Diffusion Constant Research Articles

Selenite Removal from Aqueous Solution Using Silica-Iron Oxide Nanocomposite Adsorbents.

In recent years, during industrial development, the expanding discharge of harmful metallic ions from different industrial wastes (such as arsenic, barium, cadmium, chromium, copper, lead, mercury, nickel, selenium, silver, or zinc) into different water bodies has caused serious concern, with one of the problematic elements being represented by selenium (Se) ions. Selenium represents an essential microelement for human life and plays a vital role in human metabolism. In the human body, this element acts as a powerful antioxidant, being able to reduce the risk of the development of some cancers. Selenium is distributed in the environment in the form of selenate (SeO42-) and selenite (SeO32-), which are the result of natural/anthropogenic activities. Experimental data proved that both forms present some toxicity. In this context, in the last decade, only several studies regarding selenium's removal from aqueous solutions have been conducted. Therefore, in the present study, we aim to use the sol-gel synthesis method to prepare a nanocomposite adsorbent material starting from sodium fluoride, silica, and iron oxide matrices (SiO2/Fe(acac)3/NaF), and to further test it for selenite adsorption. After preparation, the adsorbent material was characterized by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). The mechanism associated with the selenium adsorption process has been established based on kinetic, thermodynamic, and equilibrium studies. Pseudo second order is the kinetic model that best describes the obtained experimental data. Also, from the intraparticle diffusion study, it was observed that with increasing temperature the value of the diffusion constant, Kdiff, also increases. Sips isotherm was found to best describe the experimental data obtained, the maximum adsorption capacity being ~6.00 mg Se(IV) per g of adsorbent material. From a thermodynamic point of view, parameters such as ΔG0, ΔH0, and ΔS0 were evaluated, proving that the process studied is a physical one.

Transport coefficients in AdS/CFT and quantum gravity corrections due to a functional measure

The presence of a functional measure is scrutinized on both sides of the dual gauge/gravity correspondence. Corrections to the transport coefficients in relativistic hydrodynamics are obtained using the linear response procedure. In particular, using first-order hydrodynamics, the shear viscosity, entropy density, diffusion constant, and speed of sound are shown not to acquire any corrections from the functional measure of gravity, for a Minkowski background metric. On the other hand, the energy density, the pressure, the relaxation time, the bulk viscosity, the decay rate of sound waves, and coefficients of conformal traceless tensor fields, are shown to carry significant quantum corrections due to the functional measure, even for a flat background. They all acquire an imaginary part that reflects the instability of the strongly-coupled fluids on the boundary CFT. This opens up the possibility of testing quantum gravity with the quark-gluon plasma.

Thermotropic liquid crystal doped with silica, silica grafted with aniline (ANI@SiO2) and polyaniline (PANI@SiO2)

ABSTRACT Nanoparticles dispersed in liquid crystals exhibit novel and intriguing properties, which make them suitable materials for displays and photonic applications. This paper reports on the impact of non-modified silica (SiO2), silica grafted with aniline (ANI@SiO2) and silica grafted with polyaniline (PANI@SiO2) nanoparticles on the physical parameters of 7CB liquid crystal. A slight change in the nematic-isotropic phase transition temperature was observed. The results from dielectric experiments revealed an increase in free ion concentration in the doped samples. By fitting a suitable equivalent electric circuit model to the experimental data, we demonstrate changes in the electro-physical parameters of the liquid crystal in the bulk and at the liquid crystal-metal electrode interface. Therefore, we were able to calculate the ion mobility and the diffusion constant. It was also demonstrated that the doping of 7CB with the above-mentioned nanoparticles increases the response time, thresholds, and viscosity.

Diffusion and Thermal Shock Behaviour of Silicate Dental Ceramics

The purpose of this study is to examine the diffusion and thermal shock behaviour of the alternative dental silicates. The samples derived from BaO-SiO2 system have been produced by melting process and followed by the heat treatment. X-ray examinations have indicated that the amount of orthorhombic sanbornite phase rised due to treatment temperature as revealed by the peak intensities. The alteration of the morphology by treatment temperature was evident from scanning electron microscopy SEM images. Crystallization at low temperature produced small crystallites and coarsening was not observed with a rise in temperature. The failure of the dental samples after the thermal shock test was examined using SEM. A continuous crack geometry and very few crack branching were observed. Diffusivity constant (D) and diffusion rate were examined vs treatment temperature for the present system. Diffusion depth (L) was doubled when the crystallization treatment was applied. Based on the obtained results, these silicate samples might take part in the further characterization studies to be used as alternative dentistry materials.

