Random Diffusion Research Articles

The trajectory patterns of single HIV-1 virus-like particle in live CD4 cells: A real time three-dimensional multi-resolution microscopy study using encapsulated nonblinking giant quantum dot.

The exploration of virology knowledge was limited by the optical technology for the observation of virus. Previously, a three-dimensional multi-resolution real-time microscope system (3D-MRM) was developed to observe the uptake of HIV-1-tat peptide-modified nanoparticles in cell membrane. In this study, we labeled HIV-1 virus-like particles (VLPs) with passivated giant quantum dots (gQDs) and recorded their interactive trajectories with human Jurkat CD4 cells through 3D-MRM. The labeled of gQDs of the HIV-1 VLPs in sucrose-gradient purified viral lysates was first confirmed by Cryo-electronic microscopy and Western blot assay. After the infection with CD4 cells, the gQD-labeled VLPs were visualized and their extracellular and intracellular trajectories were recorded by 3D-MRM. A total of 208 prime trajectories was identified and classified into three distinct patterns: cell-free random diffusion pattern, directional movement pattern and cell-associated movement pattern, with distributions and mean durations were 72.6%/87.6s, 9.1%/402.7sand 18.3%/68.7s, respectively. Further analysis of the spatial-temporal relationship between VLP trajectories and CD4 cells revealed the three stages of interactions: (1) cell-associated (extracellular) diffusion stage, (2) cell membrane surfing stage and (3) intracellular directional movement stage. A complete trajectory of HIV-1 VLP interacting with CD4 cells was presented in animation. This encapsulating method could increase the accuracy for the observation of HIV-1-CD4 cell interaction in real time and three dimensions.

Crystal growth according to the law of proportionate effect

Abstract This paper summarizes an approach to crystal growth that was published in parts in various articles over the course of 25 years by the present author and his colleagues. Evidence for this approach, which is confirmed in detail by data in the cited publications and in the figures and equations in the supplementary material that accompanies this paper (see the Online Materials1), comes mainly from the shapes of crystal size distributions (CSDs). Such distributions reveal the growth histories of natural minerals and synthetic compounds, histories that can be used to make geological interpretations and to guide industrial syntheses. CSDs have three fundamental shapes: log-normal, asymptotic, and Ostwald. These shapes result from different degrees of supersaturation near the time of nucleation. The first two distribution shapes form according to the Law of Proportionate Effect (LPE) at moderate supersaturation, and the latter rare distribution forms by Ostwald ripening at large supersaturation. Initially, the first two distributions have mean diameters of up to tens of nanometers and grow by surface-limited growth kinetics. The slow step in this reaction is the incorporation of nanoparticles (bits of crystal or adparticles) onto the crystal surface. As the crystals become larger, their demand for nutrients, as calculated by the LPE, increases exponentially. Then the slow step in the reaction changes to the rate of transfer of nutrients to the crystal (supply- or transport-limited growth). Crystal diameters often grow the most during this latter stage, and the initial CSD shapes that originally formed during surface-limited growth are retained and scaled up proportionately. Proportionate growth during the supply-limited stage can be simulated approximately by multiplying the diameter of each crystal in a distribution by a constant. Crystals can also grow by a constant rate law in which a constant length is added to each crystal diameter in the distribution. This rare process causes the original CSD to narrow so that its initial shape is not preserved. The growth law that prevails, either proportionate or constant, is determined by the manner in which nutrients are supplied to the crystal. Supply is by advective flow during proportionate growth, with the nutrient solution moving with respect to the crystals. Constant growth relies on the random diffusion of nutrients through a quiescent solution. Proportionate growth is by far the most common growth law, and therefore, nutrient supply by diffusion alone during crystal growth is uncommon. Distributions formed by Oswald ripening and those formed by other rare processes are also discussed. During Ostwald ripening, nucleation caused by mixing reactants at large supersaturation forms crystals that are extremely fine and numerous. The larger crystals grow at the expense of the finer, less stable crystals, thereby forming, on completion, the universal steady-state CSD shape predicted by the Lifshitz-Slyozov-Wagner (LSW) theory. This unique CSD shape, as well as other rare shapes, then are scaled up to larger sizes by supply limited proportionate growth.

