Behavior Of Brownian Motion Research Articles

Distinguishing Protein Corona from Nanoparticle Aggregate Formation in Complex Biological Media Using X-ray Photon Correlation Spectroscopy.

In biological systems, nanoparticles interact with biomolecules, which may undergo protein corona formation that can result in noncontrolled aggregation. Therefore, comprehending the behavior and evolution of nanoparticles in the presence of biological fluids is paramount in nanomedicine. However, traditional lab-based colloid methods characterize diluted suspensions in low-complexity media, which hinders in-depth studies in complex biological environments. Here, we apply X-ray photon correlation spectroscopy (XPCS) to investigate silica nanoparticles (SiO2) in various environments, ranging from low to high complex biological media. Interestingly, SiO2 revealed Brownian motion behavior, irrespective of the complexity of the chosen media. Moreover, the SiO2 surface and media composition were tailored to underline the differences between a corona-free system from protein corona and aggregates formation. Our results highlighted XPCS potential for real-time nanoparticle analysis in biological media, surpassing the limitations of conventional techniques and offering deeper insights into colloidal behavior in complex environments.

Experimental In-Situ Observatory on Brownian Motion Behavior of 105 nm Sized Silica Particles During Chemical Mechanical Polishing of 4H-SiC by an Evanescent Field

The experimentally observing optical systems for on-machine measurement have been developed to study on nano-polishing phenomena during the chemical mechanical polishing process, which is a wet process in semiconductor manufacturing. The developed optical system employs an evanescent field to selectively enhance exclusively the observatory of phenomena occurring on the surface being polished, offering a lateral resolving power of approximately 400 nm, in the slurry concentration of up to 5 wt% based on the numerical aperture of the objective lens. In addition, there is also the observability of 105 nm and down to 55 nm-sized silica particles without requiring additive fluorescence agents in or around the nano-particles, even when these particles are moving on surfaces such as silica glass or hard materials (silicon carbide: 4H-SiC). Consequently, the motion behavior of nano-particles disjoining with polishing pad asperity was explored and discussed, in this paper. Experimental results revealed that the polishing pad spatially constrains the movement of particles between the pad and the substrate surface, guiding them toward the surface being polished. During pad sliding, fluidically dragged nano-particles exhibit slower movement than the polishing pad sliding speed while retaining the Brownian motion. Furthermore, 105 nm-sized silica particles did not continuously approach to attach onto the SiC surface; the nano-particles approached in steps with reduced Brownian motion in all directions before attaching. This behavior can be attributed to the effects of van der Waals attraction and electrostatic repulsion forces between the particle and the substrate surfaces.

Effective de Sitter space, quantum behaviour and large-scale spectral dimension (3+1)

De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de Sitter space-time is not fundamental but constitutes only an effective description of a more fundamental quantum gravity ground state. This cosmological ground state is a graph, appearing on large scales as a Riemannian manifold of constant negative curvature. We model the behaviour of matter near this equilibrium state as Brownian motion in the effective thermal environment of graph fluctuations, driven by a universal time parameter. We show how negative curvature dynamically induces the asymptotic emergence of relativistic coordinate time and of leading ballistic motion governed by the isometry group of an “effective Lorentzian manifold” of opposite, positive curvature, i.e. de Sitter space-time: free fall in positive curvature is asymptotically equivalent to the leading behaviour of Brownian motion in negative curvature. The local limit theorem for negative curvature implies that the large-scale spectral dimension of this “effective de Sitter space-time” is (3+1) independently of its microscopic topological dimension. In the effective description, the sub-leading component of asymptotic Brownian motion becomes Schrödinger quantum behavior on a 3D Euclidean manifold.

EXPERIMENTAL DESIGN OF BROWNIAN MOTION USING FRACTAL GEOMETRY

Brownian motion refers to the random movement of a particle, resulting from collisions with surrounding molecules. This movement appears irregular and asymmetric, occurring in random directions and at random rates. The behavior of Brownian motion can be studied using fractal geometry, as demonstrated by 2D graphics that plot particle movement along the x and y axes. These graphics are generated using a computer program written in the Pascal programming language. To analyze the pattern of Brownian motion, 30 graphics were selected as a statistical sample. Each graphic is measured from its starting point to its endpoint, following a thousand collisions. The average distance is then calculated, and each distance value is divided by the mean distance to obtain a ratio. The resulting ratios were used to construct a histogram, which represents the distribution of distances. This distribution is then compared to the ratio distribution predicted by physics theory, allowing for further analysis and interpretation of the Brownian Motion behavior. In this study, a novel approach is proposed for analyzing Brownian Motion behavior using fractal geometry and statistical analysis. Specifically, 2D graphics are used to plot particle movement, and a statistical sample of 30 graphics is analyzed to obtain distance ratios, which are then used to construct a distribution histogram. The resulting distribution is compared to the predicted ratio distribution, providing new insights into the underlying physics of Brownian Motion. This approach may have implications for understanding complex systems in fields such as physics, chemistry, and biology. Keywords: Motion, Fractal, Random Walk, Free Walk DOI： https://doi.org/10.35741/issn.0258-2724.58.2.8

