Gradient Of Solution Research Articles

High‐Performance X‐Ray Detector Based on Liquid Diffused Separation Induced Cs3Bi2I9 Single Crystal

AbstractThe recently demonstrated Cs3Bi2I9 single crystals (SCs) exhibit superior performance for X‐ray detection. More importantly, they do not contain any toxic lead element. However, compared with lead‐halide perovskites, one challenge for the Cs3Bi2I9 SC for X‐ray detection application is that it is difficult to prepare large‐sized and high‐quality SCs. Here, a liquid diffused separation induced crystallization (LDSC) method is employed to grow Cs3Bi2I9 SCs for eliminating the temperature fluctuation and convection currents caused by the thermal gradient in the growth solution. The resultant Cs3Bi2I9 SC exhibits a microstrain of 1.21 × 10–3, a resistivity of 1.12 × 109 Ω cm, a carrier mobility of 4.57 cm2 V–1 s–1, and a mobility‐lifetime product of 1.87 × 10–3 cm2 V–1. As a result, an X‐ray detector based on the high‐quality Cs3Bi2I9 SC exhibits an excellent dose rate linearity, a sensitivity of 964 µC Gyair–1 cm–2, and a limit of detection (LoD) of 44.6 nGyair s–1.

Gradient Hölder regularity for parabolic normalized p(x,t)-Laplace equation

We consider the interior Hölder regularity of spatial gradient of viscosity solution to the parabolic normalized p ( x , t ) -Laplace equation u t = ( δ i j + ( p ( x , t ) − 2 ) u i u j | D u | 2 ) u i j with some suitable assumptions on p ( x , t ) , which arises naturally from a two-player zero-sum stochastic differential game with probabilities depending on space and time.

Besov regularity for a class of singular or degenerate elliptic equations

Motivated by applications to congested traffic problems, we establish higher integrability results for the gradient of local weak solutions to the strongly degenerate or singular elliptic PDE−div((|∇u|−1)+q−1∇u|∇u|)=f,inΩ, where Ω is a bounded domain in Rn for n≥2, 1<q<∞ and (⋅)+ stands for the positive part. We assume that the datum f belongs to a suitable Sobolev or Besov space. The main novelty here is that we deal with the case of subquadratic growth, i.e. 1<q<2, which has so far been neglected. In the latter case, we also prove the higher fractional differentiability of the solution to a variational problem, which is characterized by the above equation. For the sake of completeness, we finally give a Besov regularity result also in the case q≥2.

Weighted global regularity estimates for elliptic problems with Robin boundary conditions in Lipschitz domains

Let n ≥ 2 and Ω be a bounded Lipschitz domain of R n . In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second-order elliptic equations of divergence form with real-valued, bounded, measurable coefficients on Ω. More precisely, let p ∈ ( n / ( n − 1 ) , ∞ ) . Using a real-variable argument, the authors obtain two necessary and sufficient conditions for W 1 , p estimates of solutions to Robin boundary value problems, respectively, in terms of a weak reverse Hölder inequality with exponent p or weighted W 1 , q estimates of solutions with q ∈ ( n / ( n − 1 ) , p ] and some Muckenhoupt weights. As applications, the authors establish some global regularity estimates for solutions to Robin boundary value problems of second-order elliptic equations of divergence form with small BMO coefficients, respectively, on bounded Lipschitz domains, C 1 domains or (semi-)convex domains, in the scale of weighted Lebesgue spaces, via some quite subtle approach which is different from the existing ones and, even when n = 3 in case of bounded C 1 domains, also gives an alternative correct proof of some known result under an additional assumption. By this and some technique from harmonic analysis, the authors further obtain the global regularity estimates, respectively, in Morrey spaces, (Musielak–)Orlicz spaces, and variable Lebesgue spaces.

Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

Higher integrability for parabolic systems with Orlicz growth

We prove higher integrability of the spatial gradient of weak solutions to parabolic systems with φ-growth, where φ=φ(t) is a general Orlicz function. The parabolic systems need be neither degenerate nor singular. Our result is a generalized version of the one of Kinnunen and Lewis (2000) [34] for the parabolic p-Laplace systems.

A hyperbolic Poisson solver for wall distance computation on irregular triangular grids

This paper presents an accurate and efficient Poisson solver for wall distance computations on irregular triangular grids. It is discussed that a typical formula of computing the wall distance from a numerical solution of a Poisson equation is not very accurate when solution contours are curved and the accuracy can be improved by a second-order formula derived by Taubin. However, the improved formula, as it requires second derivatives of the numerical solution, presents a challenge for a second-order method leading to zeroth-order accurate second-order derivatives on irregular grids. To overcome the difficulty, we develop a hyperbolic Poisson solver with gradients included as additional unknowns. In this method, the solution gradient can be obtained with second-order accuracy by a second-order discretization method, and therefore the second-derivatives can be obtained with first-order accuracy. Moreover, the hyperbolic method eliminates the numerical stiffness arising from the discretization of the Laplacian operator and achieves the ever-growing O(1/h) speed-up in iterative convergence, where h is a typical mesh spacing. Superior accuracy and efficiency of the developed method are demonstrated for irregular triangular grids.

P–012 A new sperm preparation technique for ICSI

Abstract Study question Is there any difference in this technique(swim-in) according to clinical results in ICSI cycles? Summary answer Fertilization rates are significantly better with this new technique(swim-in). There is no difference in pregnancy and ongoing pregnancy rates between swim-in and DGS techniques. What is known already Sperm separation is crucial in assisted reproductive technologies, based on different principles like migration, filtration, or density gradient centrifugation techniques. However, there are some studies that centrifugation steps and using gradient solutions may increase sperm DNA fragmentation. On the other hand, multiple contacts to different plastic surfaces such as pipettes, plastic tubes, etc., and also pipetting the ejaculate in sperm preparation may have detrimental effects. The ideal sperm separation technique should be non-invasive, not time-consuming, easy, and cost-effective, not cause sperm damage or non-physiological alterations of the separated sperm cells, eliminate dead spermatozoa and other cells, including leukocytes. Study design, size, duration This is a prospective randomized study between 01/02/2019...01/01/2021. Sperms were prepared either with this new technique that we call “swim-in”(n = 359) or with density gradient centrifugation(n = 404) before microinjection (ICSI). Fertilization rates, clinical pregnancy rates, and on-going pregnancy rates were compared between groups. Sperm motility is less than%20 patients are not included in the study. t-test and Chi-square test used. p &amp;lt; 0.05 significant. Participants/materials, setting, methods For this new centrifugation free technique(swim-in), a Braun injector, 21G green needle, and sperm washing medium are used. First, we pulled a 0.5 ml sperm wash medium in a Braun injector. After sperm liquefaction, we put Braun injector with the needle in the sperm cap perpendicularly and waited 30 minutes at 37-degree Celcius. Sperms swam through the needle to the injector used for ICSI. For DGC sperms were prepared according to the 2015 WHO manual. Main results and the role of chance: We try to make a centrifugation-free, gentle, cost-effective, and easy sperm preparation technique and called it a swim-in technique. Groups were comparable according to mean age, collected oocyte numbers, and oocyte maturation ratios. Fertilization rates are%73,2(1786/2438) vs%66,9(2167/3237) respectively for swim-in and DGC groups. Clinical pregnancy rates are%45,1 vs%42,3 respectively for swim-in and DGC groups. On-going pregnancy rates are%41,5 vs%39,6 for swim-in and DGC respectively. There is a significant difference between the two techniques according to fertilization rates but no difference according to clinical pregnancy and ongoing pregnancy rates. Limitations, reasons for caution Sperms can move by their own motility from ejaculate to the sperm washing medium for that reason with severe sperm problem patients are not suitable for this technique. Wider implications of the findings: This technique is centrifugation free so there are no detrimental g-forces. The needle used may mimic the physiological environment like Uterine Tube. Alternative sperm washing mediums like follicular fluid or chemical attractor progesterone rich medium can be used.DNA fragmentation rates and live birth rates should be established for future aspect. Trial registration number Not applicable

Gradient estimate for the forward conjugate heat equation of forms under the Ricci flow

We establish bounds for the gradient of solutions to the forward conjugate heat equation of differential forms on a Riemannian manifold with the metric evolves under the Ricci flow.

