Simple Diffusion Model Research Articles

A biphasic mathematical model for the release of polymer-drug conjugates from poly(vinyl alcohol) hydrogels

BackgroundHydrogels are a popular vehicle for controlled drug release. In comparison with small-soluble drugs of simple diffusion, the release of large polymer-drug conjugates is more complex and could not be predicted by a simple diffusion model. This study was aimed at mathematical modeling of the release of polymer-drug conjugates to design controlled drug-release hydrogel systems. MethodsFluorescein was used as a small model drug, whereas fluorescein isothiocyanate-dextran acted as a polymer-drug conjugates. The molecules were encapsulated in poly(vinyl alcohol)-based hydrogels with different concentrations and degrees of crosslinking. The release data were fitted using a one-diffusion coefficient (1DC) model and a two-diffusion coefficient (2DC) model, performed by Matlab. Significant findingsThe simple 1DC model fitted the release data of small molecules (< 10 kDa) very well, while the more complex 2DC model was needed to predict the release of macromolecules (10–250 kDa) for a better fit. The 2DC model proposed that a hydrogel is a heterogeneous structure with dense and loose areas, and macromolecules diffuse through the two areas with different diffusivity. We further demonstrated that the biphasic model could be applied to design hydrogel systems for precision drug release profiles.

Radical Diffusion Crossover Phenomenon in Glass-Forming Liquids.

We studied the diffusivities of a nitroxide radical at various temperatures in six glass-forming molecular liquids by electron spin resonance. By comparing the radical diffusivities and solvent self-diffusivities, we found that the radical diffusivities are lower than the self-diffusivities at high temperatures and approach them at low temperatures in all liquids. This crossover behavior was considered as evidence that a single-molecule diffusion process transforms into a collective process with temperature lowering. The crossover phenomenon was analyzed by a novel, simple diffusion model, combining collective and single-molecule diffusion processes, and it was compared to the Arrhenius crossover phenomenon. The obtained results suggest that future studies of tracer diffusion could contribute to a better understanding of diffusion mechanisms in glass-forming liquids. The proposed diffusion model could be used to study the crossover phenomena of tracer diffusion measured by other techniques, and it could serve as a base for developing more advanced models.

Nonlinear dynamics in micellar surfactant solutions. II. Diffusion

We discuss diffusion in micellar surfactant solutions in a form appropriate for analyzing experiments that involve large deviations from equilibrium. A general nonlinear dynamical model for inhomogeneous systems is developed that describes the effects of diffusion and micelle kinetics as a set of coupled partial differential equationsfor unimer concentration, micelle number concentration, average micelle aggregation number, and, optionally, the variance of the micelle aggregation number. More specialized models are developed to describe slow dynamics in situations in which the system stays in a state of partial local equilibrium or full local equilibrium. As an illustrative example of a nonlinear transport phenomenon, we discuss a simple model of diffusion from an initially homogeneous micellar solution to a rapidly created absorbing interface with fast unimer adsorption.

Part I: Hydrological properties within the eastern Indonesian throughflow region during the INDOMIX experiment

