Homogeneous Case Research Articles

Analysis of a diffusive host–pathogen epidemic model with two‐stage mechanism in a spatially heterogeneous environment

Due to the spatial heterogeneity present in many aspects of disease transmission, the rate of transmission of infectious diseases, human birth/mortality rate, and the mobility ability of infected humans should be different in different geographical locations. On the other hand, infected humans may exhibit distinct differences in symptoms during the different stages of the disease transmission. This paper aims to study threshold dynamics of a reaction–diffusion host–pathogen model governed by two‐stage mechanism and no flux boundary condition. In the model, we use bilinear and saturated incidence mechanism to model the interactions between host populations and pathogens and assume that (i) the parameters are spatially dependent and (ii) infected individuals in the first stage can random walk, while in the second stage, the diffusion rates are neglected. By carrying out strict analysis, the paper establishes the threshold‐type results with the basic reproduction number. Specifically, in a homogeneous case that all parameters are constants, we establish the global attractivity of the endemic equilibrium. To investigate the effects of small or large diffusion rates of susceptible individuals on the disease transmission in a heterogeneous environment, we explore the asymptotic profile of positive steady state whenever it exists. Our numerical results validate the theoretical results and indicate the importance of the infected humans in the second stage and pathogens in the environment in disease transmission, which greatly contribute to disease spread in a bounded domain and should not be ignored.

CD49d Expression Identifies a Biologically Distinct Subtype of Chronic Lymphocytic Leukemia with Inferior Progression-Free Survival on BTK Inhibitor Therapy.

To determine the role of CD49d for response to Bruton's tyrosine kinase inhibitors (BTKi) in patients with chronic lymphocytic leukemia (CLL). In patients treated with acalabrutinib (n = 48), CD49d expression, VLA-4 integrin activation, and tumor transcriptomes of CLL cells were assessed. Clinical responses to BTKis were investigated in acalabrutinib- (n = 48; NCT02337829) and ibrutinib-treated (n = 73; NCT01500733) patients. In patients treated with acalabrutinib, treatment-induced lymphocytosis was comparable for both subgroups but resolved more rapidly for CD49d+ cases. Acalabrutinib inhibited constitutive VLA-4 activation but was insufficient to block BCR and CXCR4-mediated inside-out activation. Transcriptomes of CD49d+ and CD49d- cases were compared using RNA sequencing at baseline and at 1 and 6 months on treatment. Gene set enrichment analysis revealed increased constitutive NF-κB and JAK-STAT signaling, enhanced survival, adhesion, and migratory capacity in CD49d+ over CD49d- CLL that was maintained during therapy. In the combined cohorts of 121 BTKi-treated patients, 48 (39.7%) progressed on treatment with BTK and/or PLCG2 mutations detected in 87% of CLL progressions. Consistent with a recent report, homogeneous and bimodal CD49d-positive cases (the latter having concurrent CD49d+ and CD49d- CLL subpopulations, irrespective of the traditional 30% cutoff value) had a shorter time to progression of 6.6 years, whereas 90% of cases homogenously CD49d- were estimated progression-free at 8 years (P = 0.0004). CD49d/VLA-4 emerges as a microenvironmental factor that contributes to BTKi resistance in CLL. The prognostic value of CD49d is improved by considering bimodal CD49d expression. See related commentary by Tissino et al., p. 3560.

Recursive relations and quantum eigensolver algorithms within modified Schrieffer-Wolff transformations for the Hubbard dimer

We derive recursive relations for the Schrieffer--Wolff (SW) transformation applied to the half-filled Hubbard dimer. While the standard SW transformation is set to block-diagonalize the transformed Hamiltonian solely at the first order of perturbation, we infer from recursive relations two types of modifications, variational or iterative, that approach, or even enforce for the homogeneous case, the desired block-diagonalization at infinite order of perturbation. The modified SW unitary transformations are then used to design an test quantum algorithms adapted to the noisy and fault-tolerant era. This work paves the way toward the design of alternative quantum algorithms for the general Hubbard Hamiltonian.