Effects of temperature, pH, feed, and fertilizer draw solution concentrations on the performance of forward osmosis process for textile wastewater treatment.

Water is crucial for enhancing the yield of agricultural land to meet the growing demand. Forward osmosis (FO) is a developing technology that utilizes the natural osmotic gradient of solutions. In this study, fertilizer drawn FO setup was considered by using potassium chloride (KCl) as the draw solution (DS) for treating textile wastewater as the feed solution (FS). This study investigated the effects of FS temperature, pH, and FS and DS concentrations. The performance investigation involved the study in terms of water flux, reverse salt flux, and specific reverse salt flux. DS and FS properties, osmotic potential, and temperature played a vital role in the performance. At 30°C FS temperature, the highest water flux (5.5 LMH) was observed. Reverse salt flux increased due to the increase in solute diffusivity. The highest value of water flux was obtained at a DS of 1.150 M and FS of 1000 mg/L. The permeation of water improved due to the difference in DS and FS concentrations at pH values above 7. The results of this study suggest that KCl as DS has a higher potential for the treatment of textile wastewater at a temperature of 30°C. Additionally, the functional groups attached to the FO membrane were identified through Fourier-transform infrared (FTIR) spectroscopic study. PRACTITIONER POINTS: Treatment of textile wastewater with the use of fertilizer draw solution (KCl) by forward osmosis process as carried out. The performance was assessed in terms of water flux, reverse salt flux, and specific reverse salt flux. The effects of feed and fertilizer draw solution concentrations; pH and temperature were evaluated on the performance of FO process.

Temporal Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Let U=U(t,x) for (t,x)∈R+×Rd and ∂xU=∂xU(t,x) for (t,x)∈R+×R be the solution and gradient solution of the fourth order linearized Kuramoto–Sivashinsky (L-KS) SPDE driven by the space-time white noise in one-to-three dimensional spaces, respectively. We use the underlying explicit kernels and symmetry analysis, yielding exact, dimension-dependent, and temporal moduli of non-differentiability for U(·,x) and ∂xU(·,x). It has been confirmed that almost all sample paths of U(·,x) and ∂xU(·,x), in time, are nowhere differentiable.

Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Thermosolutal-Convective Instability In Stern’s Type Configuration

The thermal-convective instability of a stellar atmosphere in the presence of stable solute gradient in Stern’s type configuration is studied in the presence of radiative transfer effect. A criterion for monotonic instability is obtained in terms of the source functions S. The criterion for monotonic instability is found to be unchanged in the presence of radiative transfer and rotation effects. The problem of thermosolutal-convective instability of a hydromagnetic composite medium is also studied to include the frictional effects with neutrals. The criterion derived for monotonic instability in terms of heat-loss function is found to be the same in the presence or absence of the collisional effects.

Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation

We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded uniformly in the fractional diffusion exponent $\alpha\in(0,1]$. In addition, we account for the presence of an inhomogeneous term and show a stability estimate for the gradient of the Galerkin solution. As a by-product, the proofs of error bounds for a standard finite element approximation are simplified.

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.

