140 research outputs found
Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems
In this paper, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems. Such a collection of dynamical systems may or may not have well defined ensemble averages as the existence of ensemble averages is predicated on the specification of appropriate initial conditions. A meaningful “average” dynamical system can represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average. They
can also prove to be very attractive from a computational perspective. An advantage to the construction of the meaningful average is that it involves integrating a nonlinear differential equation, of the same order as that of any member in the collection. An average dynamical system can be used in the analysis and design of hierarchical systems, and will allow one to capture approximately the response of any member of the collection
Spring-block model for a single-lane highway traffic
A simple one-dimensional spring-block chain with asymmetric interactions is
considered to model an idealized single-lane highway traffic. The main elements
of the system are blocks (modeling cars), springs with unidirectional
interactions (modeling distance keeping interactions between neighbors), static
and kinetic friction (modeling inertia of drivers and cars) and spatiotemporal
disorder in the values of these friction forces (modeling differences in the
driving attitudes). The traveling chain of cars correspond to the dragged
spring-block system. Our statistical analysis for the spring-block chain
predicts a non-trivial and rich complex behavior. As a function of the disorder
level in the system a dynamic phase-transition is observed. For low disorder
levels uncorrelated slidings of blocks are revealed while for high disorder
levels correlated avalanches dominates.Comment: 6 pages, 7 figure
Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid
The mechanical response and load bearing capacity of high performance polymer
composites changes due to diffusion of a fluid, temperature, oxidation or the
extent of the deformation. Hence, there is a need to study the response of
bodies under such degradation mechanisms. In this paper, we study the effect of
degradation and healing due to the diffusion of a fluid on the response of a
solid which prior to the diffusion can be described by the generalized
neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves
like an elastic body (i.e., it does not produce entropy) within a purely
mechanical context - creeps and stress relaxes when infused with a fluid and
behaves like a body whose material properties are time dependent. We
specifically investigate the torsion of a generalized neo-Hookean circular
cylindrical annulus infused with a fluid. The equations of equilibrium for a
generalized neo-Hookean solid are solved together with the convection-diffusion
equation for the fluid concentration. Different boundary conditions for the
fluid concentration are also considered. We also solve the problem for the case
when the diffusivity of the fluid depends on the deformation of the generalized
neo-Hookean solid.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent
Material
Delay Times and Rates for Type Ia Supernovae and Thermonuclear Explosions from Double-detonation Sub-Chandrasekhar Mass Models
We present theoretical delay times and rates of thermonuclear explosions that
are thought to produce Type Ia supernovae, including the double-detonation
sub-Chandrasekhar mass model, using the population synthesis binary evolution
code StarTrack. If detonations of sub-Chandrasekhar mass carbon-oxygen white
dwarfs following a detonation in an accumulated layer of helium on the white
dwarf's surface ("double-detonation" models) are able to produce thermonuclear
explosions which are characteristically similar to those of SNe Ia, then these
sub-Chandrasekhar mass explosions may account for at least some substantial
fraction of the observed SN Ia rate. Regardless of whether all
double-detonations look like 'normal' SNe Ia, in any case the explosions are
expected to be bright and thus potentially detectable. Additionally, we find
that the delay time distribution of double-detonation sub-Chandrasekhar mass
SNe Ia can be divided into two distinct formation channels: the 'prompt'
helium-star channel with delay times <500 Myr (~10% of all sub-Chandras), and
the 'delayed' double white dwarf channel, with delay times >800 Myr spanning up
to a Hubble time (~90%). These findings coincide with recent
observationally-derived delay time distributions which have revealed that a
large number of SNe Ia are prompt with delay times <500 Myr, while a
significant fraction also have delay times spanning ~1 Gyr to a Hubble time.Comment: MNRAS Accepted: 13 pages, shortened text, now 3 figure
Feedback control algorithms for the dissipation of traffic waves with autonomous vehicles
International audienceThis article considers the problem of traffic control in which an autonomous vehicle is used to regulate human piloted traffic to dissipate stop and go traffic waves. We first investigate the controllability of well-known microscopic traffic flow models, namely i) the Bando model (also known as the optimal velocity model), ii) the follow-the-leader model, and iii) a combined optimal velocity follow the leader model. Based on the controllability results, we propose three control strategies for an autonomous vehicle to stabilize the other, human-piloted traffic. We subsequently simulate the control effects on the microscopic models of human drivers in numerical experiments to quantify the potential benefits of the controllers. Based on the simulations, finally we conduct a field experiment with 22 human drivers and a fully autonomous-capable vehicle, to assess the feasibility of autonomous vehicle based traffic control on real human piloted traffic. We show that both in simulation and in the field test that an autonomous vehicle is able to dampen waves generated by 22 cars, and that as a consequence, the total fuel consumption of all vehicles is reduced by up to 20%
Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems
In this paper, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems. Such a collection of dynamical systems may or may not have well defined ensemble averages as the existence of ensemble averages is predicated on the specification of appropriate initial conditions. A meaningful “average” dynamical system can represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average. They can also prove to be very attractive from a computational perspective. An advantage to the construction of the meaningful average is that it involves integrating a nonlinear differential equation, of the same order as that of any member in the collection. An average dynamical system can be used in the analysis and design of hierarchical systems, and will allow one to capture approximately the response of any member of the collection.</p
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