scholarly journals On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1604
Author(s):  
Bruno Felice Filippo Flora ◽  
Armando Ciancio ◽  
Alberto d’Onofrio
Keyword(s):  
Steady State ◽  
Total Population ◽  
State Density ◽  
Internal Variables ◽  
Bounded Noise ◽  
Stochastic Perturbations ◽  
System Evolution ◽  
Active Particles ◽  
Fokker Plank Equation ◽  
Bounded Perturbations

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Active particles under confinement and effective force generation among surfaces

Soft Matter ◽  
2018 ◽  
Vol 14 (44) ◽  
pp. 9044-9054 ◽  
Author(s):  
Lorenzo Caprini ◽  
Umberto Marini Bettolo Marconi
Keyword(s):  
Steady State ◽  
Thermal Noise ◽  
Active Suspension ◽  
Force Generation ◽  
One Dimensional ◽  
Effective Force ◽  
Active Particles ◽  
Geometric Confinement

We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise.

scholarly journals Iterative solutions to the steady-state density matrix for optomechanical systems

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
P. D. Nation ◽  
J. R. Johansson ◽  
M. P. Blencowe ◽  
A. J. Rimberg
Keyword(s):  
Steady State ◽  
Density Matrix ◽  
State Density ◽  
Optomechanical Systems ◽  
Iterative Solutions

scholarly journals Ribosome flow model with extended objects

2017 ◽  
Vol 14 (135) ◽  
pp. 20170128 ◽  
Author(s):  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Mean Field ◽  
State Density ◽  
Transition Rates ◽  
Ribosome Density ◽  
Protein Production Rate ◽  
Unique Steady State

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects  (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period  T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period  T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

Dynamics of Granular Compaction

1997 ◽  
Vol 07 (05) ◽  
pp. 1159-1165 ◽  
Author(s):  
Hisao Hayakawa ◽  
Daniel C. Hong
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Granular Materials ◽  
Hard Sphere ◽  
Dimensionless Parameter ◽  
Preliminary Investigation ◽  
State Density ◽  
Dynamic Evolution ◽  
Initial State ◽  
Granular Compaction

We investigate the way the disordered granular materials organize themselves in a vibrating bed, the intensity of which is given by the dimensionless parameter Γ. Based on the recognition that an assembly of mono-disperse and cohesionless granular materials is a collection of spinless hard sphere Fermions, we first demonstrate that the time averaged steady state density profile for weak excitation with Γ ≈ 1 is given by the Fermi distribution. This is consistent with the observed experimental data and the results of Molecular dynamics. We then present a dynamic model to study the dynamics of granular compaction, namely the dynamic evolution of the initial state ultimately relaxing toward this steady state. Our preliminary investigation reveals that the relaxation is exponential, which is not inconsistent with the available experimental data for low Γ.

The influence of rotation on shelf convection

1998 ◽  
Vol 369 ◽  
pp. 23-48 ◽  
Author(s):  
P. JACOBS ◽  
G. N. IVEY
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Exchange Process ◽  
Baroclinic Instability ◽  
Slope Angle ◽  
State Density ◽  
Working Volume ◽  
Slope Topography ◽  
Lateral Heat ◽  
Lateral Exchange

A series of laboratory experiments was conducted to study the flows and exchange processes generated by turbulent convection in a shallow fluid with a combination of a shelf and slope topography in the presence of rotation. For convenience, heat loss at the ocean surface was modelled by heating from below with a buoyancy flux B0 applied to a circular portion (of radius R) of the base of a cylindrical tank, rotating with angular frequency f. The working volume was closed by an inverted model of a shelf and slope topography (with slope angle ϕ), creating a fluid height H between the forced surface and the shelf. After the initiation of the buoyancy forcing, the average temperature in the actively convecting region initially increases linearly with time but slows down once a lateral heat flux is generated by baroclinic instability at the edge of the convecting region. The wavelength of this instability is described by λ=(5.9±0.3) RD, with RD the Rossby radius of deformation, defined by (g′H)1/2/f, where g′ is the reduced gravity based on the density difference between the convecting and ambient fluids. A steady state is eventually reached when the lateral heat flux balances the (vertical) heat flux due to the forcing. The results differ from previous work in either unbounded or in constant-depth environments. It is shown that the steady-state density anomaly between the convecting and ambient regions is given by g′f=(1.6±0.2) (B0f)1/2 (R/H), while the time to reach this steady state is τ=(3.1±0.5) (f/B0)1/2R. The eddy velocity, characterizing the lateral exchange process, is given by vflux≈1.2 (B0/f)1/2. These results are consistent with the description of the lateral exchange process by eddy diffusion (rather than advection). Comparisons are made between the experimental results and field observations of convection events.

scholarly journals Towards a statistical mechanical theory of active fluids

Soft Matter ◽  
2015 ◽  
Vol 11 (45) ◽  
pp. 8768-8781 ◽  
Author(s):  
Umberto Marini Bettolo Marconi ◽  
Claudio Maggi
Keyword(s):  
Steady State ◽  
External Fields ◽  
Mechanical Theory ◽  
State Behavior ◽  
Stochastic Description ◽  
Active Particles ◽  
Statistical Mechanical ◽  
Steady State Behavior

We present a stochastic description of a model of N mutually interacting active particles in the presence of external fields and characterize its steady state behavior in the absence of currents.

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