Gradient Of Solution Research Articles

A Detergent-Free Method for Preparation of Lipid Rafts for the Shotgun Lipidomics Study.

Lipid rafts are microdomains on plasma membrane that contain high levels of cholesterol and sphingolipids. Because of the detergent-resistant property of lipid rafts, lipid rafts isolated by methods that use detergents frequently yield different results. Artifacts can also be introduced through the use of detergents. These limitations could be overcome with a detergent-free method which eliminates possible artificial influences. Importantly, lipid rafts prepared with a detergent-free method is more compatible to mass spectrometric analysis since the ion suppression effect is largely reduced.This chapter describes a detergent-free two-step method for preparation of lipid rafts. Firstly, a purified plasma membrane fraction is prepared from cells by sedimentation of the postnuclear supernatant (PNS) in a Percoll gradient. Secondly, the as-prepared plasma membranes are sonicated to release lipid rafts which are further isolated by flotation in a continuous gradient of Optiprep solution. Then, we introduce a typical shotgun lipidomics workflow that can be used as a cost-effective and relatively high throughput method to determine the lipidomes of lipid rafts.The method also makes an easy start for lipidomics studies.

Ferro-advection aided evaporation kinetics of ferrofluid droplets in magnetic field ambience

The present article discusses the physics and mechanics of evaporation of pendant, aqueous ferrofluid droplets, and modulation of the same by an external magnetic field. We show experimentally and by mathematical analysis that the presence of a horizontal magnetic field augments the evaporation rates of pendant ferrofluid droplets. First, we tackle the question of improved evaporation of the colloidal droplets compared to water and propose physical mechanisms to explain the same. Experiments show that the changes in evaporation rates aided by the magnetic field cannot be explained on the basis of changes in surface tension or based on classical diffusion driven evaporation models. Probing via particle image velocimetry shows that the internal advection kinetics of such droplets plays a direct role toward the augmented evaporation rates by modulating the associated Stefan flow. Infrared thermography reveals changes in thermal gradients within the droplet and evaluating the dynamic surface tension reveals the presence of solutal gradients within the droplet, both brought about by the external field. Based on the premise, a scaling analysis of the internal magneto-thermal and magneto-solutal ferroadvection behavior is presented. The model incorporates the role of the governing Hartmann number, the magneto-thermal Prandtl number, and the magneto-solutal Schmidt number. The analysis and stability maps reveal that the magneto-solutal ferroadvection is the more dominant mechanism, and the model is able to predict the internal advection velocities with accuracy. Furthermore, another scaling model to predict the modified Stefan flow is proposed and is found to accurately predict the improved evaporation rates.

Modeling of salt finger convection through a fluid-saturated porous interface: Representative elementary volume scale simulation and effect of initial buoyancy ratio

Simultaneous existence of solute gradients along with temperature gradients in a double diffusive system is favorable to the onset of salt finger convection and this phenomenon has been investigated for several decades due to its efficient mixing mechanism. However, relatively few works were focused on the double diffusive process through a fluid-saturated porous interface (FPI), which could be applied in a variety of scenarios such as the directional solidification of concentrated alloys or mixing zones in coastal freshwater aquifers. In this paper, we consider the evolution of double-diffusive salt finger through FPI with a single-domain approach adopted for the solution of flow in a composite region made up of a fluid layer overlying a porous layer. Comparisons with existing numerical results show great agreement and demonstrate that flows through a fluid–porous system can be predicted with good accuracy by the proposed method. Several cases spanning a range of initial buoyancy ratio N0 from 2 to 7 are conducted to study the structure and behavior of salt finger together with key issues being focused on the effect of initial buoyancy ratio on flux variations. Differing from in stratified fluid layers, salt finger through FPI shows an asymmetric structure in which the growth rate in the fluid layer is much greater and the finger column in the porous layer presents a squarer shape. It is found that under the condition of low initial buoyancy ratios, the potential energy stored in the unstable stratification of salinity converted more into kinetic energy, which enhances the mixture of heat and masses in the vertical direction.

