DETECTION OF BROWNIAN PARTICLES (EULERIAN AND LAGRANGIAN STATISTICS OF IMPURITY PARTICLE IN ATMOSPHERE)

2008 ◽  
Vol 18 (09) ◽  
pp. 2727-2731
Author(s):  
EVGENIYA Z. GRIBOVA
Keyword(s):  
Probability Distribution ◽  
Brownian Particle ◽  
Classical Problem ◽  
Impurity Particle ◽  
Stochastic Motion ◽  
Spatial Region ◽  
Brownian Particles ◽  
Potential Applications ◽  
Passive Admixture ◽  
Meteorological Problems

We study passive admixture spreading in the atmosphere considering regular (with the wind) and stochastic motion of the particles. The probability distribution of velocities on a boundary of a given spatial region (detector) is found for particles of a passive admixture. The connection between this probability distribution and the solution of the classical problem on the probability distribution of the coordinates and velocity of a Brownian particle at a fixed moment is determined. The dependence of the obtained probability density on the relation among the parameters of the problem under consideration is discussed. Some specific examples are presented. Potential applications of the results are in ecological and meteorological problems.

scholarly journals Active Brownian particles: mapping to equilibrium polymers and exact computation of moments

Soft Matter ◽  
2020 ◽  
Vol 16 (20) ◽  
pp. 4776-4787 ◽  
Author(s):  
Amir Shee ◽  
Abhishek Dhar ◽  
Debasish Chaudhuri
Keyword(s):  
Brownian Particle ◽  
Exact Calculation ◽  
Exact Computation ◽  
Brownian Particles ◽  
Active Brownian Particle ◽  
Equilibrium Polymers

A polymer-mapping of active Brownian particle (ABP)-trajectories, and exact calculation of the moments of dynamical variables provide insights into the mechanical crossovers in polymers with length, and related dynamical crossovers in ABP-motion.

scholarly journals Intermediate scattering function of an anisotropic active Brownian particle

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Christina Kurzthaler ◽  
Sebastian Leitmann ◽  
Thomas Franosch
Keyword(s):  
Brownian Particle ◽  
Rotational Diffusion ◽  
Effective Diffusion ◽  
Mean Square Displacement ◽  
Scattering Function ◽  
Directed Motion ◽  
Stochastic Motion ◽  
Length Scales ◽  
Intermediate Scattering Function ◽  
Active Brownian Particle

Abstract Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

scholarly journals Design Strategy Network: A deep hierarchical framework to represent generative design strategies in complex action spaces

2021 ◽  
pp. 1-36
Author(s):  
Ayush Raina ◽  
Jonathan Cagan ◽  
Christopher McComb
Keyword(s):  
Probability Distribution ◽  
Design Strategy ◽  
Hierarchical Architecture ◽  
Design Strategies ◽  
Generative Design ◽  
Complex Action ◽  
Spatial Region ◽  
Hierarchical Framework ◽  
State Dependent ◽  
Action Spaces

Abstract Generative design problems often encompass complex action spaces that may be divergent over time, contain state-dependent constraints, or involve hybrid (discrete and continuous) domains. To address those challenges, this work introduces Design Strategy Network (DSN), a data-driven deep hierarchical framework that can learn strategies over these arbitrary complex action spaces. The hierarchical architecture decomposes every action decision into first predicting a preferred spatial region in the design space and then outputting a probability distribution over a set of possible actions from that region. This framework comprises a convolutional encoder to work with image-based design state representations, a multi-layer perceptron to predict a spatial region, and a weight-sharing network to generate a probability distribution over unordered set-based inputs of feasible actions. Applied to a truss design study, the framework learns to predict the actions of human designers in the study, capturing their truss generation strategies in the process. Results show that DSNs significantly outperform non-hierarchical methods of policy representation, demonstrating their superiority in complex action space problems.

scholarly journals Election algorithms with random delays in trees

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Jean-François Marckert ◽  
Nasser Saheb-Djahromi ◽  
Akka Zemmari
Keyword(s):  
Probability Distribution ◽  
Distributed Algorithm ◽  
Randomized Algorithms ◽  
Classical Problem ◽  
Random Delays ◽  
International Audience

International audience The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is studied. The election amounts to removing leaves one by one until the tree is reduced to a unique node which is then elected. The algorithm assigns to each leaf a probability distribution (that may depends on the information transmitted by the eliminated nodes) used by the leaf to generate its remaining random lifetime. In the general case, the probability of each node to be elected is given. For two categories of algorithms, close formulas are provided.

scholarly journals Avalanche-like fluidization of a non-Brownian particle gel

Soft Matter ◽  
2015 ◽  
Vol 11 (46) ◽  
pp. 9026-9037 ◽  
Author(s):  
Aika Kurokawa ◽  
Valérie Vidal ◽  
Kei Kurita ◽  
Thibaut Divoux ◽  
Sébastien Manneville
Keyword(s):  
Shear Band ◽  
Brownian Particle ◽  
Moving Wall ◽  
Brownian Particles ◽  
Start Up

