Towards More Accurate Molecular Dynamics Calculation of Thermal Conductivity. Case Study: GaN Bulk Crystals

Significant differences exist among literature for thermal conductivity of various systems computed using molecular dynamics simulation. In some cases, unphysical results, for example, negative thermal conductivity, have been found. Using GaN as an example case and the direct non-equilibrium method, extensive molecular dynamics simulations and Monte Carlo analysis of the results have been carried out to quantify the uncertainty level of the molecular dynamics methods and to identify the conditions that can yield sufficiently accurate calculations of thermal conductivity. We found that the errors of the calculations are mainly due to the statistical thermal fluctuations. Extrapolating results to the limit of an infinite-size system tend to magnify the errors and occasionally lead to unphysical results. The error in bulk estimates can be reduced by performing longer time averages using properly selected systems over a range of sample lengths. If the errors in the conductivity estimates associated with each of the sample lengths are kept below a certain threshold, the likelihood of obtaining unphysical bulk values becomes insignificant. Using a Monte-Carlo approach developed here, we have determined the probability distributions for the bulk thermal conductivities obtained using the direct method. We also have observed a nonlinear effect that can become a source of significant errors. For the extremely accurate results presented here, we predict a [0001] GaN thermal conductivity of 185 $\rm{W/K \cdot m}$ at 300 K, 102 $\rm{W/K \cdot m}$ at 500 K, and 74 $\rm{W/K \cdot m}$ at 800 K. Using the insights obtained in the work, we have achieved a corresponding error level (standard deviation) for the bulk (infinite sample length) GaN thermal conductivity of less than 10 $\rm{W/K \cdot m}$, 5 $\rm{W/K \cdot m}$, and 15 $\rm{W/K \cdot m}$ at 300 K, 500 K, and 800 K respectively

Rendezvous of Heterogeneous Mobile Agents in Edge-weighted Networks

We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal times for the other agent. The goal of the agents is to meet on an edge or a node of the graph. In this scenario, we study the time required by the agents to meet, compared to the meeting time $T_{OPT}$ in the offline scenario in which the agents have complete knowledge about each others speed characteristics. When no additional assumptions are made, we show that rendezvous in our model can be achieved after time $O(n T_{OPT})$ in a $n$-node graph, and that such time is essentially in some cases the best possible. However, we prove that the rendezvous time can be reduced to $\Theta (T_{OPT})$ when the agents are allowed to exchange $\Theta(n)$ bits of information at the start of the rendezvous process. We then show that under some natural assumption about the traversal times of edges, the hardness of the heterogeneous rendezvous problem can be substantially decreased, both in terms of time required for rendezvous without communication, and the communication complexity of achieving rendezvous in time $\Theta (T_{OPT})$

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown

Ripple Texturing of Suspended Graphene Atomic Membranes

Graphene is the nature's thinnest elastic membrane, with exceptional mechanical and electrical properties. We report the direct observation and creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene sheets, using spontaneously and thermally induced longitudinal strains on patterned substrates, with control over their orientations and wavelengths. We also provide the first measurement of graphene's thermal expansion coefficient, which is anomalously large and negative, ~ -7x10^-6 K^-1 at 300K. Our work enables novel strain-based engineering of graphene devices.Comment: 15 pages, 4 figure

Simulation of dimensionality effects in thermal transport

The discovery of nanostructures and the development of growth and fabrication techniques of one- and two-dimensional materials provide the possibility to probe experimentally heat transport in low-dimensional systems. Nevertheless measuring the thermal conductivity of these systems is extremely challenging and subject to large uncertainties, thus hindering the chance for a direct comparison between experiments and statistical physics models. Atomistic simulations of realistic nanostructures provide the ideal bridge between abstract models and experiments. After briefly introducing the state of the art of heat transport measurement in nanostructures, and numerical techniques to simulate realistic systems at atomistic level, we review the contribution of lattice dynamics and molecular dynamics simulation to understanding nanoscale thermal transport in systems with reduced dimensionality. We focus on the effect of dimensionality in determining the phononic properties of carbon and semiconducting nanostructures, specifically considering the cases of carbon nanotubes, graphene and of silicon nanowires and ultra-thin membranes, underlying analogies and differences with abstract lattice models.Comment: 30 pages, 21 figures. Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations.Comment: 26 pages, 13 eps figure

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r

Climate policy and ancillary benefits : a survey and integration into the modelling of international negotiations on climate change

Currently informal and formal international negotiations on climate change take place in an intensive way since the Kyoto Protocol expires already in 2012. A post-Kyoto regulation to combat global warming is not yet stipulated. Due to rapidly increasing greenhouse gas emission levels, industrialized countries urge major polluters from the developing world like China and India to participate in a future agreement. Whether these developing countries will do so, depends on the prevailing incentives to participate in international climate protection efforts. This paper identifies ancillary benefits of climate policy to provide important incentives to attend a new international protocol and to positively affect the likelihood of accomplishing a post-Kyoto agreement which includes commitments of developing countries

An anatomy-based lumped parameter model of cerebrospinal venous circulation: can an extracranial anatomical change impact intracranial hemodynamics?

Background The relationship between extracranial venous system abnormalities and central nervous system disorders has been recently theorized. In this paper we delve into this hypothesis by modeling the venous drainage in brain and spinal column areas and simulating the intracranial flow changes due to extracranial morphological stenoses. Methods A lumped parameter model of the cerebro-spinal venous drainage was created based on anatomical knowledge and vessels diameters and lengths taken from literature. Each vein was modeled as a hydraulic resistance, calculated through Poiseuille’s law. The inputs of the model were arterial flow rates of the intracranial, vertebral and lumbar districts. The effects of the obstruction of the main venous outflows were simulated. A database comprising 112 Multiple Sclerosis patients (Male/Female = 42/70; median age ± standard deviation = 43.7 ± 10.5 years) was retrospectively analyzed. Results The flow rate of the main veins estimated with the model was similar to the measures of 21 healthy controls (Male/Female = 10/11; mean age ± standard deviation = 31 ± 11 years), obtained with a 1.5 T Magnetic Resonance scanner. The intracranial reflux topography predicted with the model in cases of internal jugular vein diameter reduction was similar to those observed in the patients with internal jugular vein obstacles. Conclusions The proposed model can predict physiological and pathological behaviors with good fidelity. Despite the simplifications introduced in cerebrospinal venous circulation modeling, the key anatomical feature of the lumped parameter model allowed for a detailed analysis of the consequences of extracranial venous impairments on intracranial pressure and hemodynamics

Sustainable Urban Systems: Co-design and Framing for Transformation

Rapid urbanisation generates risks and opportunities for sustainable development. Urban policy and decision makers are challenged by the complexity of cities as social–ecological–technical systems. Consequently there is an increasing need for collaborative knowledge development that supports a whole-of-system view, and transformational change at multiple scales. Such holistic urban approaches are rare in practice. A co-design process involving researchers, practitioners and other stakeholders, has progressed such an approach in the Australian context, aiming to also contribute to international knowledge development and sharing. This process has generated three outputs: (1) a shared framework to support more systematic knowledge development and use, (2) identification of barriers that create a gap between stated urban goals and actual practice, and (3) identification of strategic focal areas to address this gap. Developing integrated strategies at broader urban scales is seen as the most pressing need. The knowledge framework adopts a systems perspective that incorporates the many urban trade-offs and synergies revealed by a systems view. Broader implications are drawn for policy and decision makers, for researchers and for a shared forward agenda