Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.

Information and the evolution of codon bias

The informational properties of biological systems are the subject of much debate and research. I present a general argument in favor of the existence and central importance of information in organisms, followed by a case study of the genetic code (specifically, codon bias) and the translation system from the perspective of information. The codon biases of 831 Bacteria and Archeae are analyzed and modeled as points in a 64-dimensional statistical space. The major results are that (1) codon bias evolution does not follow canonical patterns, and (2) the use of coding space in organsims is a subset of the total possible coding space. These findings imply that codon bias is a unique adaptive mechanism that owes its existence to organisms' use of information in representing genes, and that there is a particularly biological character to the resulting biased coding and information use.

Geological Evolution of Coastal and Marine Environments off the Campania Continental Shelf Through Marine Geological Mapping - The Example of the Cilento Promontory

The geological evolution of coastal and marine environments offshore the Cilento Promontory through marine geological mapping is discussed here. The marine geological map n. 502 “Agropoli,” located offshore the Cilento Promontory (southern Italy), is described and put in regional geologic setting. The study area covers water depths ranging between 30 and 200 m isobaths. The geologic map has been constructed in the frame of a research program financed by the National Geological Survey of Italy (CARG Project), finalized to the construction of an up-to-date cartography of the Campania region. Geological and geophysical data on the continental shelf and slope offshore the southern Campania region have been acquired in an area bounded northward by the Gulf of Salerno and southward by the Gulf of Policastro. A high-resolution multibeam bathymetry has permitted the construction of a digital elevation model (DEM). Sidescan sonar profiles have also been collected and interpreted, and their merging with bathymetric data has allowed for the realization of the base for the marine geologic cartography. The calibration of geophysical data has been attempted through sea-bottom samples. The morpho-structures and the seismic sequences overlying the outcrops of acoustic basement reported in the cartographic representation have been studied in detail using single-channel seismics. The interpretation of seismic profiles has been a support for the reconstruction of the stratigraphic and structural setting of the Quaternary continental shelf successions and the outcrops of rocky acoustic basement in correspondence to the Licosa Cape morphostructural high. These areas result from the seaward prolongation of the stratigraphic and structural units, widely cropping out in the surrounding emerged sector of the Cilento Promontory. The cartographic approach is based on the recognition of laterally coeval depositional systems, interpreted in the frame of system tracts of the Late Quaternary depositional sequence.

Close-in planets around giant stars: lack of hot-Jupiters and prevalence of multiplanetary systems

Extrasolar planets abound in almost any possible configuration. However, until five years ago, there was a lack of planets orbiting closer than 0.5 au to giant or subgiant stars. Since then, recent detections have started to populated this regime by confirming 13 planetary systems. We discuss the properties of these systems in terms of their formation and evolution off the main sequence. Interestingly, we find that 70.0 ± 6.6% of the planets in this regime are inner components of multiplanetary systems. This value is 4.2σ higher than for main-sequence hosts, which we find to be 42.4 ± 0.1%. The properties of the known planets seem to indicate that the closest-in planets (a< 0.06 au) to main-sequence stars are massive (i.e., hot Jupiters) and isolated and that they are subsequently engulfed by their host as it evolves to the red giant branch, leaving only the predominant population of multiplanetary systems in orbits 0.06 evolution of hot Jupiters.

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

A Performance Measurement System to Manage CEN Operations, Evolution and Innovation

