Purely elastic turbulence in pressure-driven channel flows.

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.

An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids.

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

A Lifshitz-Slyozov type model for adipocyte size dynamics: limit from Becker-Döring system and numerical simulation.

Biological data show that the size distribution of adipose cells follows a bimodal distribution. In this work, we introduce a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipose cells. We prove a new convergence result from the related Becker-Döring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. Then, this result allows us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model are performed using a well-balanced scheme and compared to solutions to the transport model. Those simulations show that both bimodal and unimodal profiles can be reached asymptotically depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.

Directivity and Excitability of Ultrasonic Shear Waves Using Piezoceramic Transducers-Numerical Modeling and Experimental Investigations.

In this paper, piezoceramic-based excitation of shear horizontal waves is investigated. A thickness-shear d15 piezoceramic transducer is modeled using the finite-element method. The major focus is on the directivity and excitability of the shear horizontal fundamental mode with respect to the maximization of excited shear and minimization of Lamb wave modes. The results show that the geometry of the transducer has more effect on the directivity than on the excitability of the analyzed actuator. Numerically simulated results are validated experimentally. The experimental results show that transducer bonding significantly affects the directivity and amplitude of the excited modes. In conclusion, when the selected actuator is used for shear excitation, the best solution is to tailor the transducer in such a way that at the resonant frequency the desired directivity is achieved.

Numerical simulation and experimental study of three-phase distribution characteristics of leaked light non-aqueous phase liquid from buried pipelines in soils containing groundwater and gas.

Leakage accidents of buried pipelines have become increasingly common due to the prolonged service of some pipelines which have been in use for more than 150 years. Therefore, there is an urgent need for accurate prediction of pollution scope to aid in the development of emergency remediation strategies. This study investigated the distribution of a light non-aqueous phase liquid in soils containing gas and water through numerical simulations and laboratory experiments. Firstly, a three-dimensional porous medium model was established using ANSYS FLUENT, and for the first time, the distribution of gas and groundwater in soil environments was simulated in the model. Subsequently, the distribution of the three phases of diesel, gas, and water in soil was studied with different leakage velocities and it was found that the leakage velocity played a significant role in the distribution. The areas of diesel in soils at 60 min were 0.112 m2, 0.194 m2, 0.217 m2, and 0.252 m2, with corresponding volumes of 0.028 m3, 0.070 m3, 0.086 m3, and 0.106 m3, respectively, for leakage velocities of 1.3 m/s, 3.4 m/s, 4.6 m/s, and 4.9 m/s. Calculation formulas for distribution areas and volumes were also developed to aid in future prevention and control strategies under different leakage velocities. The study also compared the distribution areas and volumes of diesel in soils with and without groundwater, and it was found that distribution scopes were larger in soils containing groundwater due to capillary force. In order to validate the accuracy of the numerical simulation, laboratory experiments were conducted to study the diffusion of oil, gas, and water under different leakage velocities. The results showed good agreement between the experiments and the simulations. The research findings are of great significance for preventing soil pollution and provide a theoretical basis for developing scientifically sound soil remediation strategies.

A DNA Segregation Module for Synthetic Cells.

The bottom-up construction of an artificial cell requires the realization of synthetic cell division. Significant progress has been made toward reliable compartment division, yet mechanisms to segregate the DNA-encoded informational content are still in their infancy. Herein, droplets of DNA Y-motifs are formed by liquid-liquid phase separation. DNA droplet segregation is obtained by cleaving the linking component between two populations of DNA Y-motifs. In addition to enzymatic cleavage, photolabile sites are introduced for spatio-temporally controlled DNA segregation in bulk as well as in cell-sized water-in-oil droplets and giant unilamellar lipid vesicles (GUVs). Notably, the segregation process is slower in confinement than in bulk. The ionic strength of the solution and the nucleobase sequences are employed to regulate the segregation dynamics. The experimental results are corroborated in a lattice-based theoretical model which mimics the interactions between the DNA Y-motif populations. Altogether, engineered DNA droplets, reconstituted in GUVs, can represent a strategy toward a DNA segregation module within bottom-up assembled synthetic cells.

