scholarly journals Asymptotic speed of spread for a nonlocal evolutionary-epidemic system

2021 ◽  
Vol 41 (10) ◽  
pp. 4959
Author(s):  
Lara Abi Rizk ◽  
Jean-Baptiste Burie ◽  
Arnaud Ducrot
Keyword(s):  
Asymptotic Speed

The development of travelling waves in a simple isothermal chemical system III. Cubic and mixed autocatalysis

1990 ◽  
Vol 430 (1880) ◽  
pp. 509-524 ◽  
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Chemical System ◽  
Mixed System ◽  
Dimensional Parameter ◽  
Diffusion Wave ◽  
Symmetrical Form ◽  
Asymptotic Speed ◽  
Mixed Systems ◽  
Cubic Autocatalysis

Autocatalytic chemical reactions can support isothermal travelling waves of constant speed and form. This paper extends previous studies to cubic autocatalysis and to mixed systems where quadratic and cubic autocatalyses occur concurrently. A + B → 2B, rate = k q ab , (1) A + 2B → 3B, rate = k c ab 2 . (2) For pure cubic autocatalysis the wave has, at large times, a constant asymptotic speed v 0 (where v 0 = 1/√2 in the appropriate dimensionless units). This result is confirmed by numerical investigation of the initial-value problem. Perturbations to this stable wave-speed decay at long times as t -3/2 e -1/8 t . The mixed system is governed by a non-dimensional parameter μ = k q / k c a 0 which measures the relative rates of transformation by quadratic and cubic modes. In the mixed case ( μ ≠ 0) the reaction-diffusion wave has a form appropriate to a purely cubic autocatalysis so long as μ lies between ½ and 0. When μ exceeds ½, the reaction wave loses its symmetrical form, and all its properties steadily approach those of quadratic autocatalysis. The value μ = ½ is the value at which rates of conversion by the two paths are equal.

scholarly journals The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags

2020 ◽  
Vol 117 (29) ◽  
pp. 16770-16775
Author(s):  
Johan Fourdrinoy ◽  
Julien Dambrine ◽  
Madalina Petcu ◽  
Morgan Pierre ◽  
Germain Rousseaux
Keyword(s):  
Internal Waves ◽  
Laboratory Experiments ◽  
Analytical Description ◽  
Unsteady Motion ◽  
Linear Regime ◽  
Dual Nature ◽  
Asymptotic Speed ◽  
Propulsion Force ◽  
Initial Acceleration ◽  
Dead Water

A ship encounters a higher drag in a stratified fluid compared to a homogeneous one. Grouped under the same “dead-water” vocabulary, two wave-making resistance phenomena have been historically reported. The first, the Nansen wave-making drag, generates a stationary internal wake which produces a kinematic drag with a noticeable hysteresis. The second, the Ekman wave-making drag, is characterized by velocity oscillations caused by a dynamical resistance whose origin is still unclear. The latter has been justified previously by a periodic emission of nonlinear internal waves. Here we show that these speed variations are due to the generation of an internal dispersive undulating depression produced during the initial acceleration of the ship within a linear regime. The dispersive undulating depression front and its subsequent whelps act as a bumpy treadmill on which the ship would move back and forth. We provide an analytical description of the coupled dynamics of the ship and the wave, which demonstrates the unsteady motion of the ship. Thanks to dynamic calculations substantiated by laboratory experiments, we prove that this oscillating regime is only temporary: the ship will escape the transient Ekman regime while maintaining its propulsion force, reaching the asymptotic Nansen limit. In addition, we show that the lateral confinement, often imposed by experimental setups or in harbors and locks, exacerbates oscillations and modifies the asymptotic speed.

Convergence to travelling fronts in semilinear parabolic equations

1978 ◽  
Vol 80 (3-4) ◽  
pp. 213-234 ◽  
Author(s):  
Franz Rothe
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Parabolic Equations ◽  
Step Function ◽  
Wave Type ◽  
All Solutions ◽  
Asymptotic Speed ◽  
Rate Of Decay ◽  
Travelling Fronts ◽  
Semilinear Parabolic

SynopsisWe study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(x − ct) for a continuum of velocities c. In the asymptotic behavior of this equation was investigated for a step function as initial data. In this paper we obtain the asymptotic behavior for a large class of monotone initial data.All solutions with initial data in this class evolve to wave-type solutions, where the rate of decay of the initial data determines the asymptotic speed.

A SIMPLIFIED TECHNIQUE FOR HIDDEN-LINE ELIMINATION IN TERRAINS

1993 ◽  
Vol 03 (02) ◽  
pp. 167-181 ◽  
Author(s):  
FRANCO P. PREPARATA ◽  
JEFFREY SCOTT VITTER
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Full Advantage ◽  
Implicit Representation ◽  
Geometrical Properties ◽  
Asymptotic Speed ◽  
Hidden Line ◽  
The Cost ◽  
Set Of Points

In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d+n) log 2 n) time and uses O(nα(n)) space, where d is the size of the final display, and α(n) is a (very slowly growing) functional inverse of Ackermann’s function. Our implementation is especially simple and practical, because we try to take full advantage of the specific geometrical properties of the terrain. The asymptotic speed of our algorithm has been improved upon theoretically by other authors, but at the cost of higher space usage and/or high overhead and complicated code. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in O( log 2 n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.

Stick–Slip Motion of the Chaplygin Sleigh With a Piecewise-Smooth Nonholonomic Constraint

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Phanindra Tallapragada
Keyword(s):  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
Piecewise Smooth ◽  
Nonsmooth Dynamics ◽  
Chaplygin Sleigh ◽  
Stick Slip ◽  
Velocity Decay ◽  
Asymptotic Speed ◽  
Asymptotic Motion ◽  
Stick Slip Motion

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints. Such constraints often arise due to the role of a no-slip requirement imposed by friction. In the case of the Chaplygin sleigh, it is well known that its asymptotic motion is that of pure translation along a straight line. Any perturbations in angular velocity decay and result in an increase in asymptotic speed of the sleigh. Such motion of the sleigh is under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum value to the friction. The Chaplygin sleigh is then under a piecewise-smooth nonholonomic constraint and transitions between “slip” and “stick” modes. We investigate these transitions and the resulting nonsmooth dynamics of the system. We show that the reduced state space of the system can be partitioned into sets of distinct dynamics and that the stick–slip transitions can be explained in terms of transitions of the state of the system between these sets.

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