A new approach to model geomaterials with heterogeneous properties in thermo-hydro-mechanical coupled problems

The main objective of this article is to present a new approach to model coupled thermo-hydro-mechanical problems considering geomaterials with heterogeneous properties. This approach has been implemented in the software CODE_BRIGHT and it provides the possibility of considering geomaterials with a spatially correlated heterogeneous field of porosity, following a normal distribution. This spatial correlation can be isotropic or anisotropic. An important feature of this approach is that material properties such as intrinsic permeability, thermal conductivity, diffusivity, retention curve, elastic modulus or cohesion are defined as a function of porosity and, thus, they become heterogeneous with spatial correlation and, eventually, anisotropic. A validation exercise and other basic numerical examples have been carried out to illustrate the possibilities of the proposed approach. The results, which have been compared with a homogeneous case, show that considering heterogeneous fields can be relevant in different modelling problems, especially coupled thermo-hydro-mechanical problems.

Transient dispersion regimes in heterogeneous porous media: On the impact of spatial heterogeneity in permeability and exchange kinetics in mobile–immobile transport

Transport processes in the subsurface are coupled with the heterogeneity of the porous structure. Obtaining an accurate description of mass transport in such media at all time scales remains a crucial task, as the subsurface is strongly impacted by human activity. Spreading of pollutants in the transient but also in the asymptotic regime, as well as the time to reach a critical location (e.g. aquifer, well) significantly depend on the underlying heterogeneity of the permeability field. Moreover, in the case of solute retention, transport is also characterized by local exchange kinetics that depend on the local aquifer properties. Consequently, exchange (retention) times are expected to be spatially heterogeneous. In this work we focus on the influence of spatially heterogeneous permeability and exchange times on the transient and asymptotic transport regimes and provide a parametric study. To this goal, we simulate in a first part the transport in a two-dimensional heterogeneous medium under spatially varying permeability and mobile–immobile mass transfer parameters. Equations are solved using a Lattice-Boltzmann two-relaxation-time (TRT) algorithm. We assume the following relation between the local permeability K and the local exchange time: τ∝Kγ. Taking into account this relation, we investigate the impact of the Damköhler number (Da, ratio of the advection and exchange time scales), the disorder of the permeability field and the value of the exponent of the coupling function (γ) on the spatial evolution of the concentration field and breakthrough curve. We show that, depending on the parameters (Da, γ, etc.), we can observe transient, non-Fickian dispersion, which is characterized by non-exponential tails of the solute breakthrough curves and a non-linear evolution of the spatial variance of the solute distribution.In a second part, we present a new continuous time random walk (CTRW) model to upscale these transport behaviors. The model is based on a spatial Markov model for particle velocities that couples advective–dispersive transport and heterogeneous mass transfer through a compound Poisson process. The upscaled model can be fully parameterized by the statistics of permeability and the hydraulic gradient (with no fitting parameter), that is, in terms of medium and flow characteristics. The results of the CTRW model fully capture the non-Fickian transient transport regimes both for the breakthrough curves and spatial concentration variance. In the longtime limit, as expected from the central limit theorem, the CTRW model predicts normal, Fickian behavior. Finally we show, that the time to reach the asymptotic regimes in heterogeneous media (e.g. heterogeneous exchange times) is parameter dependent and in average is two orders of magnitude larger than for the respective homogeneous case. To summarize, the coupling between the heterogeneous permeability field and the local mass transfer properties can strongly influence transient and asymptotic transport regimes and potentially explain experimentally observed non-Gaussian behaviors.

Towards a novel EMHD dissipative stagnation point flow model for radiating copper-based ethylene glycol nanofluids: An unsteady two-dimensional homogeneous second-grade flow case study

A novel EMHD dissipative second-grade nanofluid flow model is proposed exclusively in this numerical inspection for radiating copper-based ethylene glycol nanofluids to reveal the dynamical and thermal aspects of the studied homogeneous mixture during its unsteady two-dimensional stagnation point flow towards a horizontal electromagnetic actuator. Based on admissible physical assumptions and authenticated experimental correlations, the governing PDEs and BCs are derived appropriately for the nanofluid flow problem under consideration. After numerous rearrangements and non-dimensionalization treatments, the resulting ODEs and BCs are handled computationally with the help of a robust GDQ algorithm under the parametric control of several influencing factors, whose strengthening magnitudes affect probably the flow control process and heat transport mechanism. In this context, it proved graphically that the nanoparticles’ loading process exhibits dissimilar dynamical and thermal impacts as compared with the influences of the nanoparticles’ diameter size. Besides, the resistive dynamical effect of the utilized electromagnetic actuator reinforces thermally the enhancing role of the thermal radiative heat flux and Joule’s heating process within the nanofluidic medium.