Image encryption algorithm based on 2D‐CLICM chaotic system

AbstractImage encryption algorithm based on a two‐dimensional Chebyshev‐Logistic‐Infinite Collapse Map (2D‐CLICM) is proposed. A new two‐dimensional chaotic map is designed, and numerical studies show that 2D‐CLICM has a larger chaotic region, better randomness and more complex chaotic behavior. An image encryption algorithm (CLICM‐IE) is developed based on the 2D‐CLICM. The randomly generated key is used to generate more random chaotic sequences and the security is greatly improved. To obtain lower computation and time complexity, the whole process performs row encryption for each image pixel. The Arnold transformation preprocesses the image and then the encryption of image pixels is accomplished by controlling the random confusion and diffusion parts with the sequence generated by 2D‐CLICM. The results show that the CLICM‐IE algorithm is deeply random and unpredictable, and resists a variety of attacks. These results can provide good basis and practical application for the chaos generation and image encryption.

Alterations in white matter integrity and network topological properties are associated with a decrease in global motion perception in older adults.

Previous studies have mainly explored the effects of structural and functional aging of cortical regions on global motion sensitivity in older adults, but none have explored the structural white matter (WM) substrates underlying the age-related decrease in global motion perception (GMP). In this study, random dot kinematogram and diffusion tensor imaging were used to investigate the effects of age-related reductions in WM fiber integrity and connectivity across various regions on GMP. We recruited 106 younger adults and 94 older adults and utilized both tract-based spatial statistics analysis and graph theoretical analysis to comprehensively investigate group differences in WM microstructural and network connections between older and younger adults at the microscopic and macroscopic levels. Moreover, partial correlation analysis was used to explore the relationship between alterations in WM and the age-related decrease in GMP. The results showed that decreased GMP in older adults was related to decreased fractional anisotropy (FA) of the inferior frontal-occipital fasciculus, inferior longitudinal fasciculus, anterior thalamic radiation, superior longitudinal fasciculus, and cingulum cingulate gyrus. Decreased global efficiency of the WM structural network and increased characteristic path length were closely associated with decreased global motion sensitivity. These results suggest that the reduced GMP in older adults may stem from reduced WM integrity in specific regions of WM fiber tracts as well as decreased efficiency of information integration and communication between distant cortical regions, supporting the "disconnection hypothesis" of cognitive aging.

Non-Local Kinetics: Revisiting and Updates Emphasizing Fractional Calculus Applications

Non-local kinetic problems spanning a wide area of problems where fractional calculus is applicable have been analyzed. Classical fractional kinetics based on the Continuum Time Random Walk diffusion model with the absence of stationary states, real-world problems from pharmacokinetics, and modern material processing have been reviewed. Fractional allometry has been considered a potential area of application. The main focus in the analysis has been paid to the memory functions in the convolution formulation, crossing from the classical power law to versions of the Mittag-Leffler function. The main idea is to revisit the non-local kinetic problems with an update updating on new issues relevant to new trends in fractional calculus.

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

AbstractWe propose a novel capsule‐based deep encoder–decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into an image‐to‐image regression encoder–decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) – retaining pose and position information related to an entity to name a few. The performance of the proposed approach is illustrated by solving two different variants of elliptic partial differential equations (PDE): a stochastic version without a source term having an input dimensionality of 1024 and a deterministic pressure Poisson equation for flow past a cylinder. The first PDE, that is, the stochastic PDE (SPDE), also governs systems in mechanics such as steady heat conduction, groundwater flow, or other diffusion processes. In this article, the problem definition for this SPDE is such that it does not restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. Finally, we also evaluate the performance of our model on the uncertainty propagation problem based on this equation. The obtained results from the performance evaluation of the developed model on the mentioned problems indicate that the proposed approach is accurate, data efficient, and robust.

An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs

An ensemble-based time stepping scheme is applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equation. The EMC scheme solves a single linear system including several right-side vectors at each time step. Stability analysis and error estimates are derived. Two numerical examples verify the theoretical results and the validity of the EMC method.

Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow

Hypothesis: The classical Schulze-Hardy rule states that the critical coagulation concentration (CCC) of colloidal particles is inversely proportional to the counter-ionic valence at powers ranging from 2 to 6. However, the inverse Schulze-Hardy rule has recently been proposed, suggesting that the CCC can also be inversely proportional to the co-ionic valence. Previous studies on these rules did not consider the effect of flow on aggregation kinetics and the CCC. This study aims to investigate the effect of multivalent counter-ions and co-ions on aggregation kinetics and the CCCs in systems with and without a mixing flow.Experiments: We measured the aggregation rate coefficients of polystyrene sulfate latex particles as a function of the salt concentration with different ionic species. Furthermore, we analyzed these measurements using theoretical models based on hydrodynamic pair-diffusion in a random flow and trajectory analysis in two steady flows. The analysis was conducted using zeta potentials determined through electrophoretic measurements.Findings: Although the trajectory analysis underestimates the CCCs, the hydrodynamic pair-diffusion model can capture the shift of critical coagulation concentrations in the mixing flow to higher values than those in Brownian aggregation and also shows a better agreement with the experimental results. This result suggests that combining random flow and Brownian diffusion is crucial for developing a consistent framework for predicting both Brownian aggregation and aggregation in a mixing flow.

