Characterizing persistence and pause dynamical behaviors in biological systems

2021 ◽  
pp. 2150133
Author(s):  
Nicholas Mwilu Mutothya ◽  
Yong Xu
Keyword(s):  
Phase Transition ◽  
Dynamical Behavior ◽  
Nonlinear Function ◽  
Switching Rate ◽  
Initial State ◽  
Average Speed ◽  
Mean Squared Displacement ◽  
The Mean ◽  
Short Times ◽  
Direction Switching

This paper analyzed motion that randomly switches between the persistent motion runs and pause periods. A two-state continuous-time Markov chain is used to model the motion, which led to a system with coupled differential equations. Using a combined Fourier–Laplace transform, an analytical expression for calculating the mean-squared displacement is derived. The overall motion is investigated and identified from the obtained mean-squared displacement. The mean-squared displacement is a nonlinear function in time that is dependent on the phase transition rate, the direction switching rate, the average speed, and the initial state. It decays and grows with increasing the direction switching and average speed, respectively. The effective diffusivity descents exponentially in short times and remains constant in long times. The waiting time in each phase decayed exponentially. The probability density function for the position of a particle at a given time tends to be Gaussian in long times. The motion can be interpreted as a super-diffusion in short times and a standard diffusion in long times with a diffusion coefficient dependent on the phase transition rates, the direction switching rate and the average speed. Persistence influences the dynamical behavior for short times while for long times diffusive behavior is exhibited.

Motion of Active Fluids: Diffusion Dynamics of Cyanobacteria

2016 ◽  
Author(s):  
Thomas Vourc’h ◽  
Julien Léopoldès ◽  
Annick Méjean ◽  
Hassan Peerhossaini
Keyword(s):  
Time Lapse ◽  
Global Behavior ◽  
Diffusion Dynamics ◽  
Mean Squared Displacement ◽  
Terrestrial Environments ◽  
The Mean ◽  
Micro Organisms ◽  
Synechocystis Sp ◽  
Time Lapse Video ◽  
Pcc 6803

Cyanobacteria are photosynthetic micro-organisms colonizing all aquatic and terrestrial environments. The motility of such living micro-organisms should make their diffusion distinct from typical Brownian motion. This diffusion can be investigated in terms of global behavior (Fickian or not) and in terms of displacement probabilities, which provide more detail about the motility process. Using cyanobacterium Synechocystis sp. PCC 6803 as the model micro-organism, we carry out time-lapse video microscopy to track and analyze the bacteria’s trajectories, from which we compute the mean-squared displacement (MSD) and the distribution function of displacement probabilities. We find that the motility of Synechocystis sp. PCC 6803 is intermittent: high-motility “run” phases are separated by low-motility “tumble” phases corresponding to trapped states. However, this intermittent motility leads to a Fickian diffusive behavior, as shown by the evolution of the MSD with time.

scholarly journals Phase diagram of the selfinteracting particle­-antiparticle boson system

2021 ◽  
Vol 29 (1) ◽  
pp. 5-14
Author(s):  
D. Anchishkin ◽  
V. Gnatovskyy ◽  
D. Zhuravel ◽  
V. Karpenko
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Diagrams ◽  
Canonical Ensemble ◽  
Bose Condensate ◽  
Mean Field ◽  
Thermodynamic Quantities ◽  
Boson System ◽  
The Mean

A system of interacting relativistic bosons at finite temperatures and isospin densities is studied within the framework of the Skyrme­like mean­field model. The mean field contains both attractive and repulsive terms. The consideration is taken within the framework of the Canonical Ensemble and the isospin­density dependencies of thermodynamic quantities is obtained, in particular as the phase diagrams. It is shown that in such a system, in addition to the formation of a Bose­Einstein condensate, a liquid­gas phase transition is possible. We prove that the multi­boson system develops the Bose condensate for particles of high­density component only.

scholarly journals Fluid models with phase transition for kinetic equations in swarming

2020 ◽  
Vol 30 (10) ◽  
pp. 2023-2065 ◽  
Author(s):  
Mihaï Bostan ◽  
José Antonio Carrillo
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Kinetic Equation ◽  
Free Parameter ◽  
Kinetic Equations ◽  
Interaction Frequency ◽  
Fluid Models ◽  
Mean Velocity ◽  
Friction Forces ◽  
The Mean

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.

Extended Dynamic Spin-Fluctuation Theory with Application to Iron

2012 ◽  
Vol 190 ◽  
pp. 55-58 ◽  
Author(s):  
B.I. Reser ◽  
N.B. Melnikov ◽  
Vladimir I. Grebennikov
Keyword(s):  
Phase Transition ◽  
Magnetic Properties ◽  
Green Function ◽  
Spin Fluctuation ◽  
Spin Fluctuations ◽  
Fluctuation Theory ◽  
Dynamic Spin ◽  
Discontinuous Phase ◽  
The Mean ◽  
Extended Dynamic

The problem of discontinuous phase transition in the dynamic spin-fluctuation theory is resolved by taking into account large anharmonic spin fluctuations and nonlocality of the mean Green function. The extended theory is applied to the calculation of magnetic properties of iron.