The Indonesian Mixing (INDOMIX) cruise of July 2010, resolves the Pacific Ocean water masses spreading from the Halmahera Sea through the Seram Sea, Manipa Strait, Banda Sea, to the Ombai Strait, and along the southern margin of Lesser Sunda Arc across the northern Savu Sea, Sumba Strait, and south of Lombok Strait. This paper focuses on the characteristics and stratification of the water masses, along this path and Part II of this study discusses the biogeochemical aspects. Two companion papers on quantification of turbulent mixing have been published elsewhere. We find: a) A marked transformation of South Pacific (SP) thermocline water within a sharp salinity front between the Halmahera Seram Seas. Tidally induced vertical mixing is the main process weakening the SP stratification, as suggested by a simple 1-dimensional diffusion model forced by vertical diffusivity of INDOMIX vertical microstructure profiler dataset. The transformation of SP water by vertical mixing can occur after 3 days, which is in good agreement with previously reported water mass residence times. Lateral advection plays a minor role; b) Interleaving salinity structure within the thermocline of the central Halmahera Sea and two deeper inflow channels. The interleaving salinity features within the central Halmahera Sea thermocline occurs where vertical diffusivity is relatively weak, compared to the vertical mixing at entry/exit portal that removes the interleaving salinity features. Two deeper inflow channels (about 950 m and 740 m depth) in the entry portal of the Halmahera Sea are mapped from the multi-beam echo sounder measurement, where both channels allow the renewal of SP thermocline water and salinity interleaving processes; c) Northward flow of thermocline water (100–200 m depth) in the Manipa Strait that injects Banda homogeneous salinity water into Seram Sea that erode Halmahera salty water via strong diapycnal mixing; d) Cyclonic upper layer circulation in Banda where eastward (westward) flow occurs in the northern (southern) Banda, confirmed by recent modeling study; and e) Relative salty Indian Ocean intermediate water flowing along southern margin of the Lesser Sunda Arc, within the South Java Undercurrent. Two distinct upper thermocline water, due to different source of Indonesian Throughflow (ITF) water, are found in the Banda Sea: fresher and colder water contrasting to saltier and warmer water that converge in this confluence region. Beneath it, Banda intermediate homogeneous salinity water and low dissolved oxygen water is dominant.

Extreme value statistics and arcsine laws for heterogeneous diffusion processes.

Heterogeneous diffusion with a spatially changing diffusion coefficient arises in many experimental systems such as protein dynamics in the cell cytoplasm, mobility of cajal bodies, and confined hard-sphere fluids. Here, we showcase a simple model of heterogeneous diffusion where the diffusion coefficient D(x) varies in a power-law way, i.e., D(x)∼|x|^{-α} with the exponent α>-1. This model is known to exhibit anomalous scaling of the mean-squared displacement (MSD) of the form ∼t^{2/2+α} and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all α, the exact probability distributions of the maximum spatial displacement M(t) and arg-maximum t_{m}(t) (i.e., the time at which this maximum is reached) till duration t. In the second part of our paper, we analyze the statistical properties of the residence time t_{r}(t) and the last-passage time t_{ℓ}(t) and compute their distributions exactly for all values of α. Our study unravels that the heterogeneous version (α≠0) displays many rich and contrasting features compared to that of the standard Brownian motion (BM). For example, while for BM (α=0), the distributions of t_{m}(t),t_{r}(t), and t_{ℓ}(t) are all identical (á la "arcsine laws" due to Lévy), they turn out to be significantly different for nonzero α. Another interesting property of t_{r}(t) is the existence of a critical α (which we denote by α_{c}=-0.3182) such that the distribution exhibits a local maximum at t_{r}=t/2 for α<α_{c} whereas it has minima at t_{r}=t/2 for α≥α_{c}. The underlying reasoning for this difference hints at the very contrasting natures of the process for α≥α_{c} and α<α_{c} which we thoroughly examine in our paper. All our analytical results are backed by extensive numerical simulations.

The effect of exposure to elevated temperatures on the microstructure and hardness of Mg–Ca–Zn alloy

Abstract The die cast Mg-5 wt.% Ca-6 wt.% Zn ternary alloy was exposed to 160 °C for different times of up to 40 days. Microstructural analysis and microhardness and hardness measurements of the samples after different exposure times enabled the thermal stability of the cast alloy to be monitored. The as-cast structure is composed mainly of α-Mg solid solution, elliptical grain boundary particles of CaMg2, and an intergranular eutectics of Mg and Ca2Mg6Zn3. The grain size of α-Mg and the structure of the alloy did not change during the treatment, but the amount of the intergranular phases increased slightly. Exposure to 160 °C resulted in a decrease in micro-hardness of the α-Mg grains, but no change in the overall hardness of the samples was observed. Microstructural analyses indicated diffusion of the solute elements from the α-Mg grains to the grain boundaries, resulting in a decrease in hardness of the α-Mg which is, however, compensated by an increase in hardness related to intergranular precipitates. Using a simple diffusion model, the diffusion coefficient of Ca atoms in Mg at 160 °C was estimated to be 2.1 · 10 –17 m2 s– 1, which is greater than that of Zn by two orders of magnitude.

DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL

AbstractTwo simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.