Nematic\u2013Isotropic Phase Transition in Liquid Crystals: A Variational Derivation of Effective Geometric Motions

In this work, we study the nematic–isotropic phase transition based on the dynamics of the Landau–De Gennes theory of liquid crystals. At the critical temperature, the Landau–De Gennes bulk potential favors the isotropic phase and nematic phase equally. When the elastic coefficient is much smaller than that of the bulk potential, a scaling limit can be derived by formal asymptotic expansions: the solution gradient concentrates on a closed surface evolving by mean curvature flow. Moreover, on one side of the surface the solution tends to the nematic phase which is governed by the harmonic map heat flow into the sphere while on the other side, it tends to the isotropic phase. To rigorously justify such a scaling limit, we prove a convergence result by combining weak convergence methods and the modulated energy method. Our proof applies as long as the limiting mean curvature flow remains smooth.

Removable singularities for Lipschitz caloric functions in time varying domains

In this paper we study removable singularities for regular (1,1/2) -Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric capacity and we study its metric and geometric properties and the connection with the L^2 boundedness of the singular integral whose kernel is given by the gradient of the fundamental solution of the heat equation.

Numerical study of non-isothermal analysis of exiting sheet thickness in the calendering of micropolar-Casson fluid

This theoretical analysis reports on the non-isothermal calendering process of micropolar-Casson fluid and studies the viscoplastic and microrotation effects by utilizing the lubrication approximation (LAT). Exact dimensionless velocity and pressure gradient solutions are achieved. Then a numerical integration technique determined other mechanical quantities. Implementing the finite difference approximations resolved the energy expression. Graphs show how material parameters influence the pressure, pressure gradient, leave-off distance, temperature distribution, force, and power function. Temperature distribution increases with increased coupling number N and decreased Casson parameter [Formula: see text]. Force and power function increase with increased coupling number and decreased Casson parameter. Both Casson and coupling number control the pressure distribution and exiting sheet thickness.

Optimization of a Ligand Exchange Chromatography Method for the Enantioselective Separation of Levofloxacin and Its Chiral Impurity.

Levofloxacin is a third-generation fluoroquinolone that has several advantages over its (R) ofloxacin isomer. It is used to treat different types of infection, including urinary infection and prostatitis. A new HPLC method for the enantioselective separation of levofloxacin and its chiral impurity was developed and validated to improve the separation of the enantiomers of levofloxacin [impurity(R) and active principle (S)] by increasing the value of the resolution between the eutomer and the distomer. Chromatographic separation was performed on a Prodigy ODS -2, 5 µm 4.6 × 150 mm column, with a gradient of buffer solution and methanol (80:20, v/v). A Box-Behnken design was considered when optimizing the enantioseparation involving the effects of many factors such as the concentration of d-phenylalanine, the pH of the buffer, the percentage of organic modifier in the mobile phase, the flow rate, the temperature of the column, and the type of column. Chiral separation was achieved with an optimal resolution of 3.8. The method was successfully validated following the International Conference on Harmonization Q2 (R1) guideline, fulfilling the acceptance criteria for selectivity [no interference in the retention time of (S) levofloxacin and (R) levofloxacin], linearity (r ≥0.999 in the range 1.25-3.75 µg/mL for all enantiomers), and precision (RSD <2%). Accuracy was assessed by the application of the analytical method to an analyte of known purity, providing evidence for the usefulness of this monitoring system. The method was successfully used for the determination of levofloxacin impurity in raw material and pharmaceutical dosage forms. The following method is accurate and robust to quantify and characterize the presence of levofloxacin impurity in raw material for pharmaceutical compounds.

Besov regularity for the gradients of solutions to non-uniformly elliptic obstacle problems

In this paper, we use the finite difference argument to prove a higher fractional differentiability in the scale of Besov spaces for the gradients of solutions of the double phase elliptic problems with unilateral obstacle:∫Ω〈A(x,Du),D(u−v)〉dx≤∫Ω〈|F|p−2F+a(x)|F|q−2F,D(u−v)〉dx. A key feature of our study consists in assuming that the nonlinearity A(x,Du) has an anisotropic (p,q)-growth for any 2≤p<q and qp<1+αn with 0≤a(⋅)∈C0,α(Ω‾) for α∈(0,1].