Synchronization transitions induced by partial time delay in a excitatory–inhibitory coupled neuronal network

Information transmission delays are an inherent factor of neuronal systems as a consequence of the finite propagation speeds and time lapses occurring by both dendritic and synaptic processes. In real neuronal systems, some delay between two neurons is too small and can be ignored, which results in partial time delay. In this paper, we focus on investigating influences of partial time delay on synchronization transitions in a excitatory–inhibitory (E–I) coupled neuronal networks. Here, we suppose time delay between two neurons equals to \(\tau \) with probability \(p_{\mathrm{delay}}\) and investigate effect of partial time delay on synchronization transitions of the neuronal networks by controlling \(\tau \) and \(p_{\mathrm{delay}}\) under three cases. In these three cases, excitatory synapses are always considered to delayed with probability \(p_{\mathrm{delay}}\), while inhibitory synapses are considered to be without delays (case I), delayed with probability \(p_{\mathrm{delay}}\) (case II), and always delayed (case III), respectively. It is revealed that, in the first two cases, partial time delay has little influences on synchronization of the neuronal network for small \(p_{\mathrm{delay}}\), while it could induce synchronization transitions at \(\tau \) around integer multiples of the period of individual neuron T when \(p_{\mathrm{delay}}\) is large enough, while in the case III, partial time delay could induce synchronization transitions at \(\tau \) being around odd integer multiples of T / 2 for small \(p_{\mathrm{delay}}\) and at \(\tau \) being around integer multiples of T for large \(p_{\mathrm{delay}}\). Most interesting observation is that partial time delay could induce frequent synchronization transitions at \(\tau \) being around integer multiples of T / 2 for intermediate \(p_{\mathrm{delay}}\). Moreover, effect of rewiring probability on synchronization transitions induced by partial time delay has been discussed. It is found that synchronization transitions induced by partial time delay are robust to rewiring probability for large \(p_{\mathrm{delay}}\) under the three cases.     

Bifurcations of a creeping air–water flow in a conical container

This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height \(H_{\mathrm{w}}\) and cone half-angle \(\beta \) vary, numerous flow metamorphoses occur. They are investigated for \(\beta =30^{\circ }, 45^{\circ }\), and \(60^{\circ }\). For small \(H_{\mathrm{w}}\), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as \(H_{\mathrm{w}}\) exceeds a threshold depending on \(\beta \). For all \(\beta \), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.     

Uniaxial experimental study of the acoustic emission and deformation behavior of composite rock based on 3D digital image correlation (DIC)

In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3 D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the θ = 0?–45?specimens had obvious plastic deformation during loading, and the brittleness of the θ = 60?–90?specimens gradually increased during the loading process. When the anisotropic angle θincreased from 0?to 90?, the peak strength, peak strain,and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories:tensile fracture across the discontinuities(θ = 0?–30?), slid-ing failure along the discontinuities(θ = 45?–75?), and tensile-split along the discontinuities(θ = 90?). The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the θ = 0?–45?specimens and was almost the same as that of the θ = 60?–90?specimens. As for the strain localization highlighted in the maximum principal strain field, the θ = 0?–30?specimens appeared in the rock matrix approximately parallel to the loading direction,while in the θ = 45?–90?specimens it appeared at the hard and weak rock layer interface.     

Measurements of Transitional and Turbulent Flow in a Randomly Packed Bed of Spheres with Particle Image Velocimetry

Particle image velocimetry (PIV) has been used to investigate transitional and turbulent flow in a randomly packed bed of mono-sized transparent spheres at particle Reynolds number, \(20<{{ Re}}_{\mathrm{p}}< 3220\). The refractive index of the liquid is matched with the spheres to provide optical access to the flow within the bed without distortions. Integrated pressure drop data yield that Darcy law is valid at \({{ Re}}_{\mathrm{p}} \approx 80\). The PIV measurements show that the velocity fluctuations increase and that the time-averaged velocity distribution start to change at lower \({{ Re}}_{\mathrm{p}}\). The probability for relatively low and high velocities decreases with \({{ Re}}_{\mathrm{p}}\) and recirculation zones that appear in inertia dominated flows are suppressed by the turbulent flow at higher \({{ Re}}_{\mathrm{p}}\). Hence there is a maximum of recirculation at about \({{ Re}}_{\mathrm{p}} \approx 400\). Finally, statistical analysis of the spatial distribution of time-averaged velocities shows that the velocity distribution is clearly and weakly self-similar with respect to \({{ Re}}_{\mathrm{p}}\) for turbulent and laminar flow, respectively.     