Pursuit problem with a stochastic prey that sees its chasers

A recent stochastic pursuit model describes a pack of chasers (hounds) that actively move toward a target (hare) that undergoes pure Brownian diffusion (Bernardi and Lindner 2022 Phys. Rev. Lett. 128 040601). Here, this model is extended by introducing a deterministic ‘escape term’, which depends on the hounds’ positions. In other words, the hare can ‘see’ the approaching hounds and run away from them, in addition to the ‘blind’ random diffusion. In the case of a single chaser, the mean capture time (CT) can still be computed analytically. At weak noise, the qualitative behavior of the system depends on whether the hare’s maximum running drift speed is above or below a critical value (the pursuers’ speed), but not on the target’s viewing range, whereas the capture statistics at strong noise is similar to those of the original model without escape term. When multiple hounds are present, the behavior of the system is surprisingly similar to the original model with purely diffusing target, because the escape terms tend to compensate each other if the prey is encircled. At weak noise levels and ‘supracritical’ maximum escape speed, the hare can slip through the chaser pack and lead to a very strong increase of the mean CT with respect to the blind case. This large difference is due to rare events, which are enhanced when the symmetry in the initial conditions is disrupted by some randomness. Comparing the median of the CT probability density (which reflects the typical CT) with the mean CT makes clear the contribution of rare events with exceptionally long CTs.

Long range chromosomal interactions and first passage process in budding yeast.

Chromosomal interaction plays a critical role for nuclear processes including DNA repair, replication, and transcription. One important step during the interaction is the encountering of two chromosome segments, which in statistical physics presents a first passage problem. Here, we use a novel method developed in our lab, chemically induced chromosomal interaction (CICI), to study chromosome motion and the first passage dynamics. We show that both random diffusion and cohesin loop extrusion contribute to intrachromosomal interactions. We also applied polymer physics models to understand the chromosome dynamics.

Slow Time Phenomena in Heterogeneous Materials: from Microscopic Fluctuations to Macroscopic Relaxation

Slow time relaxation of elastic moduli with typically logarithmic time dependence is observed in many media interesting for materials science. This phenomenon is related to internal structure and is, hence, important for the development of present-day materials. Here, we provide a general explanation showing a close link between slow time phenomena and fluctuations on the microscopic and mesoscopic scales. We look for the origin of slow time phenomena in random walk or diffusion processes on microscopic scales. Some bonds occurring in the metastable state make a transition through the energy barriers due to small fluctuations slightly perturbing the statistical equilibrium. If the number of the excited bonds is small compared to the total number of bonds in a heterogeneous material, the process of the transition as a whole can be considered as mesoscopic fluctuations. Averaging over all transient bonds or states is revealed in the observed macroscopic relaxation of elastic moduli, velocities, and others. The functional dependence on time in the relaxation process has been shown to be controlled by the profile of energy barriers. The results obtained point to their possible applications in materials science.

Numerical Study on the Heat Transfer Characteristics of Cu-Water and TiO2-Water Nanofluid in a Circular Horizontal Tube

A numerical simulation of convective heat transfer coefficient (hconv) was studied with Cu-Water and TiO2-Water nanofluids flowing through a circular tube subjected to uniform wall heat flux boundary conditions under laminar and turbulent regimes. Four different concentrations of nanofluids (ɸ = 0.5, 1, 1.5 and 2%) were used for the analysis and the Reynolds number (Re) was varied from laminar (500 to 2000) to turbulent flow regime (5000 to 20,000). The dependence of hconv on Re and ɸ was investigated using a single-phase Newtonian approach. In comparison to base fluid, average hconv enhancements of 10.4% and 7.3% were noted, respectively, for the maximum concentration (ɸ = 2%) and Re = 2000 for Cu-Water and TiO2—water nanofluids in the laminar regime. For the same ɸ under the turbulent regime (Re = 20,000), the enhancements were noted to be 14.6% and 13.2% for both the nanofluids, respectively. The random motion (Brownian motion) and heat diffusion (thermophoresis) by nanosized particles are the two major slip mechanisms that have more influence on the enhancement of hconv. In addition, the Nusselt number (Nu) of the present work was validated for water with the Shah and Dittus Boelter equation and found to have good agreement for both the regimes.

