in the 1990s. Since then, smart buildings have become a closely interconnected element of smart cities. This type of building implements Internet of Things technology and control algorithms to monitor and control their indoor environment. The aim of this paper is to develop a new stability criterion method for smart building Internet of Things (IoT) systems, subject to external disturbances. The new stability criterion is going to optimize the operation of control algorithms since this criterion does not depend on the transmission function of the control algorithm but on the data collected by the IoT system. We present a new matrix called “Laplacian IoT matrix”, containing IoT network information associated with the graph of a smart building. The proposal is supported by the results of a numerical case study.This work was developed as part of “Virtual-Ledgers-Tecnologías DLT/Blockchain y Cripto-IOT sobre organizaciones virtuales de agentes ligeros y su aplicación en la eficiencia en el transporte de última milla”, ID SA267P18, project cofinanced by Junta Castilla y León, Consejería de Educación, and FEDER funds

A Hybrid System For Pandemic Evolution Prediction

The areas of data science and data engineering have experienced strong advances in recent years. This has had a particular impact in areas such as healthcare, where, as a result of the pandemic caused by the COVID-19 virus, technological development has accelerated. This has led to a need to produce solutions that enable the collection, integration and efficient use of information for decision making scenarios. This is evidenced by the proliferation of monitoring, data collection, analysis, and prediction systems aimed at controlling the pandemic. This article proposes a hybrid model that combines the dynamics of epidemiological processes with the predictive capabilities of artificial neural networks to go beyond the prediction of the first ones. In addition, the system allows for the introduction of additional information through an expert system, thus allowing the incorporation of additional hypotheses on the adoption of containment measures./n/n/n/n/n/

Religious fasting and its impacts on individual, public, and planetary health: Fasting as a “religious health asset” for a healthier, more equitable, and sustainable society

Religious fasting is practiced by people of all faiths, including Christianity, Islam, Buddhism, Jainism, as well as Hinduism, Judaism, and Taoism. Individual/clinical, public, global, and planetary health has traditionally been studied as separate entities. Nevertheless, religious fasting, in conjunction with other religious health assets, can provide several opportunities, ranging from the individual to the population, environmental, and planetary levels, by facilitating and supporting societal transformations and changes, such as the adoption of healthier, more equitable, and sustainable lifestyles, therein preserving the Earth's systems and addressing major interconnected, cascading, and compound challenges. In this review, we will summarize the most recent evidence on the effects of religious fasting, particularly Orthodox and Ramadan Islamic fasting, on human and public health. Further, we will explore the potential effects of religious fasting on tackling current environmental issues, with a special focus on nutrition/food restriction and planetary health. Finally, specific recommendations, particularly around dietary intake during the fasting rituals, will be provided to ensure a sustainable healthy planet