A Simple Method for the Determination of Adsorption Kinetic Parameters Using Recycle Fixed-Bed Adsorber

This study focuses on the development of a novel analysis technique for determining the intraparticle diffusivity \((D_{\mathrm{S}})\) and fluid film mass transfer coefficient \((k_\mathrm{F})\) from a concentration history curve of a recycle fixed-bed reactor without using the linear driving force approximation and empirical equations for the estimation of \(k_\mathrm{F}\). The recycle fixed-bed method requires lesser amounts of working fluid for experiment purposes, which is an advantage over the usual fixed-bed method. Based on the characterization results of the concentration history curves, simulated by rigorous numerical calculations, a novel analysis technique was established. The \(D_{\mathrm{S}}\) value can be determined from the experimentally obtained time at which the concentration of the curve is minimal \((t_{C\mathrm{min}})\). The \(k_\mathrm{F}\) value can be determined from the \(D_{\mathrm{S}}\) value and Biot number (Bi), which can be estimated from the experimental ratio of the maximum concentration to the minimum concentration \((c_{\max }/c_{\min })\). The \(D_{\mathrm{S}}\) and \(k_\mathrm{F}\) values of phenol adsorption on an activated carbon material were determined experimentally using the proposed analysis method. This method enables the determination of reliable adsorption kinetic parameters through a simple and economical experiment. However, appropriate experimental data must be acquired under regulated experimental conditions, especially in the case of fluctuation of the concentration history curve.     

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s~(-iε), so that K = ■ s~(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.     

Inertial Sensitivity of Porous Microstructures

Fluid flows through porous media are subject to different regimes, ranging from linear creeping flows to unsteady, chaotic turbulence. These different flow regimes at the pore scale have repercussions at larger scales, with the macroscale drag force experienced by a fluid moving through the medium becoming a nonlinear function of the average velocity beyond the creeping flow regime. Accurate prediction of the transition between different flow regimes is an important challenge with repercussions onto many engineering applications. Here, we are interested in the first deviation from Darcy’s law, when inertia effects become sizeable. Our goal is to define a Reynolds number, \(Re_{\mathrm{C}}\), so that the inertial deviation occurs when \(Re_{\mathrm{C}}\sim 1\) for any microstructure. The difficulty in doing so is to reduce the multiple length scales characterizing the geometry of the porous structure to a single length scale, \(\ell \). We analyze the problem using the method of volume averaging and identify a length scale in the form \(\ell =C_\lambda \sqrt{\nicefrac {K_\lambda }{\epsilon _\beta }}\), with \(C_\lambda \) a parameter that indicates the sensitivity of the microstructure to inertia. The main advantage of this definition is that an explicit formula for \(C_\lambda \) is given; \(C_\lambda \) is computed from a creeping flow simulation in the porous medium; and \(Re_{\mathrm{C}}\) can be used to predict the transition to a non-Darcian regime more accurately than by using Reynolds numbers based on alternative length scales. The theory is validated numerically with data from flow simulations for a variety of microstructures.     

Direct Numerical Simulation of Head-On Quenching of Statistically Planar Turbulent Premixed Methane-Air Flames Using a Detailed Chemical Mechanism