Acceptance-Aware Mobile Crowdsourcing Worker Recruitment in Social Networks

With the increasing prominence of smart mobile devices, an innovative distributed computing paradigm, namely Mobile Crowdsourcing (MCS), has emerged. By directly recruiting skilled workers, MCS exploits the power of the crowd to complete location-dependent tasks. Currently, based on online social networks, a new and complementary worker recruitment mode, i.e., socially aware MCS, has been proposed to effectively enlarge worker pool and enhance task execution quality, by harnessing underlying social relationships. In this paper, we propose and develop a novel worker recruitment game in socially aware MCS, i.e., <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> cceptance-aware <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</b> orker <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> ecruitment ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AWR</b> ). To accommodate MCS task invitation diffusion over social networks, we design a Random Diffusion model, where workers randomly propagate task invitations to social neighbors, and receivers independently make a decision whether to accept or not. Based on the diffusion model, we formulate the AWR game as a combinatorial optimization problem, which strives to search a subset of seed workers to maximize overall task acceptance under a pre-given incentive budget. We prove its NP hardness, and devise a meta-heuristic-based evolutionary approach named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MA-RAWR</i> to balance exploration and exploitation during the search process. Comprehensive experiments using two real-world data sets clearly validate the effectiveness and efficiency of our proposed approach.

CFD modeling of influenza virus diffusion during coughing and breathing in a ventilated room

The virus diffusion in a ventilated room with the droplets produced by coughing and breathing are presented by the Lagrangian model. When the human body is located in the middle of the room with two locations of AC, in front of and behind the human body, three angles of Air Conditioning (AC) gate are applied 0°, 30°, and 60° to show droplet particle diffusion in the room in these cases. Three types of coughing velocity profiles were selected, real human coughing, sinusoidal cough, and cough jet with one velocity profile of breathing as a step function to cover the inhaling and exhaling cycle. The simulation results show that the uncovered standing in the middle of the room, are more susceptible to infection for the bouncy and forced flow around the human body. Droplet particle moves in the room as a random diffusion and it is very sensitive to the thermal load inside the room, generally depends on the bouncy force and pressure force due to convection heat transfer. when the AC location at the opposite direction of coughing flow, the droplet travels a distance of about 3 m, 2.85 m, and 2.75 m for real cough, sinusoidal cough, and cough jet respectively. While the droplet travel distance is about 3.1 m, 3.2 m, and 2.9 m when the AC location is at the same direction of coughing flow. Finally, the adopted CFD modeling was also used to show the effects of different AC locations on coughing, breathing particle droplets distribution in different indoor spaces, such as buildings, hospitals, and public transports, Also, showed good visual demonstration and representation of the real physical processes.

Population dynamics with resource-dependent dispersal: single- and two-species models.

In this paper, we consider the population models with resource-dependent dispersal for single-species and two-species with competition. For the single-species model, it is well-known that the total population supported by the environment is always greater than the environmental carrying capacity if the dispersal is simply random diffusion. However, we find that the total population supported can be equal or smaller than the environmental carrying capacity when the dispersal depends on the resource distribution. This analytical finding not only well agrees with the yeast experiment observation of Zhang et al. (Ecol Lett 20(9):1118-1128, 2017), but also indicates that resource-dependent dispersal may produce different outcomes compared to the random dispersal. For the two-species competition model, when two competing species use the same dispersal strategy up to a multiplicative constant (i.e. their dispersal strategies are proportional) or both diffusion coefficients are large, we give a classification of global dynamics. We also show, along with numerical simulations, that if the dispersal strategies are resource-dependent, even one species has slower diffusion, coexistence is possible though competitive exclusion may occur under different conditions. This is distinct from the prominent result that with random dispersal the slower diffuser always wipes out its fast competitor. Our analytical results, supported by the numerical simulations, show that the resource-dependent dispersal strategy has profound impact on the population dynamics and evolutionary processes.

An easy-to-assemble probe for in situ corrosion testing of archaeological metal

This paper describes the construction and application of an easily assembled electrochemical probe for testing the corrosion of archaeological metals in situ. The probe tip opens a gas-guiding groove to effectively solve the problem of random diffusion of electrolyte solution onto a rusted or patinated surface. After assessing the differences in EIS curves from this probe and a conventional flat cell, a bronze coin of the Northern Song Dynasty with a diameter of 2.5 cm was successfully studied using a 28-point mapping mode. The overall corrosion state of the bronze coin was assessed by fitting the charge transfer resistance (Rct) and rust resistance (Rr) as representative parameters. This is beneficial for providing clear guidance on the protection of targeted micro-areas of metal heritage objects, with broad application prospects in the field of monitoring rusted metal corrosion.

