Brownian diffusion. Medical search. Frequent questions

Macromolecular diffusion plays a fundamental role in biological processes. (biomedcentral.com)
The concept of Brownian motors is a recent one, having only been coined in 1995 by Peter Hänggi, but the existence of such motors in nature may have existed for a very long time and help to explain crucial cellular processes that require movement at the nanoscale, such as protein synthesis and muscular contraction. (wikipedia.org)
Dry deposition is the transfer of airborne dust particles to the surface through different mechanical processes, mainly Brownian diffusion, interception, inertial impaction, and sedimentation [ 10 , 11 ]. (hindawi.com)
Diffusion processes and local dynamic equilibria inside cells lead to nonuniform spatial distributions of molecules, which are essential for processes such as nuclear organization and signaling in cell division, differentiation and migration 1 . (nature.com)
We expect that FCS imaging will become a useful method for the precise characterization of cellular reaction-diffusion processes. (nature.com)

Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. (cam.ac.uk)
The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. (projecteuclid.org)

It is found that Heat transfer rate decreases with the influence of Brownian motion and thermophoresis parameters and the local Sherwood number increases with the effect of both Brownian motion and thermophoresis parameters. (journalpsij.com)
Brownian motion and thermophoresis were incorporated using the Buongiorno model. (hindawi.com)

Investigation has been carried out to analyze the effects of variable wall temperature and concentration on Magnetohydrodynamic mixed convection flow of a nanofluid over a nonlinear stretching sheet with variable Brownian and thermophoretic diffusion coefficient. (journalpsij.com)

First we state the almost sure convergence for the $k$-power second order increments of the fractional Brownian motion (fBm). (hal.science)

This is well established in terms of the depositional mechanisms of impaction, sedimentation, Brownian motion and (for fibers) interception. (cdc.gov)
The dry deposition velocities are calculated as a function of particle size, density, friction velocity, and surface characteristics and they include the contributions of turbulent transfer, Brownian diffusion, impaction, interception, gravitational settling, and particle rebound [ 15 , 16 ]. (hindawi.com)
Filtration theory holds that materials that are permeable to air and gases remove particles from the airstream using three mechanisms: interception, inertial impaction, and diffusion. (mddionline.com)
However, larger particles moving at higher flow rates are more likely to be trapped by inertial impaction, whereas lighter ones moving at slower speeds are more likely to be caught by diffusion. (mddionline.com)

A36.00009: Diffusing colloids in the vicinity of a surface: Anomalous yet Brownian diffusion? (aps.org)
Wachsmuth, M., Waldeck, W. & Langowski, J. Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. (nature.com)

normal states and abnormal conditions are easily interpreted through the use of DWI in conjunction with apparent diffusion coefficient (ADC) imaging by correlating findings of hyperintensity on DWI images with findings of hypointensity on ADC images (see the images below). (medscape.com)
On DWI commonly used to diagnose acute stroke (see the image below), diffusion is described by using the apparent diffusion coefficient (ADC). (medscape.com)
In the simplest case of free Brownian motion, the trajectory is subsequently analyzed to extract a diffusion coefficient. (nist.gov)
This latter data analysis step, diffusion coefficient estimation, is commonly accomplished using a statistical estimate of the average distance a particle moves, the mean-square displacement (MSD), as a function of time interval. (nist.gov)
Second, we used this distribution to derive an alternate data analysis procedure, a maximum likelihood estimator (MLE) that extracts the diffusion coefficient in a nearly-optimal way. (nist.gov)

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. (biomedcentral.com)
We are developing improved analysis algorithms for extracting diffusion coefficients from single-particle tracking data based on rigorous statistical methods. (nist.gov)
This is the interception of a particle with a fiber as a result of random particle movement (Brownian motion) and, for some materials, electrostatic attraction. (mddionline.com)

A primary motivation is to explore how one can pass, in the parabolic scaling limit, from geodesics, orthonormal frames, and/or volumes to diffusions, and hence their infinitesimal generators, on sub-Riemannian manifolds, which is interesting in light of the fact that there is no completely canonical notion of sub-Laplacian on a general sub-Riemannian manifold. (esaim-cocv.org)
To remove topological obstructions, we introduce Diffusion Variational Autoencoders (DeltaVAE) with arbitrary (closed) manifolds as a latent space. (ijcai.org)

By proving an Itô-Wentzell formula for jump diffusions as well as an abstract result of stochastic evolution equations, we obtain the stochastic integral partial differential equation for the inverse of the stochastic flow generated by a stochastic differential equation driven by a Brownian motion and a Poisson point process. (aimsciences.org)