Fractionation of O&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;∕N&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; and Ar∕N&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in the Antarctic ice sheet during bubble formation and bubble–clathrate hydrate transition from precise gas measurements of the Dome Fuji ice core

Abstract. The variations of δO2/N2 and δAr/N2 in the Dome Fuji ice core were measured from 112 m (bubbly ice) to 2001 m (clathrate hydrate ice). Our method, combined with the low storage temperature of the samples (−50 ∘C), successfully excludes post-coring gas-loss fractionation signals from our data. From the bubbly ice to the middle of the bubble–clathrate transition zone (BCTZ) (112–800 m) and below the BCTZ (&gt;1200 m), the δO2/N2 and δAr/N2 data exhibit orbital-scale variations similar to local summer insolation. The data in the lower BCTZ (800–1200 m) have large scatter, which may be caused by millimeter-scale inhomogeneity of air composition combined with finite sample lengths. The insolation signal originally recorded at the bubble close-off remains through the BCTZ, and the insolation signal may be reconstructed by analyzing long ice samples (more than 50 cm for the Dome Fuji core). In the clathrate hydrate zone, the scatter around the orbital-scale variability decreases with depth, indicating diffusive smoothing of δO2/N2 and δAr/N2. A simple gas diffusion model was used to reproduce the smoothing and thus constrain their permeation coefficients. The relationship between δAr/N2 and δO2/N2 is markedly different for the datasets representing bubble close-off (slope ∼ 0.5), bubble–clathrate hydrate transformation (∼1), and post-coring gas loss (∼0.2), suggesting that the contributions of the mass-independent and mass-dependent fractionation processes are different for those cases. The method and data presented here may be useful for improving the orbital dating of deep ice cores over the multiple glacial cycles and further studying non-insolation-driven signals (e.g., atmospheric composition) of these gases.

Chemical Reactions at the Interface Periphery of Colliding Droplets Studied by Raman Image Analysis

Chemical reactions at the interface of reactive solutions are of importance for a full understanding of solution reactions. We investigate the chemical reaction induced by the collision of two droplets. The extent of the reaction is measured by analyzing spectra and images of the Raman scattered light emerging from the interface of the colliding droplets of H2SO4 and NH3 aqueous solutions. The obtained product concentration is lower than that expected from a simple diffusion model. The result indicates that a fresh interface is produced at the periphery of the mixing region of the colliding droplets. This study provides the basis to extend this method to measure rapid chemical reactions at the interface of colliding droplets.

Alcohol-sensing microfiber: Dependence of conductance of a hydrated composite fiber on normal aliphatic alcohol

This paper introduces composite microfibers that can distinguish liquid, normal, aliphatic alcohols with high selectivity. The composite microfibers are composed of a hydrophilic agarose polymer and carbon nanotube (CNT) fillers. The CNTs distributed in the CNT-agarose composite microfiber (CAF) enable the material to sensitively change its electrical conductivity upon exposure to alcohols, induced by a change in the volume of the polymer matrix. When a CAF is highly hydrated, its resistance distinctly changes depending on the molecular weight of the alcohol via competitive mass transfer of alcohol and water. As a result, highly hydrated CAFs can selectively distinguish normal, aliphatic alcohols ranging from methanol to 1-pentanol. A provisional mechanism for the alcohol-dependent change in resistance of hydrated CAFs is suggested based on the permeation of alcohols and the discharge of water and is supported by numerical calculations using a simple diffusion model. The effects of the CNT loading ratio and the as-prepared CAF diameter on the alcohol-dependent resistance change are investigated. Furthermore, the highly hydrated CAFs are used to determine the volume ratios of binary mixtures of methanol/ethanol and ethanol/water. Finally, we demonstrate that a CAF alcohol sensor can identify commercial liquors with different alcohol contents.