A three-dimensional compressible Direct Numerical Simulation (DNS) analysis has been carried out for head-on quenching of a statistically planar stoichiometric methane-air flame by an isothermal inert wall. A multi-step chemical mechanism for methane-air combustion is used for the purpose of detailed chemistry DNS. For head-on quenching of stoichiometric methane-air flames, the mass fractions of major reactant species such as methane and oxygen tend to vanish at the wall during flame quenching. The absence of \(\text {OH}\) at the wall gives rise to accumulation of carbon monoxide during flame quenching because \(\text {CO}\) cannot be oxidised anymore. Furthermore, it has been found that low-temperature reactions give rise to accumulation of \(\text {HO}_{2}\) and \(\mathrm {H}_{2}\mathrm {O}_{2}\) at the wall during flame quenching. Moreover, these low temperature reactions are responsible for non-zero heat release rate at the wall during flame-wall interaction. In order to perform an in-depth comparison between simple and detailed chemistry DNS results, a corresponding simulation has been carried out for the same turbulence parameters for a representative single-step Arrhenius type irreversible chemical mechanism. In the corresponding simple chemistry simulation, heat release rate vanishes once the flame reaches a threshold distance from the wall. The distributions of reaction progress variable c and non-dimensional temperature T are found to be identical to each other away from the wall for the simple chemistry simulation but this equality does not hold during head-on quenching. The inequality between c (defined based on \(\text {CH}_{4}\) mass fraction) and T holds both away from and close to the wall for the detailed chemistry simulation but it becomes particularly prominent in the near-wall region. The temporal evolutions of wall heat flux and wall Peclet number (i.e. normalised wall-normal distance of \(T = 0.9\) isosurface) for both simple and detailed chemistry laminar and turbulent cases have been found to be qualitatively similar. However, small differences have been observed in the numerical values of the maximum normalised wall heat flux magnitude \(\left ({\Phi }_{\max } \right )_{\mathrm {L}}\) and the minimum Peclet number \((Pe_{\min })_{\mathrm {L}}\) obtained from simple and detailed chemistry based laminar head-on quenching calculations. Detailed explanations have been provided for the observed differences in behaviours of \(\left ({\Phi }_{\max }\right )_{\mathrm {L}}\) and \((Pe_{\min })_{\mathrm {L}}\). The usual Flame Surface Density (FSD) and scalar dissipation rate (SDR) based reaction rate closures do not adequately predict the mean reaction rate of reaction progress variable in the near-wall region for both simple and detailed chemistry simulations. It has been found that recently proposed FSD and SDR based reaction rate closures based on a-priori DNS analysis of simple chemistry data perform satisfactorily also for the detailed chemistry case both away from and close to the wall without any adjustment to the model parameters.     

Three-Dimensional Lattice Boltzmann Simulations of Single-Phase Permeability in Random Fractal Porous Media with Rough Pore–Solid Interface

Single-phase permeability k has intensively been investigated over the past several decades by means of experiments, theories and simulations. Although the effect of surface roughness on fluid flow and permeability in single pores and fractures as well as networks of fractures was studied previously, its influence on permeability in a random mass fractal porous medium constructed of pores of different sizes remained as an open question. In this study, we, therefore, address the effect of pore–solid interface roughness on single-phase flow in random fractal porous media. For this purpose, we apply a mass fractal model to construct porous media with a priori known mass fractal dimensions \(2.579 \le D_{\mathrm{m}} \le 2.893\) characterizing both solid matrix and pore space. The pore–solid interface of the media is accordingly roughened using the Weierstrass–Mandelbrot approach and two parameters, i.e., surface fractal dimension \(D_{\mathrm{s}}\) and root-mean-square (rms) roughness height. A single-relaxation-time lattice Boltzmann method is applied to simulate single-phase permeability in the corresponding porous media. Results indicate that permeability decreases sharply with increasing \(D_{\mathrm{s}}\) from 1 to 1.1 regardless of \(D_{\mathrm{m}}\) value, while k may slightly increase or decrease, depending on \(D_{\mathrm{m}}\), as \(D_{\mathrm{s}}\) increases from 1.1 to 1.6.     

A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds

We show that the mean wall-shear stresses in wall-modeled large-eddy simulations (WMLES) of high-speed flows can be off by up to \(\approx 100\%\) with respect to a DNS benchmark when using the van-Driest-based damping function, i.e., the conventional damping function. Errors in the WMLES-predicted wall-shear stresses are often attributed to the so-called log-layer mismatch, which, albeit also an error in wall-shear stresses \(\tau _\mathrm{w}\), is an error of about \(15\%\). The larger error identified here cannot be removed using the previously developed remedies for the log-layer mismatch. This error may be removed by using the semi-local scaling, i.e., \(l_\nu =\mu /\sqrt{\rho \tau _\mathrm{w}}\), in the damping function, where \(\mu \) and \(\rho \) are the local mean dynamic viscosity and density, respectively.     

Further Dense Properties of the Space of Circle Diffeomorphisms with a Liouville Rotation Number

In continuation of Matsumoto’s paper (Nonlinearity 25:1495–1511, 2012) we show that various subspaces are \(C^{\infty }\)-dense in the space of orientation-preserving \(C^{\infty }\)-diffeomorphisms of the circle with rotation number \(\alpha \), where \(\alpha \in {\mathbb {S}}^1\) is any prescribed Liouville number. In particular, for every odometer \({\mathcal {O}}\) of product type we prove the denseness of the subspace of diffeomorphisms which are orbit-equivalent to \({\mathcal {O}}\).     