Limiting stiffness coefficients analysis of texture foil journal bearing

The purpose of this study is to explore the limiting stiffness coefficients of a foil journal bearing with the texture bump profile of top foil. The limiting stiffness coefficients are evaluated based on simplified compressible Reynolds equation for large bearing numbers with high speeds of foil journal bearing. A limiting pressure gradient solution for a texture bump of top foil bearing is analyzed. The analytical model accounts for the top foil texture bump profile and bottom foil bump compliance. Results of linearized nondimensional stiffness coefficients obtained using infinitesimal perturbation method are compared for various top foil texture bump profiles. The influence of top foil texture bump extent and height on the limiting stiffness coefficients of a foil journal bearing are investigated.

Microfluidic‐Assisted Blade Coating of Compositional Libraries for Combinatorial Applications: The Case of Organic Photovoltaics

AbstractMicrofluidic technologies are highly adept at generating controllable compositional gradients in fluids, a feature that has accelerated the understanding of the importance of chemical gradients in biological processes. That said, the development of versatile methods to generate controllable compositional gradients in the solid‐state has been far more elusive. The ability to produce such gradients would provide access to extensive compositional libraries, thus enabling the high‐throughput exploration of the parametric landscape of functional solids and devices in a resource‐, time‐, and cost‐efficient manner. Herein, the synergic integration of microfluidic technologies is reported with blade coating to enable the controlled formation of compositional lateral gradients in solution. Subsequently, the transformation of liquid‐based compositional gradients into solid‐state thin films using this method is demonstrated. To demonstrate efficacy of the approach, microfluidic‐assisted blade coating is used to optimize blending ratios in organic solar cells. Importantly, this novel technology can be easily extended to other solution processable systems that require the formation of solid‐state compositional lateral gradients.

Higher integrability in the obstacle problem for the fast diffusion equation

We prove local higher integrability of the spatial gradient for solutions to obstacle problems of porous medium type in the fast diffusion case m<1. The result holds for the natural range of exponents that is known from other regularity results for porous medium type equations. We also cover the case of signed solutions.

Higher integrability for doubly nonlinear parabolic systems

This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.

A fourth order finite difference method for solving elliptic interface problems with the FFT acceleration

In this paper, a new Cartesian grid finite difference method is introduced based on the fourth order accurate matched interface and boundary (MIB) method and fast Fourier transform (FFT). The proposed augmented MIB method consists of two major parts for solving elliptic interface problems in two dimensions. For the interior part, in treating a smoothly curved interface, zeroth and first order jump conditions are enforced repeatedly by the MIB scheme to generate fictitious values near the interface. For the exterior part, two layers of zero-padding solutions are introduced beyond the original rectangular domain so that the FFT inversion becomes feasible. Different types of boundary conditions, including Dirichlet, Neumann, Robin and their mix combinations, can be imposed via the MIB scheme to generate fictitious values near boundaries. Based on fictitious values at both interfaces and boundaries, the augmented MIB method reconstructs Cartesian derivative jumps as auxiliary variables. Then, by treating such variables as unknowns, an enlarged linear system is obtained. In the Schur complement solution of such system, the FFT algorithm will not sense the solution discontinuities, so that the discrete Laplacian can be efficiently inverted. Therefore, the FFT-based augmented MIB not only achieves a fourth order of accuracy in dealing with interfaces and boundaries, but also produces an overall complexity of O(n2log⁡n) for a n×n uniform grid. Moreover, the augmented MIB scheme can provide fourth order accurate approximations to solution gradients and fluxes.

Local higher integrability for unsteady motion equations of generalized Newtonian fluids

In this paper, we show local higher integrability of the gradient of weak solutions for unsteady motions of generalized Newtonian fluids including electrorheological fluids under the restriction p(z)≥3n+2n+2. Moreover, this is a new result even for corresponding Stokes setting or a system with p-structure depending on the symmetric gradient under the restriction p(z)>2nn+2.