Wave Propagation through a Piezoelectric Semiconductor Infinite Space

The propagation characteristics of anti-plane waves, i.e., the quasi-shear horizontal (QSH) waves and the carrier (CA) waves through a piezoelectric semiconductor (Piezo-SEMI) infinite space are discussed in this paper. First, the elastic, piezoelectric, dielectric, carrier mobility and diffusion constants in the considered propagation coordinate system are obtained by Bonde transformation from those in the crystal axis coordinate system. For anti-plane case, the secular equation with the mechanical, electric and the carrier concentration fields of the anti-plane waves through a Piezo-SEMI infinite space is derived. We obtain all possible wave modes, i.e., QSH waves and CA waves, that propagate in the Piezo-SEMI material by solving the secular equation. Then, the wave speeds and attenuation of QSH waves and CA waves are obtained. The steady-state carrier concentration and biasing electric field have significant effects on dispersion and attenuation of the QSH waves and the CA waves, and the sensitive areas to the wave velocity and attenuation are obtained.

A Topological Mechanism of Superdiffusion on Duplex Networks

Superdiffusion is an interesting phenomenon from both theoretical and practical perspectives. We propose a sufficient condition for the occurrence of superdiffusion on duplex networks by applying the generating functionology from combinatorial mathematics. Our result indicates that, with fixed values of intra-layer diffusion constants, superdiffusion emerges from a certain combination of different network topologies, which provides a topological mechanism to regulate the whole diffusion process. On a more general ground, we provide two inter-layer linking strategies to expand the applicability of the above topological mechanism on real-world networks, and construct a class of specific duplex networks on which superdiffusion occurs. We further verify that diffusion with negative inter-layer correlation is faster than those with positive correlation from a typical duplex structure. Given the ubiquity of diffusion in the real world, our results constitute a significant step toward a better understanding of superdiffusion processes on multiplex networks.

Large eddy simulation within the smoothed particle hydrodynamics: Applications to multiphase flows

In this paper, the large eddy simulation (LES) model introduced in the smoothed particle hydrodynamics (SPH) by Di Mascio et al. [Phys. Fluids 29, 035102 (2017)] and called δ-LES-SPH, is extended to treat multiphase flows. This is achieved by modifying the multiphase δ-SPH by Hammani et al. [Comput. Methods Appl. Mech. Eng. 368, 113189 (2020)] by switching the viscous and density diffusion constants to dynamic variables evaluated as turbulence closure terms. The equation for energy conservation is also written for the presented model. The validation is performed for two-dimensional problems, by comparison with other established SPH solvers, with a finite volume method solver based on the turbulence closure corresponding to that adopted for the Lagrangian scheme, and with experimental data. The first test case investigated is a modified Taylor–Green vortex in which the introduction of macro-bubbles of a lighter fluid phase inside the domain is considered. In the second test case, a more violent problem involving wave breaking and splashing dynamics is analyzed. In the final test, the dynamic of a sloshing problem is reproduced. An analysis of turbulence resolution is conducted by considering modeled and resolved turbulent kinetic energies, as well as viscous dissipation and turbulent viscosity dissipation.

Chirality reversing active Brownian motion in two dimensions

We study the dynamics of a chirality reversing active Brownian particle (ABP), which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two time-scales set by the chirality reversing rate γ and rotational diffusion constant gives rise to four dynamical regimes, namely, (I) , (II) , (III) and (IV) , each showing different behavior. The short-time regime (I) is characterized by a strongly anisotropic and non-Gaussian position distribution, which crosses over to a diffusive Gaussian behavior in the long-time regime (IV) via an intermediate regime (II) or (III), depending on the relative strength of γ and . In regime (II), the chirality reversing active Brownian motion reduces to that of an ordinary ABP, with an effective rotation diffusion coefficient which depends on the angular velocity. Finally, we find that, the regime (III) is characterized by an effective chiral active Brownian motion.

A Novel Inter-Symbol Interference Model and Weighted Sum Detection for Diffusion-Based Molecular Communication Systems

Inter-symbol interference (ISI) may result in substantial performance degradation in molecular communication systems. In this paper, we propose a more accurate and realistic ISI model compared to the literature, by quantifying the ISI in a three-dimensional fluid environment with a spherical receiver. Moreover, due to the propagation delay in a fluid environment, a large number of the molecules absorbed earlier in a transmission interval are due to the previous transmissions. Therefore, we find the optimal delay time, that the receiver should wait at the beginning of each time interval before counting the absorbed molecules, to reduce the effect of the ISI. Further, and to enhance the performance of the system, we adopt a detection approach based on multiple molecular observations at the receiver, and introduce a weighted sum detector, in which the transmission interval is divided into a number of sub-intervals. We analytically derive the weights, assigned to different sub-intervals, that minimize the bit error rate (BER). Simulations, based on the presented approaches, show the impact of the transmitter-receiver distance, the reaction rate, and the diffusion constant of the environment on the BER performance. We also show that using a weighted sum detector significantly improves the BER performance.