Surface Density Function and Its Evolution in Homogeneous and Inhomogeneous Mixture n-Heptane MILD Combustion

ABSTRACT Moderate or intense low-oxygen dilution (MILD) combustion is a combustion technique with potential to simultaneously improve thermal efficiency and reduce emissions. This paper focuses on the mean behavior of the reactive scalar gradient characterized by the surface density function (SDF = magnitude of the reaction progress variable gradient) and its evolution for exhaust gas recirculation (EGR) type, homogeneous and inhomogeneous mixture n-heptane combustion under MILD conditions using Direct Numerical Simulations (DNS) with reduced chemical mechanism. Two oxygen concentrations have been considered here for the homogeneous mixture case, namely, 3.0% and 4.5% by volume. The characteristics of the SDF and displacement speed were also analyzed in the reaction and propagating-flame-dominated regions of the domain to illustrate the effect of combustion mode on the mean variations of these quantities. The mean values of the SDF in turbulent MILD combustion cases are found to be smaller compared to the corresponding laminar flame cases. Moreover, the effect of mixture inhomogeneity on the SDF variation is found to be marginal for the parameters considered here. It is found that increasing the dilution factor reduces the percentage of flame thickening with respect to the corresponding laminar flame thickness under identical turbulence conditions. The effects of dilatation rate are found to be weak in the studied cases due to the expected low heat release under MILD conditions which leads to weak thermal expansion effects. The effective flame normal and tangential strain rates are found to be dominated by the additional flame normal and tangential strain rates due to flame propagation, respectively. The effective flame normal strain rate has positive values across the flame which promotes flame thickening and could explain the decrease in the SDF values, while the effective flame tangential strain rate is negative throughout the flame and indicates a fractional reduction in flame area that could be attributed to flame surface interactions. The reaction-dominated regions give rise to reduced level of the SDF in the homogeneous mixture cases and increased level of in all cases compared to those calculated in the propagating-flame region.

Modeling and numerical simulations of multilane vehicular traffic by active particles methods

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the kinetic theory of active particles methods. The main idea of this theory is to consider each driver–vehicle system as a micro-system, where the microscopic state of particles is described by position, velocity, and activity which is an appropriate variable for modeling the quality of the driver-vehicle. The interactions between micro-systems are modeled by stochastic game theory. This leads to the derivation of a mathematical model within the framework of the approach of kinetic theory. The well-posedness of the related Cauchy problem for the spatially homogeneous case is established. Numerical simulations are carried out to show the ability of the proposed model to reproduce the empirical data such as the asymptotic property in time and the emerging behavior of clusters with a particular focus on the road environment conditions.

Perirectal hematoma after stapled surgery for hemorrhoidal prolapse and obstructed defecation syndrome: case series management to avoid panic-guided treatment

Perirectal hematoma (PH) is one of the most feared complications of stapling procedures. Literature reviews have reported only a few works on PH, most of them describing isolated treatment approaches and severe outcomes. The aim of this study was to analyze a homogenous case series of PH and to define a treatment algorithm for huge postoperative PHs. A retrospective analysis of a prospective database of three high-volume proctology units was performed between 2008 and 2018, and all PH cases were analyzed. In all, 3058 patients underwent stapling procedures for hemorrhoidal disease or obstructed defecation syndrome with internal prolapse. Among these, 14 (0.46%) large PH cases were reported, and 12 of these hematomas were stable and treated conservatively (antibiotics and CT/laboratory test monitoring); most of them were resolved with spontaneous drainage. Two patients with progressive PH (signs of active bleeding and peritonism) were submitted to CT and arteriography to evaluate the source of bleeding, which was subsequently closed by embolization. This approach helped ensure that no patients with PH were referred for major abdominal surgery. Most PH cases are stable and treatable with a conservative approach, evolving with self-drainage. Progressive hematomas are rare and should undergo angiography with embolization to minimize the possibility of major surgery and severe complications.