Updating Geometrically Nonlinear Reduced-Order Models Using Nonlinear Modes and Harmonic Balance

Nonlinear reduced-order models are being investigated for use as digital twins for advanced aircraft and spacecraft. In concept, the digital twin would be tuned to accurately describe the behavior of the vehicle, and then it would be updated as the vehicle is modified or ages. Unfortunately, the linear model correlation and validation techniques that are commonly used in the aerospace industry are not valid for nonlinear models, so a new set of tools is needed. This work presents an algorithm to update geometrically nonlinear reduced-order models using nonlinear normal modes as a correlation metric. The nonlinear normal modes serve as a strong metric to correlate the numerical models because they can be extracted from experiments, and they describe the dynamics of the nonlinear system over a range of amplitudes and are independent of the loading applied to the system. This paper presents a novel method of computing analytical gradients of nonlinear normal mode solutions with respect to system parameters using the multiharmonic balance method. The procedure is first tested using numerical simulations and then applied to tune the reduced-order model of a curved beam based on nominal blueprints and idealized boundary conditions to match a nonlinear normal mode that has been measured experimentally from a three-dimensional printed test specimen.

An explicitly multi-component arterial gas embolus dissolves much more slowly than its one-component approximation

We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straight-forward extensions of those for a one-component gas bubble. They were derived by using the Young–Laplace equation and Dalton’s law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry’s law for gas solubilities, and Fick’s law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O2, N2, He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N2-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N2 partial pressure can be quite high (e.g.∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygen-rich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.

Adaptive dynamic multilevel simulation of fractured geothermal reservoirs

An algebraic dynamic multilevel (ADM) method for fully-coupled simulation of flow and heat transport in heterogeneous fractured geothermal reservoirs is presented. Fractures are modeled explicitly using the projection-based embedded discrete method (pEDFM), which accurately represents fractures with generic conductivity values, from barriers to highly-conductive manifolds. A fully implicit scheme is used to obtain the coupled discrete system including mass and energy balance equations with two main unknowns (i.e., pressure and temperature) at fine-scale level. The ADM method is then developed to map the fine-scale discrete system to a dynamic multilevel coarse grid, independently for matrix and fractures. To obtain the ADM map, multilevel multiscale coarse grids are constructed for matrix as well as for each fracture at all coarsening levels. On this hierarchical nested grids, multilevel multiscale basis functions (for flow and heat) are solved locally at the beginning of the simulation. They are used during the ADM simulation to allow for accurate multilevel systems in presence of parameter heterogeneity. The resolution of ADM simulations is defined dynamically based on the solution gradient (i.e. front tracking technique) using a user-defined threshold. The ADM mapping occurs algebraically using the so-called ADM prolongation and restriction operators, for all unknowns. A variety of 2D and 3D fractured test cases with homogeneous and heterogeneous permeability maps are studied. It is shown that ADM is able to model the coupled mass-heat transport accurately by employing only a fraction of fine-scale grid cells. Therefore, it promises an efficient approach for simulation of large and real-field scale fractured geothermal reservoirs. All software developments of this paper is publicly available at https://gitlab.com/DARSim2simulator.

Lorentz improving estimates for the [formula omitted]-Laplace equations with mixed data

The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Dirichlet p-Laplace equation of type div(|∇u|p−2∇u)=f+div(|F|p−2F)inΩ,u=gon∂Ω, in Lorentz space, with given data F∈Lp(Ω;Rn), f∈Lpp−1(Ω), g∈W1,p(Ω) for 1<p<∞ and Ω⊂Rn (n≥2) satisfying a Reifenberg flat domain condition or a p-capacity uniform thickness condition, which are considered in several recent papers. To better specify our result, the proofs of regularity estimates involve fractional maximal operators and valid for a more general class of quasilinear nonhomogeneous elliptic equations with mixed data. This paper not only deals with the Lorentz estimates for a class of more general problems with mixed data but also improves the good-λ approach technique proposed in our preceding works (Tran, 2019; Tran and Nguyen, 2019; Tran and Nguyen, 2020; Tran and Nguyen (in press)), to achieve the global Lorentz regularity estimates for gradient of weak solutions in terms of fractional maximal operators.

Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process**Project supported by the National Natural Science Foundation of China (Grant No. 11804296), the Joint Key Project of Yunnan Province, China (Grant Nos. 2018FY001-020 and 2018ZI002), and the Fund from the Educational Department of Yunnan Province, China (Grant No. 2016CYH05).

Ray tracing method is used to study the propagation of collimated beams in a liquid–core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile Ce(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C) = D0 × (1 + α1C + α2C2 + α3C3 + ⋅). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z, t). The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z, t) with Ce(z,t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

Electrodeposition of Copper Using Polyelectrolyte Membranes: Effective Ion Transport through Solid-Liquid Interface

The widespread demand of coating, corrosion protection, metallurgy, and microelectronics industries for electrodeposition has been met by developing current successful, commercially-available deposition baths containing metallic salts at higher concentration, highly concentrated supporting electrolytes, and various kinds of organic additives, enabling higher deposition rate, greater current efficiency, and long-term stability for the baths. However, developing effective deposition systems for high-performance electrodeposition is challenging, because, (1) in product point of view, the additives sometimes and rather often cause mechanical and/or electrical problems for deposited metal circuit elements due to inclusion of such additives during deposition process, and, (2) in processing point of view, commercial electrodeposition setups cause huge amount of detrimental effluents that can be a serious environmental and cost problems. These issues may be a product of compromise that is particularly relevant for structure and properties of the deposited metals (film resistivity, surface roughness, mechanical and adhesion strength), and processing (costs and manufacturing steps including rinsing and detrimental effluents treatment). The current solution-based electrodeposition systems are generally incapable of significantly increasing reaction rate (deposition rate constant) form dilute electrolyte solution, because diffusion-limiting current that needs to be higher for industrial manufacturing depends on the concentration (and its gradient) of electrolyte solution, which can be described by Fick’s first law in a steady-state electrodeposition. Additionally, current electrodeposition systems are optimized for large area substrate and mass production manufacturing, thereby cannot be suitable for small-lot, on-demand, and multi-product microfabrication. These have inspired the use of polyelectrolyte membranes to encapsulate metallic ions within inside their channels to concentrate from electrolyte solution while maintaining efficient ion transport properties owing to high density anionic counterparts inside channels and the swelling nature of the membrane.We now show that when the polyelectrolyte membrane does not anchor itself to the cathode substrate, stable electrodeposition of metals on cathode surface is achieved, not as much like a solution-phase electrodeposition, resulting in a new type of solid-state electrodeposition (SED) system (Fig. 1).The SED system consists of cathode electrode, polyelectrolyte membrane (PE), electrolyte solution, and anode electrode.PE works as an additional interfacial phase, in which metal ions are transferred through ion exchange reaction based on concentration gradient of metal ions bound with sulfonic acid functional groups in PE layer. Most important feature of the use of PE at the electrode surface is their ability for metal ions to be concentrated in inner ion transport channels with high density sulfonic anions inside the channels (Fig.1).In the current contribution, we describe transfer process of copper ions between electrodes where the additional PE-solution interfacial layer has been introduced to explain concentration behavior of PE layer for copper ions and electrodeposition characteristics in the present system. From detailed theoretical (both thermodynamic and kinetic) and experimental study regarding with the ion concentration process for PE membrane suggest that (1) the “ion penetration” process is slower than ion exchange (diffusion) process inside PE layer and is therefore rate-determining step for ion concentration, and (2) ion penetration rate increases exponentially as the concentration of copper ions in PE layer decreases.The effect of cation concentration, temperature, and electrochemical deposition conditions on the current efficiency, deposition rate, growth process and morphology of the films has been investigated to optimize the deposition conditions to achieve higher deposition rate. This strategy can be suitable for small-lot, on-demand, and multi-product microfabrication. Figure 1

Sharp estimates for the gradient of solutions to the heat equation

Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belo ...