Hydrophobic and electrostatic interactions modulate protein escape at the ribosomal exit tunnel

After translation, nascent proteins must escape the ribosomal exit tunnel to attain complete folding to their native states. This escape process also frees up the ribosome tunnel for a new translation job. In this study, we investigate the impacts of energetic interactions between the ribosomal exit tunnel and nascent proteins on the protein escape process by molecular dynamics simulations using partially coarse-grained models that incorporate hydrophobic and electrostatic interactions of the ribosome tunnel of Haloarcula marismortui with nascent proteins. We find that, in general, attractive interactions slow down the protein escape process, whereas repulsive interactions speed it up. For the small globular proteins considered, the median escape time correlates with both the number of hydrophobic residues, Nh, and the net charge, Q, of a nascent protein. A correlation coefficient exceeding 0.96 is found for the relation between the median escape time and a combined quantity of Nh + 5.9Q, suggesting that it is ∼6 times more efficient to modulate the escape time by changing the total charge than the number of hydrophobic residues. The estimated median escape times are found in the submillisecond-to-millisecond range, indicating that the escape does not delay the ribosome recycling. For various types of the tunnel model, with and without hydrophobic and electrostatic interactions, the escape time distribution always follows a simple diffusion model that describes the escape process as a downhill drift of a Brownian particle, suggesting that nascent proteins escape along barrier-less pathways at the ribosome tunnel.

Low-radio frequency observations of seven nearby galaxies with GMRT

ABSTRACT We have observed seven nearby large-angular-sized galaxies at 0.33 GHz using Giant Metrewave Radio Telescope with an angular resolution of ∼10 arcsec and sub-mJy sensitivity. Using archival higher frequency data at 1.4 or ∼6 GHz, we have then determined their spatially resolved non-thermal spectrum. As a general trend, we find that the spectral indices are comparatively flat at the galaxy centres and gradually steepen with increasing galactocentric distances. Using archival far-infrared (FIR) MIPS 70-${\mu }\mathrm{m}$ data, we estimate the exponent of radio–FIR correlation. One of the galaxies (NGC 4826) was found to have an exponent of the correlation of ∼1.4. Average exponent from 0.33-GHz data for the rest of the galaxies was 0.63 ± 0.06 and is significantly flatter than the exponent 0.78 ± 0.04 obtained using 1.4-GHz data. This indicates cosmic-ray electron (CRe) propagation to have reduced the correlation between FIR and 0.33-GHz radio. Assuming a model of simple isotropic diffusion of CRe, we find that the scenario can explain the frequency-dependent CRe propagation length-scales for only two galaxies. Invoking streaming instability could, however, explain the results for the majority of the remaining ones.

A mathematical model and numerical solution for brain tumor derived using fractional operator

In this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a solution for this model, a numerical technique is presented which is based on operational matrix. First, we assume the solution of the problem under the study is as an expansion of the Bernoulli polynomials. Then with combination of the operational matrix based on the Bernoulli polynomials and collocation method, the problem under the study is changed to a system of nonlinear algebraic equations. Finally, the proposed technique is simulated and tested on three types of the FBEs to confirm the superiority and accuracy.

The effect of the convective momentum transfer on the acoustic boundary condition of perforated liners with grazing mean flow

The interaction of sound with sound-permeable hard walls subjected to grazing mean flow is investigated with a focus on the sound-induced exchange of streamwise momentum between the mean flow and the wall. Two generic wall types have to be distinguished, the homogeneously permeable wall and the wall with clearly separated openings, which is a more realistic model of technically feasible walls. To begin with, the focus is on the shear stress that drives the dynamics of the shearing mean flow over the homogeneous wall. This is analyzed by means of two simple mathematical models of shear stress diffusion, which come as two equivalent pairs of differential equations either for the acoustic shear stress and the wall-normal displacement, or for the streamwise and the wall-normal components of the acoustic velocity. The physical analysis is concentrated on the relation between shear stress and the wall-normal displacement of the fluid elements, which determines the effective admittance of the wall. The shear stress is represented by the momentum transfer impedance which is defined as the ratio between the acoustic wall shear stress and the in-wall velocity evaluated at the wall. It turns out that the strong increase of the acoustic wall shear stress due to transfer of mean flow momentum to the wall is the dominating mechanism which affects the effective admittance of the wall. Nevertheless, the suitability of the momentum transfer impedance as part of a complete boundary condition of the wall is questioned. The disagreement between the predicted momentum transfer impedance and some rare experimental data obtained with real inhomogeneous walls is considered as a strong indication that some further mechanisms are invoked by the inhomogeneity of real walls which are briefly discussed with regard to future studies.

