scholarly journals Kink dynamics in spatially inhomogeneous media: The role of internal modes

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
Jorge A. González ◽  
Sara Cuenda ◽  
Angel Sánchez
Keyword(s):  
Inhomogeneous Media ◽  
Spatially Inhomogeneous

scholarly journals Space-time caustics

1986 ◽  
Vol 9 (3) ◽  
pp. 531-540 ◽  
Author(s):  
Arthur D. Gorman
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Series Solution ◽  
Asymptotic Series ◽  
Inhomogeneous Media ◽  
Linear Differential Equations ◽  
Spatially Inhomogeneous ◽  
Asymptotic Series Solution ◽  
Linear Differential

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. Here the formalism is adapted to determine a class of asymptotic solutions at caustic points for those equations modelling wave propagation in media with both spatial and temporal inhomogeneities. The analogous Schrodinger equation is also considered.

UNIFORM Lp-STABILITY ESTIMATE FOR THE SPATIALLY INHOMOGENEOUS BOLTZMANN EQUATION NEAR VACUUM

2008 ◽  
Vol 05 (04) ◽  
pp. 713-739 ◽  
Author(s):  
SEUNG-YEAL HA ◽  
MITSURU YAMAZAKI ◽  
SEOK-BAE YUN
Keyword(s):  
Stability Analysis ◽  
Boltzmann Equation ◽  
Stability Estimate ◽  
Functional Approach ◽  
Classical Solutions ◽  
Nonlinear Functional ◽  
Spatially Inhomogeneous ◽  
Nonlinear Functionals ◽  
Spatially Inhomogeneous Boltzmann Equation

We present a new uniform Lp-stability theory for the spatially inhomogeneous Boltzmann equation near vacuum via the nonlinear functional approach proposed by the first author. Our stability analysis is based on new nonlinear functionals which are equivalent to the pth power of Lp-distance. The L1-nonlinear functionals play the key role of "modulators" which make the accumulative functional be non-increasing in time t along classical solutions.

scholarly journals Odorant-regulated Ca2+ gradients in rat olfactory neurons.

1993 ◽  
Vol 102 (5) ◽  
pp. 907-924 ◽  
Author(s):  
D Restrepo ◽  
Y Okada ◽  
J H Teeter
Keyword(s):  
Royal Society ◽  
Brain Research ◽  
Large Percentage ◽  
Concomitant Increase ◽  
Olfactory Neurons ◽  
Fura 2 ◽  
Spatially Inhomogeneous ◽  
Royal Society Of London

Olfactory neurons respond to odors with a change in conductance that mediates an influx of cations including Ca2+. The concomitant increase in [Cai] has been postulated to play a role in the adaptation to maintained odorant stimulation (Kurahashi, T., and T. Shibuya. 1990. Brain Research. 515:261-268. Kramer, R. H., and S. A. Siegelbaum. 1992. Neuron. 9:897-906. Zufall, F., G. M. Shepherd, and S. Firestein. 1991. Proceedings of the Royal Society of London, B. 246:225-230.) We have imaged the distribution of [Cai] in rat olfactory neurons (RON) using the Ca2+ indicator fura-2. A large percentage of the RON (42%, n = 35) responded to odorants with an increase in [Cai]. About half of the responding neurons displayed an increase in [Cai] at the apical end of the cell, but not at the soma. Moreover, in those cells that responded to odors with a standing [Cai] gradient, the gradient could be maintained for long periods of time (minutes) provided that the cells were continuously stimulated. In contrast, K(+)-induced depolarization elicited a more homogeneous increase in [Cai]. The spatially inhomogeneous increase in [Cai] elicited by odorants in some cells has important implications for the role of Ca2+ in adaptation because channels and enzymes regulated by Ca2+ will be affected differently depending on their location.

New nonreciprocal optical effects in spatially inhomogeneous media

1996 ◽  
Vol 26 (8) ◽  
pp. 659-660
Author(s):  
Nikolai V Kravtsov ◽  
N N Kravtsov ◽  
Anatolii S Chirkin
Keyword(s):  
Inhomogeneous Media ◽  
Spatially Inhomogeneous ◽  
Optical Effects

scholarly journals Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering

2021 ◽  
Author(s):  
Frank den Hollander ◽  
Shubhamoy Nandan
Keyword(s):  
Random Walks ◽  
Seed Bank ◽  
Seed Banks ◽  
Model Parameters ◽  
Geographic Space ◽  
Spatially Inhomogeneous ◽  
And Migration ◽  
Coalescing Random Walks ◽  
Colony Migration

AbstractWe consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. The colonies are labelled by $${\mathbb {Z}}^d$$ Z d , $$d \ge 1$$ d ≥ 1 , playing the role of a geographic space. The sizes of the active and the dormant population are finite and depend on the location of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper, under a mild condition on the sizes of the active populations, the system is well defined and has a dual. The dual consists of a system of interacting coalescing random walks in an inhomogeneous environment that switch between an active state and a dormant state. We analyse the dichotomy of coexistence (= multi-type equilibria) versus clustering (= mono-type equilibria) and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank enhances genetic diversity. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.

THE BOLTZMANN EQUATION AND THE GROUP TRANSFORMATIONS

1993 ◽  
Vol 03 (04) ◽  
pp. 443-476 ◽  
Author(s):  
A.V. BOBYLEV
Keyword(s):  
Boltzmann Equation ◽  
Special Role ◽  
Spatially Inhomogeneous ◽  
The Boltzmann Equation ◽  
Symmetry Properties ◽  
Full Equation ◽  
Spatially Inhomogeneous Boltzmann Equation ◽  
Spatially Homogeneous ◽  
Spatially Homogeneous Boltzmann Equation

This paper is devoted to the investigation of group properties of the nonlinear Boltzmann equation. The complete Lie group of invariant transformations for the spatially inhomogeneous Boltzmann equation is constructed. The generalization to the Lie-Backlund groups is given for the spatially homogeneous case. It is shown that there are only two non-trivial group transformations for the Boltzmann equation in the wide class of Lie and Lie-Backlund transformations. Some consequences of these symmetry properties are discussed. The special role of Galileo group and the analogy between the spatially homogeneous Boltzmann equation and the full equation are also investigated.

scholarly journals Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

2005 ◽  
Vol 69 (5-6) ◽  
pp. 537-552 ◽  
Author(s):  
G. Theocharis ◽  
D.J. Frantzeskakis ◽  
P.G. Kevrekidis ◽  
R. Carretero-González ◽  
B.A. Malomed
Keyword(s):  
Dark Soliton ◽  
Inhomogeneous Media ◽  
Soliton Dynamics ◽  
Spatially Inhomogeneous ◽  
Bose Einstein

scholarly journals Role of translational entropy in spatially inhomogeneous, coarse-grained models

2018 ◽  
Vol 148 (9) ◽  
pp. 094112 ◽  
Author(s):  
Marcel Langenberg ◽  
Nicholas E. Jackson ◽  
Juan J. de Pablo ◽  
Marcus Müller
Keyword(s):  
Coarse Grained ◽  
Spatially Inhomogeneous ◽  
Translational Entropy
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