scholarly journals REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations

2019 ◽  
Vol 491 (2) ◽  
pp. 2885-2901 ◽  
Author(s):  
Daniel Tamayo ◽  
Hanno Rein ◽  
Pengshuai Shi ◽  
David M Hernandez

ABSTRACT Symplectic methods, in particular the Wisdom–Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes are not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces, which often strongly suppress integration errors. Furthermore, we demonstrate that so-called ‘symplectic correctors’ (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as ‘weak splitting correctors’. Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an open-source C library for incorporating additional effects into REBOUNDN-body integrations, together with a convenient python wrapper. All effects are machine independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.

2014 ◽  
Vol 16 (1) ◽  
pp. 169-200 ◽  
Author(s):  
Jian Deng ◽  
Cristina Anton ◽  
Yau Shu Wong

AbstractThe construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochastic Hamiltonian systems preserving Hamiltonian functions, the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes. A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators. The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.


2006 ◽  
Vol 18 (12) ◽  
pp. 2959-2993 ◽  
Author(s):  
Eduardo Ros ◽  
Richard Carrillo ◽  
Eva M. Ortigosa ◽  
Boris Barbour ◽  
Rodrigo Agís

Nearly all neuronal information processing and interneuronal communication in the brain involves action potentials, or spikes, which drive the short-term synaptic dynamics of neurons, but also their long-term dynamics, via synaptic plasticity. In many brain structures, action potential activity is considered to be sparse. This sparseness of activity has been exploited to reduce the computational cost of large-scale network simulations, through the development of event-driven simulation schemes. However, existing event-driven simulations schemes use extremely simplified neuronal models. Here, we implement and evaluate critically an event-driven algorithm (ED-LUT) that uses precalculated look-up tables to characterize synaptic and neuronal dynamics. This approach enables the use of more complex (and realistic) neuronal models or data in representing the neurons, while retaining the advantage of high-speed simulation. We demonstrate the method's application for neurons containing exponential synaptic conductances, thereby implementing shunting inhibition, a phenomenon that is critical to cellular computation. We also introduce an improved two-stage event-queue algorithm, which allows the simulations to scale efficiently to highly connected networks with arbitrary propagation delays. Finally, the scheme readily accommodates implementation of synaptic plasticity mechanisms that depend on spike timing, enabling future simulations to explore issues of long-term learning and adaptation in large-scale networks.


2020 ◽  
Vol 98 (Supplement_4) ◽  
pp. 4-5
Author(s):  
Martyna E Lagoda ◽  
Laura A Boyle ◽  
Joanna Marchewka ◽  
Julia A Calderón Díaz

Abstract Aggressive behavior resulting from mixing to establish a dominance hierarchy is a welfare concern for group-housed sows. The associated stress could negatively impact reproductive performance (RP). Objectives of this study were to investigate associations between 1) mixing aggression intensity and RP within and between parities one (P1) and two (P2), and 2) aggression intensity, floor type and RP. A total of 164 gilts were followed through two parities. Gilts were mixed into stable groups of eight unfamiliar individuals four days after insemination, and housed on fully-slatted floors, either uncovered (CON; n = 84) or covered (RUB; n = 80) by a rubber slat-mat until farrowing (for both parities). Skin lesion scores (SLS) (proxy for mixing aggression intensity), were recorded 24–72 hrs post-mixing (0 = no lesions to 5 = severe lesions) on five body regions on left and right sides, and on the tail, in both parities. Total SLS was calculated for each sow. RP data were retrospectively acquired from farm records for both parities. Data were analyzed using GLMM in PROC GLIMMIX of SAS (v9.4) where 1) each parity analyzed separately, and 2) SLS in P1 used to predict RP in P2. Gilts with higher SLS in P2 had higher piglet mortality (P = 0.021) and longer cycle length (P = 0.003) in P2. Gilts with higher SLS in P1 had more non-productive days (P < 0.001) in P2. CON gilts had higher SLS than RUB gilts (P = 0.017) in P1, but not in P2 (P > 0.05). CON gilts also had more piglets born dead (P = 0.004) and tended to crush more piglets (P = 0.097) in P2. Our results confirm that mixing aggression impacts RP in the current parity negatively. They also suggest that mixing aggression experienced by gilts may have long-term negative carry-over effects on performance in subsequent parities. Use of rubber flooring appears to mitigate detrimental effects of mixing aggression, perhaps through improved sow comfort.


2021 ◽  
pp. 43-50
Author(s):  
Clemens Tesch-Römer ◽  
Hans-Werner Wahl ◽  
Suresh I. S. Rattan ◽  
Liat Ayalon

In this chapter the authors argue that physical, spatial, and technological environments are relevant to successful ageing both in a conceptual and in a practical sense. Conceptually, efforts towards ageing successfully cannot be discussed separately from the various external forces that serve as constraining or enhancing influences in this respect. From a practical point of view, interventions aimed at improving one’s environment become increasingly relevant as an individual’s resources and reserve capacities dwindle. Environments for ageing successfully may be characterized in terms of person–environment docility vs proactivity, person–environment fit vs lack of fit, and person–environment agency vs belonging. The authors link these concepts with various models of successful ageing and discuss practical implications for housing, long-term care environments, neighbourhoods, municipalities, and use of digital technology.