Numerical investigation of MHD convective free stream nanofluid flow influenced by radiation and chemical reaction over stretching cylinder

AbstractChemically reacting magnetohydrodynamic radiative flow of convective free stream nanofluid through a stretching cylinder using Buongiorno's model is discussed. The behavior of Brownian motion and thermophoresis is also appropriate. By adopting the similarity transformation, the partial differential equation is diminished into a first‐order ordinary differential equation (ODE). Since transformed equations are highly nonlinear these ODEs are solved by using mathematical simulation. The shooting procedure has been adopted to resolve converted equations along the attendant Runge–Kutta–Fehlberg technique. The reason behind the present work is to research the effects of different parameters of fluid, namely, magnetic parameter, free stream velocity, Brownian motion, thermophoresis, chemical reaction, heat radiation, Lewis number on nanoparticle concentration, temperature, and velocity distribution. The impact of significantly participating parameters on velocity, concentration, and temperature distribution is distinguished with appropriate physical significance. The convergence of solutions for temperature, velocity, and concentration profiles is studied carefully. The measured challenges of nanofluids are scale‐up capacity, increase in nanofluid viscosity, nanoparticle dispersion, and nanofluid cost. It is observed that nanoparticle temperature rises for more value of Brownian motion parameter while it declines for higher Lewis number. The current study in the cylindrical region is related to novel free stream flow in the presence of chemical reactions along with convective conditions which find applications in electronic systems like microprocessors and in a wide variety of industries and in the field of biotechnology. The current research helps control the transport phenomena, helping production companies to find the quality of the desired product.

The three‐dimensional bioconvective flow of Sisko nanofluid under Robin's conditions

AbstractThe proposed model investigates three‐dimensional bioconvective Sisko nanofluid flow under Robin's conditions. The Sisko nanofluid has versatile implications in drilling fluids, cement slurries, waterborne coatings, and so on. Furthermore, the inclusion of gyrotactic microorganisms prevents the deposition and agglomeration of the nanoparticles in the base fluid. Buongiorno's model is included to explore the behavior of Brownian motion and thermophoretic factors. The energy and mass transmissions along with the gyrotactic microorganism density are illustrated by the partial differential expression system with Robin's conditions. These are further reframed into an ordinary differential equation system with the aid of similarity transformation. The developing model is tackled by using the MAPLE inbuilt package BVP. The nanofluid acts as a good cooling agent for higher values of the thermophoresis parameter. Furthermore, the pseudoplastic nanofluid performs better than the dilatant nanofluid. The developed model is very useful in energy production and engineering products.

Particle Brownian motion due to random classical radiation: superfluid-like behavior in the presence of classical zero-point radiation

Nonrelativistic classical mechanics allows no fundamental transition between low-velocity and high-velocity forms of behavior, nor between low-temperature and high-temperature forms. In contrast, classical electrodynamics, which is a relativistic theory, allows fundamental transitions in velocity. Furthermore, the inclusion within the classical theory of Lorentz-invariant classical zero-point radiation allows classical electrodynamics to distinguish high-temperature and low-temperature forms of behavior. Because electromagnetism is a relativistic theory, it may provide a thermal radiation bath which gives rise to phenomena in Brownian motion which are not included in a model with a thermal bath based upon nonrelativistic particles. Here we explore the Brownian motion of a classical electric-dipole particle in random classical radiation, making use of the calculations of Einstein and Hopf. The Brownian motion as a function of temperature is analyzed in terms of the mean-square velocity and the diffusion constant for four different classical radiation spectra: the Rayleigh–Jeans spectrum, the Planck spectrum without zero-point radiation, the zero-point radiation spectrum, and the Planck spectrum including zero-point radiation. We illustrate how the inclusion of classical electromagnetic zero-point radiation alters Brownian motion behavior between high-temperature and low-temperature forms. For the Planck spectrum with zero-point radiation, the high-temperature Brownian motion agrees with some aspects found from nonrelativistic mechanics, while the low-temperature behavior includes some aspects analogous to superfluid behavior. At sufficiently low temperatures, the Brownian particle has an increasing mean-square velocity and more rapid diffusion with decreasing temperature due to the increasing dominance of the classical electromagnetic zero-point radiation.

