8,285 research outputs found
Opening the system to the environment: new theories and tools in classical and quantum settings
The thesis is organized as follows. Section 2 is a first, unconventional, approach to the topic of EPs. Having grown interest in the topic of combinatorics and graph theory, I wanted to exploit its very abstract and mathematical tools to reinterpret something very physical, that is, the EPs in wave scattering. To do this, I build the interpretation of scattering events from a graph theory perspective and show how EPs can be understood within this interpretation. In Section 3, I move from a completely classical treatment to a purely quantum one. In this section, I consider two quantum resonators coupled to two baths and study their dynamics with local and global master equations. Here, the EPs are the key physical features used as a witness of validity of the master equation. Choosing the wrong master equation in the regime of interest can indeed mask physical and fundamental features of the system. In Section 4, there are no EPs. However I transition towards a classical/quantum framework via the topic of open systems. My main contribution in this work is the classical stochastic treatment and simulation of a spin coupled to a bath. In this work, I show how a natural quantum--to--classical transition occurs at all coupling strengths when certain limits of spin length are taken. As a key result, I also show how the coupling to the environment in this stochastic framework induces a classical counterpart to quantum coherences in equilibrium. After this last topic, in Section 5, I briefly present the key features of the code I built (and later extended) for the latter project. This, in the form of a Julia registry package named SpiDy.jl, has seen further applications in branching projects and allows for further exploration of the theoretical framework. Finally, I conclude with a discussion section (see Sec. 5) where I recap the different conclusions gathered in the previous sections and propose several possible directions.Engineering and Physical Sciences Research Council (EPSRC
The infrared structure of perturbative gauge theories
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders. © 2022 Elsevier B.V
Activating Methane and Other Small Molecules: Computational study of Zeolites and Actinides
Exploring the catalytic properties and reactivity of actinide complexes towards activation of small molecules is important as human activities have led to the increased distribution of these species in nature. Toward this end, it is important to have a computational protocol for studying these species, in this thesis we provide details on the performance of multiconfigurational pair-density functional theory (MC-PDFT) in actinide chemistry. MC-PDFT and Kohn-Sham Density Functional Theory (KS-DFT) perform well for these species with indications that the former can be used for species with even greater static electron correlation effect. In addition, we study the activity of organometallic trans-uranium complexes towards the electrocatalytic reduction of water. We conclude that, with a guided choice of ligand, neptunium complexes can provide similar reactivity when compared to organometallic uranium complexes.Conversion of methane to methanol has been a major focus of research interest over the years. This is largely due to the abundance of natural gas, of which methane is the major constituent. Copper-exchanged zeolites have been shown to be able to kinetically trap activated methane as strongly-bound methoxy groups, preventing over-oxidation to CO2, CO and HCOOH. In this stepwise process, there are three cycles; an initial activation step to form the copper oxo active site, methane C-H activation and lastly simultaneous desorption of methanol and re -activation of the active site.. We provide detailed description of the pathway for the formation of over oxidation products. It is observed that to ensure high selectivity to methanol and prevent further hydrogen atom abstraction by extra-framework species, the methyl group must be stabilized from the copper-oxo active sites. There is a temperature gradient between the steps in the methane-to-methanol conversion cycle which is an impediment to industrial adoption of this approach for methane-to-methanol conversion. To mitigate this, we have investigated the impact of heterometallic extra-framework motifs on the temperature gradients of each step. Using periodic DFT, we provide detailed descriptions of the mechanistic pathways for each of the three steps. We were subsequently able to design motif(s) with great methane C-H activities as well as the abilities to be formed and regenerated at nearly the same temperatures. We found [Cu-O-Ag] and [Cu-O-Pd] to be potential candidates for isothermal or near-isothermal operations of the methane-to-methanol conversion cycle.
Finally, we provide insights to the changes in optical spectra of activated copper-exchanged zeolites, gaining an understanding of the evolution of these systems on a molecular level will provide opportunities to achieve improved reactivity
Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model
Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Satellite remote sensing of surface winds, waves, and currents: Where are we now?