We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles. Shear start up experiments evidence a heterogeneous yielding scenario: a shear band grows until complete fluidization of the material through sudden avalanche-like events that are distributed heterogeneously along the vorticity direction and correlated to the slip at the moving wall.

scholarly journals Efficient lattice Boltzmann algorithm for Brownian suspensions

2011 ◽  
Vol 369 (1944) ◽  
pp. 2237-2245 ◽  
Author(s):  
Mahesh Mynam ◽  
P. Sunthar ◽  
Santosh Ansumali
Keyword(s):  
Lattice Boltzmann ◽  
Thermal Noise ◽  
Hybrid Methods ◽  
Brownian Particle ◽  
Thermal Fluctuations ◽  
Fluid Level ◽  
Brownian Particles ◽  
Long Time ◽  
Short Time ◽  
Diffusive Behaviour

A lattice Boltzmann (LB)-based hybrid method is developed to simulate suspensions of Brownian particles. The method uses conventional LB discretization (without fluid- level fluctuations) for suspending fluid, and treats Brownian particles as point masses with a stochastic thermal noise. LB equations are used to compute the velocity perturbations induced by the particle motion. It is shown that this method correctly reproduces the short-time and long-time diffusive behaviour of a Brownian particle. Unlike the earlier hybrid methods that use thermal fluctuations in the fluid, this method correctly reproduces the temperature of the particle and does not require an empirical rescaling of the bare friction coefficient to obtain the correct diffusive behaviour. It is observed that the present method is at least twice as fast as the earlier method. This method is best suited for flows of polymers and Brownian suspensions in microfluidic devices.

THEORY OF RANDOM ADVECTION IN TWO DIMENSIONS

1996 ◽  
Vol 10 (18n19) ◽  
pp. 2273-2309 ◽  
Author(s):  
M. CHERTKOV ◽  
G. FALKOVICH ◽  
I. KOLOKOLOV ◽  
V. LEBEDEV
Keyword(s):  
Velocity Field ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Classical Problem ◽  
Passive Scalar ◽  
Two Dimensions ◽  
Change Of Variables ◽  
The Matrix ◽  
Two Dimensional Flow ◽  
Non Gaussian

The steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described at scales less than the correlation length of the flow and larger than the diffusion scale. The probability distribution of the scalar is expressed via the probability distribution of the line stretching rate. The description of the line stretching can be reduced to the classical problem of studying the product of many matrices with a unit determinant. We found a change of variables which allows one to map the matrix problem into a scalar one and to prove thus a central limit theorem for the statistics of the stretching rate. The proof is valid for any finite correlation time of the velocity field. Whatever be the statistics of the velocity field, the statistics of the passive scalar in the inertial interval of scales is shown to approach Gaussianity as one increases the Peclet number Pe (the ratio of the pumping scale to the diffusion one). The first n < ln (Pe) simultaneous correlation functions are expressed via the flux of the squared scalar and only one unknown factor depending on the velocity field: the mean stretching rate. That factor can be calculated analytically for the limiting cases. The non-Gaussian tails of the probability distributions at finite Pe are found to be exponential.

scholarly journals Whirligig beetles as corralled active Brownian particles

2021 ◽  
Vol 18 (177) ◽  
Author(s):  
Harvey L. Devereux ◽  
Colin R. Twomey ◽  
Matthew S. Turner ◽  
Shashi Thutupalli
Keyword(s):  
Phase Separation ◽  
Condensed Phase ◽  
Open Space ◽  
Brownian Particle ◽  
Low Density ◽  
Speed Scaling ◽  
New Model ◽  
Density Dependent ◽  
Brownian Particles ◽  
Active Brownian Particle

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density-dependent speed scaling like v ∼ ρ − ν with ν ≈ 0.4 over two orders of magnitude in density (ii) an inertial delay for velocity alignment of approximately 13 ms and (iii) coexisting high and low-density phases, consistent with motility-induced phase separation (MIPS). We modify a standard active Brownian particle (ABP) model to a corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that an motility-induced phase separation (MIPS) (or a MIPS like effect) can explain the co-occurrence of high- and low-density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for N = 200 and the absence of such a phase for smaller group sizes N = 50, 100.

scholarly journals Morphological transitions of active Brownian particle aggregates on porous walls

Soft Matter ◽  
2020 ◽  
Vol 16 (31) ◽  
pp. 7250-7255 ◽  
Author(s):  
Suchismita Das ◽  
Raghunath Chelakkot
Keyword(s):  
Brownian Particle ◽  
Morphological Transition ◽  
Brownian Particles ◽  
Particle Aggregates ◽  
Morphological Transitions ◽  
Porous Walls ◽  
Active Brownian Particle

Cluster of aggregated active Brownian particles (ABPs) undergoes morphological transition on porous walls.

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