Numerical modeling and analysis of bioconvection on MHD flow due to an upper paraboloid surface of revolution

This article gives brief summary about the boundary layer flow characteristics of magnetic generalized Newtonian fluid due to a paraboloid revolution under bioconvection and chemical reactive species. The nanofluid model utilized in this work includes the behavior of Brownian motion and thermophoresis. The differential equations can be determined by a similarity solution. The determined ordinary differential equations have been solved numerically by fifth order Runge–Kutta Fehlberg method-based shooting technique. The behavior of different physical controlling dimensionless parameters on the base flow velocity, temperature, concentration, skin friction heat and mass transfer rates are analyzed numerically and graphically. We observed that the velocity, temperature and concentration profile reduce for increasing values of Hartmann number, Weissenberg number, wall thickness, stretching index, bioconvection, Prandtl number, Lewis number and Brownian motions whilst behavior is noticed for power law index. Moreover, for increases the values of Brownian and thermophoresis parameter the temperature profile shown increasing behavior. Comparison has been with represents date and found that the results have good agreement.

Unsteady stagnation point flow of Oldroyd-B nanofluid with heat generation/absorption and nonlinear thermal radiation

This article addresses unsteady stagnation point flow of Oldroyd-B nanofluid past an impermeable stretching sheet. Characteristics of heat transfer are described within the frame of heat generation/absorption and nonlinear radiative process. Intention in present analysis is to develop a model for nanomaterial containing Brownian motion and thermophoresis phenomena. The resulting nonlinear differential systems have been solved for the convergent homotopic solutions. Behavior of sundry variable for the velocity, temperature and concentration are addressed. Numerical values examined the local Nusselt number. It is revealed that velocity field enhances for dimensionless retardation time while reverse situation is observed regarding dimensionless relaxation time. Temperature and heat transfer rate are enhanced via larger nonlinear thermal radiation and temperature parameters. Moreover, behavior of Brownian motion and thermophoresis on the concentration field is quite reverse.

Study of heat and mass transfer on MHD Walters [formula omitted] nanofluid flow induced by a stretching porous surface

This communication deals with the role of heat and mass transfer in a Walters B′ (non-Newtonian) nanofluid fluid flow through a stretching vertical porous surface. The behavior of Brownian motion, chemical reaction, thermophoresis and heat generation/absorption are also taken into consideration. A suitable similarity transformation variable is utilized to model the equations of nanoparticle concentration, momentum, and thermal energy. These ordinary differential equations are solved analytically by means of perturbation technique and then solved numerically using fourth-fifth order Runge–Kutta method. The behavior of all the sundry parameters are discussed and demonstrated via graphs. Furthermore, Sherwood number, Nusselt number and skin friction coefficient are also displayed via graphs. A numerical comparison is also presented against skin friction coefficient, Nusselt number and Sherwood number with previously published data.

Simulating the extrinsic regulation of the sinoatrial node cells using a unified computational model

The aim of this work is to develop a computational model to study the extrinsic regulation of the heart rate variability (HRV) during sympathetic and/or vagal stimulation. The model here proposed is based on two recent models of the sinoatrial node cell (SANC) action potential and the influence of the autonomic nervous system (ANS) on the activity of ionic channels of SANCs. The HRV was simulated by applying a random frequency stimulation using both a normal and a beta probability density function (PDF) for different ranges of stimulation frequencies. The HRV was then analyzed by computing the scale exponent using detrended fluctuation analysis. We found that our model reproduces the value of the scale exponent observed in healthy humans (α = 1.07 ± 0.05) when simultaneous vagal and sympathetic stimulus (with beta and normal PDFs, respectively) over the frequency range from 0 to 10 Hz are applied. Our model also predicts a Brownian motion behavior when the muscarinic receptors are blocked (α = 1.8) and the white noise behavior when the b-adrenergic receptors are blocked (α = 0.5). Our results shed light on how the ANS regulates the HRV in healthy conditions, where it is not enough to consider only one stimulation pathway with a simple normal PDF.

Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy

Here we analyze the mixed convective flow of magneto-nanofluid bounded by a vertical stretchable surface considering Brownian motion and thermophoretic diffusion effects. Additionally, the aspects of chemical reaction and activation energy are introduced. Formulation is made through the newly suggested assumption of zero particle flux at the boundary. Equations governing the locally similar flow are tackled through a numerical approach and the influences of involved parameters on the flow fields are displayed graphically. Buoyancy effects resulting from the temperature and concentration differences accelerate the fluid flow in vertical direction. Brownian motion has no influence on the heat flux from stretching wall. Heat flux from the wall diminishes upon increasing the chemical reaction rate constant. Nanoparticle concentration is directly proportional to the activation energy of chemical reaction and the behavior of Brownian motion on nanoparticle concentration is qualitative opposite to that of thermophoretic force. To our knowledge, the nanofluid flow in the regimes of chemical reaction and activation energy is just discussed in this paper.