Modeling the damage-induced softening behavior of brain white matter using a coupled hyperelasticty-damage model

White matter in the brain is structurally anisotropic consisting of large bundle of aligned axonal fibers. Hyperelastic, transversely isotropic constitutive models are typically used in the modeling and simulation of such tissues. However, most studies constrain the material models to describe the mechanical behavior of white matter in the limit of small deformation, without considering the experimentally observed damage initiation and damage-induced material softening in large strain regime. In this study, we extend a previously developed transversely isotropic hyperelasticity model for white matter by coupling it with damage equations within the framework of thermodynamics and using continuum damage mechanics method. Two homogeneous deformation cases are used to demonstrate the proposed model's capability in capturing the damage-induced softening behaviors of white matter under uniaxial loading and simple shear, along with the investigation of fiber orientation effect on such behaviors and material stiffness. As a demonstration case of inhomogeneous deformation, the proposed model is also implemented into finite element codes to reproduce the experimental data (nonlinear material behavior and damage initiation) from an indentation configuration of porcine white matter. Good agreement between numerical results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of white matter considering damage at large strain.

Development of a generalized Richards equation for predicting spontaneous imbibition of highly shear-thinning liquids in gas recovery applications

A new generalized Richards equation (GRE) valid for highly shear-thinning liquids obeying the power-law model is developed using the concept of the effective viscosity. The mathematical model developed this way is validated against experimental data reported recently for one-dimensional spontaneous imbibition of two pusher liquids by a tight sandstone. The GRE model was then used for evaluating the applicability of shear-thinning liquids for enhanced gas recovery. For a homogenous tight sandstone, it is shown that shear-thinning can dramatically shorten the time needed for the gas recovery to reach equilibrium. Based on the obtained numerical results, the mass of the gas recovered using spontaneous imbibition is increased if use is made of highly shear-thinning liquids. At prolonged times, however, it is predicted that gas recovery might slightly drop below its Newtonian counterpart even for highly shear-thinning fluids. The effect was attributed to the fact that, in spontaneous imbibition, the viscosity of power-law fluids increases with time and can eventually become larger than its Newtonian counterpart. For a two-layered non-homogeneous system, numerical results suggest that depending on the microstructure of the two layers, the liquid mass uptake can be smaller than that of the homogenous case. It is predicted that if the liquid is sufficiently shear-thinning, gas recovery can reach levels much above the homogeneous case.

The semidiscrete damped wave equation with a fractional Laplacian

In this paper we completely solve the open problem of finding the fundamental solution of the semidiscrete fractional-spatial damped wave equation. We combine operator theory and Laplace transform methods with properties of Bessel functions to show an explicit representation of the solution when initial conditions are given. Our findings extend known results from the literature and also provide new insights into the qualitative behavior of the solutions for the studied model. As an example, we show the existence of almost periodic solutions as well as their profile in the homogeneous case.

In situ x-ray absorption investigations of a heterogenized molecular catalyst and its interaction with a carbon nanotube support.

A highly active heterogenized molecular CO2 reduction catalyst on a conductive carbon support is investigated to identify if its improved catalytic activity can be attributed to strong electronic interactions between catalyst and support. The molecular structure and electronic character of a [Re+1(tBu-bpy)(CO)3Cl] (tBu-bpy = 4,4'-tert-butyl-2,2'-bipyridine) catalyst deposited on multiwalled carbon nanotubes are characterized using ReL3-edge x-ray absorption spectroscopy under electrochemical conditions and compared to the homogeneous catalyst. The Reoxidation state is characterized from the near-edge absorption region, while structural changes of the catalyst are assessed from the extended x-ray absorption fine structure under reducing conditions. Chloride ligand dissociation and a Re-centered reduction are both observed under applied reducing potential. The results confirm weak coupling of [Re(tBu-bpy)(CO)3Cl] with the support, since the supported catalyst exhibits the same oxidation changes as the homogeneous case. However, these results do not preclude strong interactions between a reduced catalyst intermediate and the support, preliminarily investigated here using quantum mechanical calculations. Thus, our results suggest that complicated linkage schemes and strong electronic interactions with the initial catalyst species are not required to improve the activity of heterogenized molecular catalysts.