2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Xuan Wang ◽  
Qiaozhen Ma

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert spaceD(A)×H2(Ω)∩H01(Ω), where the nonlinearityg(u,t)is translation compact and the time-dependent external forcesh(x,t)only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mario Krapp ◽  
Robert M. Beyer ◽  
Stephen L. Edmundson ◽  
Paul J. Valdes ◽  
Andrea Manica

AbstractCurated global climate data have been generated from climate model outputs for the last 120,000 years, whereas reconstructions going back even further have been lacking due to the high computational cost of climate simulations. Here, we present a statistically-derived global terrestrial climate dataset for every 1,000 years of the last 800,000 years. It is based on a set of linear regressions between 72 existing HadCM3 climate simulations of the last 120,000 years and external forcings consisting of CO2, orbital parameters, and land type. The estimated climatologies were interpolated to 0.5° resolution and bias-corrected using present-day climate. The data compare well with the original HadCM3 simulations and with long-term proxy records. Our dataset includes monthly temperature, precipitation, cloud cover, and 17 bioclimatic variables. In addition, we derived net primary productivity and global biome distributions using the BIOME4 vegetation model. The data are a relevant source for different research areas, such as archaeology or ecology, to study the long-term effect of glacial-interglacial climate cycles for periods beyond the last 120,000 years.


Information ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 324 ◽  
Author(s):  
Fausto Pedro García Márquez ◽  
Isaac Segovia Ramírez ◽  
Behnam Mohammadi-Ivatloo ◽  
Alberto Pliego Marugán

New wind turbines are becoming more complex and reliability analysis of them rising in complexity. The systems are composed of many components. Fault tree is used as an useful tool to analyze these interrelations and provide a scheme of the wind turbine, to get a quick overview of the behavior of the system under certain conditions of the components. However, it is complicated and in some cases not possible, to identify the conditions that would generate a wind turbine failure. A quantitative and qualitative reliability analysis of the wind turbine is proposed in this study. Binary decision diagrams are employed as a suitable and operational method to facilitate this analysis and to get an analytical expression by the Boolean functions. The size of the binary decision diagram, i.e., the computational cost for solving the problem, has an important dependence on the order of the components or events considered. Different heuristic ranking methods are used to find an optimal order or one closed, and to validate the results: AND, level, top-down-left-right, deep-first search and breadth-first-search. Birnbaum and criticality importance measures are proposed to evaluate the relevance of each component. This analysis leads to classify the events according to their importance with respect to the probability of the top event. This analysis provides the basis for making medium and long-term maintenance strategies.


2020 ◽  
Author(s):  
Teddy Chataigner ◽  
Marissa Yates ◽  
Nicolas Le Dantec

<p>Understanding shoreline evolution, and in particular, the consequences of shoreline erosion is a<br>major societal concern that threatens to become even more important in the future with the impacts<br>of climate change. Thus, it is necessary to improve both knowledge of the dominant physical processes<br>controlling medium to long-term shoreline evolution and the capabilities of morphological evolution<br>models to simulate beach changes at these spatial and temporal scales.<br>Empirical models may be an ideal choice for modelling complex and dynamic environments such as<br>sandy beaches at large spatial (beach) and long temporal (years to decades) scales. They reproduce<br>the effects of the main morphodynamical processes with low computational cost and relatively high<br>accuracy, in particular when high quality, long-term data are available for calibration.<br>Here, to broaden its range of application, a cross-shore equilibrium model, which has demon-<br>strated its accuracy and efficiency in reproducing shoreline and intertidal beach profile changes at<br>several micro and macrotidal beaches, is extended to couple it with a longshore beach evolution<br>modelling approach. The selection of a particular longshore model (based on a one-line approach),<br>and its implementation and validation with benchmark test cases of shoreline evolution caused by<br>the effects of diffusion, high angle wave instabilities, and coastal structures are presented.<br>The new hybrid model is applied at Narrabeen beach to reproduce the long-term evolution of<br>beach contours near the shoreline. The model is calibrated and tested using the 40-year timeseries of<br>monthly subaerial beach profile surveys conducted along 5 cross-shore profiles along the 3.6km-long<br>Narrabeen-Collaroy embayment. The novelty of the current work is to focus on reproducing changes<br>at different altitudes, with the objective of assessing the cross-shore variability of the longshore<br>sediment flux, which is assumed constant in most one-line longshore transport models. The coupled<br>model performance is discussed, and the results are compared to existing studies that have simulated<br>shoreline evolution at Narrabeen using other morphological change models.</p>


Subject The political and economic outlook for Mongolia. Significance Mongolia is recovering from a largely self-inflicted financial crisis that resulted in an IMF bailout two years ago. Meanwhile, isolationism in the United States and weakened political unity in the EU leave Mongolia with little choice but to slide further towards the neighbouring powers, China and Russia -- an uncomfortable trend for the sole liberal democracy in the region. Mongolia’s return to growth and relative political calm is dampened by external forces including weakness in metals prices and emerging market currencies. Impacts The government will focus on strengthening the economy; the direction of economic policy bodes well for continued growth. Infrastructure needs, such as energy and secure long-term water supplies for the capital, will see significant progress towards resolution. The 'truce' between the two major parties makes political conditions ripe for disruption by a new political movement or politician.


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