Experimental investigation of the instability of a sedimenting suspension of fibres

2007 ◽  
Vol 575 ◽  
pp. 307-332 ◽  
Author(s):  
BLOEN METZGER ◽  
JASON E. BUTLER ◽  
ÉLISABETH GUAZZELLI
Keyword(s):  
Vertical Component ◽  
Orientation Distribution ◽  
Velocity Fluctuations ◽  
Image Velocimetry ◽  
Wide Range ◽  
Fluid Properties ◽  
The Mean ◽  
Using Data ◽  
Horizontal Wavelength ◽  
Short Times

Observations of the flow structures formed by rigid fibres of high aspect ratio sedimenting within a viscous fluid at a Reynolds number of approximately 10−4 confirm the existence of an instability as reported in previous theories, experiments, and numerical simulations. Using data generated from particle image velocimetry measurements, we quantify the sedimentation structures over a wide range of parameters, which include the height of fluid, cross-section of the sedimentation cell, fibre dimensions, fluid properties, and volume fractions ranging from dilute to semi-dilute. Alternating structures of streamers and backflow regions which span the height of the sedimentation cell form at short times and transition from large wavelengths to smaller wavelength as the sedimentation proceeds. No simple dependence of the horizontal wavelength on the length scales and concentration was observed in the experiments, suggesting the need for additional analysis. We also report the mean velocities and velocity fluctuations; the strength of the velocity fluctuations strongly correlates with the size of the vertical component of the sedimentation structure. Measurements of the orientation distribution, using an efficient and newly employed technique, agree with previously published results. A movie is available with the online version of the paper.

scholarly journals A Note on Nonlinearity Bias and Dichotomous Choice CVM: Implications for Aggregate Benefits Estimation

1996 ◽  
Vol 25 (1) ◽  
pp. 54-59 ◽  
Author(s):  
R.A. Souter ◽  
J.M. Bowker
Keyword(s):  
Logit Model ◽  
Nonlinear Models ◽  
Nonlinear Function ◽  
Dichotomous Choice ◽  
Sample Mean ◽  
Mean Values ◽  
Concomitant Variables ◽  
The Mean ◽  
Using Data ◽  
Single Response

It is a generally known statistical fact that the mean of a nonlinear function of a set of random variables is not equivalent to the function evaluated at the means of the variables. However, in dichotomous choice contingent valuation studies a common practice is to calculate an overall mean (or median) by integrating over offer space (numerically or analytically) an estimated logit or probit function in which sample mean values for the concomitant variables are used. We demonstrate this procedure to be incorrect and we statistically test the procedure against the correct method for nonlinear models. Using data resulting in a well-behaved logit model, we reject the hypothesis of congruence between the two means. Such a finding should be considered in future single response dichotomous choice CVM studies, particularly when aggregation is of interest.

scholarly journals Phase Transition at the Metric Elastic Universe

1996 ◽  
Vol 168 ◽  
pp. 569-570
Author(s):  
Alexander Gusev
Keyword(s):  
Phase Transition ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Vacuum State ◽  
Space Time ◽  
Deformation Tensor ◽  
De Sitter ◽  
Initial State ◽  
Deformation State ◽  
The Universe

At the last time the concept of the curved space-time as the some medium with stress tensor σαβon the right part of Einstein equation is extensively studied in the frame of the Sakharov - Wheeler metric elasticity(Sakharov (1967), Wheeler (1970)). The physical cosmology pre- dicts a different phase transitions (Linde (1990), Guth (1991)). In the frame of Relativistic Theory of Finite Deformations (RTFD) (Gusev (1986)) the transition from the initial stateof the Universe (Minkowskian's vacuum, quasi-vacuum(Gliner (1965), Zel'dovich (1968)) to the final stateof the Universe(Friedmann space, de Sitter space) has the form of phase transition(Gusev (1989) which is connected with different space-time symmetry of the initial and final states of Universe(from the point of view of isometric groupGnof space). In the RTFD (Gusev (1983), Gusev (1989)) the space-time is described by deformation tensorof the three-dimensional surfaces, and the Einstein's equations are viewed as the constitutive relations between the deformations ∊αβand stresses σαβ. The vacuum state of Universe have the visible zero physical characteristics and one is unsteady relatively quantum and topological deformations (Gunzig & Nardone (1989), Guth (1991)). Deformations of vacuum state, identifying with empty Mikowskian's space are described the deformations tensor ∊αβ, wherethe metrical tensor of deformation state of 3-geometry on the hypersurface, which is ortogonaled to the four-velocityis the 3 -geometry of initial state,is a projection tensor.

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

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