Efficient prediction of MRI gradient-induced heating for guiding safety testing of conductive implants.

PURPOSE: To propose an efficient numerical method to predict the temperature increase of an implantable medical device induced by any linearly polarized homogeneous magnetic field, according to the ISO 10974 methodology for testing of gradient-induced device heating. THEORY AND METHODS: The concepts of device-specific power and temperature tensors are introduced to mathematically describe the electromagnetic and thermal anisotropic behavior of the device, from which the device heating for an arbitrary exposure direction can be predicted. The proposed method is compared to a brute-force approach based on simulations, and validated by applying it to four reference orthopedic implants with a commercial simulation software. RESULTS: The proposed method requires about 5 % $$ \% $$ of the time required by the brute-force approach, and 30 % $$ \% $$ of the memory occupancy. The temperature increase predicted by the proposed method over a range of incident magnetic field exposures deviated from brute-force direct simulations by less than ± $$ \pm $$ 0.3 % $$ \% $$ . CONCLUSION: The proposed method allows efficient prediction of the heating of an implantable medical device induced by any linearly polarized homogeneous magnetic field using a small fraction of the simulations required by the brute-force approach. The results can be used to predict the worst-case orientation of the gradient field, for subsequent experimental characterization according to the ISO 10974 standard.

A simple method for the assessment of electrophoretic mobility in porous media.

Developing paper-based electrophoretic methods involve dealing with significant uncertainty levels when compared to their capillary counterparts. Critical information for developing these kinds of methods are the electrophoretic mobility of background electrolytes and samples. This work presents the design and characterization of a device for measuring the electrophoretic mobilities of dyes in porous media. The device was developed with the aim of validating a previously presented model and also proposing a protocol for the straightforward determination of electrophoretic mobilities in porous media when open-channel values are already known. Whatman #1 paper was used as a model substrate as far as it is the most common porous medium substrate for paper-based electrophoresis. The device was designed using a numerical simulation-assisted approach, utilizing OpenFOAM® and specific solvers for capillary transport and electromigration, namely porousMicroTransport and electroMicroTransport, respectively. The electrophoretic mobilities of five dyes were analyzed experimentally with the proposed device. To establish appropriate comparative values at different pHs, experiments in fused silica capillaries were also performed. An effective parameter model for describing the electrophoretic behavior of dyes in porous media, that is, the constriction factor, was found consistent with previous reports for the Whatman #1 paper. This consistency was found after considering (via direct measurements) the chromatographic effect of the medium over each dye. Consequently, the recorded values hold significant worth due to their potential for direct application in designing new experiments or devices in Whatman #1 paper. With the validation of the model through the experiments with the proposed device, those researchers interested on developing electrophoretic methods in porous substrates can make use of the open-channel electrophoretic mobilities reported in the literature, or in the well-known software databases, and correct them for the media of interest just by performing two simple characterization steps.

A parameter study of strato-rotational low-frequency modulations: impacts on momentum transfer and energy distribution.

Previous comparisons of experimental data with nonlinear numerical simulations of density stratified Taylor-Couette (TC) flows revealed nonlinear interactions of strato-rotational instability (SRI) modes that lead to periodic changes in the SRI spirals and their axial propagation. These pattern changes are associated with low-frequency velocity modulations that are related to the dynamics of two competing spiral wave modes propagating in opposite directions. In the present paper, a parameter study of the SRI is performed using direct numerical simulations to evaluate the influence of the Reynolds numbers, the stratification, and of the container geometry on these SRI low-frequency modulations and spiral pattern changes. The results of this parameter study show that the modulations can be considered as a secondary instability that are not observed for all SRI unstable regimes. The findings are of interest when the TC model is related to star formation processes in accretion discs. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Epicardial Dispersion of Repolarization Promotes the Onset of Reentry in Brugada Syndrome: A Numerical Simulation Study.