The impact of permeability barriers on steam-solvent coinjection – A mechanistic study using a physical model

Coinjection of steam and condensate has been studied for improving the energy efficiency of steam-assisted gravity drainage (SAGD) as solvent-assisted SAGD or SA-SAGD. However, it is not well understood how tortuous hydraulic paths under heterogeneous permeability can influence the compositional and thermal flow characteristics in SA-SAGD. We addressed this question by performing an experiment of the coinjection of steam and condensate for bitumen recovery. This paper discusses the experimental results and gives our mechanistic analysis of how the tortuous hydraulic paths affected the thermal and compositional flow and the properties of the produced bitumen in the experiment.The physical model was a cylindrical pressure vessel with a diameter of 0.425 m and a length of 1.2 m, which was filled with unconsolidated sands. Two shale plates were horizontally installed above the well pair at different elevations so that they could represent permeability barriers to cause tortuous flow paths during the SA-SAGD experiment. The porosity and permeability of the sandpack was 0.34 and 5.6 D, respectively. Initially, the oil and water saturations were 95% and 5%, respectively.After preheating for 1 day, a mixture of 98.2 mol% steam and 2.8 mol% condensate was injected at 3500 kPa for 4 days (35 cm3/min of steam, cold water equivalent). The injection and production histories along with the real-time temperature distribution were recorded during the experiment. Produced oil samples were frequently taken and analyzed for density and asphaltene content. After the experiment, the sandpack was excavated and sampled from different locations to analyze the saturation and asphaltene content of the remaining oil. The experimental results in this paper were compared with the previous SAGD and SA-SAGD experiments that used the same experimental set up with a homogeneous sandpack.Results showed that, in comparison to the homogeneous SAGD case, SA-SAGD was able to lower the cumulative steam-oil ratio (SOR) by a factor of two to three even in the presence of shale plates. Analysis of the temperature profiles indicated that the steam chamber vertically expanded from the lower part to the upper part through tortuous paths at lower temperatures. An emerging steam chamber above the shale plates occurred by convective heat from the injection well through lower-temperature flow paths between shale plates, involving light to intermediate solvent components that enabled the steam chamber to expand away from the injection well. This highlights the important role of volatile solvent components in the growth of a steam chamber in SA-SAGD under heterogeneity. The produced bitumen density in this research was closer to the original bitumen than in the homogeneous SA-SAGD case because the bitumen dilution and the solvent retention increased by the tortuous flow regime resulted in efficient drainage of oil at lower temperature.

Resilient Service Provisioning for Edge Computing

We study the problem of resilient service provisioning for edge computing (RSPE), i.e., how to determine a service placement strategy to maximize the expected overall utility by service provisioning, in the presence of uncertain service failures. RSPE is extremely challenging to tackle, because the explicit expression of its objective function is difficult to obtain, and it is a resilient max–min problem subject to knapsack constraints, which is unexplored so far and cannot be addressed by existing resilient optimization techniques. We first explore the potential properties of the implicit objective function, and reveal that it is monotone submodular under certain conditions. We further prove that the knapsack constraints form a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -independence system constraint, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q&gt;0$ </tex-math></inline-formula> is a constant related to the constraints. We propose two novel solutions for the general RSPE and homogeneous case, respectively. First, for the general problem, we propose a “two-step greedy” algorithm achieving a constant approximation ratio within polynomial time. Second, for the homogeneous case where one of the knapsack constraints reduces to a matroid constraint, we propose an improved “first-greedy-then-local search” polynomial time algorithm achieving better approximation ratio than the previous one. Both extensive simulations and field experiments validate the effectiveness of our proposed algorithms.

