scholarly journals A Simple Model for Spatio-Temporal Chaos in an Unstable Burgers Equation

2000 ◽  
Vol 103 (4) ◽  
pp. 703-711 ◽  
Author(s):  
H. Sakaguchi
Keyword(s):  
Simple Model ◽  
Burgers Equation ◽  
Spatio Temporal

scholarly journals Chaoticon: localized pattern with permanent dynamics

2014 ◽  
Vol 372 (2027) ◽  
pp. 20140011 ◽  
Author(s):  
N. Verschueren ◽  
U. Bortolozzo ◽  
M. G. Clerc ◽  
S. Residori
Keyword(s):  
Simple Model ◽  
Kuramoto Model ◽  
Brownian Motor ◽  
Uniform State ◽  
Spatio Temporal ◽  
Front Dynamics

An analytical mechanism that support localized spatio-temporal chaos is provided. We consider a simple model— the Nagumo Kuramoto model —which contains the crucial ingredients for observing localized spatio-temporal chaos, namely, the spatio-temporal chaotic pattern and its coexistence with a uniform state. This model allows us to unveil the front dynamics and to show that it can be described by a chaotic motor corresponding to the deterministic counterpart of a Brownian motor. Front interaction is identified as the mechanism at the origin of the localized spatio-temporal chaotic structures.

scholarly journals Dynamic stop pooling for flexible and sustainable ride sharing

2022 ◽  
Author(s):  
Charlotte Lotze ◽  
Philip Marszal ◽  
Malte Schröder ◽  
Marc Timme
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Travel Time ◽  
Human Mobility ◽  
A Priori ◽  
Trade Off ◽  
Ride Sharing ◽  
Route Length ◽  
Spatio Temporal ◽  
Demand Patterns

Abstract Ride sharing -- the bundling of simultaneous trips of several people in one vehicle -- may help to reduce the carbon footprint of human mobility. However, the complex collective dynamics pose a challenge when predicting the efficiency and sustainability of ride-sharing systems. Standard door-to-door ride sharing services trade reduced route length for increased user travel times and come with the burden of many stops and detours to pick up individual users. Requiring some users to walk to nearby shared stops reduces detours, but could become inefficient if spatio-temporal demand patterns do not well fit the stop locations. Here, we present a simple model of dynamic stop pooling with flexible stop positions. We analyze the performance of ride sharing services with and without stop pooling by numerically and analytically evaluating the steady state dynamics of the vehicles and requests of the ride sharing service. Dynamic stop pooling does a-priori not save route length, but occupancy. Intriguingly, it also reduces the travel time, although users walk parts of their trip. Together, these insights explain how dynamic stop pooling may break the trade-off between route lengths and travel time in door-to-door ride sharing, thus enabling higher sustainability and service quality.

scholarly journals Nonlinear effects in memristors with mobile vacancies

2021 ◽  
Vol 8 (10) ◽  
Author(s):  
I. V. Boylo ◽  
K. L. Metlov
Keyword(s):  
Relaxation Time ◽  
Simple Model ◽  
Electric Field ◽  
Nonlinear Boundary ◽  
Burgers Equation ◽  
Switching Time ◽  
Nonlinear Effects ◽  
Nonlinear Boundary Conditions ◽  
Local Concentration ◽  
Applied Current

Because local concentration of vacancies in any material is bounded, their motion must be accompanied by nonlinear effects. Here, we look for such effects in a simple model for electric field-driven vacancy motion in a memristor, solving the corresponding nonlinear Burgers’ equation with impermeable nonlinear boundary conditions exactly. We find non-monotonous relaxation of the resistance while switching between the stable (‘on’ and ‘off’) states, and qualitatively different dependencies of switching time (under applied current) and relaxation time (under no current) on the memristor length. Our solution can serve as a useful benchmark for simulations of more complex memristor models.

E3 ubiquitin ligases

2005 ◽  
Vol 41 ◽  
pp. 15-30 ◽  
Author(s):  
Helen C. Ardley ◽  
Philip A. Robinson
Keyword(s):  
Protein Complexes ◽  
Loss Of Function ◽  
Direct Role ◽  
Cellular Processes ◽  
Substrate Protein ◽  
Protein Ubiquitination ◽  
C Terminus ◽  
Full Complement ◽  
Spatio Temporal ◽  
Eukaryotic Organisms

The selectivity of the ubiquitin–26 S proteasome system (UPS) for a particular substrate protein relies on the interaction between a ubiquitin-conjugating enzyme (E2, of which a cell contains relatively few) and a ubiquitin–protein ligase (E3, of which there are possibly hundreds). Post-translational modifications of the protein substrate, such as phosphorylation or hydroxylation, are often required prior to its selection. In this way, the precise spatio-temporal targeting and degradation of a given substrate can be achieved. The E3s are a large, diverse group of proteins, characterized by one of several defining motifs. These include a HECT (homologous to E6-associated protein C-terminus), RING (really interesting new gene) or U-box (a modified RING motif without the full complement of Zn2+-binding ligands) domain. Whereas HECT E3s have a direct role in catalysis during ubiquitination, RING and U-box E3s facilitate protein ubiquitination. These latter two E3 types act as adaptor-like molecules. They bring an E2 and a substrate into sufficiently close proximity to promote the substrate's ubiquitination. Although many RING-type E3s, such as MDM2 (murine double minute clone 2 oncoprotein) and c-Cbl, can apparently act alone, others are found as components of much larger multi-protein complexes, such as the anaphase-promoting complex. Taken together, these multifaceted properties and interactions enable E3s to provide a powerful, and specific, mechanism for protein clearance within all cells of eukaryotic organisms. The importance of E3s is highlighted by the number of normal cellular processes they regulate, and the number of diseases associated with their loss of function or inappropriate targeting.

Elucidating cyclic AMP signaling in subcellular domains with optogenetic tools and fluorescent biosensors

2019 ◽  
Vol 47 (6) ◽  
pp. 1733-1747 ◽  
Author(s):  
Christina Klausen ◽  
Fabian Kaiser ◽  
Birthe Stüven ◽  
Jan N. Hansen ◽  
Dagmar Wachten
Keyword(s):  
Cyclic Amp ◽  
Adenosine Monophosphate ◽  
Adenylyl Cyclases ◽  
Temporal Precision ◽  
Fluorescent Biosensors ◽  
Subcellular Domains ◽  
Spatio Temporal ◽  
Hydrolysis Of ◽  
Shed Light ◽  
Cyclic Amp Signaling

The second messenger 3′,5′-cyclic nucleoside adenosine monophosphate (cAMP) plays a key role in signal transduction across prokaryotes and eukaryotes. Cyclic AMP signaling is compartmentalized into microdomains to fulfil specific functions. To define the function of cAMP within these microdomains, signaling needs to be analyzed with spatio-temporal precision. To this end, optogenetic approaches and genetically encoded fluorescent biosensors are particularly well suited. Synthesis and hydrolysis of cAMP can be directly manipulated by photoactivated adenylyl cyclases (PACs) and light-regulated phosphodiesterases (PDEs), respectively. In addition, many biosensors have been designed to spatially and temporarily resolve cAMP dynamics in the cell. This review provides an overview about optogenetic tools and biosensors to shed light on the subcellular organization of cAMP signaling.

Chaos and secular cycles in a structurally simple model society

2012 ◽  
Author(s):  
Alexander Medvinsky ◽  
Alexey Rusakov
Keyword(s):  
Simple Model
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