13,830 research outputs found
Autonomous engines driven by active matter: Energetics and design principles
Because of its nonequilibrium character, active matter in a steady state can
drive engines that autonomously deliver work against a constant mechanical
force or torque. As a generic model for such an engine, we consider systems
that contain one or several active components and a single passive one that is
asymmetric in its geometrical shape or its interactions. Generally, one expects
that such an asymmetry leads to a persistent, directed current in the passive
component, which can be used for the extraction of work. We validate this
expectation for a minimal model consisting of an active and a passive particle
on a one-dimensional lattice. It leads us to identify thermodynamically
consistent measures for the efficiency of the conversion of isotropic activity
to directed work. For systems with continuous degrees of freedom, work cannot
be extracted using a one-dimensional geometry under quite general conditions.
In contrast, we put forward two-dimensional shapes of a movable passive
obstacle that are best suited for the extraction of work, which we compare with
analytical results for an idealised work-extraction mechanism. For a setting
with many noninteracting active particles, we use a mean-field approach to
calculate the power and the efficiency, which we validate by simulations.
Surprisingly, this approach reveals that the interaction with the passive
obstacle can mediate cooperativity between otherwise noninteracting active
particles, which enhances the extracted power per active particle
significantly.Comment: 21 pages, 8 figure
Finite-horizon operations planning for a lean supply chain system
This dissertation studies an operational policy for a lean supply chain system consisting of a manufacturer, multiple suppliers and multiple buyers. The manufacturer procures raw materials from the suppliers and converts them into finished products, which are then shipped in batches to the buyers at certain intervals of times. Three distinct but inseparable problems are addressed: single supplier and single buyer with fixed delivery size (FD), multiple suppliers and multiple buyers with individual delivery schedule (MD), and time dependent delivery quantity with trend demand (TD). The mathematical formulations of these supply systems are categorized as mixed-integer, nonlinear programming problems (MINLAP) with discrete, non-convex objective functions and constraints. The operations policy determines the number of orders of raw material, beginning and ending times of cycles, production batch size, production start time, and beginning and ending inventories. The goal is to minimize the cost of the two-stage, just-in-time inventory system that integrates raw materials ordering and finished goods production system. The policy is designed for a finite planning horizon with various phases of life cycle demands such as inception (increasing), maturity (level) and phasing out (declining). Analytical results that characterize the exact, optimal policy for the problems described above are devised to develop efficient and optimal computational procedures. A closed-form heuristic that provides a near-optimal solution and tight lower bound is proposed for the problem FD. A network model to represent the problems is proposed and network-based algorithms are implemented to solve the problems FD, MD and TD optimally. The computational complexities of the algorithms are Θ(N2) or O(N3) where N is the total number of shipments in the planning horizon. Numerical tests to assess the robustness and quality of the methods show that the present research provides superior results. Production and supply chain management play an important role in ensuring that the necessary amounts of materials and parts arrive at the appropriate time and place. A manager, using the models obtained in this research, can quickly respond to consumers\u27 demand by effectively determining the right policies to order raw materials, to deliver finished goods, and to efficiently manage their production schedule
Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package
The spectral representation of stationary Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions for use in various statistical models. I describe the representation in detail and introduce the spectralGP package in R for computations. Because of the large number of basis coefficients, some form of shrinkage is necessary; I focus on a natural Bayesian approach via a particular parameterized prior structure that approximates stationary Gaussian processes on a regular grid. I review several models from the literature for data that do not lie on a grid, suggest a simple model modification, and provide example code demonstrating MCMC sampling using the spectralGP package. I describe reasons that mixing can be slow in certain situations and provide some suggestions for MCMC techniques to improve mixing, also with example code, and some general recommendations grounded in experience.
CASTRO: A New Compressible Astrophysical Solver. II. Gray Radiation Hydrodynamics
We describe the development of a flux-limited gray radiation solver for the
compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with
block-structured adaptive mesh refinement based on a nested hierarchy of
logically-rectangular variable-sized grids with simultaneous refinement in both
space and time. The gray radiation solver is based on a mixed-frame formulation
of radiation hydrodynamics. In our approach, the system is split into two
parts, one part that couples the radiation and fluid in a hyperbolic subsystem,
and another parabolic part that evolves radiation diffusion and source-sink
terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov
scheme, whereas the parabolic part is solved implicitly with a first-order
backward Euler method.Comment: accepted for publication in ApJS, high-resolution version available
at https://ccse.lbl.gov/Publications/wqzhang/castro2.pd
Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene
The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars
Metric for attractor overlap
We present the first general metric for attractor overlap (MAO) facilitating
an unsupervised comparison of flow data sets. The starting point is two or more
attractors, i.e., ensembles of states representing different operating
conditions. The proposed metric generalizes the standard Hilbert-space distance
between two snapshots to snapshot ensembles of two attractors. A reduced-order
analysis for big data and many attractors is enabled by coarse-graining the
snapshots into representative clusters with corresponding centroids and
population probabilities. For a large number of attractors, MAO is augmented by
proximity maps for the snapshots, the centroids, and the attractors, giving
scientifically interpretable visual access to the closeness of the states. The
coherent structures belonging to the overlap and disjoint states between these
attractors are distilled by few representative centroids. We employ MAO for two
quite different actuated flow configurations: (1) a two-dimensional wake of the
fluidic pinball with vortices in a narrow frequency range and (2)
three-dimensional wall turbulence with broadband frequency spectrum manipulated
by spanwise traveling transversal surface waves. MAO compares and classifies
these actuated flows in agreement with physical intuition. For instance, the
first feature coordinate of the attractor proximity map correlates with drag
for the fluidic pinball and for the turbulent boundary layer. MAO has a large
spectrum of potential applications ranging from a quantitative comparison
between numerical simulations and experimental particle-image velocimetry data
to the analysis of simulations representing a myriad of different operating
conditions.Comment: 33 pages, 20 figure
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