scholarly journals Irreversibility in Active Matter: General Framework for Active Ornstein-Uhlenbeck Particles

2021 ◽  
Vol 8 ◽  
Author(s):  
Lennart Dabelow ◽  
Ralf Eichhorn
Keyword(s):  
Brownian Motion ◽  
Technical Note ◽  
Active Matter ◽  
Directed Motion ◽  
Central Importance ◽  
Uhlenbeck Process ◽  
Particle Distributions ◽  
Minimal Description ◽  
The Individual ◽  
Log Ratio

Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called active Ornstein-Uhlenbeck particles an extension of passive Brownian motion where activity is represented by an additional fluctuating non-equilibrium “force” with simple statistical properties (Ornstein-Uhlenbeck process). While in passive Brownian motion, entropy production along trajectories is well-known to relate to irreversibility in terms of the log-ratio of probabilities to observe a certain particle trajectory forward in time in comparison to observing its time-reversed twin trajectory, the connection between these concepts for active matter is less clear. It is therefore of central importance to provide explicit expressions for the irreversibility of active particle trajectories based on measurable quantities alone, such as the particle positions. In this technical note we derive a general expression for the irreversibility of AOUPs in terms of path probability ratios (forward vs. backward path), extending recent results from [PRX 9, 021009 (2019)] by allowing for arbitrary initial particle distributions and states of the active driving.

The Fluctuating Lattice Boltzmann

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Brownian Motion ◽  
Fluid Flow ◽  
Lattice Boltzmann ◽  
Thermal Fluctuations ◽  
Directed Motion ◽  
Statistical Fluctuations ◽  
Lattice Boltzmann Models ◽  
Motion Versus ◽  
The Way

Fluid flow at nanoscopic scales is characterized by the dominance of thermal fluctuations (Brownian motion) versus directed motion. Thus, at variance with Lattice Boltzmann models for macroscopic flows, where statistical fluctuations had to be eliminated as a major cause of inefficiency, at the nanoscale they have to be summoned back. This Chapter illustrates the “nemesis of the fluctuations” and describe the way they have been inserted back within the LB formalism. The result is one of the most active sectors of current Lattice Boltzmann research.

DIRECTED MOTION OF BROWNIAN MOTORS: A RATCHET MODEL OF TWO-COUPLED MOLECULAR MOTORS

2007 ◽  
Vol 21 (28) ◽  
pp. 1915-1921 ◽  
Author(s):  
SHUTANG WEN ◽  
HONGWEI ZHANG ◽  
LEIAN LIU ◽  
XIAOFENG SUN ◽  
YUXIAO LI
Keyword(s):  
Molecular Motors ◽  
Particle System ◽  
Langevin Equations ◽  
Transition Rates ◽  
Neck Length ◽  
Directed Motion ◽  
Mean Velocity ◽  
Positive Direction ◽  
Brownian Motors ◽  
The Individual

We investigated the motion of two-head Brownian motors by introducing a model in which the two heads coupled through an elastic spring is subjected to a stochastic flashing potential. The ratchet potential felt by the individual head is anti-correlated. The mean velocity was calculated based on Langevin equations. It turns out that we can obtain a unidirectional current. The current is sensitive to the transition rates and neck length and other parameters. The coupling of transition rate and neck length leads to variations both in the values and directions of currency. With a larger neck length, the bi-particle system has a larger velocity in one direction, while with a smaller neck length, it has a smaller velocity in the other direction. This is very likely the case of myosins with a larger neck length and larger velocity in the positive direction of filaments and kinesins with a smaller neck length and smaller velocity in the negative direction of microtubules. We also further investigated how current reversal depended on the neck length and the transition rates.

scholarly journals Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 716 ◽  
Author(s):  
Pavel Kříž ◽  
Leszek Szała
Keyword(s):  
Brownian Motion ◽  
Least Squares ◽  
Fractional Brownian Motion ◽  
Numerical Experiments ◽  
Covariance Structure ◽  
Mesh Size ◽  
Uhlenbeck Process ◽  
Least Squares Estimators ◽  
Discrete Time Observations ◽  
Drift Parameter

We introduce three new estimators of the drift parameter of a fractional Ornstein–Uhlenbeck process. These estimators are based on modifications of the least-squares procedure utilizing the explicit formula for the process and covariance structure of a fractional Brownian motion. We demonstrate their advantageous properties in the setting of discrete-time observations with fixed mesh size, where they outperform the existing estimators. Numerical experiments by Monte Carlo simulations are conducted to confirm and illustrate theoretical findings. New estimation techniques can improve calibration of models in the form of linear stochastic differential equations driven by a fractional Brownian motion, which are used in diverse fields such as biology, neuroscience, finance and many others.