Effects of memory response and impedance barrier on reflection of plane waves in a nonlocal micropolar porous thermo-diffusive medium

This research problem is an investigation of reflection amplitude in a nonlocal porous-thermo-micropolar diffusion half-space under memory dependent derivative (MDD) thermo-elasticity subjected to impedance boundary reflecting surface. The governing equations for nonlocal porous-thermo-micropolar diffusion medium in MDD theory are formulated. This research challenge is solved analytically for a two-dimensional model in order to demonstrate the presence of four coupled longitudinal waves and two paired transverse waves denoted as coupled longitudinal displacement wave ( cLDW − I ), coupled longitudinal thermal wave ( cLDW − II ), coupled longitudinal mass diffusion wave ( cLDW − III ), coupled longitudinal void volume fraction wave ( cLDW − IV ), and coupled transverse displacement wave ( cTDW ) and coupled transverse micro-rotational wave ( cTMW ). When there is nonlocality, diffusion, and porous characteristics in the medium, it is discovered to have an impact on these coupled longitudinal waves, making them dispersive and attenuating. The transverse wave is non-attenuating but dispersive, it is unaffected by diffusion and porous characteristics. To find the expression for the reflection coefficients of reflected waves, the plane wave reflection from a thermally insulated surface subjected to an impedance boundary is explored. For a specific material, the reflection coefficients of the reflected waves are calculated, and graphic representations of the fluctuations of the reflection coefficients versus the incidence angle, nonlocality, diffusion and porous constants are provided. For further investigation, energy ratio can be studied in future.

Nonparametric adaptive estimation for interacting particle systems

AbstractWe consider a stochastic system of interacting particles with constant diffusion coefficient and drift linear in space, time‐depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on for fixed and large . We define two collections of projection estimators belonging to finite‐dimensional subspaces of . We study the ‐risks of these estimators, where the risk is defined either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data‐driven choice of the dimensions and study the risk of the adaptive estimators. The results are illustrated by numerical experiments on simulated data.

Differences in Water Dynamics between the Hydrated Chitin and Hydrated Chitosan Determined by Quasi-Elastic Neutron Scattering.

Recently, it was reported that chitin and chitosan exhibited high-proton conductivity and function as an electrolyte in fuel cells. In particular, it is noteworthy that proton conductivity in the hydrated chitin becomes 30 times higher than that in the hydrated chitosan. Since higher proton conductivity is necessary for the fuel cell electrolyte, it is significantly important to clarify the key factor for the realization of higher proton conduction from a microscopic viewpoint for the future development of fuel cells. Therefore, we have measured proton dynamics in the hydrated chitin using quasi-elastic neutron scattering (QENS) from the microscopic viewpoint and compared the proton conduction mechanism between hydrated chitin and chitosan. QENS results exhibited that a part of hydrogen atoms and hydration water in chitin are mobile even at 238 K, and the mobile hydrogen atoms and their diffusion increase with increasing temperature. It was found that the diffusion constant of mobile protons is two times larger and that the residence time is two times faster in chitin than that in chitosan. In addition, it is revealed from the experimental results that the transition process of dissociable hydrogen atoms between chitin and chitosan is different. To realize proton conduction in the hydrated chitosan, the hydrogen atoms of the hydronium ions (H3O+) should be transferred to another hydration water. By contrast, in hydrated chitin, the hydrogen atoms can transfer directly to the proton acceptors of neighboring chitin. It is deduced that higher proton conductivity in the hydrated chitin compared with that in the hydrated chitosan is yielded by the difference of diffusion constant and the residence time by hydrogen-atom dynamics and the location and number of proton acceptors.

