1,157 research outputs found
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
Interacting with digital media at home via a second screen
In recent years Interactive Television (iTV) has become a household technology on a global scale. However, iTV is still a new technology in the early stages of its evolution.
Our previous research looked at how everyday users of iTV feel about the interactive part of iTV. In a series of studies we investigated how people use iTV services; their likes, dislikes, preferences and opinions. We then developed a second screen-based prototype device in response to these findings and tested it with iTV users in their own homes. This is a work in progress paper that outlines the work carried previously in the area of controlling interactive Television via a second screen. The positive user responses led us to extend the scope of our previous research to look into other related areas such as barriers to digital interactive media and personalisation of digital interactive media at home
Recent Studies of the North Magnetic Dip Pole
Reviews post-war studies on the secular motion of the dip pole and predicts its position for epoch 1960. 0:74.8 ± 0.3 N., 99.6 ± 1.2 W. The daily track during moderate magnetic disturbance approximates an ellipse with a north-south long axis of ca. 30 mi and an east-west axis of ca. 18 mi. Estimated and observed tracks 1600-1950 are mapped, and sources and magnitudes of errors are discussed. The secular motion, as estimated by various methods, averages 5.5 mi/yr to the north and 0.7 mi/yr to the east
Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
In a certain class of differential-difference equations for dissipative
systems, we show that hyperbolic tangent model is the only the nonlinear system
of equations which can admit some particular solutions of the Toda lattice. We
give one parameter family of exact solutions, which include as special cases
the Toda lattice solutions as well as the Whitham's solutions in the Newell's
model. Our solutions can be used to describe temporal-spatial density patterns
observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur
Supernova Hosts for Gamma-Ray Burst Jets: Dynamical Constraints
I constrain a possible supernova origin for gamma-ray bursts by modeling the
dynamical interaction between a relativistic jet and a stellar envelope
surrounding it. The delay in observer's time introduced by the jet traversing
the envelope should not be long compared to the duration of gamma-ray emission;
also, the jet should not be swallowed by a spherical explosion it powers. The
only stellar progenitors that comfortably satisfy these constraints, if one
assumes that jets move ballistically within their host stars, are compact
carbon-oxygen or helium post-Wolf-Rayet stars (type Ic or Ib supernovae); type
II supernovae are ruled out. Notably, very massive stars do not appear capable
of producing the observed bursts at any redshift unless the stellar envelope is
stripped prior to collapse. The presence of a dense stellar wind places an
upper limit on the Lorentz factor of the jet in the internal shock model;
however, this constraint may be evaded if the wind is swept forward by a photon
precursor. Shock breakout and cocoon blowout are considered individually;
neither presents a likely source of precursors for cosmological GRBs.
These envelope constraints could conceivably be circumvented if jets are
laterally pressure-confined while traversing the outer stellar envelope. If so,
jets responsible for observed GRBs must either have been launched from a region
several hundred kilometers wide, or have mixed with envelope material as they
travel. A phase of pressure confinement and mixing would imprint correlations
among jets that may explain observed GRB variability-luminosity and
lag-luminosity correlations.Comment: 17 pages, MNRAS, accepted. Contains new analysis of pressure-confined
jets, of jets that experience oblique shocks or mix with their cocoons, and
of cocoons after breakou
Recommended from our members
Infant-mortality testing of high-energy-density capacitors used on Nova
Nova is a solid-state large laser for inertial-confinement fusion research. Its flashlamps are driven by a 60-MJ capacitor bank. Part of this bank is being built with high-energy-density capacitors, 52-..mu..F, 22 kV, 12.5 kJ. A total of 2645 of these capacitors have been purchased from two manufacturers. Each capacitor was infant-mortality tested. The first test consisted of a high-potential test, bushing-to-case, since these capacitors have dual bushings. Then the capacitors were discharged 500 times with circuit conditions approximating the capacitors normal flashlamp load. Failure of either of these tests or if the capacitor was leaking was cause for rejection
Hydrodynamic singularities and clustering in a freely cooling inelastic gas
We employ hydrodynamic equations to follow the clustering instability of a
freely cooling dilute gas of inelastically colliding spheres into a
well-developed nonlinear regime. We simplify the problem by dealing with a
one-dimensional coarse-grained flow. We observe that at a late stage of the
instability the shear stress becomes negligibly small, and the gas flows solely
by inertia. As a result the flow formally develops a finite time singularity,
as the velocity gradient and the gas density diverge at some location. We argue
that flow by inertia represents a generic intermediate asymptotic of unstable
free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure
Ecological and Evolutionary Interaction Network Exploration: Addressing the Complexity of Biological Interactions in Natural Systems with Community Genetics and Statistics
Symposium Pape
Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models
A system of first-order differential-difference equations with time lag
describes the formation of density waves, called as quasi-solitons for
dissipative systems in this paper. For co-moving density waves, the system
reduces to some exactly solvable lattice models. We construct a shock-wave
solution as well as one-quasi-soliton solution, and argue that there are
pseudo-conserved quantities which characterize the formation of the co-moving
waves. The simplest non-trivial one is given to discuss the presence of a
cascade phenomena in relaxation process toward the pattern formation.Comment: REVTeX, 4 pages, 1 figur
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