A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Parametric POMDPs for planning in continuous state spaces

This thesis is concerned with planning and acting under uncertainty in partially-observable continuous domains. In particular, it focusses on the problem of mobile robot navigation given a known map. The dominant paradigm for robot localisation is to use Bayesian estimation to maintain a probability distribution over possible robot poses. In contrast, control algorithms often base their decisions on the assumption that a single state, such as the mode of this distribution, is correct. In scenarios involving significant uncertainty, this can lead to serious control errors. It is generally agreed that the reliability of navigation in uncertain environments would be greatly improved by the ability to consider the entire distribution when acting, rather than the single most likely state. The framework adopted in this thesis for modelling navigation problems mathematically is the Partially Observable Markov Decision Process (POMDP). An exact solution to a POMDP problem provides the optimal balance between reward-seeking behaviour and information-seeking behaviour, in the presence of sensor and actuation noise. Unfortunately, previous exact and approximate solution methods have had difficulty scaling to real applications. The contribution of this thesis is the formulation of an approach to planning in the space of continuous parameterised approximations to probability distributions. Theoretical and practical results are presented which show that, when compared with similar methods from the literature, this approach is capable of scaling to larger and more realistic problems. In order to apply the solution algorithm to real-world problems, a number of novel improvements are proposed. Specifically, Monte Carlo methods are employed to estimate distributions over future parameterised beliefs, improving planning accuracy without a loss of efficiency. Conditional independence assumptions are exploited to simplify the problem, reducing computational requirements. Scalability is further increased by focussing computation on likely beliefs, using metric indexing structures for efficient function approximation. Local online planning is incorporated to assist global offline planning, allowing the precision of the latter to be decreased without adversely affecting solution quality. Finally, the algorithm is implemented and demonstrated during real-time control of a mobile robot in a challenging navigation task. We argue that this task is substantially more challenging and realistic than previous problems to which POMDP solution methods have been applied. Results show that POMDP planning, which considers the evolution of the entire probability distribution over robot poses, produces significantly more robust behaviour when compared with a heuristic planner which considers only the most likely states and outcomes

A Pre-Landing Assessment of Regolith Properties at the InSight Landing Site

This article discusses relevant physical properties of the regolith at the Mars InSight landing site as understood prior to landing of the spacecraft. InSight will land in the northern lowland plains of Mars, close to the equator, where the regolith is estimated to be ≥3--5 m thick. These investigations of physical properties have relied on data collected from Mars orbital measurements, previously collected lander and rover data, results of studies of data and samples from Apollo lunar missions, laboratory measurements on regolith simulants, and theoretical studies. The investigations include changes in properties with depth and temperature. Mechanical properties investigated include density, grain-size distribution, cohesion, and angle of internal friction. Thermophysical properties include thermal inertia, surface emissivity and albedo, thermal conductivity and diffusivity, and specific heat. Regolith elastic properties not only include parameters that control seismic wave velocities in the immediate vicinity of the Insight lander but also coupling of the lander and other potential noise sources to the InSight broadband seismometer. The related properties include Poisson’s ratio, P- and S-wave velocities, Young’s modulus, and seismic attenuation. Finally, mass diffusivity was investigated to estimate gas movements in the regolith driven by atmospheric pressure changes. Physical properties presented here are all to some degree speculative. However, they form a basis for interpretation of the early data to be returned from the InSight mission.Additional co-authors: Nick Teanby and Sharon Keda

STRUCTURAL ORDERING RELATED TO CHEMICAL BONDS IN RANDOM NETWORKS

No abstract availabl

Visualizing lithium-ion migration pathways in battery materials

10.1002/chem.201301504Chemistry - A European Journal194615535-15544CEUJ