Nonsingular Gradient Solutions in Crack Mechanics and the Concept of Stress Concentration

We consider the fracture mechanics problem for the finite and semi-infinite cracks in the gradient elasticity. Local stress fields that define the fracture the strength of materials are found as solutions of the inhomogeneous Helmholtz equations in which the inhomogeneity is determined by classical stresses. To construct solutions, the radial factors method and the Papkovich-Neuber representation are used. It is shown that, in problems of crack mechanics. We show that the local stresses in the vicinity of crack tips are non-singular, have the form characteristic of stress concentration, and depend only on the level of acting stresses and the scale parameter, which is found as a result of mechanical testing of material samples.

Salivary Zinc level and Taste Detection Thresholds in Hypertensive Patients on Amlodipine and on Losartan (A Comparative Study)

High blood pressure (hypertension) is one of greatest risk factors for cardiovascular disease,whichis a remarkable cause of morbidity and mortality worldwide. The outcome of hypertension (HTN) andcardiovascular disease (CVD) is influenced by a wide variation of risk factors like use of tobacco; excessivealcohol consumption; unhealthy diet, few physical activity ,overweight and obesity; high blood glucose,and abnormal blood lipids. The objectives of this study were to evaluate taste detection thresholds (offour basic tastes) of hypertensive patients on Amlodipine 5 mg and on Losartan 50 mg. And to estimateZinc level in saliva of those patients and compare it with control subjects. A total of 90 subjects wereincorporated in this study they were divided into three groups: 1-Thirty patients on Amlodipine (5mg)2-Thirty patients on Losartan (50mg) and 3- Thirty healthy control subjects. Unstimulated whole saliva wascollected from all subjects including in this study. Volume of 5 ml of each taste gradient solution,was offeredto the participants. The samples were subjected to biomechanical analysis to estimate zinc level by usingthe atomic absorption spectrophotometer.The result showed that the taste detection threshold of sucrose andsault were significantly higher in patients on Amlodipine and on Losartan treatment than in control subjects.While the taste detection threshold of sour and bitter showed no significant differences between the studygroups. Also there is un alteration in salivary Zinc, Zinc in patients on Amlodipine and on Losartan wassignificantly lower compared to control group.

Overlapping finite element meshes in AMORE

The AMORE scheme of “automatic meshing with overlapping and regular elements” has been recently proposed, in which the concept of overlapping finite elements plays a central role. In earlier work we focused on the overlapping of individual elements. In this paper, we present a technique to overlap finite element meshes so that elements from different meshes can overlap in any geometric form. Meshes for different parts of the analysis domain can be independently spanned, which is an effective way to adapt meshes to various geometric features and solution gradients. Hence, the meshing effort is much reduced and high solution accuracy is achieved. We formulate the new scheme, analyze its solvability and convergence, and propose an implementation. The solutions of some engineering problems are given to illustrate the use and performance of the new scheme.

Effective high-order energy stable flux reconstruction methods for first-order hyperbolic linear and nonlinear systems

The paper devises high-order energy stable flux reconstruction method towards first-order hyperbolic linear advection-diffusion and nonlinear Navier-Stokes problems (HFR). The underlying idea is to take the advantages of high-order differential framework from flux reconstruction and accurate gradient solution from first-order hyperbolic system. By means of the additional gradient equation, the linear advection-diffusion system is recast as hyperbolic formulation, which is equivalent to original equation when pseudo time derivatives are dropped, and then diffusive fluxes are directly solved by flux reconstruction. The resulting scheme has compact stencils and high accuracy without increasing computation cost. Mathematical analysis is presented to confirm that HFR method is consistent and stable for all orders of accuracy, at least for linear problems. In addition, numerical results for linear and nonlinear problems demonstrate that HFR method can achieve the desired accuracy for both primitive and gradient variable, reduce the absolute error of gradient variable, and allow a larger maximum CFL number compared to the existing methods, such as BR2 and direct flux reconstruction (DFR). It indicates that HFR method is potential in accuracy and efficiency for solving steady viscous problems.