Part 16: Performance Measurement Systems

SOVLENT REACTIVITY AND INTERFACE EVOLUTION AT MODEL ELECTRODES FOR ENERGY APPLICATIONS

The Li-ion rechargeable battery (LIB) is widely used as an energy storage device, but has significant limitations in battery cycle life and safety. During initial charging, decomposition of the ethylene carbonate (EC)-based electrolytes of the LIB leads to the formation of a passivating layer on the anode known as the solid electrolyte interphase (SEI). The formation of an SEI has great impact on the cycle life and safety of LIB, yet mechanistic aspects of SEI formation are not fully understood. In this dissertation, two surface science model systems have been created under ultra-high vacuum (UHV) to probe the very initial stage of SEI formation at the model carbon anode surfaces of LIB. The first model system, Model System I, is an lithium-carbonate electrolyte/graphite C(0001) system. I have developed a temperature programmed desorption/temperature programmed reaction spectroscopy (TPD/TPRS) instrument as part of my dissertation to study Model System I in quantitative detail. The binding strengths and film growth mechanisms of key electrolyte molecules on model carbon anode surfaces with varying extents of lithiation were measured by TPD. TPRS was further used to track the gases evolved from different reduction products in the early-stage SEI formation. The branching ratio of multiple reaction pathways was quantified for the first time and determined to be 70.% organolithium products vs. 30% inorganic lithium product. The obtained branching ratio provides important information on the distribution of lithium salts that form at the very onset of SEI formation. One of the key reduction products formed from EC in early-stage SEI formation is lithium ethylene dicarbonate (LEDC). Despite intensive studies, the LEDC structure in either the bulk or thin-film (SEI) form is unknown. To enable structural study, pure LEDC was synthesized and subject to synchrotron X-ray diffraction measurements (bulk material) and STM measurements (deposited films). To enable studies of LEDC thin films, Model System II, a lithium ethylene dicarbonate (LEDC)-dimethylformamide (DMF)/Ag(111) system was created by a solution microaerosol deposition technique. Produced films were then imaged by ultra-high vacuum scanning tunneling microscopy (UHV-STM). As a control, the dimethylformamide (DMF)-Ag(111) system was first prepared and its complex 2D phase behavior was mapped out as a function of coverage. The evolution of three distinct monolayer phases of DMF was observed with increasing surface pressure — a 2D gas phase, an ordered DMF phase, and an ordered Ag(DMF)2 complex phase. The addition of LEDC to this mixture, seeded the nucleation of the ordered DMF islands at lower surface pressures (DMF coverages), and was interpreted through nucleation theory. A structural model of the nucleation seed was proposed, and the implication of ionic SEI products, such as LEDC, in early-stage SEI formation was discussed.

Experimentation of Rational Trust Evolution and Sustainability in Dynamic VOs

Part 10: Sustainability and Trust

Artificial immune systems

The human immune system has numerous properties that make it ripe for exploitation in the computational domain, such as robustness and fault tolerance, and many different algorithms, collectively termed Artificial Immune Systems (AIS), have been inspired by it. Two generations of AIS are currently in use, with the first generation relying on simplified immune models and the second generation utilising interdisciplinary collaboration to develop a deeper understanding of the immune system and hence produce more complex models. Both generations of algorithms have been successfully applied to a variety of problems, including anomaly detection, pattern recognition, optimisation and robotics. In this chapter an overview of AIS is presented, its evolution is discussed, and it is shown that the diversification of the field is linked to the diversity of the immune system itself, leading to a number of algorithms as opposed to one archetypal system. Two case studies are also presented to help provide insight into the mechanisms of AIS; these are the idiotypic network approach and the Dendritic Cell Algorithm.

Pressure management in water distribution systems: current status, proposals, and future trends

Pressure management (PM) is commonly used in water distribution systems (WDSs). In the last decade, a strategic objective in the field has been the development of new scientific and technical methods for its implementation. However, due to a lack of systematic analysis of the results obtained in practical cases, progress has not always been reflected in practical actions. To address this problem, this paper provides a comprehensive analysis of the most innovative issues related to PM. The methodology proposed is based on a case-study comparison of qualitative concepts that involves published work from 140 sources. The results include a qualitative analysis covering four aspects: (1) the objectives yielded by PM; (2) types of regulation, including advanced control systems through electronic controllers; (3) new methods for designing districts; and (4) development of optimization models associated with PM. The evolution of the aforementioned four aspects is examined and discussed. Conclusions regarding the current status of each factor are drawn and proposals for future research outlined

El Estribo Volcanic Complex: Evolution from a shield volcano to a cinder cone, Pátzcuaro Lake, Michoacán, México