Improvement of the glass transition temperature in novel molybdenum carbide doped polyaniline nanocomposites

Several studies have revealed that the glass transition temperature (Tg) of polymer nanocomposites (PNCs) may change upon the loading of even a small number of nanoparticles (NPs). However, the exact phenomenon behind such shifting in Tg is still not well known. This study uses experimental and MD simulation approaches to explore the physics of the Tg of polyaniline (PANI) nanocomposite with molybdenum carbide (Mo2C) nanoparticles at different weight percentage loading of NPs. The experimental study shows that, at a lower wt-% loading of NPs, the Tg of the resulting PNCs decreases slowly, and above a particular loading wt-%* (30 wt-%), the depression in Tg becomes more serious. The SEM images show that for wt-% < wt-%*, NPs remain diffuse in the polymer matrix, and for wt-%t > wt-%* a large number of NPs surround the polymer. The MD simulation reveals a slow increase in the diffusion of polymer and NPs for wt-% < wt-%* and a sudden increase for wt-%t > wt-%*. The measurement of the radius of gyration of the polymer reveals swelling of the polymer for wt-% < wt-%* and contraction of the polymer for wt-%t > wt-%*. Moreover, the variations of the diffusion constants and the radius of gyration of the polymer are consistent with the Tg behaviour of PNCs.

Reduced order modeling for elliptic problems with high contrast diffusion coefficients

We consider a parametric elliptic PDE with a scalar piecewise constant diffusion coefficient taking arbitrary positive values on fixed subdomains. This problem is not uniformly elliptic, as the contrast can be arbitrarily high, contrarily to the Uniform Ellipticity Assumption (UEA) that is com- monly made on parametric elliptic PDEs. We construct reduced model spaces that approximate uniformly well all solutions with estimates in relative error that are independent of the contrast level. These estimates are sub-exponential in the reduced model dimension, yet exhibiting the curse of dimensionality as the number of subdomains grows. Similar es- timates are obtained for the Galerkin projection, as well as for the state estimation and parameter estimation inverse problems. A key ingredient in our construction and analysis is the study of the convergence towards limit solutions of stiff problems when diffusion tends to infinity in certain domains.

Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail.

Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients, and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid, and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing us to subtract the periodic boundary condition effects. By this, we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from simulations with rather small box sizes.

Theoretical description for nonlinear dynamic light scattering based on stimulated Raman effect (NLDLS‐SRS)

AbstractDynamic light scattering (DLS) is a method to analyze the diffusion constant and mesostructure of colloidal systems based on refractive index fluctuations. For example, DLS evaluates particle size distribution, particle drift velocity, and the typical length of the cooperative diffusion in gels. However, DLS inherently lacks chemical sensitivity since it detects the spatial Fourier component of the refractive index at the scattering vector (q). This work theoretically demonstrates the feasibility of nonlinear dynamic light scattering (NLDLS) of stimulated Raman effect that reflects molecular vibration. Specifically, we show that by interfering with two pump beams (in the pump‐probe method terminology), it is possible to extract the spatial Fourier component of the imaginary part of the third‐order nonlinear susceptibility. Here, the phase modulation of either of the two beams is effective for mode‐selective detection of the Fourier component. The difference in the wavevectors of these beams corresponds to q in DLS. The result is the same as DLS in mesostructural sensitivity but has a molecular vibration selectivity. The proposed assay in the present paper enables qualitative and chemical‐structure analysis of the colloidal systems without labeling and size differentiation in a mesopic regime.

Fourth-order multiple-relaxation-time lattice Boltzmann model and equivalent finite-difference scheme for one-dimensional convection-diffusion equations.

In this paper, we first develop a fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional convection-diffusion equation(CDE) with the constant velocity and diffusion coefficient, where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is used. We also perform the Chapman-Enskog analysis to recover the CDE from the MRT-LB model. Then an explicit four-level finite-difference (FLFD) scheme is derived from the developed MRT-LB model for the CDE. Through the Taylor expansion, the truncation error of the FLFD scheme is obtained, and at the diffusive scaling, the FLFD scheme can achieve the fourth-order accuracy in space. After that, we present a stability analysis and derive the same stability condition for the MRT-LB model and FLFD scheme. Finally, we perform some numerical experiments to test the MRT-LB model and FLFD scheme, and the numerical results show that they have a fourth-order convergence rate in space, which is consistent with our theoretical analysis.

Self-consistent hopping theory of activated relaxation and diffusion of dilute penetrants in dense crosslinked polymer networks.

