scholarly journals Traveling and standing waves mediate pattern formation in cellular protrusions

2020 ◽  
Vol 6 (32) ◽  
pp. eaay7682
Author(s):  
Sayak Bhattacharya ◽  
Tatsat Banerjee ◽  
Yuchuan Miao ◽  
Huiwang Zhan ◽  
Peter N. Devreotes ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Traveling Waves ◽  
Standing Waves ◽  
Cell Cortex ◽  
Theoretical Studies ◽  
Direct Transformation ◽  
Diffusion Parameters ◽  
Excitable Systems ◽  
Mutant Strains ◽  
The Stability

The mechanisms regulating protrusions during amoeboid migration exhibit excitability. Theoretical studies have suggested the possible coexistence of traveling and standing waves in excitable systems. Here, we demonstrate the direct transformation of a traveling into a standing wave and establish conditions for the stability of this conversion. This theory combines excitable wave stopping and the emergence of a family of standing waves at zero velocity, without altering diffusion parameters. Experimentally, we show the existence of this phenomenon on the cell cortex of some Dictyostelium and mammalian mutant strains. We further predict a template that encompasses a spectrum of protrusive phenotypes, including pseudopodia and filopodia, through transitions between traveling and standing waves, allowing the cell to switch between excitability and bistability. Overall, this suggests that a previously-unidentified method of pattern formation, in which traveling waves spread, stop, and turn into standing waves that rearrange to form stable patterns, governs cell motility.

Critical Stability of a Hinged Beam With Dynamic Moment: With and Without External Flow

2019 ◽  
Author(s):  
Mahmoud Abdullatif ◽  
Ranjan Mukherjee ◽  
Aren Hellum
Keyword(s):  
Critical Point ◽  
Dynamic Model ◽  
Traveling Waves ◽  
Galerkin Approximation ◽  
Standing Waves ◽  
External Flow ◽  
Critical Stability ◽  
The Stability ◽  
The Moment ◽  
Dynamic Moment

Abstract The stability characteristics of a hinged beam subjected to a dynamic moment is investigated. The moment is proportional to the curvature of the beam at some point along its length. The stability investigations are carried out using a Galerkin approximation, both in the presence and absence of external flow. In the absence of external flow, stability is lost through divergence and flutter depending on the location of the point of measurement of curvature and the sign of the applied moment. In the presence of external flow, additional terms are introduced in the dynamic model. This alters the mechanism of flutter, reduces the value of the parameter at the critical point, and changes the nature of oscillations from standing waves to traveling waves.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

scholarly journals Structural Properties of G,T-Parallel Duplexes

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Aviñó ◽  
Elena Cubero ◽  
Raimundo Gargallo ◽  
Carlos González ◽  
Modesto Orozco ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Structural Properties ◽  
Theoretical Calculations ◽  
Md Simulations ◽  
Theoretical Studies ◽  
Duplex Structure ◽  
Strong Stabilization ◽  
The Stability ◽  
The Impact

The structure of G,T-parallel-stranded duplexes of DNA carrying similar amounts of adenine and guanine residues is studied by means of molecular dynamics (MD) simulations and UV- and CD spectroscopies. In addition the impact of the substitution of adenine by 8-aminoadenine and guanine by 8-aminoguanine is analyzed. The presence of 8-aminoadenine and 8-aminoguanine stabilizes the parallel duplex structure. Binding of these oligonucleotides to their target polypyrimidine sequences to form the corresponding G,T-parallel triplex was not observed. Instead, when unmodified parallel-stranded duplexes were mixed with their polypyrimidine target, an interstrand Watson-Crick duplex was formed. As predicted by theoretical calculations parallel-stranded duplexes carrying 8-aminopurines did not bind to their target. The preference for the parallel-duplex over the Watson-Crick antiparallel duplex is attributed to the strong stabilization of the parallel duplex produced by the 8-aminopurines. Theoretical studies show that the isomorphism of the triads is crucial for the stability of the parallel triplex.

scholarly journals Synaptic propagation in neuronal networks with finite-support space dependent coupling

2020 ◽  
Author(s):  
Ricardo Erazo Toscano ◽  
Remus Osan
Keyword(s):  
Time Constant ◽  
Sensory Processing ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Neuronal Networks ◽  
Evolution Equations ◽  
Network Connectivity ◽  
Space Constant ◽  
The Stability ◽  
The Brain

1AbstractTraveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves’ evolution are synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model to investigate the propagation characteristics of traveling wave activity. We formulated a set of evolution equations based on the network connectivity parameters. We numerically investigated the stability of the traveling wave propagation with a series of perturbations with biological relevance.

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