Après-ski: The spread of coronavirus from Ischgl through Germany

Abstract The Austrian ski resort of Ischgl is commonly claimed to be ground zero for the diffusion of the SARS-CoV-2 virus in the first wave of infections experienced by Germany. Drawing on data for 401 German counties, we find that conditional on geographical latitude and testing behavior by health authorities, road distance to Ischgl is indeed an important predictor of infection cases, but – in line with expectations – not of fatality rates. Were all German counties located as far from Ischgl as the most distant county of Vorpommern-Rügen, Germany would have seen about 45 % fewer COVID-19 cases. A simple diffusion model predicts that the absolute value of the distance-to-Ischgl elasticity should fall over time when inter- and intra-county mobility are unrestricted. We test this hypothesis and conclude that the German lockdown measures have halted the spread of the virus.

Decoupling bulk and surface recombination properties in silicon by depth-dependent carrier lifetime measurements

Muons, as a bulk probe of materials, have been used to study the depth profile of charge carrier kinetics in Si wafers by scanning the muon implantation depth. The photoexcited muon spin spectroscopy technique can optically generate excess carriers in semiconductor wafers, while muons can measure the excess carrier density. As a result, carrier recombination lifetime spectra can be obtained. The depth-dependent lifetime spectra enable us to accurately measure the bulk carrier lifetime and surface recombination velocity by fitting the spectra to a simple one-dimensional diffusion model. Unlike other traditional lifetime spectroscopy techniques, the bulk and surface recombination properties can be readily de-convoluted in this method. Here, we have applied the technique to study silicon wafers both with and without passivation treatment and have demonstrated that the model can correctly describe the carrier kinetics in these two cases.

Diffusivity and Solubility of H2 in Ice Ih: Implications for the Behavior of H2 in Polar Ice

AbstractReconstructions of paleoatmospheric H2 using polar firn air and ice cores would lead to a better understanding of the H2 biogeochemical cycle and how it is influenced by climate change and human activity. In this study, the permeability, diffusivity, and solubility of H2 are determined experimentally in ice Ih at temperatures relevant to polar ice sheets (199–253 K). The experimental data are used in conjunction with simplified diffusion models to assess the implications for: (a) Diffusion of H2 from pressurized closed bubbles to open pores in polar firn, (b) diffusive smoothing of H2 gradients in the ice sheet, and (c) post‐coring diffusive losses of H2 from ice core samples. The results indicate that diffusive equilibrium between open and closed pores is likely achieved in the firn lock‐in zone. Diffusive smoothing of atmospheric variations is significant and should be accounted for in atmospheric reconstructions on millennial time scales. Diffusive losses from a bubbly ice sample are sufficiently slow that samples may be meaningfully analyzed for H2 after storage on the order of a year. These results suggest that the mobility of H2 in ice should not preclude the reconstruction of paleoatmospheric H2 from firn air and ice cores.

Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit

&lt;p style='text-indent:20px;'&gt;We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, e.g., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems.&lt;/p&gt;

Critical theory for the breakdown of photon blockade

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.

Origin and hydrodynamics of xylem sap in tree stems, and relationship to root uptake of soil water

Although 10 years have passed since Japan’s Fukushima nuclear accident, the future radiation risk from 137Cs contamination of wood via root uptake is a serious concern. We estimated the depth at which the roots of evergreen coniferous sugi (Cryptomeria japonica) and broadleaf deciduous konara (Quercus serrata) trees actively take up soil water by using positive δD values from the artificial D2O tracer and seasonal changes in the δ18O values of soil water as a natural environmental tracer. We compared the tracer concentration changes in xylem sap with those in the soil water and ascertained that both tree species primarily took up water from a depth of 20 cm, though with mixing of water from other depths. Using sap hydrodynamics in tree stems, we found that water circulation was significantly slower in heartwood than in sapwood. Heartwood water was not supplied by direct root uptake of soil water. The measured diffusion coefficients for D2O, K+, Cs+, and I− in xylem stems were greater in sapwood than in heartwood, and their magnitude was inversely correlated with their molecular weights. The distribution of D2O and 137Cs concentrations along the radial stem could be explained by simulations using the simple advective diffusion model.