Brownian motion refers to the erratic random movement of microscopic particles suspended in a fluid. (sfu.ca)
The theory behind Brownian motors relies on the phenomenon of Brownian motion, random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid. (wikipedia.org)
The Brownian motor, like the phenomenon of Brownian motion that underpinned its underlying theory, was also named after 19th century Scottish botanist Robert Brown, who, while looking through a microscope at pollen of the plant Clarkia pulchella immersed in water, famously described the random motion of pollen particles in water in 1827. (wikipedia.org)
Rather than fighting it, Brownian motors take advantage of the ceaseless noise to move particles efficiently and reliably. (wikipedia.org)
In this talk we present a one-dimensional diffusion process on BBM particles which is symmetric with respect to a certain random martingale measure. (cam.ac.uk)
The Brownian diffusion affects very fine particles, typically smaller than 0.1 μ m. (hindawi.com)
Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. (aip.org)
Essential physics of MIPS has been well captured by linear swimmer models such as active Brownian particles (ABPs), 2,3 run-and-tumble particles (RTPs), 4,5 and active Ornstein-Uhlenbeck particles (AOUPs). (aip.org)

Tracer diffusion at water-oil interfaces studied by fluorescence correlation spectroscopy. (mpg.de)
Here we describe a microscope based on light-sheet illumination 2 that allows massively parallel fluorescence correlation spectroscopy (FCS) 3 measurements and use it to visualize the diffusion and interactions of proteins in mammalian cells and in isolated fly tissue. (nature.com)
Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements. (nature.com)

Diffusion, or brownian movement, denotes the random motion of molecules. (medscape.com)
Diffusion of isolated surface-active molecules at the air/water interface. (mpg.de)
Different alternatives are compared for chemically reacting molecules moving by Brownian diffusion in two and three dimensions. (global-sci.com)
The diffusion ellipsoid defines the magnitude and direction of the diffusion of water molecules in each voxel in the brain. (medscape.com)
The eigenvector corresponding to the largest eigenvalue, termed the principal eigenvector, defines the main direction of diffusion of water molecules in that voxel (see the image below). (medscape.com)

In the classical view, cell membrane proteins undergo isotropic random motion, that is a 2D Brownian diffusion that should result in an homogeneous distribution of concentration. (biomedcentral.com)
A more recent NMR pulsed-gradient, spin-echo misfolded proteins (Kelly, 1998), and the nucleation, growth, (PGSE) self-diffusion study concluded that BPTI is pre- and polymorphism of protein crystals (Rosenberger et al. (lu.se)

The new theory is tested using Brownian dynamics simulations. (purdue.edu)

Brownian Dynamics (BD) is a coarse-grained implicit-solvent simulation method that is routinely used to investigate binary protein association dynamics, but due to its efficiency in handling large simulation v. (biomedcentral.com)

In a simple fluid, Brownian motion exhibits two key properties: the mean-squared displacement (MSD) increases linearly with time (the proportionality constant is the diffusivity D) and the displacement distribution is Gaussian. (sfu.ca)
Axial fluid-attenuated inversion recovery (FLAIR) image (top left), diffusion-weighted image (DWI) (top right), and axial and sagittal T1-weighted (T1W) images (bottom) in a 40-year-old man with a history of intravenous drug abuse and fever demonstrate multiple enhancing focal brain lesions in the gray-white matter junction (arrow) compatible with septic emboli. (medscape.com)
Axial diffusion-weighted image (DWI) (top left), T2-weighted (T2W) image (top right), fluid-attenuated inversion recovery (FLAIR) image (bottom left), and contrast-enhanced T1W (bottom right) image demonstrate a right convexity meningioma, which appears hypointense on DWI image. (medscape.com)
We present an unconditionally energy stable and uniquely solvable finite difference scheme for the Cahn-Hilliard-Brinkman (CHB) system, which is comprised of a Cahn-Hilliard-type diffusion equation and a generalized Brinkman equation modeling fluid flow. (global-sci.com)

Here, we report experiments on a simple system where D(x, t) is known: the Brownian motion of a colloidal sphere near a boundary wall. (sfu.ca)

This process is obtained by a time-change of a standard Brownian motion in terms of the associated positive continuous additive functional. (cam.ac.uk)
To discretize the diffusion terms, we use the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches. (global-sci.com)

The next step is to recognize that a Wiener process, that is, an $\mathscr{F}_t$-adapted Brownian Motion $W_t$, is a Markov Process and as such possesses the so called Markov Property. (stackexchange.com)

The model of connected compartments exhibits the length-scale dependent diffusion that is observed in many heterogeneous environments, such as porous catalysts and biological environments. (purdue.edu)
The new theory generalizes the classic Smoluchowski diffusion limit to the case of heterogeneous environments. (purdue.edu)

Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation. (thenakedscientists.com)
These trees can also be grown easily in an electrodeposition cell, and are the direct result of diffusion-limited aggregation. (thenakedscientists.com)