Dynamics of a diffusive competition model with memory effect and spatial heterogeneity

In this paper, a diffusive competition model is formulated by considering the memory-based diffusions of species in their movement and spatial heterogeneity of the resource. The global existence of solution for the proposed model is proved. Under weak competition, the existence and stability of the positive steady state are obtained, when the random diffusion rates are large enough, by using implicit function theorem and some priori estimations. However, when memory-based diffusions dominate the dynamics, spatial-temporal patterns can be observed. We also consider the case that both competition coefficients equal to one, showing that the stabilities of semi-trivial steady states, existence of positive steady state by the method of upper and lower solutions, and bistable dynamics of the model. The results reveal that the memory-based diffusion plays an important role on the competition outcomes. Specifically, the species with slower random diffusion may not help itself to wipe out its competitor because of disadvantageous memory-based diffusion, while the species with faster random diffusion but with advantageous memory-based diffusion may win the competition.

Chaotic Image Encryption Using Piecewise-Logistic-Sine Map

The classical one-dimension chaotic maps are not adequately secure, and some improved maps usually have a high time complexity. To address these problems, this paper presents a new Piecewise-Logistic-Sine map (PLSM). The bifurcation diagrams, Lyapunov exponent, and running time of the proposed PLSM are analyzed, and the outcomes show that it has better chaotic behavior with low time complexity. Furthermore, diffusion by certain rules is vulnerable to attack, so a PLSM-based image encryption scheme with random exclusive OR diffusion is proposed. Using a 256-bit secret key, the initial value and parameters of PLSM are calculated by the key distribution method. Then four chaotic sequences are generated by PLSM, they are used in three rounds of random exclusive OR diffusion. This scheme can spread a small change in the original image to all pixels, and the performance evaluation shows the security of this image encryption scheme.

Global boundedness in a parabolic-parabolic-elliptic attraction-repulsion chemotaxis system with nonlinear productions

This paper investigates the global boundedness of the semilinear attraction-repulsion chemotaxis system with nonlinear productions and logistic source: \begin{document}$ \begin{cases} u_{t} = \Delta u-\chi\nabla\cdot(u\nabla v)+\xi\nabla\cdot(u\nabla w)+u(a-bu^s), \ (x, t)\in \Omega\times (0, T), \\[6pt] v_t = \Delta v+\alpha u^k-\beta v, \ (x, t)\in \Omega\times (0, T), \\[6pt] 0 = \Delta w+\gamma u^l-\delta w, \ (x, t)\in\Omega\times (0, T), \end{cases} $\end{document} with $ \alpha, \beta, \gamma, \delta, \chi, \xi, a, b, s, k, l&gt;0 $, subject to the homogeneous Neumann boundary conditions in a bounded domain $ \Omega\subset\mathbb{R}^n $ ($ n\ge1 $) with smooth boundary. Hong et al. (J. Math. Anal. Appl. 484: 12703, 2020) have established the global boundedness criteria for the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system. With the help of the maximum Sobolev regularity, this paper generalizes the results to the parabolic-parabolic-elliptic case. It is proved that if one of the random diffusion, logistic source and repulsion mechanisms dominates the attraction with $ \max\{l, s, \frac{2}{n}\}&gt;k $, the solutions would be globally bounded. Under the balance situations, the boundedness of solutions will be determined by the sizes of the coefficients involved, but Hong et al only considered the balance of logistic source and repulsion mechanisms with $ \max\{l, s\} = k $, the balance produced by random diffusion was not taken into account, this paper consider the balance of random diffusion, logistic source and repulsion mechanisms with $ \max\{l, s, \frac{2}{n}\} = k $, the clear characterization of the global boundedness criteria is obtained for the parabolic-parabolic-elliptic attraction-repulsion chemotaxis system.

Global existence and boundedness of solutions in a reaction-diffusion system of Michaelis-Menten-type predator-prey model with nonlinear prey-taxis and random diffusion

This article deals with a 2 ? 2 reaction-diffusion-taxis model consisting of Michaelis-Menten functional response predator-prey system. The critical section of this model is that temporal-spatial evolution of the predators? velocity depends largely on the gradient of prey. But beyond that, this system also inscribes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which leads to the collection of u). By using contraction mapping principle, Lp estimates and Schauder estimates of parabolic equations, we prove the global existence and uniqueness of classical solutions to this model. In addition to this, we prove the global boundedness of solutions by overcome the difficulties brought by nonlinear prey-taxis.