Role of inhomogeneities in resonance light absorption and luminescence of molecular aggregates

Within the linear response theory, we have calculated the resonance absorption of the light and resonance luminescence for the one-dimensional molecular aggregate. We have shown that the randomness of the distribution of signs of the interaction between dipoles of the aggregate dramatically changes the parameters of the absorption and luminescence. In the homogeneous case, the resonance response of the exciton band of the molecular aggregate produces narrow lines at edges of the band. On the other hand, inhomogeneities yield contributions to optical characteristics of all excitons of the band.

Enhanced Direct Electron Transfer Mediated Contaminant Degradation by Fe(IV) Using a Carbon Black-Supported Fe(III)-TAML Suspension Electrode System.

Iron complexes of tetra-amido macrocyclic ligands (Fe-TAML) are recognized to be effective catalysts for the degradation of a wide range of organic contaminants in homogeneous conditions with the high valent Fe(IV) and Fe(V) species generated on activation of the Fe-TAML complex by hydrogen peroxide (H2O2) recognized to be powerful oxidants. Electrochemical activation of Fe-TAML would appear an attractive alternative to H2O2 activation, especially if the Fe-TAML complex could be attached to the anode, as this would enable formation of high valent iron species at the anode and, importantly, retention of the valuable Fe-TAML complex within the reaction system. In this work, we affix Fe-TAML to the surface of carbon black particles and apply this "suspension anode" process to oxidize selected target compounds via generation of high valent iron species. We show that the overpotential for Fe(IV) formation is 0.17 V lower than the potential required to generate Fe(IV) electrochemically in homogeneous solution and also show that the stability of the Fe(IV) species is enhanced considerably compared to the homogeneous Fe-TAML case. Application of the carbon black-supported Fe-TAML suspension anode reactor to degradation of oxalate and hydroquinone with an initial pH value of 3 resulted in oxidation rate constants that were up to three times higher than could be achieved by anodic oxidation in the absence of Fe-TAML and at energy consumptions per order of removal substantially lower than could be achieved by alternate technologies.

A Continuous Gradient Colloidal Glass (Adv. Mater. 7/2023)

Photonic Colloidal Glass Continuous gradients in self-assembled materials can provide functionality exceeding that of the homogenous case. In article number 2208745, Markus Retsch and co-workers present a synthesis method that provides gradient size distributions via a controlled extraction emulsion process (CrEEP). The high degree of control allows the fabrication of a continuous-gradient photonic glass with enhanced broadband reflectance.

The heterogeneous helicoseir

We study the rotations of a heavy string (helicoseir) about a vertical axis with one free endpoint and with arbitrary density, under the action of the gravitational force. We show that the problem can be transformed into a nonlinear eigenvalue equation, as in the uniform case. The eigenmodes of this equation represent equilibrium configurations of the rotating string in which the shape of the string does not change with time. As previously proved by Kolodner for the homogeneous case, the occurrence of new modes of the nonlinear equation is tied to the spectrum of the corresponding linear equation. We have been able to generalize this result to a class of densities ρ(s)=γ(1−s)γ−1, which includes the homogeneous string as a special case (γ=1).We also show that the solutions to the nonlinear eigenvalue equation (NLE) for an arbitrary density are orthogonal and that a solution of this equation with a given number of nodes contains solutions of a different helicoseir, with a smaller number of nodes. Both properties hold also for the homogeneous case and had not been established before.

Simulation of Phobos gravity field estimation from Tianwen-1 flybys and implications for the modelling of Phobos’ internal structure

ABSTRACT Doppler radio tracking data from Tianwen-1, China’s first Mars mission, could contribute to a better estimate of the gravity field of Phobos. In this study, we show that a determination up to degree and order 3 is feasible by considering five additional flybys of Phobos by the Tianwen-1 spacecraft, in addition to the previous flybys already done by the Mars Express spacecraft, and probably degree and order 5 is within reach. Three cases of mass repartition are considered: (i) a homogeneous case, (ii) a core-dominated Phobos, and (iii) a mantle-dominated Phobos. The case of a mantle-dominated Phobos is the easiest to detect, followed by a homogeneous Phobos, and finally by a core-dominated Phobos. We also discuss implications about the modelling of the internal structure of Phobos.