Macro and micro mechanics behavior of granite after heat treatment by cluster model in particle flow code

In this paper, a cluster model in particle flow code was used to simulate granite specimens after heat treatment under uniaxial compression. The results demonstrated that micro-cracks are randomly distributed in the specimen when the temperature is below 300?C, and have partial coalescence when the temperature is up to 450?C, then form macro-cracks when the temperature is above 600?C. There is more inter-granular cracking than intra-granular cracking, and their ratio increases with increasing temperature.The micro-cracks are almost constant when the temperature decreases from 900?C to room temperature, except for quartz α–β phase transition temperature(573?C). The fracture evolution process is obviously affected by these cracks, especially at 600–900?C. Elevated temperature leads to easily developed displacement between the grains, and the capacity to store strain energy becomes weaker, corresponding to the plasticity of granite after heat treatment.     

Direct Numerical Simulation of Flow over Periodic Hills up to $\text {Re}_{H}= 10{,}595$

We present fully resolved computations of flow over periodic hills at the hill-Reynolds numbers \(\text {Re}_{H}=?5{,}600\) and \(\text {Re}_{H}=?10{,}595\) with the highest fidelity to date. The calculations are performed using spectral incompressible discontinuous Galerkin schemes of \(8^{\text {th}}\) and \(7^{\text {th}}\) order spatial accuracy, \(3^{\text {rd}}\) order temporal accuracy, as well as 34 and 180 million grid points, respectively. We show that the remaining discretization error is small by comparing the results to h- and p-coarsened simulations. We quantify the statistical averaging error of the reattachment length, as this quantity is widely used as an ‘error norm’ in comparing numerical schemes. The results exhibit good agreement with the experimental and numerical reference data, but the reattachment length at \(\text {Re}_{H}=?10{,}595\) is predicted slightly shorter than in the most widely used LES references. In the second part of this paper, we show the broad range of capabilities of the numerical method by assessing the scheme for underresolved simulations (implicit large-eddy simulation) of the higher Reynolds number in a detailed h/p convergence study.     

A Spectral Criterion for Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We show that the question of stability of a steady incompressible Navier-Stokes flow \({\mathrm{V}}\) in a 3D exterior domain \({\Omega}\) is essentially a finite-dimensional problem (Theorem 3.2). Although the associated linearized operator has an essential spectrum touching the imaginary axis, we show that certain assumptions on the eigenvalues of this operator guarantee the stability of flow \({\mathrm{V}}\) (Theorem 4.1). No assumption on the smallness of the steady flow \({\mathrm{V}}\) is required.     

Insight into Heterogeneity Effects in Methane Hydrate Dissociation via Pore-Scale Modeling

A large number (1253) of high-quality streaming potential coefficient (\(C_\mathrm{sp})\) measurements have been carried out on Berea, Boise, Fontainebleau, and Lochaline sandstones (the latter two including both detrital and authigenic overgrowth forms), as a function of pore fluid salinity (\(C_\mathrm{f})\) and rock microstructure. All samples were saturated with fully equilibrated aqueous solutions of NaCl (10\(^{-5}\) and 4.5 mol/dm\(^{3})\) upon which accurate measurements of their electrical conductivity and pH were taken. These \(C_\mathrm{sp}\) measurements represent about a fivefold increase in streaming potential data available in the literature, are consistent with the pre-existing 266 measurements, and have lower experimental uncertainties. The \(C_\mathrm{sp}\) measurements follow a pH-sensitive power law behaviour with respect to \(C_\mathrm{f}\) at medium salinities (\(C_\mathrm{sp} =-\,1.44\times 10^{-9} C_\mathrm{f}^{-\,1.127} \), units: V/Pa and mol/dm\(^{3})\) and show the effect of rock microstructure on the low salinity \(C_\mathrm{sp}\) clearly, producing a smaller decrease in \(C_\mathrm{sp}\) per decade reduction in \(C_\mathrm{f}\) for samples with (i) lower porosity, (ii) larger cementation exponents, (iii) smaller grain sizes (and hence pore and pore throat sizes), and (iv) larger surface conduction. The \(C_\mathrm{sp}\) measurements include 313 made at \(C_\mathrm{f} > 1\) mol/dm\(^{3}\), which confirm the limiting high salinity \(C_\mathrm{sp}\) behaviour noted by Vinogradov et al., which has been ascribed to the attainment of maximum charge density in the electrical double layer occurring when the Debye length approximates to the size of the hydrated metal ion. The zeta potential (\(\zeta \)) was calculated from each \(C_\mathrm{sp}\) measurement. It was found that \(\zeta \) is highly sensitive to pH but not sensitive to rock microstructure. It exhibits a pH-dependent logarithmic behaviour with respect to \(C_\mathrm{f}\) at low to medium salinities (\(\zeta =0.01133 \log _{10} \left( {C_\mathrm{f} } \right) +0.003505\), units: V and mol/dm\(^{3})\) and a limiting zeta potential (zeta potential offset) at high salinities of \({\zeta }_\mathrm{o} = -\,17.36\pm 5.11\) mV in the pH range 6–8, which is also pH dependent. The sensitivity of both \(C_\mathrm{sp}\) and \(\zeta \) to pH and of \(C_\mathrm{sp}\) to rock microstructure indicates that \(C_\mathrm{sp}\) and \(\zeta \) measurements can only be interpreted together with accurate and equilibrated measurements of pore fluid conductivity and pH and supporting microstructural and surface conduction measurements for each sample.     

