857 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
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
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
Kink Solution in a Fluid Model of Traffic Flows
Traffic jam in a fluid model of traffic flows proposed by Kerner and
Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is
analyzed. An analytic scaling solution is presented near the critical point of
the hetero-clinic bifurcation. The validity of the solution has been confirmed
from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure
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
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
Long-term insect herbivory slows soil development in an arid ecosystem
Although herbivores are well known to alter litter inputs and soil nutrient fluxes, their long-term influences on soil development are largely unknown because of the difficulty of detecting and attributing changes in carbon and nutrient pools against large background levels. The early phase of primary succession reduces this signal-to-noise problem, particularly in arid systems where individual plants can form islands of fertility. We used natural variation in tree-resistance to herbivory, and a 15 year herbivore-removal experiment in an Arizona piñon-juniper woodland that was established on cinder soils following a volcanic eruption, to quantify how herbivory shapes the development of soil carbon (C) and nitrogen (N) over 36–54 years (i.e., the ages of the trees used in our study). In this semi-arid ecosystem, trees are widely spaced on the landscape, which allows direct examination of herbivore impacts on the nutrient-poor cinder soils. Although chronic insect herbivory increased annual litterfall N per unit area by 50% in this woodland, it slowed annual tree-level soil C and N accumulation by 111% and 96%, respectively. Despite the reduction in soil C accumulation, short-term litterfall-C inputs and soil C-efflux rates per unit soil surface were not impacted by herbivory. Our results demonstrate that the effects of herbivores on soil C and N fluxes and soil C and N accumulation are not necessarily congruent: herbivores can increase N in litterfall, but over time their impact on plant growth and development can slow soil development. In sum, because herbivores slow tree growth, they slow soil development on the landscape. http://dx.doi.org/10.1890/ES12-00411.
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