Transience and recurrence of a Brownian path with limited local time

In this paper, we study the behavior of Brownian motion conditioned on the event that its local time at zero stays below a given increasing function $f$ up to time $T$. For a class of nonincreasing functions $f$, we show that the conditioned process converges, as $T\rightarrow\infty$, to a limit process and we derive necessary and sufficient conditions for the limit to be transient. In the transient case, the limit process is described explicitly, and in the recurrent case we quantify the entropic repulsion phenomenon by describing the repulsion envelope, stating how much slower than $f$ the local time of the process grows as a result of the conditioning. The methodology is based on a fine analysis of the subordinator given by the inverse local time of the Brownian motion. We describe the probability of general subordinator to stay above a given curve up to time $T$ via the solution of a general ordinary linear differential equation. For the specific case of the inverse local time of the Brownian motion, we explicitly and precisely compute the asymptotics of this probability for a large class of functions.

Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles.

Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles.

Dynamical properties of single-file diffusion

We study the statistics of a tagged particle in single-file diffusion, a one-dimensional interacting infinite-particle system in which the order of particles never changes. We compute the two-time correlation function for the displacement of the tagged particle for an arbitrary single-file system. We also discuss single-file analogs of the arcsine law and the law of the iterated logarithm characterizing the behavior of Brownian motion. Using a macroscopic fluctuation theory we devise a formalism giving the cumulant generating functional. In principle, this functional contains the full statistics of the tagged particle trajectory—the full single-time statistics, all multiple-time correlation functions, etc are merely special cases.

Self-powered macroscopic Brownian motion of spontaneously running liquid metal motors

We disclosed the interiorly driven macroscopic Brownian motion behavior of self-powered liquid metal motors. Such tiny motors in millimeter scale move randomly at a velocity magnitude of centimeters per second in aqueous alkaline solution, well resembling the classical Brownian motion. However, unlike the existing phenomena, where the particle motions were caused by collisions from the surrounding molecules, the current random liquid metal motions are internally enabled and self-powered, along with the colliding among neighboring motors, the substrate and the surrounding electrolyte molecules. Through uniformly dissolving only 1% (mass percentage) Al into GaIn10, many tiny motors can be quickly fabricated and activated to take the Brownian-like random motions. Further, we introduced an experimental approach of using optical image contrast, which works just like the Wilson cloud chamber, to distinctively indicate the motor trajectory resulted from the generated hydrogen gas stream. A series of unusual complicated multi-phase fluid mechanics phenomena were observed. It was also identified that the main driving factor of the motors comes from the H2 bubbles generated at the bottom of these tiny motors, which is different from the large size self-fueled liquid metal machine. Several typical mechanisms for such unconventional Brownian-like motion phenomena were preliminarily interpreted.

On the stochastic behaviour of optional processes up to random times

In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomised stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to financial mathematics, as well as to the study of the stochastic behaviour of Brownian motion with drift up to its time of overall maximum as well as up to last-passage times over finite intervals. Furthermore, a novel proof of the Jeulin-Yor decomposition formula via Girsanov's theorem is provided.

Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet

This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet.

The long time behavior of Brownian motion in tilted periodic potentials

A variety of phenomena in physics and other fields can be modeled as Brownian motion in a heat bath under tilted periodic potentials. We are interested in the long time average velocity considered as a function of the external force, that is, the tilt of the potential. In many cases, the long time behavior–pinning and de-pinning phenomenon–has been observed. We use the method of stochastic differential equation to study the Langevin equation describing such diffusion. In the over-damped limit, we show the convergence of the long time average velocity to that of the Smoluchowski–Kramers approximation, and carry out asymptotic analysis based on Risken’s and Reimann et al.’s formula. In the under-damped limit, applying Freidlin et al.’s theory, we first show the existence of three pinning and de-pinning thresholds of the normalized tilt, corresponding to the bi-stability phenomenon; and second, as noise approaches zero, derive formulas of the mean transition times between the pinning and running states.

New correlation equations for predicting the initial collection efficiency of aerosols in granular media

The new correlation equations for predicting the initial collection efficiency of aerosols are presented. Based on the Brownian dynamic simulation method of using the parabolic type constricted tube model and taking the deposition mechanisms of inertial impaction, interception, gravitational force and Brownian diffusion into consideration, two new correlation equations are obtained by regressing against a broad range of parameter values governing aerosol collection in granular media. The new correlation equations are able to describe previous experimental results well, especially for the sub-micro-aerosol particles with significant Brownian motion behavior.