167 research outputs found
ANNUAL REPORT, SEPTEMBER 1, 1970--AUGUST 31, 1971.
This year has seen the completion of initial versions of all programs for the transient analysis of arbitrary networks and the linking together of these packages. A diagram showing the organization of the major parts of the software system is given in Figure 1. A brief description of the purpose of each package is given in section 2 in the report
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems
In "equation-free" multiscale computation a dynamic model is given at a fine,
microscopic level; yet we believe that its coarse-grained, macroscopic dynamics
can be described by closed equations involving only coarse variables. These
variables are typically various low-order moments of the distributions evolved
through the microscopic model. We consider the problem of integrating these
unavailable equations by acting directly on kinetic Monte Carlo microscopic
simulators, thus circumventing their derivation in closed form. In particular,
we use projective multi-step integration to solve the coarse initial value
problem forward in time as well as backward in time (under certain conditions).
Macroscopic trajectories are thus traced back to unstable, source-type, and
even sometimes saddle-like stationary points, even though the microscopic
simulator only evolves forward in time. We also demonstrate the use of such
projective integrators in a shooting boundary value problem formulation for the
computation of "coarse limit cycles" of the macroscopic behavior, and the
approximation of their stability through estimates of the leading "coarse
Floquet multipliers".Comment: Submitted to Journal of Computational Physic
Projective and Coarse Projective Integration for Problems with Continuous Symmetries
Temporal integration of equations possessing continuous symmetries (e.g.
systems with translational invariance associated with traveling solutions and
scale invariance associated with self-similar solutions) in a ``co-evolving''
frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with
the evolving solution) leads to improved accuracy because of the smaller time
derivative in the new spatial frame. The slower time behavior permits the use
of {\it projective} and {\it coarse projective} integration with longer
projective steps in the computation of the time evolution of partial
differential equations and multiscale systems, respectively. These methods are
also demonstrated to be effective for systems which only approximately or
asymptotically possess continuous symmetries. The ideas of projective
integration in a co-evolving frame are illustrated on the one-dimensional,
translationally invariant Nagumo partial differential equation (PDE). A
corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is
used to illustrate the coarse-grained method. A simple, one-dimensional
diffusion problem is used to illustrate the scale invariant case. The
efficiency of projective integration in the co-evolving frame for both the
macroscopic diffusion PDE and for a random-walker particle based model is again
demonstrated
Algorithm for numerical integration of the rigid-body equations of motion
A new algorithm for numerical integration of the rigid-body equations of
motion is proposed. The algorithm uses the leapfrog scheme and the quantities
involved are angular velocities and orientational variables which can be
expressed in terms of either principal axes or quaternions. Due to specific
features of the algorithm, orthonormality and unit norms of the orientational
variables are integrals of motion, despite an approximate character of the
produced trajectories. It is shown that the method presented appears to be the
most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur
Interaction of free-floating planets with a star-planet pair
The recent discovery of free-floating planets and their theoretical
interpretation as celestial bodies, either condensed independently or ejected
from parent stars in tight clusters, introduced an intriguing possibility.
Namely, that some exoplanets are not condensed from the protoplanetary disk of
their parent star. In this novel scenario a free-floating planet interacts with
an already existing planetary system, created in a tight cluster, and is
captured as a new planet. In the present work we study this interaction process
by integrating trajectories of planet-sized bodies, which encounter a binary
system consisting of a Jupiter-sized planet revolving around a Sun-like star.
To simplify the problem we assume coplanar orbits for the bound and the
free-floating planet and an initially parabolic orbit for the free-floating
planet. By calculating the uncertainty exponent, a quantity that measures the
dependence of the final state of the system on small changes of the initial
conditions, we show that the interaction process is a fractal classical
scattering. The uncertainty exponent is in the range (0.2-0.3) and is a
decreasing function of time. In this way we see that the statistical approach
we follow to tackle the problem is justified. The possible final outcomes of
this interaction are only four, namely flyby, planet exchange, capture or
disruption. We give the probability of each outcome as a function of the
incoming planet's mass. We find that the probability of exchange or capture (in
prograde as well as retrograde orbits and for very long times) is
non-negligible, a fact that might explain the possible future observations of
planetary systems with orbits that are either retrograde or tight and highly
eccentric.Comment: 19 pages, 12 figure
Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian Flow
Equation-free methods make possible an analysis of the evolution of a few
coarse-grained or macroscopic quantities for a detailed and realistic model
with a large number of fine-grained or microscopic variables, even though no
equations are explicitly given on the macroscopic level. This will facilitate a
study of how the model behavior depends on parameter values including an
understanding of transitions between different types of qualitative behavior.
These methods are introduced and explained for traffic jam formation and
emergence of oscillatory pedestrian counter flow in a corridor with a narrow
door
Spatial rigid-multi-body systems with lubricated spherical clearance joints : modeling and simulation
The dynamic modeling and simulation of spatial rigid-multi-body systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.Fundação para a Ciência e a Tecnologia (FCT
On the contact detection for contact-impact analysis in multibody systems
One of the most important and complex parts of the simulation of multibody systems with contact-impact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time step integration algorithms are used and the pre-impact dynamics does not involve high-frequencies the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time step integration algorithms, in the vicinity of contact of multibody systems. The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency and its ability to deal with the transitions between non contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.Fundação para a Ciência e a Tecnologia (FCT
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