This review paper reports on the state-of-the-art concerning observations of surface winds, waves, and currents from space and their use for scientific research and subsequent applications. The development of observations of sea state parameters from space dates back to the 1970s, with a significant increase in the number and diversity of space missions since the 1990s. Sensors used to monitor the sea-state parameters from space are mainly based on microwave techniques. They are either specifically designed to monitor surface parameters or are used for their abilities to provide opportunistic measurements complementary to their primary purpose. The principles on which is based on the estimation of the sea surface parameters are first described, including the performance and limitations of each method. Numerous examples and references on the use of these observations for scientific and operational applications are then given. The richness and diversity of these applications are linked to the importance of knowledge of the sea state in many fields. Firstly, surface wind, waves, and currents are significant factors influencing exchanges at the air/sea interface, impacting oceanic and atmospheric boundary layers, contributing to sea level rise at the coasts, and interacting with the sea-ice formation or destruction in the polar zones. Secondly, ocean surface currents combined with wind- and wave- induced drift contribute to the transport of heat, salt, and pollutants. Waves and surface currents also impact sediment transport and erosion in coastal areas. For operational applications, observations of surface parameters are necessary on the one hand to constrain the numerical solutions of predictive models (numerical wave, oceanic, or atmospheric models), and on the other hand to validate their results. In turn, these predictive models are used to guarantee safe, efficient, and successful offshore operations, including the commercial shipping and energy sector, as well as tourism and coastal activities. Long-time series of global sea-state observations are also becoming increasingly important to analyze the impact of climate change on our environment. All these aspects are recalled in the article, relating to both historical and contemporary activities in these fields
Variational quantum eigensolver for causal loop Feynman diagrams and acyclic directed graphs
We present a variational quantum eigensolver (VQE) algorithm for the
efficient bootstrapping of the causal representation of multiloop Feynman
diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of
acyclic configurations in directed graphs. A loop Hamiltonian based on the
adjacency matrix describing a multiloop topology, and whose different energy
levels correspond to the number of cycles, is minimized by VQE to identify the
causal or acyclic configurations. The algorithm has been adapted to select
multiple degenerated minima and thus achieves higher detection rates. A
performance comparison with a Grover's based algorithm is discussed in detail.
The VQE approach requires, in general, fewer qubits and shorter circuits for
its implementation, albeit with lesser success rates.Comment: 32 pages, 7 figures. Improved discussion and success rates of
multi-run VQ
Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures
In this work we present a non-parametric online market regime detection
method for multidimensional data structures using a path-wise two-sample test
derived from a maximum mean discrepancy-based similarity metric on path space
that uses rough path signatures as a feature map. The latter similarity metric
has been developed and applied as a discriminator in recent generative models
for small data environments, and has been optimised here to the setting where
the size of new incoming data is particularly small, for faster reactivity.
On the same principles, we also present a path-wise method for regime
clustering which extends our previous work. The presented regime clustering
techniques were designed as ex-ante market analysis tools that can identify
periods of approximatively similar market activity, but the new results also
apply to path-wise, high dimensional-, and to non-Markovian settings as well as
to data structures that exhibit autocorrelation.
We demonstrate our clustering tools on easily verifiable synthetic datasets
of increasing complexity, and also show how the outlined regime detection
techniques can be used as fast on-line automatic regime change detectors or as
outlier detection tools, including a fully automated pipeline. Finally, we
apply the fine-tuned algorithms to real-world historical data including
high-dimensional baskets of equities and the recent price evolution of crypto
assets, and we show that our methodology swiftly and accurately indicated
historical periods of market turmoil.Comment: 65 pages, 52 figure
GNN-Assisted Phase Space Integration with Application to Atomistics
Overcoming the time scale limitations of atomistics can be achieved by
switching from the state-space representation of Molecular Dynamics (MD) to a
statistical-mechanics-based representation in phase space, where approximations
such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic
ensemble in a time-coarsened fashion. In practice, this requires the
computation of expensive high-dimensional integrals over all of phase space of
an atomistic ensemble. This, in turn, is commonly accomplished efficiently by
low-order numerical quadrature. We show that numerical quadrature in this
context, unfortunately, comes with a set of inherent problems, which corrupt
the accuracy of simulations -- especially when dealing with crystal lattices
with imperfections. As a remedy, we demonstrate that Graph Neural Networks,
trained on Monte-Carlo data, can serve as a replacement for commonly used
numerical quadrature rules, overcoming their deficiencies and significantly
improving the accuracy. This is showcased by three benchmarks: the thermal
expansion of copper, the martensitic phase transition of iron, and the energy
of grain boundaries. We illustrate the benefits of the proposed technique over
classically used third- and fifth-order Gaussian quadrature, we highlight the
impact on time-coarsened atomistic predictions, and we discuss the
computational efficiency. The latter is of general importance when performing
frequent evaluation of phase space or other high-dimensional integrals, which
is why the proposed framework promises applications beyond the scope of
atomistics
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