Long-time Dynamics of Resonant Weakly Nonlinear CGL Equations

Consider a weakly nonlinear CGL equation on the torus \(\mathbb {T}^d\):

$$\begin{aligned} u_t+i\Delta u=\epsilon [\mu (-1)^{m-1}\Delta ^{m} u+b|u|^{2p}u+ ic|u|^{2q}u]. \end{aligned}$$

(*)

Here \(u=u(t,x)\), \(x\in \mathbb {T}^d\), \(0<\epsilon <<1\), \(\mu \geqslant 0\), \(b,c\in \mathbb {R}\) and \(m,p,q\in \mathbb {N}\). Define \(I(u)=(I_{\mathbf {k}},\mathbf {k}\in \mathbb {Z}^d)\), where \(I_{\mathbf {k}}=v_{\mathbf {k}}\bar{v}_{\mathbf {k}}/2\) and \(v_{\mathbf {k}}\), \(\mathbf {k}\in \mathbb {Z}^d\), are the Fourier coefficients of the function \(u\) we give. Assume that the equation \((*)\) is well posed on time intervals of order \(\epsilon ^{-1}\) and its solutions have there a-priori bounds, independent of the small parameter. Let \(u(t,x)\) solve the equation \((*)\). If \(\epsilon \) is small enough, then for \(t\lesssim {\epsilon ^{-1}}\), the quantity \(I(u(t,x))\) can be well described by solutions of an effective equation:

$$\begin{aligned} u_t=\epsilon [\mu (-1)^{m-1}\Delta ^m u+ F(u)], \end{aligned}$$

where the term \(F(u)\) can be constructed through a kind of resonant averaging of the nonlinearity \(b|u|^{2p}+ ic|u|^{2q}u\).

     

Chaotic characteristics analysis of the sintering process system with unknown dynamic functions based on phase space reconstruction and chaotic invariables

We develop a local discontinuous Galerkin finite element method for the distributed-order time and Riesz space-fractional convection–diffusion and Schrödinger-type equations. The stability of the presented schemes is proved and optimal order of convergence \(\mathcal {O}(h^{N+1}+(\Delta t)^{1+\frac{\theta }{2}}+\theta ^{2})\) for the Riesz space-fractional diffusion and Schrödinger-type equations with distributed order in time, an order of convergence of \(\mathcal {O}(h^{N+\frac{1}{2}}+(\Delta t)^{1+\frac{\theta }{2}}\) \(+\theta ^{2})\) is provided for the Riesz space-fractional convection–diffusion equations with distributed order in time where h, \(\theta \) and \(\Delta t\) are space step size, the distributed-order variables and the step sizes in time, respectively. Finally, the performed numerical examples confirm the optimal convergence order and illustrate the effectiveness of the method.     