scholarly journals Apparent Phototaxis Enabled by Brownian Motion

2020 ◽  
Author(s):  
Lukas Niese ◽  
Linlin Wang ◽  
Sayan Das ◽  
Juliane Simmchen
Keyword(s):  
Brownian Motion ◽  
Phototrophic Bacteria ◽  
Active Matter ◽  
Obvious Reason ◽  
Theoretical Considerations ◽  
Phototactic Behaviour ◽  
Do So

Biomimetic behaviour in artificially created active matter that allow deterministic and controlled motility has become of growing interest in recent years. It is well known that phototrophic bacteria optimize their position with respect to light by phototaxis. Here, we describe how our magnetic, photocatalytic microswimmers apparently undergo phototactic behaviour. Since there is no obvious reason for the particles to do so, we analyze different influences and elucidate through experiments and theoretical considerations from which physical circumstances this behaviour originates.

The unification of neural activity

1968 ◽  
Vol 171 (1024) ◽  
pp. 353-359 ◽  
Keyword(s):  
Nervous System ◽  
Neural Activity ◽  
Nerve Cells ◽  
General Nature ◽  
Central Importance ◽  
Stimulus Response ◽  
Simple Hypothesis ◽  
Neural Organization ◽  
The Individual ◽  
The Brain

In studying the brain, two levels of investigation emerge naturally. One of these concerns itself with properties of nerve cells, their numbers, patterns of firing, interconnexions, and so forth. The other considers the whole nervous system in what one may call ‘macroscopic’ terms. Thus it discusses ‘stimulus’, ‘response’, ‘decision’, etc. At this latter level, the nervous system operates with considerable unity. The individual nerve cells must therefore be linked in a well-integrated manner and the general nature of this integration has been recognized, especially by neurophysiologists such as Sherrington, to present a problem of central importance for our understanding of the brain. In previously published work, I have put forward a theory of how this unification of neural activity might be achieved and of a possible molecular biological basis of the necessary neural organization. In this talk I restrict myself to the first of these and thus give an account of what might be called the basic logic of the unification. I also indicate briefly how a simple hypothesis about the basis of memory would fit into such a theory.

scholarly journals On conditional Ornstein–Uhlenbeck processes

1984 ◽  
Vol 16 (04) ◽  
pp. 920-922
Author(s):  
P. Salminen
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Bessel Process ◽  
Uhlenbeck Process ◽  
Brownian Motions ◽  
Ornstein Uhlenbeck Process ◽  
The Law ◽  
Similar Description

It is well known that the law of a Brownian motion started from x > 0 and conditioned never to hit 0 is identical with the law of a three-dimensional Bessel process started from x. Here we show that a similar description is valid for all linear Ornstein–Uhlenbeck Brownian motions. Further, using the same techniques, it is seen that we may construct a non-stationary Ornstein–Uhlenbeck process from a stationary one.

scholarly journals Continuous-variable tomography of solitary electrons

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
J. D. Fletcher ◽  
N. Johnson ◽  
E. Locane ◽  
P. See ◽  
J. P. Griffiths ◽  
...  
Keyword(s):  
Wigner Function ◽  
Information Technologies ◽  
Wide Band ◽  
Quantum Tomography ◽  
Continuous Variable ◽  
State Density ◽  
Electronic Excitations ◽  
Particle Distributions ◽  
Experimental Resolution ◽  
The Individual

AbstractA method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated from the Fermi sea. While we cannot resolve the pure state Wigner function of our excitations due to classical fluctuations, we can partially resolve the chirp and squeezing of the Wigner function imposed by emission conditions and quantify the quantumness of the source. This tomography scheme, when implemented with sufficient experimental resolution, will enable quantum-limited measurements, providing information on electron coherence and entanglement at the individual particle level.

scholarly journals On the Entropy of Fractionally Integrated Gauss–Markov Processes

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2031
Author(s):  
Mario Abundo ◽  
Enrica Pirozzi
Keyword(s):  
Dynamical System ◽  
Stochastic Process ◽  
Brownian Motion ◽  
Markov Process ◽  
Markov Processes ◽  
Numerical Approximation ◽  
Uhlenbeck Process ◽  
Sample Paths ◽  
Ornstein Uhlenbeck Process ◽  
Application Fields

This paper is devoted to the estimation of the entropy of the dynamical system {Xα(t),t≥0}, where the stochastic process Xα(t) consists of the fractional Riemann–Liouville integral of order α∈(0,1) of a Gauss–Markov process. The study is based on a specific algorithm suitably devised in order to perform the simulation of sample paths of such processes and to evaluate the numerical approximation of the entropy. We focus on fractionally integrated Brownian motion and Ornstein–Uhlenbeck process due their main rule in the theory and application fields. Their entropy is specifically estimated by computing its approximation (ApEn). We investigate the relation between the value of α and the complexity degree; we show that the entropy of Xα(t) is a decreasing function of α∈(0,1).

Sign in / Sign up

Export Citation Format

Share Document