The Brugada syndrome (BrS) is a cardiac arrhythmic disorder responsible for sudden cardiac death associated with the onset of ventricular arrhythmias, such as reentrant ventricular tachycardia and fibrillation. The mechanisms which lead to the onset of such electrical disorders in patients affected by BrS are not completely understood, yet. The aim of the present study is to investigate by means of numerical simulations the electrophysiological mechanisms at the basis of the morphology of electrocardiogram (ECG) and the onset of reentry associated with BrS. To this end, we consider the Bidomain equations coupled with the ten Tusscher-Panfilov membrane model, on an idealized wedge of human right ventricular tissue. The results have shown that: (1) epicardial dispersion of repolarization, generated by the coexistence of regions of early and late repolarization, due to different modulation of the [Formula: see text] current, produces ECG waveforms exhibiting qualitatively the typical BrS morphology, characterized by ST elevation and partially negative T-waves; (2) epicardial dispersion of repolarization promotes the onset of reentry during the implementation of the programmed stimulation protocol, because of the conduction block occurring when a premature beat reaches the border of late repolarizing regions; and (3) the modulation of the [Formula: see text] current affects the duration of reentry, which becomes sustained with a remarkable increase of [Formula: see text] in the subepicardial layers.

A Mathematical Study of Metal Biosorption on Algal-Bacterial Granular Biofilms.

A multiscale mathematical model describing the metals biosorption on algal-bacterial photogranules within a sequencing batch reactor (SBR) is presented. The model is based on systems of partial differential equations (PDEs) derived from mass conservation principles on a spherical free boundary domain with radial symmetry. Hyperbolic PDEs account for the dynamics of sessile species and their free sorption sites, where metals are adsorbed. Parabolic PDEs govern the diffusion, conversion and adsorption of nutrients and metals. The dual effect of metals on photogranule ecology is also modelled: metal stimulates the production of EPS by sessile species and negatively affects the metabolic activities of microbial species. Accordingly, a stimulation term for EPS production and an inhibition term for metal are included in all microbial kinetics. The formation and evolution of the granule domain are governed by an ordinary differential equation with a vanishing initial value, accounting for microbial growth, attachment and detachment phenomena. The model is completed with systems of impulsive differential equations describing the evolution of dissolved substrates, metals, and planktonic and detached biomasses within the granular-based SBR. The model is integrated numerically to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and adsorption properties of biofilm components on the metal removal. Numerical results show an accurate description of the photogranules evolution and ecology and confirm the applicability of algal-bacterial photogranule technology for metal-rich wastewater treatment.

The role of A[Formula: see text] and Tau proteins in Alzheimer's disease: a mathematical model on graphs.

In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as two superposed graphs where toxic proteins diffuse, the connectivity graph which represents the neural network, and the proximity graph which takes into account the extracellular space. Toxic proteins such as [Formula: see text] amyloid and Tau play in fact a crucial role in the development of Alzheimer's disease and, separately, have been targets of medical treatments. Recent biomedical literature stresses the potential impact of the synergetic action of these proteins. We numerically test various modelling hypotheses which confirm the relevance of this synergy.

The Effect of the Method of Downhole Deployment on Distributed Acoustic Sensor Measurements: Field Experiments and Numerical Simulations.

Distributed acoustic sensing (DAS) is a promising technology for seismic data acquisition, particularly in downhole applications. However, downhole DAS measurements can be affected by the deployment method of the fibre-optic cable. These effects were explored in a field trial in two wells (one vertical and one deviated) drilled at the Otway International Test Centre. The trial in the vertical well shows that (1) fibre-optic cables cemented behind the casing provide data of the highest quality due to the best coupling to the formation, and (2) tubing-conveyed cable shows only slightly weaker coupling, but the data quality can be severely degraded by source-generated noise. A cable loosely suspended in the deviated well provided data quality comparable to that of the cemented DAS cable. To better understand the nature of the observed effects, the field experiments were supplemented by numerical modelling with a 1.5D full wave reflectivity algorithm (3D wave propagation in a 1D model), where cement, casing and wellbore were represented by infinite vertical layers. The results show that (1) a cement layer has only a slight effect (<5%) on the DAS amplitude; (2) the vertical strain in a liquid-filled borehole is comparable to that in the formation; and (3) the strain amplitude in the cable is of the same order of magnitude both in the formation and in the fluid. The strain in the cable is zero both when the cable's Poisson's ratio is zero and when the borehole fluid is air. The results confirm the feasibility of borehole DAS measurements with fibre-optic cables suspended in a borehole liquid (but not gas!).