We generalize a microscopic statistical mechanical theory of the activated dynamics of dilute spherical penetrants in glass-forming liquids to study the influence of crosslinking in polymer networks on the penetrant relaxation time and diffusivity over a wide range of temperature and crosslink fraction (fn). Our calculations are relevant to recent experimental studies of a nm-sized molecule diffusing in poly-(n-butyl methacrylate) networks. The theory predicts the penetrant relaxation time increases exponentially with the glass transition temperature, Tg(fn), which grows roughly linearly with the square root of fn due to the coupling of local hopping to longer-range collective elasticity. Moreover, Tg is also found to be proportional to a geometric confinement parameter defined as the ratio of the penetrant diameter to the mean network mesh size. The decoupling ratio of the penetrant and Kuhn segment alpha times displays a complex non-monotonic dependence on fn and temperature that is well collapsed based on the variable Tg(fn)/T. A model for the penetrant diffusion constant that combines activated relaxation and entropic mesh confinement is proposed, which results in a significantly stronger suppression of mass transport with degree of effective supercooling than predicted for the penetrant alpha time. This behavior corresponds to a new network-based type of "decoupling" of diffusion and relaxation. In contrast to the diffusion of larger nanoparticles in high temperature rubbery networks, our analysis in the supercooled regime suggests that for the penetrants studied the mesh confinement effects are of secondary importance relative to the consequences of crosslink-induced slowing down of activated hopping of glassy physics origin.

A particle-size dependent smoothing scheme for polydisperse Euler-Lagrange simulations

In Euler-Lagrange models for particulate systems, the information exchange of multiphase coupling terms, i.e. drag force, heat transfer, or mass transfer, is often smoothed from particles' location to nearby computational cells when the cell and particle sizes are comparable. The diffusion-based smoothing is among the most popular approach. However, when it comes to polydisperse systems, the state-of-the-art constant diffusivity approach does not consider variation in particle sizes, resulting in an even smoothing of exchanged information across all particles with different sizes.In this paper, a particle-size dependent smoothing scheme named “non-constant diffusivity approach” is proposed. This approach distributes the exchanged information based on the local Sauter diameter d32 such that the area of influence per particle varies by size. The one-dimensional analytical solution of the non-constant diffusivity approach is first derived and two control parameters L⁎ and S are identified, where L⁎ determines the characteristic length of the diffusivity and S determines the magnitude of the diffusivity. Together they control the characteristic length scale ℓ˜c of the smoothing operation. In the one-dimensional study, it is found that the proposed smoothing method is most suitable for the dilute particulate regime. The investigation is extended to a three-dimensional dilute particle flow based on the experiment of the CRIEPI (Central Research Institute of Electric Power Industry) pulverized coal burner. It is shown that using the non-constant diffusivity smoothing, the prediction of the O2 concentration is more accurate than when using the constant diffusivity smoothing approach, which assumes a universal smoothing length for all sizes of particles. The findings suggest that when it comes to polydisperse particulate systems, the area of influence per particle on the fluid depends on the particle size. The proposed non-constant diffusivity approach can describe that with the benefits of cheap computational cost, conservation of exchanged quantities, and easy-to-implement.

Benchmarking Molecular Dynamics Force Fields for All-Atom Simulations of Biological Condensates.

Proteins containing intrinsically disordered regions are integral parts of the cellular signaling pathways and common components of biological condensates. Point mutations in the protein sequence, genetic at birth or acquired through aging, can alter the properties of the condensates, marking the onset of neurodegenerative diseases such as ALS and dementia. While the all-atom molecular dynamics method can, in principle, elucidate the conformational changes that arise from point mutations, the applications of this method to protein condensate systems is conditioned upon the availability of molecular force fields that can accurately describe both structured and disordered regions of such proteins. Using the special-purpose Anton 2 supercomputer, we benchmarked the efficacy of nine presently available molecular force fields in describing the structure and dynamics of a Fused in sarcoma (FUS) protein. Five-microsecond simulations of the full-length FUS protein characterized the effect of the force field on the global conformation of the protein, self-interactions among its side chains, solvent accessible surface area, and the diffusion constant. Using the results of dynamic light scattering as a benchmark for the FUS radius of gyration, we identified several force fields that produced FUS conformations within the experimental range. Next, we used these force fields to perform ten-microsecond simulations of two structured RNA binding domains of FUS bound to their respective RNA targets, finding the choice of the force field to affect stability of the RNA-FUS complex. Taken together, our data suggest that a combination of protein and RNA force fields sharing a common four-point water model provides an optimal description of proteins containing both disordered and structured regions and RNA-protein interactions. To make simulations of such systems available beyond the Anton 2 machines, we describe and validate implementation of the best performing force fields in a publicly available molecular dynamics program NAMD. Our NAMD implementation enables simulations of large (tens of millions of atoms) biological condensate systems and makes such simulations accessible to a broader scientific community.