Aspects of Brownian Motion (Mansuy & Yor) give an expression for the joint Laplace transform of $B_t$ and $\int_0^t B_s^2 ds$ (section 2.1). (mathoverflow.net)

Since the early 1980's physicists have started to investigate analytical and probabilistic problems on fractals, for instance questions about heat diffusion, Brownian motion and vibration. (europa.eu)

Diffusion is termed isotropic if the motion is equal in all directions. (medscape.com)
This is sufficient for pathologies in areas such as gray matter, where diffusion is usually isotropic. (medscape.com)

where W is a standard complex Brownian bridge. (mathoverflow.net)
We consider the one-dimensional diffusion $X$ that satisfies the stochastic differential equation $$dX_t = b(X_t) \, dt + \sigma (X_t) \, dW_t $$ in the interior $int(I) = \mbox{} ]\alpha, \beta[$ of a given interval $I \subseteq [-\infty, \infty]$, where $b, \sigma: int(I)\rightarrow \mathbb{R}$ are Borel-measurable functions and $W$ is a standard one-dimensional Brownian motion. (projecteuclid.org)

Diffusion tensor imaging can be used to measure anisotropy per voxel and provides directional information relevant for magnetic resonance tractography or fiber tracking in vivo. (medscape.com)

Diffusion-weighted imaging (DWI) is a well-established magnetic resonance imaging (MRI) method for diagnosing cerebral ischemia. (medscape.com)
[ 1 , 2 ] Imaging and interpretation of water diffusion have improved with the development of diffusion tensor imaging (DTI). (medscape.com)
Diffusion tensor imaging has shown strong momentum in research performed to evaluate the neural fibers of the central nervous system (CNS). (medscape.com)
Diffusion-weighted imaging has been shown to be useful in the investigation of brain disorders such as epilepsy , multiple sclerosis , brain abscesses , brain tumors, mild traumatic brain injury, and hypertensive encephalopathy (see the images below). (medscape.com)
Diffusion tensor imaging allows direct examination of the brain microstructure and has become a useful tool for investigating brain disorders such as stroke, epilepsy, multiple sclerosis (MS), brain tumors, and demyelinating and dysmyelinating disorders. (medscape.com)
Imaging the mobility of heterochromatin protein HP1α (ref. 4 ) in cell nuclei we could provide high-resolution diffusion maps that reveal euchromatin areas with heterochromatin-like HP1α-chromatin interactions. (nature.com)
Figure 2: 1D- and 2D-FCS imaging of protein diffusion in Madin-Darby canine kidney (MDCK) cells. (nature.com)
Figure 3: 2D-FCS imaging of protein diffusion in Drosophila wing imaginal discs. (nature.com)

If this is the case, Brownian motors may have implications for the foundations of life itself. (wikipedia.org)

The applications of Brownian motors are most obvious in nanorobotics due to its inherent reliance on directed motion. (wikipedia.org)

But it is worth mentioning that when the distribution of noise of the accumulation tends to a more heavy-tailed distribution, low values of the noise are less likely to happen, and then the accumulation process between two jumps is less noisy than in the diffusion model. (mathpsych.org)
In contrast with the previous evidence accumulation models that include only one noise distribution, the Levy-Brownian model utilizes both Gaussian and Levy white noises simultaneously in a way that the noise of the accumulation process is a weighted summation of the Gaussian (its weight is equal to lambda) and the Levy (its weight is equal to 1). (mathpsych.org)
We have tested the performance of this model on some perceptual and lexical decision tasks and the obtained results exhibit a better performance of the model in comparison with the Levy Flight and diffusion models. (mathpsych.org)

In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. (ijcai.org)

Brownian motors are nanoscale or molecular machines that use chemical reactions to generate directed motion in space. (wikipedia.org)

In more recent times, humans have attempted to apply this knowledge of natural Brownian motors to solve human problems. (wikipedia.org)

Duality formula for the bridges of a Brownian diffusion. (wias-berlin.de)

Does the hitting time of +1/-1 of a Brownian motion posess a density? (mathoverflow.net)

Chemicals and Drugs5

Analytical, Diagnostic and Therapeutic Techniques and Equipment9

Phenomena and Processes14

Disciplines and Occupations3

Information Science4

Health Care2

Processes5

Branching Brownian motion2

Motion and thermophoresis2

Thermophoretic diffusion1

Fractional Browni1

Impaction4

Anomalous2

Coefficient5

Particle3

Manifolds2

Stochastic integral1

Particles8

Fluorescence3

Molecules5

Proteins2

Simulations1

Dynamics1

Fluid4

Boundary1

Continuous2

Wiener1

Environments2

Aggregation2

Aspects1

Heat1

Isotropic2

Standard2

Fiber1

Imaging8

Case1

Applications1

Model3

Properties1

Space1

Problems1

Formula1

Time1