Optimal Frequency and Wireless Power Budget for Miniature Receivers in Obese People.

This study investigates wireless power transfer for deep in-body receivers, determining the optimal frequency, power budget, and design for the transmitter and receiver. In particular, the focus is on small, in-body receivers at large depths up to 20 cm for obese patients. This enables long-term monitoring of the gastrointestinal tract for all body types. Numerical simulations are used to investigate power transfer and losses as a function of frequency and to find the optimal design at the selected frequency for an obese body model. From all ISM-frequencies in the investigated range (1 kHz-10 GHz), the value of 13.56 MHz yields the best performance. This optimum corresponds to the transition from dominant copper losses in conductors to dominant losses in conductive tissue. At this frequency, a transmitting and receiving coil are designed consisting of 12 and 23 windings, respectively. With a power transfer efficiency of 2.70×10-5, 18 µW can be received for an input power of 0.68 W while still satisfying exposure guidelines. The power transfer is validated by measurements. For the first time, efficiency values and the power budget are reported for WPT through 20 cm of tissue to mm sized receivers. Compared to WPT at higher frequencies, as commonly used for small receivers, the proposed system is more suitable for WPT to large depths in-body and comes with the advantage that no focusing is required, which can accommodate multiple receivers and uncertainty about receiver location more easily. The received power allows long-term sensing in the gastrointestinal tract by, e.g., temperature, pressure, and pH sensors, motility sensing, or even gastric stimulation.

The Reducing Agents in Sonochemical Reactions without Any Additives.

It has been experimentally reported that not only oxidation reactions but also reduction reactions occur in aqueous solutions under ultrasound without any additives. According to the numerical simulations of chemical reactions inside an air or argon bubble in water without any additives under ultrasound, reducing agents produced from the bubbles are H, H2, HO2 (which becomes superoxide anion (O2-) in liquid water), NO, and HNO2 (which becomes NO2- in liquid water). In addition, H2O2 sometimes works as a reducing agent. As the reduction potentials of H and H2 (in strongly alkaline solutions for H2) are higher than those of RCHOH radicals, which are usually used to reduce metal ions, H and H2 generated from cavitation bubbles are expected to reduce metal ions to produce metal nanoparticles (in strongly alkaline solutions for H2 to work). It is possible that the superoxide anion (O2-) also plays some role in the sonochemical reduction of some solutes. In strongly alkaline solutions, hydrated electrons (e-aq) formed from H atoms in liquid water may play an important role in the sonochemical reduction of solutes because the reduction potential is extremely high. The influence of ultrasonic frequency on the amount of H atoms produced from a cavitation bubble is also discussed.

Effect of cross-border migration on the healthcare system of a destination community: Insights from mathematical modelling of COVID-19 in a developing country.

The movement of persons during the pandemic has played a significant role in increasing the disease transmission rates as well as the spread of COVID-19 variants from one region to another. Although, strict restrictions on movement of persons across borders had been imposed early on in the pandemic, countries had to open up their borders to travel as a way of trying to resuscitate their economies that were declining due to closure of businesses and restriction on both local and international travel. Although the lifting of travel bans was done under strict regulations, there has since been a spike in the number of infection cases and spread of virus variants. These increases have certainly put a lot of strain on the rather limited resources allocated to fighting COVID-19 in most regions including the Eastern and Southern Africa. In this manuscript, we examine the potential role played by cross-border movements on the number of detected cases in a developing country. Here, we consider cases where persons cross borders through either designated controlled border points with proper facilitation for screening and detection of potentially infected cases, as well as border crossings through ungazatted points. The persons crossing borders are considered to be either susceptible, exposed or infected with no or mild symptom. A mathematical model was formulated to cater for the aforementioned classifications as well as additional important dynamics related to the disease. The behaviour of solutions for the model is determined and the conditions for existence of the disease free equilibrium as well as the disease persistent equilibrium ascertained. Finally, a dynamically consistent nonstandard finite difference scheme is proposed to replicate the properties of the continuous model. The baseline model was fitted to data of two waves, parameter values were determined and used to obtain numerical results. Our results show that, an increase in cross border movement can result in an increase in the number of detected cases. We observed that if the number of persons who cross-border points while positive for COVID-19 is reduced by 60%, the total number of detected cases can be reduced by up to 58%. In addition, an 83% increase in immigration of exposed persons can increase the disease burden in a destination country by at least 14%. These results justify border points closures during a pandemic or imposing very stringent measure across borders to curtail the importation of positive cases in a country.