In Situ Chemically-Selective Monitoring of Multiphase Displacement Processes in a Carbonate Rock Using 3D Magnetic Resonance Imaging

Accurate monitoring of multiphase displacement processes is essential for the development, validation and benchmarking of numerical models used for reservoir simulation and for asset characterization. Here we demonstrate the first application of a chemically-selective 3D magnetic resonance imaging (MRI) technique which provides high-temporal resolution, quantitative, spatially resolved information of oil and water saturations during a dynamic imbibition core flood experiment in an Estaillades carbonate rock. Firstly, the relative saturations of dodecane (\(S_{\mathrm{o}})\) and water (\(S_{\mathrm{w}})\), as determined from the MRI measurements, have been benchmarked against those obtained from nuclear magnetic resonance (NMR) spectroscopy and volumetric analysis of the core flood effluent. Excellent agreement between both the NMR and MRI determinations of \(S_{\mathrm{o}}\) and \(S_{\mathrm{w}}\) was obtained. These values were in agreement to 4 and 9% of the values determined by volumetric analysis, with absolute errors in the measurement of saturation determined by NMR and MRI being 0.04 or less over the range of relative saturations investigated. The chemically-selective 3D MRI method was subsequently applied to monitor the displacement of dodecane in the core plug sample by water under continuous flow conditions at an interstitial velocity of \(1.27\times 10^{-6}\,\hbox {m}\,\hbox {s}^{-1}\) (\(0.4\,\hbox {ft}\,\hbox {day}^{-1})\). During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of \(0.31\,\hbox {mm}\times 0.39\,\hbox {mm} \times 0.39\,\hbox {mm}\) were acquired on a timescale of 16 min per image. Using this technique the spatial and temporal dynamics of the displacement process have been monitored. This MRI technique will provide insights to structure–transport relationships associated with multiphase displacement processes in complex porous materials, such as those encountered in petrophysics research.     

Physical Clogging of Uniformly Graded Porous Media Under Constant Flow rates

This study investigated the physical clogging of uniformly graded porous media under constant flow rates using natural porous media and suspensions. The porous media selected for this experimental study was a fine-to-medium sandy soil fractioned into thirteen uniformly graded beds: seven unisize beds and six uniform beds. The physical clogging of the beds was studied using two types of silt suspensions as along with two suspension concentrations and three water discharges. It was found that the permeability reduction due to physical clogging \([(K_\mathrm{i} - K_\mathrm{t})/K_\mathrm{i}]\) increased with decreasing \({D}_{15}/{d}_{85}\) ratios until a critical value of \({D}_{15}/{d}_{85}\), after which a surface mat of suspension was formed on the porous media. It was also found that the value of reduced permeability at any time (at any number of pore volumes of injected suspension-laden water), \(K_\mathrm{t}\), is directly proportional to square of \({D}_{15}\) and inversely proportional to \({C}_{\mathrm{u}}\) of the porous media and \({d}_{85}\) of suspensions. The effects of suspension type and flow rates on physical clogging seemed to depend on the size of the pores in the porous media.     

On the Justification of Viscoelastic Elliptic Membrane Shell Equations

We consider a family of linearly viscoelastic shells with thickness \(2\varepsilon\), clamped along their entire lateral face, all having the same middle surface \(S=\boldsymbol{\theta}(\bar{\omega})\subset \mathbb{R}^{3}\), where \(\omega\subset\mathbb{R}^{2}\) is a bounded and connected open set with a Lipschitz-continuous boundary \(\gamma\). We make an essential geometrical assumption on the middle surface \(S\), which is satisfied if \(\gamma\) and \(\boldsymbol{\theta}\) are smooth enough and \(S\) is uniformly elliptic. We show that, if the applied body force density is \(O(1)\) with respect to \(\varepsilon\) and surface tractions density is \(O(\varepsilon)\), the solution of the scaled variational problem in curvilinear coordinates, \(\boldsymbol{u}( \varepsilon)\), defined over the fixed domain \(\varOmega=\omega\times (-1,1)\) for each \(t\in[0,T]\), converges to a limit \(\boldsymbol{u}\) with \(u_{\alpha}(\varepsilon)\rightarrow u_{\alpha}\) in \(W^{1,2}(0,T,H ^{1}(\varOmega))\) and \(u_{3}(\varepsilon)\rightarrow u_{3}\) in \(W^{1,2}(0,T,L^{2}(\varOmega))\) as \(\varepsilon\to0\). Moreover, we prove that this limit is independent of the transverse variable. Furthermore, the average \(\bar{\boldsymbol{u}}= \frac{1}{2}\int_{-1}^{1} \boldsymbol{u}dx_{3}\), which belongs to the space \(W^{1,2}(0,T, V_{M}( \omega))\), where

$$V_{M}(\omega)=H^{1}_{0}(\omega)\times H^{1}_{0}(\omega)\times L ^{2}(\omega), $$

satisfies what we have identified as (scaled) two-dimensional equations of a viscoelastic membrane elliptic shell, which includes a long-term memory that takes into account previous deformations. We finally provide convergence results which justify those equations.