El Estribo Volcanic Complex (EVC) is located in the northern part of the Michoacán–Guanajuato Volcanic Field within the Trans-Mexican Volcanic Belt (TMVB). El Estribo is located at the southern edge of the E-W Pátzcuaro fault that belongs to the Pátzcuaro-Jarácuaro graben, a western extension of the E-W Morelia–Acambay fault system. Stratigraphy, geochronology, chemistry, and mineral assemblages suggest that the volcanic complex was constructed in two periods separated by a ~ 100 ka volcanic hiatus: a) emission of lava flows that constructed a shield volcano between 126 ka, and b) mixed phreatomagmatic to Strombolian activity that formed a cinder cone ~ 28 ka. The magmas that fed these monogenetic volcanoes were able to use the same feeding system. The cinder cone itself was constructed by Strombolian fallouts and remobilized scoria beds, followed by an erosion period, and by a mixed phreatomagmatic to magmatic phase (Strombolian fallouts ending with lava flows). Soft-sedimentary deformation of beds and impact sags, cross-bedding, as well as pitting and hydrothermal cracks found in particles support the phreatomagmatic phase. The erupted magmas through time ejected basaltic andesitic lava flows (56.21–58.88% SiO2) that built the shield volcano and then basaltic andesitic scoria (57.65–59.05% SiO2) that constructed the cinder cone. Although they used the same feeding system, the geochemical data and the mineral chemistry of the magmas indicate that the shield volcano and the cinder cone were fed by different magma batches erupted thousands of years apart. Therefore, the location of El Estribo Volcanic Complex along an E-W fault that has generated two sector collapses of the shield volcano to the north may be directly linked to this complex redistribution of the magmatic paths to the surface. Our findings show that magmatic feeding systems within monogenetic volcanic fields could be long lived, questioning the classic view of the monogenetic nature of their volcanoes and yielding information about the potential volcanic risk of these settings, usually considered risk-free.

An updated evolutionary classification of CRISPR–Cas systems

The evolution of CRISPR–cas loci, which encode adaptive immune systems in archaea and bacteria, involves rapid changes, in particular numerous rearrangements of the locus architecture and horizontal transfer of complete loci or individual modules. These dynamics complicate straightforward phylogenetic classification, but here we present an approach combining the analysis of signature protein families and features of the architecture of cas loci that unambiguously partitions most CRISPR–cas loci into distinct classes, types and subtypes. The new classification retains the overall structure of the previous version but is expanded to now encompass two classes, five types and 16 subtypes. The relative stability of the classification suggests that the most prevalent variants of CRISPR–Cas systems are already known. However, the existence of rare, currently unclassifiable variants implies that additional types and subtypes remain to be characterized.

DIFFUSE-INTERFACE FIELD APPROACH TO MODELING SELF-ASSEMBLY OF HETEROGENEOUS COLLOIDAL SYSTEMS AND RELATED DIPOLE-DIPOLE INTERACTION PHENOMENA

Colloid self-assembly under external control is a new route to fabrication of advanced materials with novel microstructures and appealing functionalities. The kinetic processes of colloidal self-assembly have attracted great interests also because they are similar to many atomic level kinetic processes of materials. In the past decades, rapid technological progresses have been achieved on producing shape-anisotropic, patchy, core-shell structured particles and particles with electric/magnetic charges/dipoles, which greatly enriched the self-assembled structures. Multi-phase carrier liquids offer new route to controlling colloidal self-assembly. Therefore, heterogeneity is the essential characteristics of colloid system, while so far there still lacks a model that is able to efficiently incorporate these possible heterogeneities. This thesis is mainly devoted to development of a model and computational study on the complex colloid system through a diffuse-interface field approach (DIFA), recently developed by Wang et al. This meso-scale model is able to describe arbitrary particle shape and arbitrary charge/dipole distribution on the surface or body of particles. Within the framework of DIFA, a Gibbs-Duhem-type formula is introduced to treat Laplace pressure in multi-liquid-phase colloidal system and it obeys Young-Laplace equation. The model is thus capable to quantitatively study important capillarity related phenomena. Extensive computer simulations are performed to study the fundamental behavior of heterogeneous colloidal system. The role of Laplace pressure is revealed in determining the mechanical equilibrium of shape-anisotropic particles at fluid interfaces. In particular, it is found that the Laplace pressure plays a critical role in maintaining the stability of capillary bridges between close particles, which sheds light on a novel route to in situ firming compact but fragile colloidal microstructures via capillary bridges. Simulation results also show that competition between like-charge repulsion, dipole-dipole interaction and Brownian motion dictates the degree of aggregation of heterogeneously charged particles. Assembly and alignment of particles with magnetic dipoles under external field is studied. Finally, extended studies on the role of dipole-dipole interaction are performed for ferromagnetic and ferroelectric domain phenomena. The results reveal that the internal field generated by dipoles competes with external field to determine the dipole-domain evolution in ferroic materials.

A Transcriptome Atlas of Physcomitrella patens Provides Insights into the Evolution and Development of Land Plants

Post-print version of the article.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.