Effect of wall slip on the viscoelastic particle ordering in a microfluidic channel.

The formation of a line of equally spaced particles at the centerline of a microchannel, referred as "particle ordering," is desired in several microfluidic applications. Recent experiments and simulations highlighted the capability of viscoelastic fluids to form a row of particles characterized by a preferential spacing. When dealing with non-Newtonian fluids in microfluidics, the adherence condition of the liquid at the channel wall may be violated and the liquid can slip over the surface, possibly affecting the ordering efficiency. In this work, we investigate the effect of wall slip on the ordering of particles suspended in a viscoelastic liquid by numerical simulations. The dynamics of a triplet of particles in an infinite cylindrical channel is first addressed by solving the fluid and particle governing equations. The relative velocities computed for the three-particle system are used to predict the dynamics of a train of particles flowing in a long microchannel. The distributions of the interparticle spacing evaluated at different slip coefficients, linear particle concentrations, and distances from the channel inlet show that wall slip slows down the self-assembly mechanism. For strong slipping surfaces, no significant change of the initial microstructure is observed at low particle concentrations, whereas strings of particles in contact form at higher concentrations. The detrimental effect of wall slip on viscoelastic ordering suggests care when designing microdevices, especially in case of hydrophobic surfaces that may enhance the slipping phenomenon.

Prevention and control of OQDS (olive quick decline syndrome) outbreaks caused by Xylella fastidiosa.

In Southern Italy, since 2013, there has been an ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium Xylella fastidiosa, which has caused a dramatic impact from both socio-economic and environmental points of view. The main players involved in OQDS are represented by the insect vector, Philaenus spumarius, its host plants (olive trees and weeds) and the bacterium, X. fastidiosa. Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones, with later installment of olive cultivars more resistant to the bacterium infection. Unfortunately, both of these practices are having an undesirable impact on the environment (most of these olive trees were monumental ones) and on the economy. Based on a mathematical model expressed in terms of a nontrivial system of ordinary differential equations, our analysis has provided a clear picture of all possible steady states (feasible equilibria) and their stability properties, corresponding to a variety of different parameter scenarios; all of this has been illustrated by a set of computational experiments. A significant original contribution of this paper is the proof of the global asymptotic stability of each of the feasible equilibria under its existence assumptions, a fact that excludes multiple equilibria under the given conditions. It has emerged that the removal of a suitable amount of weed biomass (host plants of the juvenile stages of the insect vector of X. fastidiosa) from olive orchards and surrounding areas leads to the eradication of the epidemic, without requiring neither the removal nor the substitution of the existing olive trees.

A mathematical model to study the impact of intra-tumour heterogeneity on anti-tumour CD8+ T cell immune response.

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Secondly, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.

Rate of formation of caustics in heavy particles advected by turbulence.

The rate of collision and the relative velocities of the colliding particles in turbulent flows are a crucial part of several natural phenomena, e.g. rain formation in warm clouds and planetesimal formation in protoplanetary discs. The particles are often modelled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three-dimensional turbulent flows, we calculate the rate of formation of caustics, [Formula: see text] as a function of the Stokes number ([Formula: see text]). The best approximation to our data is [Formula: see text], in the limit [Formula: see text] where [Formula: see text] is a non-universal constant. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.